Abrasive Wear Performance of Fe2B Layers Applied on Steel Substrates

*Armando Irvin Martínez Pérez, Edgar Ernesto Vera Cárdenas, Manuel Vite Torres, José Luis Bernal Ponce, Karina Alemán Ayala and Marisa Moreno Rios*

### **Abstract**

The resistance of dry abrasive wear in Fe2B layer deposited on AISI D2 and 1040 steel substrates, using the powder-pack boriding process, was evaluated. The boriding process was carried out at temperatures of 1220 and 1320 K for a time of 8 h. A Rockwell hardness tester was used to assess the Daimler-Benz adhesion test. The abrasive wear tests were carried out in dry conditions according to the ASTM G65 test standard. The test parameters used were a sand flow of 400 g/min, a nominal rubber wheel constant rotation of 200 rpm, a load of 122 N, and a sliding distance of 716.28 m. The type of abrasive used was steel round grit with a grain size of 260 μm and a hardness of 1100 HV. The total time for each test was 30 min, removing the specimens every 5 min to determine the amount of mass loss using an analytical balance (sensitivity of 0.0001 g). The average value of volume loss and wear rates is reported. Optical microscopy and SEM were carried out in order to identify the wear mechanisms. The wear mechanisms presented in this study were two-body abrasive wear, pitting action, and plastic deformation.

**Keywords:** dry abrasive wear, Fe2B layer, steel substrates, boriding, wear mechanisms

### **1. Introduction**

Abrasive wear occurs when a hard particle slides on a surface, causing loss of material. This type of wear depends on factors such as hardness, roughness, and particle geometry [1–4].

Different coatings are used as anti-abrasive wear materials. Some of them are as follows: ceramics coatings, such as, Al2O3/TiO2, SiO2/TiO2/Cr2O3, SiC, B4C, ZrO2, CaO, CrN/AlCrN, CrN/BCN, SiO2, WC, and TiC [5, 6]; polymer coatings [7, 8]; and DLC coatings [9, 10].

On the other hand, some works have been developed using boron coatings as anti-wear material. Boronizing is a thermo-diffusion process in which boron atoms, due to their small diameter and high mobility at elevated temperatures, diffuse into a metal surface and form intermetallic compounds with atoms of base metal [11]. Abrasive wear tests were carried out using boronizing on SAE 1010, 1040, D2, and 304 steels [12]. It was seen that boronizing improved the wear strengths

considerably. The best abrasive wear strengths were obtained in boronizing for 8 h at 900°C for SAE 1010 and SAE 1040 steels, 4 h at 900°C for D2 steel, and 6 h at 900°C for 304 steel. In another work [13], abrasive wear resistance of boride layers on Fe-15Cr alloy was studied. It was found that the dry abrasive wear resistance of borided alloy samples was around 45 times greater than that of non-borided ones. In another study [14], the micro-abrasive wear of boride layers on AISI D2 tool steel was investigated. Some results indicated that wear resistance of the borided samples was superior to the hardened, uncoated AISI D2 steel. According to literature [15], wear resistance of boronized steels in abrasive wear conditions depends on the phase composition and hardness of the layer and its stress state, but the hardness of abrasive particles also has a significant importance on the wear speed.

The objective of this work was to evaluate the resistance of dry abrasive wear in Fe2B layer deposited on AISI D2 and 1040 steel substrates without a previous heat treatment (hardened and tempered) using the powder-pack boriding process. The substrate materials were selected in order to compare the wear abrasion behavior of a plain carbon (1040) versus a high-carbon, high-chromium steel (D2). AISI 1040 steel is frequently cold drawn to specified physical properties for use without heat treatment for some practical applications such as cylinder head studs. AISI D2 tool steel has desirable properties such as abrasion resistance, high hardness, and no deforming characteristics, and is used in lamination and stamping dies, shear blades, master tools, etc. The wear resistance of D2 tool steel is approximately eight times that of plain carbon steels, so also was of interest to know if this great difference in wear behavior could increase or decrease in borided conditions.

### **2. Experimental work**

### **2.1 Test specimens**

The specimens had a rectangular shape with dimensions of 50 × 25 mm and 10 mm in thickness. The chemical composition of the AISI D2 and 1040 steels is shown in **Table 1** [16, 17].

The boriding process used in the specimens of AISI D2 and 1040 steel substrates was the same as reported in a previous work [18]. The only difference is that for this work, two boriding temperatures were employed (1220 and 1320 K).

It is important to mention that, based on the Fe-B phase diagram and the high iron content of the AISI D2 and 1040 steels [19], in addition to the diffusion of boron at high temperatures (1220 and 1320 K) and the treatment time of 8 h, the formation of a Fe2B monolayer is ensured under the conditions of the boriding process proposed in this work. Because the Fe-B phase is formed on the surface of the sample, which generates the Fe-B/Fe interface between the Fe-B phase and the steel, this allows the gradual formation of the Fe2B phase that grows when the thickness of the boride is increased and at the same time the Fe-B phase decreases. At the


**5**

*Abrasive Wear Performance of Fe2B Layers Applied on Steel Substrates*

end of the 8 h, corresponding to the treatment time, the Fe-B phase was consumed

The tests were performed according to the ASTM G65 test standard [21]. **Figure 1** shows the experimental rig and a simplified schematic diagram of the dry/sand rubber

The test parameters used were a sand flow of 400 g/min, a nominal rubber wheel constant rotation of 200 rpm, a load of 122 N, and a total sliding distance of 716.28 m, using a 228.6 mm diameter wheel rotating. The wheel consists of a steel disk with an outer layer of neoprene rubber tire molded to its periphery with hardness A60. As the rubber wheel reduces in diameter, the number of wheel revolutions was adjusted to equal the sliding distance of the new wheel. The type of abrasive used was steel round grit with a grain size of 260 μm and a hardness of 1100 HV. The total time for each test was 30 min, removing the specimens every 5 min to determine the amount of mass loss using an analytical balance (sensitivity of 0.0001 g). Before the overall tests were performed, the specimens were cleaned by washing in ethanol in an ultrasonic bath

The average value of volume loss (*V*), wear rates (*Q*), and wear coefficients (*k*) are reported. Optical microscopy and SEM were carried out on the damaged surfaces in order to identify the wear mechanisms. Additionally, the profiles of the

A load of 100 g was used to evaluate the hardness of Fe2B layers with a Vickers indenter. The variation of the hardness, depending on the depth of layers, is shown in **Figure 2**. Also, the roughness of specimens was obtained with a Mitutoyo

wear scars are presented using a Mitutoyo Surftest Profilometer.

completely, and so the only phase present (Fe2B) stops growing [20].

wheel apparatus used in this research work [22].

*(a) Experimental setup and (b) schematic diagram of the apparatus.*

*DOI: http://dx.doi.org/10.5772/intechopen.83814*

**2.2 Test procedure**

**Figure 1.**

(Fisherbrand 11020).

**3. Results and discussion**

Surftest Profilometer, see **Table 2**.

**3.1 Fe2B layer hardness**

### **Table 1.**

*Chemical composition of specimens (wt.%).*

*Abrasive Wear Performance of Fe2B Layers Applied on Steel Substrates DOI: http://dx.doi.org/10.5772/intechopen.83814*

**Figure 1.** *(a) Experimental setup and (b) schematic diagram of the apparatus.*

end of the 8 h, corresponding to the treatment time, the Fe-B phase was consumed completely, and so the only phase present (Fe2B) stops growing [20].

### **2.2 Test procedure**

*Friction, Lubrication and Wear*

borided conditions.

**2.1 Test specimens**

**2. Experimental work**

shown in **Table 1** [16, 17].

considerably. The best abrasive wear strengths were obtained in boronizing for 8 h at 900°C for SAE 1010 and SAE 1040 steels, 4 h at 900°C for D2 steel, and 6 h at 900°C for 304 steel. In another work [13], abrasive wear resistance of boride layers on Fe-15Cr alloy was studied. It was found that the dry abrasive wear resistance of borided alloy samples was around 45 times greater than that of non-borided ones. In another study [14], the micro-abrasive wear of boride layers on AISI D2 tool steel was investigated. Some results indicated that wear resistance of the borided samples was superior to the hardened, uncoated AISI D2 steel. According to literature [15], wear resistance of boronized steels in abrasive wear conditions depends on the phase composition and hardness of the layer and its stress state, but the hardness of

The objective of this work was to evaluate the resistance of dry abrasive wear in Fe2B layer deposited on AISI D2 and 1040 steel substrates without a previous heat treatment (hardened and tempered) using the powder-pack boriding process. The substrate materials were selected in order to compare the wear abrasion behavior of a plain carbon (1040) versus a high-carbon, high-chromium steel (D2). AISI 1040 steel is frequently cold drawn to specified physical properties for use without heat treatment for some practical applications such as cylinder head studs. AISI D2 tool steel has desirable properties such as abrasion resistance, high hardness, and no deforming characteristics, and is used in lamination and stamping dies, shear blades, master tools, etc. The wear resistance of D2 tool steel is approximately eight times that of plain carbon steels, so also was of interest to know if this great difference in wear behavior could increase or decrease in

The specimens had a rectangular shape with dimensions of 50 × 25 mm and 10 mm in thickness. The chemical composition of the AISI D2 and 1040 steels is

work, two boriding temperatures were employed (1220 and 1320 K).

**Steel Composition**

The boriding process used in the specimens of AISI D2 and 1040 steel substrates was the same as reported in a previous work [18]. The only difference is that for this

It is important to mention that, based on the Fe-B phase diagram and the high iron content of the AISI D2 and 1040 steels [19], in addition to the diffusion of boron at high temperatures (1220 and 1320 K) and the treatment time of 8 h, the formation of a Fe2B monolayer is ensured under the conditions of the boriding process proposed in this work. Because the Fe-B phase is formed on the surface of the sample, which generates the Fe-B/Fe interface between the Fe-B phase and the steel, this allows the gradual formation of the Fe2B phase that grows when the thickness of the boride is increased and at the same time the Fe-B phase decreases. At the

AISI D2 1.55 0.35 0.35 11.8 0.85 0.85 0.03 0.03 84.22 AISI 1040 0.38 0.6 0.1 0 0 0 0.02 0.02 98.87

**C Mn Si Cr Mo V S P Fe**

abrasive particles also has a significant importance on the wear speed.

**4**

**Table 1.**

*Chemical composition of specimens (wt.%).*

The tests were performed according to the ASTM G65 test standard [21]. **Figure 1** shows the experimental rig and a simplified schematic diagram of the dry/sand rubber wheel apparatus used in this research work [22].

The test parameters used were a sand flow of 400 g/min, a nominal rubber wheel constant rotation of 200 rpm, a load of 122 N, and a total sliding distance of 716.28 m, using a 228.6 mm diameter wheel rotating. The wheel consists of a steel disk with an outer layer of neoprene rubber tire molded to its periphery with hardness A60. As the rubber wheel reduces in diameter, the number of wheel revolutions was adjusted to equal the sliding distance of the new wheel. The type of abrasive used was steel round grit with a grain size of 260 μm and a hardness of 1100 HV. The total time for each test was 30 min, removing the specimens every 5 min to determine the amount of mass loss using an analytical balance (sensitivity of 0.0001 g). Before the overall tests were performed, the specimens were cleaned by washing in ethanol in an ultrasonic bath (Fisherbrand 11020).

The average value of volume loss (*V*), wear rates (*Q*), and wear coefficients (*k*) are reported. Optical microscopy and SEM were carried out on the damaged surfaces in order to identify the wear mechanisms. Additionally, the profiles of the wear scars are presented using a Mitutoyo Surftest Profilometer.

### **3. Results and discussion**

### **3.1 Fe2B layer hardness**

A load of 100 g was used to evaluate the hardness of Fe2B layers with a Vickers indenter. The variation of the hardness, depending on the depth of layers, is shown in **Figure 2**. Also, the roughness of specimens was obtained with a Mitutoyo Surftest Profilometer, see **Table 2**.

**Figure 2.** *Variation of hardness.*


**Table 2.**

*Properties of the specimens.*

### **3.2 SEM, X-ray diffraction, and EDS**

**Figure 3** shows the cross-sectional view of SEM micrographs. A zigzag teeth shape is observed in both steels. This columnar shape comes from the direction in which diffusion is preferred, and the boride is of stronger (002) texture [23]. The presence of this typical morphology for good adhesion between coating and substrate is necessary.

The boriding is a diffusive process highly anisotropic [24]. In **Figure 3**, it was observed that the boride on the surface of AISI D2 steel presents a columnar morphology; in the case of boride formed on the surface of AISI 1040 mold steel is observed a dense structure due to alloying elements it has. Depending on the conditions of processing time, temperature, and chemical composition of substrates, the depth obtained of the boride layer was an interval of 10–60 μm (**Figure 2**). It was observed that the depth of borides formed on AISI D2 is more homogeneous than that of AISI 1040.

The results of X-ray diffraction studies are presented in **Figure 4**. The XRD analysis shows well-defined peaks at 42.67 and 45.11° confirming Fe2B phase. Also, the presence of chromium boride (CrB) phase in the borided AISI D2 steel was determined. This is due to the significant presence of chromium in AISI D2 steel as an alloying element [25, 26]; apparently, during powder-pack boriding, it reacted with boron atoms and formed a little intermediate phase of CrB.

**7**

**Figure 4.**

*1220 K, and (d) AISI D2 at 1320 K.*

**Figure 3.**

*Abrasive Wear Performance of Fe2B Layers Applied on Steel Substrates*

The EDS analysis obtained by SEM, for the borided steels, is shown in **Figure 5a–d**. The presence of borides formed on the surfaces of the steels was

*Diffraction patterns of borided specimens: (a) AISI 1040 at 1220 K, (b) AISI 1040 at 1320 K, (c) AISI D2 at* 

*SEM cross-sectional micrograph, and XRD of borided samples: (a) AISI D2 at 1220 K, (b) AISI 1040 at* 

confirmed considering the presence of boron and iron.

*1220 K, (c) AISI D2 at 1320 K and (d) AISI 1040 at 1320 K.*

*DOI: http://dx.doi.org/10.5772/intechopen.83814*

*Abrasive Wear Performance of Fe2B Layers Applied on Steel Substrates DOI: http://dx.doi.org/10.5772/intechopen.83814*

### **Figure 3.**

*Friction, Lubrication and Wear*

**Boriding temperature (K) Borided steel Vickers hardness (HV) Roughness (Ra)** 

AISI 1040 964.4 1.14

AISI 1040 1179.5 0.35

1220 AISI D2 1270.7 0.86

1320 AISI D2 1354.5 0.22

**Figure 3** shows the cross-sectional view of SEM micrographs. A zigzag teeth shape is observed in both steels. This columnar shape comes from the direction in which diffusion is preferred, and the boride is of stronger (002) texture [23]. The presence of this typical morphology for good adhesion between coating and

The boriding is a diffusive process highly anisotropic [24]. In **Figure 3**, it was observed that the boride on the surface of AISI D2 steel presents a columnar morphology; in the case of boride formed on the surface of AISI 1040 mold steel is observed a dense structure due to alloying elements it has. Depending on the conditions of processing time, temperature, and chemical composition of substrates, the depth obtained of the boride layer was an interval of 10–60 μm (**Figure 2**). It was observed that the depth of borides formed on AISI D2 is more homogeneous than that of AISI 1040. The results of X-ray diffraction studies are presented in **Figure 4**. The XRD analysis shows well-defined peaks at 42.67 and 45.11° confirming Fe2B phase. Also, the presence of chromium boride (CrB) phase in the borided AISI D2 steel was determined. This is due to the significant presence of chromium in AISI D2 steel as an alloying element [25, 26]; apparently, during powder-pack boriding, it reacted

with boron atoms and formed a little intermediate phase of CrB.

**(μm)**

**6**

**Table 2.**

**Figure 2.**

*Variation of hardness.*

*Properties of the specimens.*

substrate is necessary.

**3.2 SEM, X-ray diffraction, and EDS**

*SEM cross-sectional micrograph, and XRD of borided samples: (a) AISI D2 at 1220 K, (b) AISI 1040 at 1220 K, (c) AISI D2 at 1320 K and (d) AISI 1040 at 1320 K.*

The EDS analysis obtained by SEM, for the borided steels, is shown in **Figure 5a–d**. The presence of borides formed on the surfaces of the steels was confirmed considering the presence of boron and iron.

### **Figure 4.**

*Diffraction patterns of borided specimens: (a) AISI 1040 at 1220 K, (b) AISI 1040 at 1320 K, (c) AISI D2 at 1220 K, and (d) AISI D2 at 1320 K.*

### **Figure 5.**

*EDS spectrum of borided samples. (a) AISI D2 at 1220 K, (b) AISI 1040 at 1220 K, (c) AISI D2 at 1320 K, and (d) AISI 1040 at 1320 K.*

### **3.3 Fe2B layer adhesion test**

A Cientec Rockwell hardness tester model 200HR-150 was used to assess the Daimler-Benz adhesion tests [27]. **Figure 6** shows the indentations on the surfaces. For the AISI D2 steel, some small cracks and no visible delamination are observed (**Figure 6a** and **c**), and the adhesion strength quality is related to HF1 map [28]. In the case of AISI 1040 steel (**Figure 6b** and **d**), microcracks and small delamination are observed, and the adhesion category belongs to the HF4 level.

### **3.4 Wear profile**

The abrasion tests carried out caused wear damage on surfaces. The wear profiles were measured using a Mitutoyo Surftest profilometer and are shown in **Figure 7**. The results are compatible with the volume loss (**Figure 8**), where 1040 steel borided at 1220 K has the greatest wear volume and the D2 steels at 1320 K had the minor wear.

### **3.5 Volume loss**

The volume loss was obtained for all the borided and unborided steel substrates. These data were calculated using Eq. (1). The mass loss was obtained weighing the specimens before and after the test. The graph of the **Figure 8** shows that the AISI D2 steel borided at 1320 K exhibited a higher wear resistance compared to the other specimens. The results also show the great difference in volume loss between borided and unborided steels. The reason that the D2 steel had a greater wear resistance is due most likely to the mechanical properties conferred by a high content of C and Cr, which is higher than in the 1040 steel (see **Table 1**). According to **Figure 8**, the abrasion wear resistance of borided D2 tool steel is approximately 16 times greater than borided 1040 plain carbon steel. This could justify the use of this tool steel for abrasion wear applications when it is borided to the conditions used in this work,

**9**

treatment.

**Figure 6.**

distance (m).

*Abrasive Wear Performance of Fe2B Layers Applied on Steel Substrates*

without a previous heat treatment, as usual. These results also indicate that its core strength was not affected due to high temperatures of powder-pack boriding

*Indentations on surfaces. (a) AISI D2 borided at 1220 K, (b) AISI 1040 borided at 1220 K, (c) AISI D2* 

*Q* = *V*/*d*. (2)

/m), *V* = volume loss (mm3

**Figure 9** shows the wear rates obtained every 716 m of the borided and unborided D2 and 1040 steels. AISI D2 borided steels at 1320 and 1220 K had the best performance against the dry abrasive wear conditions. It was due to its good mechanical properties and chemical composition. Additionally, the adhesion tests on this steel showed an excellent performance. On the other hand, the 1040 steel borided at 1320 K had a good behavior, almost similar to the D2 steel. For the AISI 1040 steels borided at 1220 K, an abnormal value was observed at a sliding distance of 716 m, where the wear rate had a great increase. This performance was mainly

)) × 1000 (1)

), and *d* = sliding

Volume loss (mm3) = (Mass loss (g)/density (g/cm<sup>3</sup>

**3.6 Wear rates (Q ) and wear coefficients (k)**

*borided at 1320 K, and (d) AISI 1040 borided at 1320 K.*

where *Q* = wear rate (mm3

due to the running in period of the test.

The wear rates were obtained from Eq. (2).

*DOI: http://dx.doi.org/10.5772/intechopen.83814*

*Abrasive Wear Performance of Fe2B Layers Applied on Steel Substrates DOI: http://dx.doi.org/10.5772/intechopen.83814*

### **Figure 6.**

*Friction, Lubrication and Wear*

**Figure 5.**

*(d) AISI 1040 at 1320 K.*

**3.4 Wear profile**

**3.5 Volume loss**

**3.3 Fe2B layer adhesion test**

*EDS spectrum of borided samples. (a) AISI D2 at 1220 K, (b) AISI 1040 at 1220 K, (c) AISI D2 at 1320 K, and* 

A Cientec Rockwell hardness tester model 200HR-150 was used to assess the Daimler-Benz adhesion tests [27]. **Figure 6** shows the indentations on the surfaces. For the AISI D2 steel, some small cracks and no visible delamination are observed (**Figure 6a** and **c**), and the adhesion strength quality is related to HF1 map [28]. In the case of AISI 1040 steel (**Figure 6b** and **d**), microcracks and small delamination

The abrasion tests carried out caused wear damage on surfaces. The wear profiles were measured using a Mitutoyo Surftest profilometer and are shown in **Figure 7**. The results are compatible with the volume loss (**Figure 8**), where 1040 steel borided at 1220 K has the greatest wear volume and the D2 steels at 1320 K had the minor wear.

The volume loss was obtained for all the borided and unborided steel substrates. These data were calculated using Eq. (1). The mass loss was obtained weighing the specimens before and after the test. The graph of the **Figure 8** shows that the AISI D2 steel borided at 1320 K exhibited a higher wear resistance compared to the other specimens. The results also show the great difference in volume loss between borided and unborided steels. The reason that the D2 steel had a greater wear resistance is due most likely to the mechanical properties conferred by a high content of C and Cr, which is higher than in the 1040 steel (see **Table 1**). According to **Figure 8**, the abrasion wear resistance of borided D2 tool steel is approximately 16 times greater than borided 1040 plain carbon steel. This could justify the use of this tool steel for abrasion wear applications when it is borided to the conditions used in this work,

are observed, and the adhesion category belongs to the HF4 level.

**8**

*Indentations on surfaces. (a) AISI D2 borided at 1220 K, (b) AISI 1040 borided at 1220 K, (c) AISI D2 borided at 1320 K, and (d) AISI 1040 borided at 1320 K.*

without a previous heat treatment, as usual. These results also indicate that its core strength was not affected due to high temperatures of powder-pack boriding treatment.

$$\text{Volume loss } \left(\text{mm}^3\right) = \left(\text{Mass loss } \left(\text{g}\right) / \text{density } \left(\text{g}/\text{cm}^3\right)\right) \times 1000 \tag{1}$$

### **3.6 Wear rates (Q ) and wear coefficients (k)**

The wear rates were obtained from Eq. (2).

$$\mathbf{Q} = \mathbf{V}/d.\tag{2}$$

where *Q* = wear rate (mm3 /m), *V* = volume loss (mm3 ), and *d* = sliding distance (m).

**Figure 9** shows the wear rates obtained every 716 m of the borided and unborided D2 and 1040 steels. AISI D2 borided steels at 1320 and 1220 K had the best performance against the dry abrasive wear conditions. It was due to its good mechanical properties and chemical composition. Additionally, the adhesion tests on this steel showed an excellent performance. On the other hand, the 1040 steel borided at 1320 K had a good behavior, almost similar to the D2 steel. For the AISI 1040 steels borided at 1220 K, an abnormal value was observed at a sliding distance of 716 m, where the wear rate had a great increase. This performance was mainly due to the running in period of the test.

**Figure 7.** *Roughness profiles of wear scars.*

**Figure 8.**

*Volume loss of borided and unborided steels.*

### **3.7 Wear mechanisms**

**Figure 10a–f** shows the wear on the surface of the unborided and borided specimens. In both steels, as expected, the wear damage was more severe on the unborided specimens (**Figure 10a** and **b**). In the case of the borided steels, AISI 1040 at 1220 K (**Figure 10c**) showed the greater damage and the AISI D2 borided at 1320 K (**Figure 10d**) showed the lower damage. This was in accordance to the results of the wear profiles showed in **Figure 7** and wear rates showed in **Figure 9**. In the case of borided steels, the main wear mechanism observed in the wear scars was the two-body abrasive wear due to the presence of parallel lines to the sliding direction. These parallel lines were produced by wear debris acting as indenters causing, in some cases, depth grooves.

**Figure 11a**–**d** shows the SEM micrographs of the wear damage of the borided steels. In the case of AISI 1040 steel borided at 1220 K (**Figure 11a**), wear debris was observed, which was derived from the three-body abrasion situation, where hard particles were trapped between the two sliding surfaces. Also, severe pitting action was observed, caused by the particles of material and abrasive particles. Finally,

**11**

**Figure 11.**

*(d) AISI D2 at 1320 K.*

**Figure 9.**

**Figure 10.**

*Wear rate of borided and unborided steels.*

*borided—1320 K, and (f) D2 borided—1320 K.*

*Abrasive Wear Performance of Fe2B Layers Applied on Steel Substrates*

*(a) 1040 steel substrate, (b) D2 steel substrate (c) 1040 borided—1220 K, (d) D2 borided—1220 K, (e) 1040* 

*SEM micrographs of wear scars. (a) AISI 1040 at 1220 K, (b) AISI D2 at 1220 K, (c) AISI 1040 at 1320 K, and* 

*DOI: http://dx.doi.org/10.5772/intechopen.83814*

*Abrasive Wear Performance of Fe2B Layers Applied on Steel Substrates DOI: http://dx.doi.org/10.5772/intechopen.83814*

**Figure 9.** *Wear rate of borided and unborided steels.*

### **Figure 10.**

*Friction, Lubrication and Wear*

**10**

**3.7 Wear mechanisms**

*Volume loss of borided and unborided steels.*

**Figure 8.**

**Figure 7.**

*Roughness profiles of wear scars.*

causing, in some cases, depth grooves.

**Figure 10a–f** shows the wear on the surface of the unborided and borided specimens. In both steels, as expected, the wear damage was more severe on the unborided specimens (**Figure 10a** and **b**). In the case of the borided steels, AISI 1040 at 1220 K (**Figure 10c**) showed the greater damage and the AISI D2 borided at 1320 K (**Figure 10d**) showed the lower damage. This was in accordance to the results of the wear profiles showed in **Figure 7** and wear rates showed in **Figure 9**. In the case of borided steels, the main wear mechanism observed in the wear scars was the two-body abrasive wear due to the presence of parallel lines to the sliding direction. These parallel lines were produced by wear debris acting as indenters

**Figure 11a**–**d** shows the SEM micrographs of the wear damage of the borided steels. In the case of AISI 1040 steel borided at 1220 K (**Figure 11a**), wear debris was observed, which was derived from the three-body abrasion situation, where hard particles were trapped between the two sliding surfaces. Also, severe pitting action was observed, caused by the particles of material and abrasive particles. Finally,

*(a) 1040 steel substrate, (b) D2 steel substrate (c) 1040 borided—1220 K, (d) D2 borided—1220 K, (e) 1040 borided—1320 K, and (f) D2 borided—1320 K.*

### **Figure 11.**

*SEM micrographs of wear scars. (a) AISI 1040 at 1220 K, (b) AISI D2 at 1220 K, (c) AISI 1040 at 1320 K, and (d) AISI D2 at 1320 K.*

plastic deformation occurred due mainly to the sliding action. **Figure 11b** (AISI D2 steel at 1220 K) shows a typical effect of abrasive wear, where sharp asperities plowed the surface, causing permanent deformation. This plowing action produced a groove in the softer material. Also, parallel lines were observed caused by wear debris probably inlaid in the rubber wheel. In the case of AISI 1040 steel borided at 1320 K (**Figure 11c**), severe micropitting action and plastic deformation were observed. Finally, in the case of the AISI D2 steel at 1320 K, wear debris and pitting action were observed, but to a lesser degree. This matches with the results of wear rates obtained and indicated in **Figure 9**.

### **4. Conclusions**


**13**

Mexico

**Author details**

Manuel Vite Torres3

and Marisa Moreno Rios2

Pachuca, Hidalgo, Mexico

Orizaba, Veracruz, Mexico

Armando Irvin Martínez Pérez1

provided the original work is properly cited.

*Abrasive Wear Performance of Fe2B Layers Applied on Steel Substrates*

*DOI: http://dx.doi.org/10.5772/intechopen.83814*

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

5 Autonomous University of the State of Hidalgo, Mineral de la Reforma, Hidalgo,

, Edgar Ernesto Vera Cárdenas2

, José Luis Bernal Ponce4

1 Polytechnic University of Pachuca, Zempoala, Hidalgo, Mexico

2 National Technology of Mexico/Technological Institute of Pachuca,

3 National Polytechnic Institute, ESIME Zacatenco, Mexico City, Mexico

4 National Technology of Mexico/Technological Institute of Orizaba,

\*Address all correspondence to: eevc2000@hotmail.com

\*,

, Karina Alemán Ayala<sup>5</sup>

*Abrasive Wear Performance of Fe2B Layers Applied on Steel Substrates DOI: http://dx.doi.org/10.5772/intechopen.83814*

### **Author details**

*Friction, Lubrication and Wear*

**4. Conclusions**

sliding action.

rates obtained and indicated in **Figure 9**.

time the Fe-B phase decreases.

and some delamination was observed.

tests on this steel showed an excellent performance.

plastic deformation occurred due mainly to the sliding action. **Figure 11b** (AISI D2 steel at 1220 K) shows a typical effect of abrasive wear, where sharp asperities plowed the surface, causing permanent deformation. This plowing action produced a groove in the softer material. Also, parallel lines were observed caused by wear debris probably inlaid in the rubber wheel. In the case of AISI 1040 steel borided at 1320 K (**Figure 11c**), severe micropitting action and plastic deformation were observed. Finally, in the case of the AISI D2 steel at 1320 K, wear debris and pitting action were observed, but to a lesser degree. This matches with the results of wear

1.The formation of a Fe2B monolayer is ensured under the conditions of the

process of boron powder-pack proposed in this work. The Fe-B phase is formed on the surface of the sample, which generated the Fe-B/Fe interface between the Fe-B phase and the steel, which allowed the gradual formation of the Fe2B phase that grows when the thickness of the boride is increased and at the same

2.The Rockwell-C adhesion tests showed that for the AISI D2 steel, the adhesion strength quality, of Fe2B layers, is related to HF1 map, showing some small microcraks and the AISI 1040 steel fits to HF4 category, where microcracks

3.AISI D2 steel specimens borided at 1320 K showed a higher wear resistance, in accordance to the wear rates and wear coefficients results. It was due to its good mechanical properties and chemical composition. Additionally, the adhesion

4.The wear mechanisms presented in this study were as follows: two-body abrasive wear, which was due to the presence of parallel lines to the sliding direction; pitting action, which was caused by the particles of the material and abrasive particles; and plastic deformation, which occurred due mainly to the

**12**

Armando Irvin Martínez Pérez1 , Edgar Ernesto Vera Cárdenas2 \*, Manuel Vite Torres3 , José Luis Bernal Ponce4 , Karina Alemán Ayala5 and Marisa Moreno Rios2

1 Polytechnic University of Pachuca, Zempoala, Hidalgo, Mexico

2 National Technology of Mexico/Technological Institute of Pachuca, Pachuca, Hidalgo, Mexico

3 National Polytechnic Institute, ESIME Zacatenco, Mexico City, Mexico

4 National Technology of Mexico/Technological Institute of Orizaba, Orizaba, Veracruz, Mexico

5 Autonomous University of the State of Hidalgo, Mineral de la Reforma, Hidalgo, Mexico

\*Address all correspondence to: eevc2000@hotmail.com

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

### **References**

[1] Rabinowicz E. Friction and Wear of Materials. New York, USA: Wiley; 1965

[2] Bhushan B. Introduction to Tribology. New York, USA: Wiley; 2002

[3] Khruschov MM. Principles of abrasive wear. Wear. 1974;**28**:69-88

[4] ASTM G40-17. Standard Terminology Relating to Wear and Erosion. 2017

[5] Mo JL, Zhu MH. Sliding tribological behaviors of PVD CrN and AlCrN coatings against Si3N4 ceramic and pure titanium. Wear. 2009;**267**: 874-881

[6] Czerwinski F. Thermochemical Treatment of Metals. Croatia: Intech; 2012

[7] Zhu F, Wang J, Li S, Zhang J. Preparation and characterization of anodic films on AZ31B Mg alloy formed in the silicate electrolytes with ethylene glycol oligomers as additive. Applied Surface Science. 2012;**258**:8985-8990

[8] Brzeziński S, Kowalczyk D, Borak B, Jasiorski M. Applying the sol–gel method to the deposition of nanocoats on textiles to improve their abrasion resistance. Journal of Applied Polymer Science. 2012;**125**:3058-3067

[9] Corbella C, Rubio-Roy M, Bertran E, Polo MC, Pascual E, Andújar JL. Low friction and protective diamondlike carbon coatings deposited by asymmetric bipolar pulsed plasma. Diamond and Related Materials. 2009;**18**:1035-1038

[10] He F, Wong PL, Zhou X. Wear properties of DLC-coated steel rollers running with highly contaminated lubrication. Tribology International. 2010;**43**:990-996

[11] Milinović A, Krumes D, Marković R. An investigation of boride layers growth kinetics on carbon steels. Tehnički vjesnik. 2012;**19**:27-31

[12] Atik E, Yunker U, Meric C. The effects of conventional heat treatment and boronizing on abrasive wear and corrosion of SAE 1010, SAE 1040, D2 and 304 steels. Tribology International. 2003;**36**:155-161

[13] Dybkov VI, Goncharuk LV, Khoruzha VG, Samelyuk AV, Sidorko VR. Growth kinetics and abrasive wear resistance of boride layers on Fe–15Cr alloy. Materials Science and Technology. 2011;**27**:1502-1512

[14] Oliveira CK, Lombardi AN, Totten GE, Casteletti LC. Micro-abrasive wear of boride layers on AISI D2 tool steel produced by the thermoreactive process. International Journal of Microstructure and Materials Properties. 2008;**3**:241-253

[15] Krukovich MG, Prusakov BA, Sizov IG. Plasticity of Boronized Layers. Russia: Springer; 2016. pp. 250-253

[16] ASTM A681-08. Standard Specification for Tool Steels Alloy; 2015 (Reapproved)

[17] ASTM A510-03. Standard Specification for General Requirements for Wire Rods and Coarse Round Wire, Carbon Steel. 2003

[18] Vera Cardenas E, Lewis R, Martinez Perez A, Bernal Ponce J, Perez Pinal F, Ortiz Dominguez M, et al. Characterization and wear performance of boride phases over tool steel substrates. Advances in Mechanical Engineering. 2016;**8**(2):1-10

[19] Repovský P, Homolová V, Čiripová L, Kroupa A, Zemanová A. Experimental study and thermodynamic modelling of the

**15**

*Abrasive Wear Performance of Fe2B Layers Applied on Steel Substrates*

[28] Verein Deutscher Ingenieure Normen VDI 3198. Düsseldorf: VDI-Verlag (Coating (CVD, PVD) of cold

forging tools); 1991. pp. 1-8

*DOI: http://dx.doi.org/10.5772/intechopen.83814*

B-Fe-Mn ternary system. CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry. 2016;**55**:252-259

[20] Yu LG, Chen XJ, Khor KA, Sundararajan G. Fe-B/Fe2B phase transformation during SPS packboriding: Boride layer growth kinetics. Acta Materialia. 2005;**53**:2361-2368

[21] ASTM G65-04. Standard Test Method for Measuring Abrasion Using the Dry Sand/Rubber Wheel Apparatus.

[22] Vite Torres M, Moreno Rios M, Gallardo Hernandez E, Laguna Camacho J. A study of the abrasive resistance of sputtered CrN coatings deposited on AISI 316 and AISI H13 steel substrates using steel particles.

Wear. 2011;**271**:1273-1279

2004;**39**:933-937

2007;**28**:1819-1826

1958;**12**:1476-1480

2015;**266**:167-176

[23] Martini C, Palombarini G, Carbucicchio M. Mechanism of

thermochemical growth of iron borides on iron. Journal of Materials Science.

[24] Uslu I, Comert H, Ipek M, Celebi FG, Ozdemir O, Bindal C. A comparison of borides formed on AISI 1040 and AISI P20 steels. Materials and Design.

[25] Aronsson B, Aselius J. The effect of boron on the formation of α-FeCr at 700°C. Acta Chemical Scandinavica.

[26] Nedfors N, Primetzhofer D, Wang L, Lu J, Hultman L, Jansson U. Characterization of magnetron sputtered Cr–B and Cr–B–C thin films for electrical contact applications. Surface and Coatings Technology.

[27] Taktak S, Tasgetiren S. Identification of delamination failure of boride layer on common Cr-based steels. Journal of Materials Engineering and Performance. 2006;**15**:570-573

2010

*Abrasive Wear Performance of Fe2B Layers Applied on Steel Substrates DOI: http://dx.doi.org/10.5772/intechopen.83814*

B-Fe-Mn ternary system. CALPHAD: Computer Coupling of Phase Diagrams and Thermochemistry. 2016;**55**:252-259

[20] Yu LG, Chen XJ, Khor KA, Sundararajan G. Fe-B/Fe2B phase transformation during SPS packboriding: Boride layer growth kinetics. Acta Materialia. 2005;**53**:2361-2368

[21] ASTM G65-04. Standard Test Method for Measuring Abrasion Using the Dry Sand/Rubber Wheel Apparatus. 2010

[22] Vite Torres M, Moreno Rios M, Gallardo Hernandez E, Laguna Camacho J. A study of the abrasive resistance of sputtered CrN coatings deposited on AISI 316 and AISI H13 steel substrates using steel particles. Wear. 2011;**271**:1273-1279

[23] Martini C, Palombarini G, Carbucicchio M. Mechanism of thermochemical growth of iron borides on iron. Journal of Materials Science. 2004;**39**:933-937

[24] Uslu I, Comert H, Ipek M, Celebi FG, Ozdemir O, Bindal C. A comparison of borides formed on AISI 1040 and AISI P20 steels. Materials and Design. 2007;**28**:1819-1826

[25] Aronsson B, Aselius J. The effect of boron on the formation of α-FeCr at 700°C. Acta Chemical Scandinavica. 1958;**12**:1476-1480

[26] Nedfors N, Primetzhofer D, Wang L, Lu J, Hultman L, Jansson U. Characterization of magnetron sputtered Cr–B and Cr–B–C thin films for electrical contact applications. Surface and Coatings Technology. 2015;**266**:167-176

[27] Taktak S, Tasgetiren S. Identification of delamination failure of boride layer on common Cr-based steels. Journal of Materials Engineering and Performance. 2006;**15**:570-573

[28] Verein Deutscher Ingenieure Normen VDI 3198. Düsseldorf: VDI-Verlag (Coating (CVD, PVD) of cold forging tools); 1991. pp. 1-8

**14**

*Friction, Lubrication and Wear*

[1] Rabinowicz E. Friction and Wear of Materials. New York, USA: Wiley; 1965

[11] Milinović A, Krumes D, Marković R. An investigation of boride layers growth kinetics on carbon steels. Tehnički

[12] Atik E, Yunker U, Meric C. The effects of conventional heat treatment and boronizing on abrasive wear and corrosion of SAE 1010, SAE 1040, D2 and 304 steels. Tribology International.

[13] Dybkov VI, Goncharuk LV, Khoruzha VG, Samelyuk AV, Sidorko VR. Growth kinetics and abrasive wear resistance of boride layers on Fe–15Cr alloy. Materials Science and Technology.

[14] Oliveira CK, Lombardi AN, Totten GE, Casteletti LC. Micro-abrasive wear of boride layers on AISI D2 tool steel produced by the thermoreactive

[15] Krukovich MG, Prusakov BA, Sizov IG. Plasticity of Boronized Layers. Russia: Springer; 2016. pp. 250-253

Specification for Tool Steels Alloy; 2015

Specification for General Requirements for Wire Rods and Coarse Round Wire,

process. International Journal of Microstructure and Materials Properties. 2008;**3**:241-253

[16] ASTM A681-08. Standard

[17] ASTM A510-03. Standard

[18] Vera Cardenas E, Lewis R, Martinez Perez A, Bernal Ponce J, Perez Pinal F, Ortiz Dominguez M, et al. Characterization and wear performance of boride phases over tool steel substrates. Advances in Mechanical

Engineering. 2016;**8**(2):1-10

L, Kroupa A, Zemanová A. Experimental study and

thermodynamic modelling of the

[19] Repovský P, Homolová V, Čiripová

(Reapproved)

Carbon Steel. 2003

vjesnik. 2012;**19**:27-31

2003;**36**:155-161

2011;**27**:1502-1512

Tribology. New York, USA: Wiley; 2002

[5] Mo JL, Zhu MH. Sliding tribological behaviors of PVD CrN and AlCrN coatings against Si3N4 ceramic and pure titanium. Wear. 2009;**267**:

[6] Czerwinski F. Thermochemical Treatment of Metals. Croatia: Intech;

[7] Zhu F, Wang J, Li S, Zhang J. Preparation and characterization of anodic films on AZ31B Mg alloy formed

in the silicate electrolytes with ethylene glycol oligomers as additive. Applied Surface Science.

Science. 2012;**125**:3058-3067

[8] Brzeziński S, Kowalczyk D, Borak B, Jasiorski M. Applying the sol–gel method to the deposition of nanocoats on textiles to improve their abrasion resistance. Journal of Applied Polymer

[9] Corbella C, Rubio-Roy M, Bertran E, Polo MC, Pascual E, Andújar JL. Low friction and protective diamondlike carbon coatings deposited by asymmetric bipolar pulsed plasma. Diamond and Related Materials.

[10] He F, Wong PL, Zhou X. Wear properties of DLC-coated steel rollers running with highly contaminated lubrication. Tribology International.

2012;**258**:8985-8990

2009;**18**:1035-1038

2010;**43**:990-996

[2] Bhushan B. Introduction to

[3] Khruschov MM. Principles of abrasive wear. Wear. 1974;**28**:69-88

[4] ASTM G40-17. Standard Terminology Relating to Wear and

Erosion. 2017

**References**

874-881

2012

**17**

**Chapter 2**

**Abstract**

lubrication, helix oil

**1. Introduction**

Experimental Results of the

Tribology of Aluminum in the

Presence of Polytron Additive

*Syed Mohammad Hassan Ahmer, Nusratullah Khan,* 

Friction is an ever-present obstacle that causes energy loss in mechanical parts. To alleviate this nuisance, we carried out experimental studies on a brand new additive called Polytron to assess its role in the minimization of friction and wear. The wear, the volume wear rate, the wear coefficient, and the coefficient of friction of the aluminum surface were measured at room temperature with pin-on-disk tribometer without and with 10% Polytron in Helix oil. In the base oil Helix, their

respectively, which with the incorporation of Polytron additive in the Helix oil

**Keywords:** friction, wear rate, polytron additive, aluminum metal,

experimental verdict points to an ionic character of the additive in that it impregnates the crystal structure of the metal, thereby prompting a hard surface layer

Whenever and wherever two surfaces and/or two parts move against each other in the form of translation, rotation, or oscillation, an opposition is encountered. This opposing or resistive force to motion is described as friction. In fact, friction is an ever-present irritant and is the real source of energy and power losses in every industry and every activity whatsoever. This can be realized in our everyday life and the different industries like automotive, aerospace, agriculture, marine, electronics, and telecommunication, and even the so-called cosmetics industry, and the movements of the human joints are not exempt from this scourge one way or another. The word friction derives from the Latin verb fricare, which means to rub. It is of interest to know that the word tribology, introduced in 1966 by the Jost Report, derives from the Greek word τριβοσ (tribos), which also means rubbing. As indicated by this report, tribology was defined as the science and technology of interacting surfaces in relative motion. Nevertheless, a better definition of tribology might be the science and technology of lubrication, friction, and wear of moving or stationary parts [1, 2]. Even if the term tribology is difficult for the general public to comprehend, the dawn of computer disk drives, micro-devices, and nanotechnology has driven friction science

/min, 1.27 × 10−10 m<sup>2</sup>

/min, 4.22 <sup>×</sup> <sup>10</sup>−11 <sup>m</sup><sup>2</sup> \_\_\_

/N, and 0.012,

<sup>N</sup> , and 0.004. The

*S. Inayat Ali Shah and Lal Said Jan*

values were found to be 70 μm, 1.28 × 10−3 mm<sup>3</sup>

correspondingly reduced to 20μm, 6.08 × 10−5 mm<sup>3</sup>

which subsequently curtails wear and friction.

### **Chapter 2**

### Experimental Results of the Tribology of Aluminum in the Presence of Polytron Additive

*Syed Mohammad Hassan Ahmer, Nusratullah Khan, S. Inayat Ali Shah and Lal Said Jan*

### **Abstract**

Friction is an ever-present obstacle that causes energy loss in mechanical parts. To alleviate this nuisance, we carried out experimental studies on a brand new additive called Polytron to assess its role in the minimization of friction and wear. The wear, the volume wear rate, the wear coefficient, and the coefficient of friction of the aluminum surface were measured at room temperature with pin-on-disk tribometer without and with 10% Polytron in Helix oil. In the base oil Helix, their values were found to be 70 μm, 1.28 × 10−3 mm<sup>3</sup> /min, 1.27 × 10−10 m<sup>2</sup> /N, and 0.012, respectively, which with the incorporation of Polytron additive in the Helix oil correspondingly reduced to 20μm, 6.08 × 10−5 mm<sup>3</sup> /min, 4.22 <sup>×</sup> <sup>10</sup>−11 <sup>m</sup><sup>2</sup> \_\_\_ <sup>N</sup> , and 0.004. The experimental verdict points to an ionic character of the additive in that it impregnates the crystal structure of the metal, thereby prompting a hard surface layer which subsequently curtails wear and friction.

**Keywords:** friction, wear rate, polytron additive, aluminum metal, lubrication, helix oil

### **1. Introduction**

Whenever and wherever two surfaces and/or two parts move against each other in the form of translation, rotation, or oscillation, an opposition is encountered. This opposing or resistive force to motion is described as friction. In fact, friction is an ever-present irritant and is the real source of energy and power losses in every industry and every activity whatsoever. This can be realized in our everyday life and the different industries like automotive, aerospace, agriculture, marine, electronics, and telecommunication, and even the so-called cosmetics industry, and the movements of the human joints are not exempt from this scourge one way or another. The word friction derives from the Latin verb fricare, which means to rub. It is of interest to know that the word tribology, introduced in 1966 by the Jost Report, derives from the Greek word τριβοσ (tribos), which also means rubbing. As indicated by this report, tribology was defined as the science and technology of interacting surfaces in relative motion. Nevertheless, a better definition of tribology might be the science and technology of lubrication, friction, and wear of moving or stationary parts [1, 2]. Even if the term tribology is difficult for the general public to comprehend, the dawn of computer disk drives, micro-devices, and nanotechnology has driven friction science

and tribology to the front position. Now, the designers have to deal with the challenge of controlling friction of interacting surfaces in relative motion at sizes far too small for the naked eye to see. This is the nano-mechanical device and nano-tribological regime where the ultimate source of friction is perceived to be van der Waals force and Coulomb force [3–7]. In addition to friction, an associated observable fact with the protracted mechanical motion or rubbing of the mating surfaces is the wreckage of the surfaces and generation of heat and pressure in the surrounding area which will definitely curtail the useful life of the mechanical parts. This scoring of the coupling surfaces is termed as wear. The critical issue is to minimize the amount of wear and friction being produced in any mechanical operation so as to avoid any possible mechanical malfunction. It is hard to stop wear of the surfaces and generation of heat and pressure; but there are different ways to minimize the effects, and one of them is lubrication [7]. A lubricant is any substance that is interposed between two surfaces in relative motion for the purpose of reducing the friction and wear between them. By and large, lubricants can be solids, liquids, or gases; but in any case, they reduce the negative influence in the moving parts. Other than friction reduction, lubricants carry away heat and wear particles as well and can serve as the means to distribute corrosion inhibitors and biocides. Lubricating films should support the pressure between opposing surfaces, separate them, and reduce the sliding or rolling resistance in the interface. To reduce friction, the liquid lubricants are formulated in such a way that chemical species within it react with the surface of the bodies to form lubricative films. This chemical species is named as additive. The function of the additive is to provide a smooth surface plus reduce the amount of wear; that is, they are expected to have antifriction and antiwear properties. For example, calcium sulfonate causes the formation of protective layers on highly loaded surfaces. Phosphorus can react with frictional hot spots on ferrous surfaces and thus can reduce wear and friction. Friction modifiers and antiwear additives to oils are the focus of extensive research in oil companies. The amount of the above-mentioned components and their nano-sized counterparts can vary, depending upon the application, in the range of 1–20 wt% [7–15]. By the same token, it has been noticed that the variation of friction and wear rate depends on various interfacial conditions. There are a number of studies in the literature which report that wear and friction primarily change with load, speed, and/or temperature [16–22], surface roughness [23, 24], type of material or mating component, and other environmental dynamics [25–30]. Yet, a group of researchers argue that friction and wear rate vary with geometry, relative surface motion, surface roughness of the rubbing surfaces, type of the material, system rigidity, stick-slip, lubrication, and vibration and/or type of additive, which means that wear and friction are functions of the specific tribosystem [31–52]. Even then, in many applications, the wear reduction mechanism and quantitative analysis of the additives are not well known and a thorough exploration is still inevitable. A literature survey reveals that there is a peculiar and unexplored additive with the brand name of Polytron which has not been thoroughly investigated by the tribological community. Accordingly, this chapter has been devoted to an academic research on the Polytron additive. Polytron is an oily fluid mixture of petroleum-based chemicals mixed with oxidation inhibitors and detergent chemicals and behaves exactly like a stable grease at ambient pressure and temperature in stark contrast to the conventional lubricants. Polytron additive is petroleum based and thus contains no solid particles; hence, it is compatible with all the lubricants available in the market whether mineral, synthetic, vegetable, or animal. Polytron comprises 80% para and 20% meta polytron. In this chapter, we will focus on the metal treatment concentrate (MTC) trademark of polytron having an inherent ionic/polar nature due to which it is attracted to metallic surfaces and develops a durable polished-like microscopic layer through metallurgical process that can resist wear, extreme pressure, and excessive temperature.

**19**

**Figure 2.**

*Pin-on-disk tribotester machine.*

**Figure 1.**

*were 8 mm (*l*) × 163 mm (dia).*

*Experimental Results of the Tribology of Aluminum in the Presence of Polytron Additive*

Wear tests were conducted on pin-on-disk tribotester (Ducom TR-20LE) wear testing machine. **Figure 1** gives a schematic sketch of the pin and disk while **Figure 2**

In **Figure 1**, FN stands for the normal force that is the load on the aluminum pin whereas FR represents the resistive force called friction that arises from the sliding contact of the aluminum pin on the steel disk. In **Figure 2**, the pin is firmly attached to the pin support and then linked to the rotating plain disk with the desired load which is usually applied through a pulley system. Lubricant is pumped continuously from the machine. To simplify the contact geometry, a hemispherical pin is used which directly touches the disk surface at the beginning of the experiment. A hygrometer measures the relative humidity of the air in the chamber whereas the rpm of the rotating shaft that supports the disk is measured with the help of tachometer. The variation of friction coefficient with friction time is recorded automatically. Necessary information regarding stainless steel disk and aluminum pin is presented in **Tables 1**–**3**. The aluminum pin is in fact an alloy of aluminum and silicon. In addition, the data sheets for the Helix oil and Polytron additive are given in **Tables 4** and **5**. The data and basic information with reference

*Sketch of the pin-on-disk. The dimensions of the pin were 32 mm (l) × 10 mm(dia) and dimensions of the disk* 

*DOI: http://dx.doi.org/10.5772/intechopen.84620*

displays the actual tribometer device.

**2. Experimental details**

**2.1 Tribometer machine**

*Experimental Results of the Tribology of Aluminum in the Presence of Polytron Additive DOI: http://dx.doi.org/10.5772/intechopen.84620*

### **2. Experimental details**

*Friction, Lubrication and Wear*

and tribology to the front position. Now, the designers have to deal with the challenge of controlling friction of interacting surfaces in relative motion at sizes far too small for the naked eye to see. This is the nano-mechanical device and nano-tribological regime where the ultimate source of friction is perceived to be van der Waals force and Coulomb force [3–7]. In addition to friction, an associated observable fact with the protracted mechanical motion or rubbing of the mating surfaces is the wreckage of the surfaces and generation of heat and pressure in the surrounding area which will definitely curtail the useful life of the mechanical parts. This scoring of the coupling surfaces is termed as wear. The critical issue is to minimize the amount of wear and friction being produced in any mechanical operation so as to avoid any possible mechanical malfunction. It is hard to stop wear of the surfaces and generation of heat and pressure; but there are different ways to minimize the effects, and one of them is lubrication [7]. A lubricant is any substance that is interposed between two surfaces in relative motion for the purpose of reducing the friction and wear between them. By and large, lubricants can be solids, liquids, or gases; but in any case, they reduce the negative influence in the moving parts. Other than friction reduction, lubricants carry away heat and wear particles as well and can serve as the means to distribute corrosion inhibitors and biocides. Lubricating films should support the pressure between opposing surfaces, separate them, and reduce the sliding or rolling resistance in the interface. To reduce friction, the liquid lubricants are formulated in such a way that chemical species within it react with the surface of the bodies to form lubricative films. This chemical species is named as additive. The function of the additive is to provide a smooth surface plus reduce the amount of wear; that is, they are expected to have antifriction and antiwear properties. For example, calcium sulfonate causes the formation of protective layers on highly loaded surfaces. Phosphorus can react with frictional hot spots on ferrous surfaces and thus can reduce wear and friction. Friction modifiers and antiwear additives to oils are the focus of extensive research in oil companies. The amount of the above-mentioned components and their nano-sized counterparts can vary, depending upon the application, in the range of 1–20 wt% [7–15]. By the same token, it has been noticed that the variation of friction and wear rate depends on various interfacial conditions. There are a number of studies in the literature which report that wear and friction primarily change with load, speed, and/or temperature [16–22], surface roughness [23, 24], type of material or mating component, and other environmental dynamics [25–30]. Yet, a group of researchers argue that friction and wear rate vary with geometry, relative surface motion, surface roughness of the rubbing surfaces, type of the material, system rigidity, stick-slip, lubrication, and vibration and/or type of additive, which means that wear and friction are functions of the specific tribosystem [31–52]. Even then, in many applications, the wear reduction mechanism and quantitative analysis of the additives are not well known and a thorough exploration is still inevitable. A literature survey reveals that there is a peculiar and unexplored additive with the brand name of Polytron which has not been thoroughly investigated by the tribological community. Accordingly, this chapter has been devoted to an academic research on the Polytron additive. Polytron is an oily fluid mixture of petroleum-based chemicals mixed with oxidation inhibitors and detergent chemicals and behaves exactly like a stable grease at ambient pressure and temperature in stark contrast to the conventional lubricants. Polytron additive is petroleum based and thus contains no solid particles; hence, it is compatible with all the lubricants available in the market whether mineral, synthetic, vegetable, or animal. Polytron comprises 80% para and 20% meta polytron. In this chapter, we will focus on the metal treatment concentrate (MTC) trademark of polytron having an inherent ionic/polar nature due to which it is attracted to metallic surfaces and develops a durable polished-like microscopic layer through metallurgical process that can resist

**18**

wear, extreme pressure, and excessive temperature.

### **2.1 Tribometer machine**

Wear tests were conducted on pin-on-disk tribotester (Ducom TR-20LE) wear testing machine. **Figure 1** gives a schematic sketch of the pin and disk while **Figure 2** displays the actual tribometer device.

In **Figure 1**, FN stands for the normal force that is the load on the aluminum pin whereas FR represents the resistive force called friction that arises from the sliding contact of the aluminum pin on the steel disk. In **Figure 2**, the pin is firmly attached to the pin support and then linked to the rotating plain disk with the desired load which is usually applied through a pulley system. Lubricant is pumped continuously from the machine. To simplify the contact geometry, a hemispherical pin is used which directly touches the disk surface at the beginning of the experiment. A hygrometer measures the relative humidity of the air in the chamber whereas the rpm of the rotating shaft that supports the disk is measured with the help of tachometer. The variation of friction coefficient with friction time is recorded automatically. Necessary information regarding stainless steel disk and aluminum pin is presented in **Tables 1**–**3**. The aluminum pin is in fact an alloy of aluminum and silicon. In addition, the data sheets for the Helix oil and Polytron additive are given in **Tables 4** and **5**. The data and basic information with reference

### **Figure 1.**

*Sketch of the pin-on-disk. The dimensions of the pin were 32 mm (l) × 10 mm(dia) and dimensions of the disk were 8 mm (*l*) × 163 mm (dia).*

**Figure 2.** *Pin-on-disk tribotester machine.*


### **Table 1.**

*Specification and composition of stainless steel disk (SUS304) [53–55].*


### **Table 2.**

*Chemical composition of aluminum pin (A390) [53–55].*


**21**

*Experimental Results of the Tribology of Aluminum in the Presence of Polytron Additive*

**Property Method Shell Helix Ultra** SAE viscosity grade 5W–40

C cSt IP 71 81.1

C cSt IP 71 14.5 Viscosity index IP 226 187

C (kg/L) IP 365 0.856

C) IP 15 –39

HTHS viscosity @ 150°C (mPa s) 3.68

C ) IP 34 206

to aluminum metal, steel disk, Helix oil, and polytron are taken from the research work of Ahmer et al. [53], John [54], and Ahmer et al. [55]. One can guess from **Table 5** that Polytron is marketed in a liquid state and is yellowish in color and, unlike other solid additives, it is odorless. Its flash point is beyond 200°C whereas its

boiling point is further than 300° C and it is scarcely soluble in water.

F SUS 391

F SUS 61

C) Low Evaporation point Higher than ether (>34.6°C)

The experimental work was performed in the Tribology Laboratory of Universiti Kebangsaan Malaysia, UKM,at ambient temperature (300 K) and pressure (760 mmHG) and approximately 70% relative humidity. Helix oil was chosen as representative base oil for the experiment and its brand 5W–40 was supplied by Shell Oils. The additive was Polytron MTC which was supplied by the Malaysian Association of Productivity. We used soft aluminum-silicon alloy A390 and stainless steel SUS304 as pin and disk material, respectively. Separate test runs were taken for the base oil stock and the 10% polytron additive plus the base oil stock. The runs were executed for 240 min in each case and the wear rates of the pin were then calculated from the measured weight loss. The mass and volume of the pin

**2.2 Materials and chemicals**

*DOI: http://dx.doi.org/10.5772/intechopen.84620*

Kinematic viscosity

@40°

@100°

Density @15°

Pour point (

Viscosity @100°

Viscosity @210°

**Table 5.**

Water solubility (<sup>T</sup> <sup>=</sup> <sup>20</sup>°

*Data sheet of Polytron [53–55].*

**Table 4.**

Flash point PMCC (

°

°

*Typical physical properties of Shell Helix Ultra oil (5*W–*40) [53–55].*

**Physical/chemical property Remarks** State Liquid Color Yellowish clear Smell Odorless Specific gravity 60/60 ≈ 1.00 Boiling point range >300°C Flash point >200°C

### **Table 3.**

*Mechanical properties of the aluminum pin and steel disc [53–55].*

*Experimental Results of the Tribology of Aluminum in the Presence of Polytron Additive DOI: http://dx.doi.org/10.5772/intechopen.84620*


### **Table 4.**

*Friction, Lubrication and Wear*

Chemical composition (weight percent)

**Composition Min (weight percent) Max (weight percent)**

**Component Specification/weight percent** Disk dimensions 165 nm (diameter) × 8 mm (height) Counter bore M5 holes from bottom × 4 nos. Counter bore M5 holes from top × 4 nos. Holes M4 tapped holes × 2 nos.

Carbon (C) ≤ 0.08% Silicon (Si) ≤ 1.00% Manganese (Mn) ≤ 2% Phosphorous (P) ≤ 0.045% Sulfur (S) ≤ 0.30% Nickel (Ni) ≤ 8 –10.5% Chromium (Cr) ≤ 18.00–20.00%

Silicon 0.4% 0.8% Iron — 0.7% Copper 0.15% 0.15% Manganese — 0.15% Magnesium 0.8% 1.2% Chromium 0.04% 0.35% Zinc — 0.25% Titanium — 0.15% Aluminum 95.85% 98.56%

*Specification and composition of stainless steel disk (SUS304) [53–55].*

**20**

**Table 3.**

**Table 2.**

**Table 1.**

*Chemical composition of aluminum pin (A390) [53–55].*

*Mechanical properties of the aluminum pin and steel disc [53–55].*

**Property Alloy**

Density 2.72 g/cm<sup>3</sup> 8000 kg/m<sup>3</sup> Hardness 112.65 VHN 88 HB Tensile strength 250.00 520 MPa Yield strength — 240 MPa Young's modulus — 190 GPa Poisson ratio — 0.27–0.30

**Aluminum pin A390 Steel disk SUS304**

*Typical physical properties of Shell Helix Ultra oil (5*W–*40) [53–55].*


### **Table 5.**

*Data sheet of Polytron [53–55].*

to aluminum metal, steel disk, Helix oil, and polytron are taken from the research work of Ahmer et al. [53], John [54], and Ahmer et al. [55]. One can guess from **Table 5** that Polytron is marketed in a liquid state and is yellowish in color and, unlike other solid additives, it is odorless. Its flash point is beyond 200°C whereas its boiling point is further than 300° C and it is scarcely soluble in water.

### **2.2 Materials and chemicals**

The experimental work was performed in the Tribology Laboratory of Universiti Kebangsaan Malaysia, UKM,at ambient temperature (300 K) and pressure (760 mmHG) and approximately 70% relative humidity. Helix oil was chosen as representative base oil for the experiment and its brand 5W–40 was supplied by Shell Oils. The additive was Polytron MTC which was supplied by the Malaysian Association of Productivity. We used soft aluminum-silicon alloy A390 and stainless steel SUS304 as pin and disk material, respectively. Separate test runs were taken for the base oil stock and the 10% polytron additive plus the base oil stock. The runs were executed for 240 min in each case and the wear rates of the pin were then calculated from the measured weight loss. The mass and volume of the pin


### **Table 6.**

*Recorded data of the wear test for helix base oil (5*W–*40).*


### **Table 7.**

*Recorded data of the wear test for the Helix oil plus 10% polytron.*

were measured both before and after running the experiment and the data set are presented in **Tables 6** and **7**.

### **2.3 Procedure and calculations**

In the experiment, an aluminum pin having a diameter of 10 mm was slid against the steel disk. The applied load was 20.0 kg. In the first instance, 100%

**23**

**Table 8.**

by Eq. (4).

equations are recorded in **Table 8**.

Mass wear rate 3.33 × 10−3

Volume wear rate 1.28 × 10−3

*Computed tribological parameters for the aluminum pin.*

*Experimental Results of the Tribology of Aluminum in the Presence of Polytron Additive*

Helix oil was used and its volume in the graduated cylinder was 2000 mL. In the second instance, 90% Helix oil having a volume of 1800 mL was mixed with 10% polytron additive which amounted to 200 mL volume of polytron. Before running the test, the disk was completely covered with the lubricant by keeping a steady flow rate of the lubricant at nearly 0.5 mL/min. The wear volume was calculated from the diameter of the wear scar generated by the pin. Typical wear versus time curves were obtained with the help of MatLab software and were polynomially

Wear process is in general quantified by the wear rate. Wear rate is defined as the volume or mass of material removed per unit time or per unit sliding distance. In order to determine the extraordinary contribution of the polytron additive in the helix lubricant, we calculated three key tribological parameters, namely, mass wear rate, volume wear rate, and wear coefficient. The defining equations for these

Mass wear rate = m/t (1)

Volume wear rate = V/t (2)

Wear coefficient (k) = (V × H)/(N × S) (3)

The coefficient of friction μ is obtainable from the experimentally obtained data. The popular defining expression for the coefficient of friction is like that described

μ = FR/N (4)

In the above equations, the variable m stands for the worn out mass of the aluminum pin, t represents the time span of the experimental run, V refers to the worn out volume of the pin called the wear volume, H points to the hardness of the sliding pin, FR is the tangential resistive force between the pin and the disk and is termed as friction force, N is the normal load, and S is the sliding distance on the disk. It is to be noted that the friction coefficient μ is a convenient way to characterize the resistance to relative motion between the surfaces, but it is not a material property nor is it a physical constant. The effect of the polytron additive on different tribological parameters in the experiment and the computed values from the above-mentioned

**Parameter Helix base oil (100%) Helix oil (90%) plus Polytron (10%)**

mm<sup>3</sup>

mg/min 8.33 × 10−4

/min 6.08 × 10−5

mg/min

/N

mm<sup>3</sup> /min

Wear 70 μm 20 μm

Coefficient of friction 0.012 0.004 Wear coefficient (k) — 4.22 × 10−11m2

Total mass loss 0.7992 mg 0.1992 mg Total volume loss 0.3079 mm<sup>3</sup> 0.01459 mm<sup>3</sup>

parameters are specified by Eqs. (1–3) as written down below [56].

Eq. (3) is the famous Archard equation of tribology.

*DOI: http://dx.doi.org/10.5772/intechopen.84620*

fitted in order to decide the data trend.

*Experimental Results of the Tribology of Aluminum in the Presence of Polytron Additive DOI: http://dx.doi.org/10.5772/intechopen.84620*

Helix oil was used and its volume in the graduated cylinder was 2000 mL. In the second instance, 90% Helix oil having a volume of 1800 mL was mixed with 10% polytron additive which amounted to 200 mL volume of polytron. Before running the test, the disk was completely covered with the lubricant by keeping a steady flow rate of the lubricant at nearly 0.5 mL/min. The wear volume was calculated from the diameter of the wear scar generated by the pin. Typical wear versus time curves were obtained with the help of MatLab software and were polynomially fitted in order to decide the data trend.

Wear process is in general quantified by the wear rate. Wear rate is defined as the volume or mass of material removed per unit time or per unit sliding distance. In order to determine the extraordinary contribution of the polytron additive in the helix lubricant, we calculated three key tribological parameters, namely, mass wear rate, volume wear rate, and wear coefficient. The defining equations for these parameters are specified by Eqs. (1–3) as written down below [56].

$$\text{Mass\,\,weak\,\,rate = m/t} \tag{1}$$

$$\text{Volume\\_wear rate} = \mathbf{V}/\mathbf{t} \tag{2}$$

$$\text{Wear coefficient (k)} = (\text{V} \times \text{H}) / (\text{N} \times \text{S}) \tag{3}$$

Eq. (3) is the famous Archard equation of tribology.

The coefficient of friction μ is obtainable from the experimentally obtained data. The popular defining expression for the coefficient of friction is like that described by Eq. (4).

$$
\boldsymbol{\mu} = \mathbf{F}\_{\mathcal{R}} / \mathbf{N} \tag{4}
$$

In the above equations, the variable m stands for the worn out mass of the aluminum pin, t represents the time span of the experimental run, V refers to the worn out volume of the pin called the wear volume, H points to the hardness of the sliding pin, FR is the tangential resistive force between the pin and the disk and is termed as friction force, N is the normal load, and S is the sliding distance on the disk. It is to be noted that the friction coefficient μ is a convenient way to characterize the resistance to relative motion between the surfaces, but it is not a material property nor is it a physical constant. The effect of the polytron additive on different tribological parameters in the experiment and the computed values from the above-mentioned equations are recorded in **Table 8**.


### **Table 8.**

*Computed tribological parameters for the aluminum pin.*

*Friction, Lubrication and Wear*

**Before the wear run**

**During the wear run**

**After the wear run**

**Before the wear run**

**During the wear run**

**After the wear run**

*Recorded data of the wear test for helix base oil (5*W–*40).*

**Table 6.**

**Test variable Assessed value**

Material of the wear disk Stainless steel S304 Diameter of the wear disk 80 mm Mass of the pin 6.4480 g Length of the pin 32.00 mm

Speed of the wear disk 500 rpm Time allocated 240 min≈ 14,400 s Sliding speed 2.09 m/s Sliding distance 30.163 km ≈ 30,163.2 m

Mass of the pin 6.4470 g Length of the Pin 31.981 mm

**Test variable Assessed value**

Quantity of Helix plus Polytron 2000 mL Load 196.2 N Material of the pin Al▬Si alloy A390 Pin diameter 10.00 mm Length of the pin 32.00 mm Material of the wear disk Stainless steel SUS 304 Diameter of the wear disk 80 mm

Speed of the wear disk 500 rpm Time allocated 240 min≈ 14,400 s Sliding speed 2.09 m/s Sliding distance 30.163 km ≈ 30163.2 m

Mass of the pin 6.4472 g Length of the pin 31.996 mm

**22**

**Table 7.**

presented in **Tables 6** and **7**.

**2.3 Procedure and calculations**

*Recorded data of the wear test for the Helix oil plus 10% polytron.*

were measured both before and after running the experiment and the data set are

In the experiment, an aluminum pin having a diameter of 10 mm was slid against the steel disk. The applied load was 20.0 kg. In the first instance, 100%

### **3. Results and discussion**

The experimentally obtained data and their polynomial fits for the wear behavior of the aluminum metallic pin are displayed in **Figures 3** and **4** for two different configurations in which the experiment was carried out. The adopted test configurations in the experiment were: aluminum pin versus Helix oil-on-steel disk, tagged as AHS configuration, and aluminum pin versus 10% polytron plus 90% Helix oil-on-steel disk, which will be referred to as the APS configuration in the forthcoming discussion.

**Figures 3** and **4** show the plot of the wear pattern of the aluminum pin with the passage of time and then the sliding distance on the steel disk of the experiment under consideration. The red line represents wear in the AHS configuration whereas the blue line symbolizes the wear in the APS configuration. It is very much clear from this plot that the polytron additive provides excellent let-up the wear of the tribosystem consisting of an aluminum pin on a steel disk interposed by an oil film of 10% Polytron and 90% Helix. It shows that that the wear in the AHS configuration starts from 70 micron and then stabilizes at approximately 65 micron, but in the APS

### **Figure 3.**

*Graph of the wear of aluminum pin against time in the AHS and APS configurations. The time for the experiment was 240 min.*

### **Figure 4.**

*Graph of the wear of aluminum vs. sliding distance in the AHS and APS configuration. The sliding distance for the experiment was 30.163 km.*

**25**

in **Figures 5** and **6**.

*experiment was 30.161 km.*

**Figure 6.**

**Figure 5.**

that the ratio in the

*Experimental Results of the Tribology of Aluminum in the Presence of Polytron Additive*

*Evolution of the COF with time in AHS and APS configuration. The experimental time was 240 min.*

configuration wear stays at nearly 20 micron. Then, for the same two configurations and under the same experimental conditions, the evolution of the coefficient of friction μ with reference to time span and sliding distance has been plotted as shown

*Evolution of COF with sliding distance in the AHS and APS configuration. The sliding distance for the* 

It is perceivable from the graph of **Figures 5** and **6** that in the AHS format, the initial value of the friction coefficient is almost zero and increases almost linearly to a value of 0.012 in a time span of 100 min of rubbing after which COF stands stable at this very value. The low value of μ in the initial stage of rubbing is probably due to the presence of a layer of foreign material on the disk surface which may be due to some moisture or oxide of the aluminum metal because it readily oxidizes in air. Conversely, in the APS setup, the coefficient of friction starts from a value of 0.005 and then further declines to virtually 0.004. It is recognizable that polytron reduces the wear of the aluminum pin significantly and one can predict

APS configuration is effectively more than 30% in comparison with AHS configuration. Despite the fact that in our experiment the normal force and sliding distance had very large values in difference with other experimenters, nevertheless the evolved coefficient of friction had negligibly small value when meager 10% polytron was added to 90% helix which in turn endorsed the positive contribution of the polytron in friction minimization. These findings in our tribological

*DOI: http://dx.doi.org/10.5772/intechopen.84620*

*Experimental Results of the Tribology of Aluminum in the Presence of Polytron Additive DOI: http://dx.doi.org/10.5772/intechopen.84620*

**Figure 5.**

*Friction, Lubrication and Wear*

**3. Results and discussion**

ing discussion.

The experimentally obtained data and their polynomial fits for the wear behavior of the aluminum metallic pin are displayed in **Figures 3** and **4** for two different configurations in which the experiment was carried out. The adopted test configurations in the experiment were: aluminum pin versus Helix oil-on-steel disk, tagged as AHS configuration, and aluminum pin versus 10% polytron plus 90% Helix oil-on-steel disk, which will be referred to as the APS configuration in the forthcom-

**Figures 3** and **4** show the plot of the wear pattern of the aluminum pin with the passage of time and then the sliding distance on the steel disk of the experiment under consideration. The red line represents wear in the AHS configuration whereas the blue line symbolizes the wear in the APS configuration. It is very much clear from this plot that the polytron additive provides excellent let-up the wear of the tribosystem consisting of an aluminum pin on a steel disk interposed by an oil film of 10% Polytron and 90% Helix. It shows that that the wear in the AHS configuration starts from 70 micron and then stabilizes at approximately 65 micron, but in the APS

*Graph of the wear of aluminum pin against time in the AHS and APS configurations. The time for the* 

*Graph of the wear of aluminum vs. sliding distance in the AHS and APS configuration. The sliding distance for* 

**24**

**Figure 4.**

*the experiment was 30.163 km.*

**Figure 3.**

*experiment was 240 min.*

*Evolution of the COF with time in AHS and APS configuration. The experimental time was 240 min.*

### **Figure 6.**

*Evolution of COF with sliding distance in the AHS and APS configuration. The sliding distance for the experiment was 30.161 km.*

configuration wear stays at nearly 20 micron. Then, for the same two configurations and under the same experimental conditions, the evolution of the coefficient of friction μ with reference to time span and sliding distance has been plotted as shown in **Figures 5** and **6**.

It is perceivable from the graph of **Figures 5** and **6** that in the AHS format, the initial value of the friction coefficient is almost zero and increases almost linearly to a value of 0.012 in a time span of 100 min of rubbing after which COF stands stable at this very value. The low value of μ in the initial stage of rubbing is probably due to the presence of a layer of foreign material on the disk surface which may be due to some moisture or oxide of the aluminum metal because it readily oxidizes in air. Conversely, in the APS setup, the coefficient of friction starts from a value of 0.005 and then further declines to virtually 0.004. It is recognizable that polytron reduces the wear of the aluminum pin significantly and one can predict that the ratio in the

APS configuration is effectively more than 30% in comparison with AHS configuration. Despite the fact that in our experiment the normal force and sliding distance had very large values in difference with other experimenters, nevertheless the evolved coefficient of friction had negligibly small value when meager 10% polytron was added to 90% helix which in turn endorsed the positive contribution of the polytron in friction minimization. These findings in our tribological

### **Figure 7.**

*Graph of the mass loss of aluminum pin vs. time for the AHS and APS configuration. The time of the experiment was 240 min.*

### **Figure 8.**

*Experimental graph of the mass loss of aluminum pin vs. sliding distance in the AHS and APS configuration. Sliding distance for the experiment was 30.161 km.*

### **Figure 9.**

*Graph of the volume loss of aluminum pin vs. time in the AHS and APS configuration. Time for the experiment was 240 min.*

experiment with polytron additive in Helix oil are significantly superior in comparison with the findings of other researchers like Nuruzzaman and Chowdhury [57], Bhushan and Kulkarni [58], and Le and Lin [59].

To further clarify the effect of polytron additive, we examined the mass and volume losses of the aluminum pin with regard to time as well as sliding distance and separate graphs were drawn for both the AHS and APS configurations. The comparison plots for the mass losses are shown in **Figures 7** and **8** while the comparison graphs for the volume losses are illustrated in **Figures 9** and **10**. A deep examination of all the figures reveals that the mass as well as volume loss cannot be controlled with Helix oil alone; rather, it will damage the contact surfaces in a

**27**

steel.

**4. Conclusions**

1.28 × 10<sup>−</sup><sup>3</sup>

attaining a value of 8.33×10<sup>−</sup><sup>4</sup>

mm3

*Experimental Results of the Tribology of Aluminum in the Presence of Polytron Additive*

short while, whereas only a scanty addition of 10% of Polytron reduces the mass as well as the volume losses to almost zero level. This is a tremendous change and is visible to the naked eye and directly identifies the supreme antifriction and antiwear capability of the polytron additive. This observation with the addition of polytron additive is fairly divergent with the high wear rate results of researchers like Suarez et al. [60] who studied the popular ZDDP additive in

*Graph of the volume loss of aluminum vs. time in the AHS and APS configuration. The sliding distance for the* 

In the same vein, the tribological parameters in our research work are much better than those of Anand et al. [61] who used phosphonium ionic liquid additives in diesel engine lubricants. More to the point, the experimental predictions in our research effort on wear and friction minimization are even far superior to the findings of Chen et al. [62] and Su et al. [63] who used nano-additives in different lubricating media. With an advantage, the calculated values of mass and volume losses of the aluminum pin show that polytron additive attenuates the mass wear rate by an order of magnitude while the volume wear rate of aluminum is alleviated by two orders of magnitude and these outcomes in sequence yield just a nominal value for the wear coefficient as can be noticed from **Table 8**. This outstanding performance identifies that polytron had the capability of permeation into the metal crystal structure of aluminum and subsequent adherence to the metallic surface as an unbreakable surface film that diminished the wear of aluminum surface and consequently curtailed friction between the rubbing surfaces of aluminum and

1.The wear of the aluminum metal surface in the Helix base oil was circa 70 μm. The addition of 10% of Polytron additive declined the wear to 20 μm, repre-

which decreased by an order of magnitude in the Helix plus Polytron mixture,

/min and it decreased by two orders of magnitude in the Helix

mm3

/min.

mg/min

senting an excess of 2/3 decrement in the wear of the metal.

2.The mass wear rate of the aluminum pin in the Helix base oil was 3.3×10<sup>−</sup><sup>3</sup>

mg/min.

3.The mass wear rate of the aluminum pin in the Helix base oil was

plus Polytron mixture by assuming a value 6.08 × 10<sup>−</sup><sup>5</sup>

*DOI: http://dx.doi.org/10.5772/intechopen.84620*

mineral oil stock.

*experiment was 30.161 km.*

**Figure 10.**

*Experimental Results of the Tribology of Aluminum in the Presence of Polytron Additive DOI: http://dx.doi.org/10.5772/intechopen.84620*

**Figure 10.**

*Friction, Lubrication and Wear*

**Figure 7.**

**Figure 8.**

**Figure 9.**

*was 240 min.*

*Sliding distance for the experiment was 30.161 km.*

*experiment was 240 min.*

**26**

experiment with polytron additive in Helix oil are significantly superior in comparison with the findings of other researchers like Nuruzzaman and Chowdhury

*Graph of the volume loss of aluminum pin vs. time in the AHS and APS configuration. Time for the experiment* 

*Experimental graph of the mass loss of aluminum pin vs. sliding distance in the AHS and APS configuration.* 

*Graph of the mass loss of aluminum pin vs. time for the AHS and APS configuration. The time of the* 

To further clarify the effect of polytron additive, we examined the mass and volume losses of the aluminum pin with regard to time as well as sliding distance and separate graphs were drawn for both the AHS and APS configurations. The comparison plots for the mass losses are shown in **Figures 7** and **8** while the comparison graphs for the volume losses are illustrated in **Figures 9** and **10**. A deep examination of all the figures reveals that the mass as well as volume loss cannot be controlled with Helix oil alone; rather, it will damage the contact surfaces in a

[57], Bhushan and Kulkarni [58], and Le and Lin [59].

*Graph of the volume loss of aluminum vs. time in the AHS and APS configuration. The sliding distance for the experiment was 30.161 km.*

short while, whereas only a scanty addition of 10% of Polytron reduces the mass as well as the volume losses to almost zero level. This is a tremendous change and is visible to the naked eye and directly identifies the supreme antifriction and antiwear capability of the polytron additive. This observation with the addition of polytron additive is fairly divergent with the high wear rate results of researchers like Suarez et al. [60] who studied the popular ZDDP additive in mineral oil stock.

In the same vein, the tribological parameters in our research work are much better than those of Anand et al. [61] who used phosphonium ionic liquid additives in diesel engine lubricants. More to the point, the experimental predictions in our research effort on wear and friction minimization are even far superior to the findings of Chen et al. [62] and Su et al. [63] who used nano-additives in different lubricating media. With an advantage, the calculated values of mass and volume losses of the aluminum pin show that polytron additive attenuates the mass wear rate by an order of magnitude while the volume wear rate of aluminum is alleviated by two orders of magnitude and these outcomes in sequence yield just a nominal value for the wear coefficient as can be noticed from **Table 8**. This outstanding performance identifies that polytron had the capability of permeation into the metal crystal structure of aluminum and subsequent adherence to the metallic surface as an unbreakable surface film that diminished the wear of aluminum surface and consequently curtailed friction between the rubbing surfaces of aluminum and steel.

### **4. Conclusions**


### **Acknowledgements**

The authors are obliged to the management of Universiti Kebangsaan Malaysia for providing laboratory facilities and are especially thankful to the cooperative technical staff of the tribology laboratory. S. M. H. Ahmer and L. S. Jan pay special thanks to Dr. Mohamed Ahmed Siddig of Al-Neelain University, Sudan, and Dr. Siti Fazlili Abdullah of Universiti Tenaga Nasional, Malaysia, for their valuable suggestions.

### **Conflict of interest**

The authors declare that there is no conflict of interest regarding the publication of this paper.

**29**

**Author details**

and Lal Said Jan4

Pakhtunkhwa, Pakistan

KSA

Syed Mohammad Hassan Ahmer1

\*

provided the original work is properly cited.

\*Address all correspondence to: lalsaidjan@gmail.com

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

, Nusratullah Khan2

1 Department of Physics, Yanbu University College, Yanbu al Sinaiyah, KSA

3 Islamia College University, Peshawar, Khyber Pakhtunkhwa, Pakistan

2 Department of Computer Science, Yanbu University College, Yanbu al Sinaiyah,

4 Department of Physics, Government Postgraduate College, Timergara, Khyber

, S. Inayat Ali Shah3

*Experimental Results of the Tribology of Aluminum in the Presence of Polytron Additive*

*DOI: http://dx.doi.org/10.5772/intechopen.84620*

### **Nomenclature**


*Experimental Results of the Tribology of Aluminum in the Presence of Polytron Additive DOI: http://dx.doi.org/10.5772/intechopen.84620*

### **Author details**

*Friction, Lubrication and Wear*

**Acknowledgements**

**Conflict of interest**

of this paper.

**Nomenclature**

MTC metal treatment concentrate

ZDDP zinc dialkyl-diethylthiophosphate μ coefficient of friction (COF)

F N normal force/(load) F R resistive force/friction TCP tricresylphosphate

4.The value of the coefficient of friction in the Helix oil was estimated at 0.012 which trimmed down to an extremely low value of 0.004 in the combination

5.Polytron, due to its polar nature, proves to be an effective antiwear additive in the Helix base oil and hence can intrinsically reduce friction by orders of magnitude in mechanical processes and consequently prolong the life span of mechanical parts and, in turn, contribute to considerable fuel and oil economy.

The authors are obliged to the management of Universiti Kebangsaan Malaysia for providing laboratory facilities and are especially thankful to the cooperative technical staff of the tribology laboratory. S. M. H. Ahmer and L. S. Jan pay special thanks to Dr. Mohamed Ahmed Siddig of Al-Neelain University, Sudan, and Dr. Siti Fazlili Abdullah of Universiti Tenaga Nasional, Malaysia, for their valuable suggestions.

The authors declare that there is no conflict of interest regarding the publication

of 10% polytron additive and 90% Helix oil.

**28**

Syed Mohammad Hassan Ahmer1 , Nusratullah Khan2 , S. Inayat Ali Shah3 and Lal Said Jan4 \*

1 Department of Physics, Yanbu University College, Yanbu al Sinaiyah, KSA

2 Department of Computer Science, Yanbu University College, Yanbu al Sinaiyah, KSA

3 Islamia College University, Peshawar, Khyber Pakhtunkhwa, Pakistan

4 Department of Physics, Government Postgraduate College, Timergara, Khyber Pakhtunkhwa, Pakistan

\*Address all correspondence to: lalsaidjan@gmail.com

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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[14] Wang WZ, Chen H, Hu YZ, Wang H. Effect of surface roughness parameters on mixed lubrication characteristics. Tribology International. 2006;**39**:522-527. DOI: 10.1016/j. triboint.2005.03.10.018

[15] Bressan JD, Daros DP, Sokolowski A, Mesquita RA, Barbosa CA. Influence of hardness on the wear resistance of 17-4 PH stainless steel evaluated by the pin-on-disc testing. Journal of Materials Processing Technology. 2008;**205**:353-359. DOI: 10.1016/j. jmatprotec.2007.11.251

[16] Oktay ST, Suh NP. Wear debris formation and agglomeration. Journal of Tribology. 1992;**114**:379-393. DOI: 10.1115/1.2920897

[17] Zhang SC, Pan QL, Yan J, Huang X. Effects of sliding velocity and

**31**

*Experimental Results of the Tribology of Aluminum in the Presence of Polytron Additive*

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[26] Petlyuk AM, Adams RJ. Oxidation stability and tribological behavior of vegetable oil hydraulic fluids. Tribology Transactions. 2004;**47**:182-187. DOI:

[27] Du L, Xu B, Dong S, Yang H, Tu W. Study of tribological characteristics and wear mechanism of nano-particle strengthened nickel-based composite coatings under abrasive contaminant lub-rication. Wear. 2004;**257**:1058-1063.

10.1080/05698190490431849

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10.1016/j.triboint.2007.08.005

net/KEM.767.181

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[30] Ligier JL, Noel B. Friction reduction and reliability for engines bearings. Lubricants. 2015;**3**:569-596. DOI: 10.3390/lubricants3030569

[31] Tung SC, McMillan ML. Automotive tribology overview of current advances and challenges for the future. Tribology International. 2004;**37**:517-536. DOI: 10.1016/j.triboint.2004.01.013

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[33] Qu J, Luo H, Chi M, Ma C, Blau PJ, Dai S. Comparison of an oil-miscible

molecules14082888

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10.1115/1.2837065

*DOI: http://dx.doi.org/10.5772/intechopen.84620*

normal load on tribological behavior of aged Al-Sn-Cu alloy. Transactions of Nonferrous Metals Society of China. 2016;**26**:1809-1819. DOI: 10.1016/

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**30**

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[35] Totolin V, Minami I, Gabler C, Brenner J, Dörr N. Lubrication

mechanism of phosphonium phosphate ionic liquid additive in alkylborane– imidazole complexes. Tribology Letters. 2014;**53**:421-432. DOI: 10.1007/

[36] González R, Battez AH, Viesca J, Higuera-Garrido A, Fernández-González A. Lubrication of DLC

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[38] Battez AH, González R, Viesca JL, Blanco D, Asedegbega E, Osorio A. Tribological behavior of two

imidazolium ionic liquids as lubricant additives for steel/steel contacts. Wear. 2009;**266**:1224-1228. DOI: 10.1016/j.

[39] Blanco D, González R, Hernández

(pentafluoroethyl) trifluorophosphate as base oil additive in the lubrication

BA, Viesca J, Fernández GA. Use of ethyl-dimethyl-2 methoxyethylammonium tris

coatings with two tris(pentafluoroethyl)

triboint.2013.11.010

am502980m

s11249-013-0281-0

trifluorophosphate anionbased ionic liquids. Tribology Transactions. 2013;**56**:887-895. DOI: 10.1080/10402004.2013.810319

431-443. DOI: 10.1007/ s11249-013-0226-7

wear.2009.03.043

ionic liquid and ZDP as a lubricant antiwear additive. Tribology International.

of TiN PVD coating. Tribology International. 2011;**44**:645-650. DOI:

10.1016/j.triboint.2011.01.004

[41] Saka N, Liou MJ, Suh NP. The role of tribology in electrical contact phenomena. Wear. 1984;**100**:77-105. DOI: 10.1016/0043-1648(84)90007-3

Vedeneeva LM, Parenago OP, Migdal CA, et al. Surfacecapped molybdenum sulphide nanoparticles—A novel type of

2004;**16**:207-214. DOI: 10.1002/

[43] Liu YB, Lim SC, Ray S, Rohatgi PK. Friction and wear of aluminumgraphite composites: The smearing process of graphite during sliding. Wear. 1992;**159**:201-205. DOI: 10.1016/0043-16489(92)90303-p

[44] Zhang L, Chen L, Wan H, Chen J, Zhou H. Synthesis and tribological properties of stearic acid-modified anatase (TiO2) nanoparticles. Tribology Letters. 2011;**41**:409-416. DOI: 10.1007/

[45] Zhang BS, Xu BS, Xu Y, Gao F, Shi PJ, Wu YX. Copper nanoparticles effect on the tribological properties

[46] Cumings J, Zettl A. Low-friction nano-scale linear bearing realized from multiwall carbon nanotubes. Science. 2000;**289**:602-604. DOI: 10.1126/

of hydro-silicate powders as lubricant additive for steel-steel contacts. Tribology International. 2011;**44**:878-886. DOI: 10.1016/j.

ls.3010160302

s11249-010-9724-z

triboint.2011.03.002

science.289.5479.602

[42] Bakunin VN, Suslov AY, Kuzmina GN,

lubricant additive. Lubrication Science.

wear.2012.04.015

[40] Yu B, Bansal DG, Qu J, Sun X, Luo H, Dai S. Oil-miscible and noncorrosive phosphonium-based ionic liquids as candidate lubricant additives. Wear. 2012;**289**:58-64. DOI: 10.1016/j.

**32**

[48] Quaroni L, Chumanov G. Preparation of polymer-coated functionalized silver nanoparticles. Journal of the American Chemical Society. 1999;**121**:10642-10643. DOI: 10.1021/ja992088q

[49] Mandal T, Fleming MS, Walt DR. Preparation of polymer-coated gold nanoparticles by surface-confined living radical polymerization at ambient temperature. Nano Letters. 2002;**2**:3-7. DOI: 10.1021/nl015582c

[50] Benabdallah HS, Wei JJ. Effects of lubricants on the friction and wear properties of PTFE and POM. Journal of Tribology. 2005;**127**:766-775. DOI: 10.1115/1.2005276

[51] Zhang Z, Liu W, Xue Q. Study on lubricating mechanisms of La(OH)3 nano-cluster modified by compound containing nitrogen in liquid paraffin. Wear. 1998;**218**:139-144. DOI: 10.1016/ S0043-1648(98)00225-7

[52] Hu ZS, Dong JX. Study on antiwear and reducing friction additive of nanometer titanium oxide. Wear. 1998;**216**:92-96. DOI: 10.1016/ S0043-1648(97)00252-4

[53] Ahmer SMH, Jan LS, Siddig MA, Abdullah SF. Experimental results of the tribology of aluminum measured with a pin-on-disk tribometer: Testing configuration and additive effects. Friction. 2016;**4**:124-134. DOI: 10.1007/ s40544-016-0109-7

[54] John EH. Aluminum: Properties and Physical Metallurgy. Ohio: ASM International; 1984. pp. 11-20. DOI: 10.1361/appm1984p025

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[57] Nuruzzaman DM, Chowdhury MA. Effect of load and sliding velocity on friction coefficient of aluminum sliding against different pin materials. American Journal of Materials Science. 2012;**2**:26-31. DOI: 10.5923/j. materials.20120201.05

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[61] Anand M, Hadfield M, Viesca JL, Thomas B, Hernández Battez A, Austen S. Ionic liquids as tribological performance improving additive for in-service and used fully-formulated diesel engine lubricants. Wear. 2015;**334**:67-74. DOI: 10.1016/j. wear.2015.01.055

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Chapter 3

Abstract

Sergey Fedorov

of the Friction

contacts of real tribosystems are proposed.

nanostructure, wear standard

1. Introduction

transformations.

35

Structural-Energy Interpretation

The structural-energy model of elastic-plastic deformation is considered as the main mechanism of transformation and dissipation of energy under friction. The equations of friction energy balance are proposed. The energy interpretation of the coefficient of friction is given. A structural-energy diagram of the friction surfaces is proposed. The energy regularities of evolution of tribological contact (elementary tribosystem) are discussed. The idea of the smallest structural element of dissipative friction structures (mechanical (nano) quantum) is discussed. Mechanical quantum is dynamic oscillator of dissipative friction structure. The nano-quantum model of the surfaces damping is proposed. Calculations for some Hertzian heavily loaded

Modern tribology considers elastic-plastic deformation of friction surfaces as the

The macroscopic phenomenon of plastic deformation, damage and destruction of a solid element is considered as a set of a huge number of microscopic elementary acts of atomic-molecular rearrangements, causing the generation (reproduction) by sources, movement, interaction and destruction of various kinds of elementary defects on the drains. Each defect is a carrier of excess potential energy and on its

From the thermodynamic point of view, the whole variety of mechanisms and structural levels of plastic flow can be divided into two most characteristic groups adaptive and dissipative types. The first group should include the mechanism of nucleation and accumulation in the local volumes of various kinds of elementary defects and damages of the structure. The second group includes elementary acts of atomic-molecular rearrangements associated with the movement and destruction of

main mechanism of transformation and dissipation of energy during friction. The modern view of plastic deformation offers ergodynamics of deformable solids [1–3]. Ergodynamics of deformable solids is a synthesis to the problem of deformation most general laws of thermodynamics for non-reversable processes, molecular kinetics and dislocation theory in their mutual, dialectical tie on the basis of a most general law of nature—the law of energy conservation at its

formation is spent strictly defined work of external forces.

various defects on the drains, that is, controlling the dynamic return.

Keywords: energy balance, contact evolution, adaptation, dissipation,

[63] Su Y, Gong L, Chen D. An investigation on tribological properties and lubrication mechanism of graphite nanoparticles as vegetable based oil additive. Journal of Nanomaterials. 2015;1−7. DOI: 10.1155/2015/276753

### Chapter 3

*Friction, Lubrication and Wear*

the antiwear ability of the prepared nanoparticles as additive in liquid paraffin. Wear. 1998;**218**:153-158. DOI: 10.1016/S0043-1648(98)00220-8

investigation on tribological properties and lubrication mechanism of graphite nanoparticles as vegetable based oil additive. Journal of Nanomaterials. 2015;1−7. DOI: 10.1155/2015/276753

[63] Su Y, Gong L, Chen D. An

**34**

### Structural-Energy Interpretation of the Friction

Sergey Fedorov

### Abstract

The structural-energy model of elastic-plastic deformation is considered as the main mechanism of transformation and dissipation of energy under friction. The equations of friction energy balance are proposed. The energy interpretation of the coefficient of friction is given. A structural-energy diagram of the friction surfaces is proposed. The energy regularities of evolution of tribological contact (elementary tribosystem) are discussed. The idea of the smallest structural element of dissipative friction structures (mechanical (nano) quantum) is discussed. Mechanical quantum is dynamic oscillator of dissipative friction structure. The nano-quantum model of the surfaces damping is proposed. Calculations for some Hertzian heavily loaded contacts of real tribosystems are proposed.

Keywords: energy balance, contact evolution, adaptation, dissipation, nanostructure, wear standard

### 1. Introduction

Modern tribology considers elastic-plastic deformation of friction surfaces as the main mechanism of transformation and dissipation of energy during friction.

The modern view of plastic deformation offers ergodynamics of deformable solids [1–3]. Ergodynamics of deformable solids is a synthesis to the problem of deformation most general laws of thermodynamics for non-reversable processes, molecular kinetics and dislocation theory in their mutual, dialectical tie on the basis of a most general law of nature—the law of energy conservation at its transformations.

The macroscopic phenomenon of plastic deformation, damage and destruction of a solid element is considered as a set of a huge number of microscopic elementary acts of atomic-molecular rearrangements, causing the generation (reproduction) by sources, movement, interaction and destruction of various kinds of elementary defects on the drains. Each defect is a carrier of excess potential energy and on its formation is spent strictly defined work of external forces.

From the thermodynamic point of view, the whole variety of mechanisms and structural levels of plastic flow can be divided into two most characteristic groups adaptive and dissipative types. The first group should include the mechanism of nucleation and accumulation in the local volumes of various kinds of elementary defects and damages of the structure. The second group includes elementary acts of atomic-molecular rearrangements associated with the movement and destruction of various defects on the drains, that is, controlling the dynamic return.

Such structural-energy interpretation of plastic deformation (friction of contact volumes) determines kinetic and competitive regularities of the process [1–3].

characteristic of these processes is the specific power of the thermal effect q\_ of

<sup>i</sup> þ ν ue

ð Þ <sup>σ</sup>0; <sup>T</sup> exp � <sup>U</sup><sup>0</sup>

<sup>i</sup>ð Þ <sup>σ</sup>0; <sup>T</sup> exp � <sup>U</sup>″

<sup>i</sup>ð Þ¼ σ0; T U″

<sup>σ</sup>V<sup>0</sup>

<sup>0</sup>i, <sup>U</sup>″0<sup>i</sup> is the activation energy of the formation and diffusion of the <sup>i</sup>th

0, U″

defect, respectively; σ0, σ<sup>i</sup> is the hydrostatic stress and stress intensity; V<sup>0</sup> is the atomic volume; k is the Boltzmann constant; h is the Planck constant; T is the

From the thermodynamic point of view, the process of plastic deformation and destruction is characterized by the competition of two opposite, interrelated and simultaneously occurring trends in the body element—the growth of the latent energy density ue of various defects and damages arising and accumulating in the material due to the work of external forces ωр, and its reduction (release) due to relaxation processes occurring inside the deformable body element; in this case, the first trend is associated with the deformation hardening and material damage, the second-with the dynamic return and dissipation of strain energy, causing the

A significant part of the dissipation energy q is not retained in the deformable element of the body, passes through it as if in transit and dissipates in the environ-

mulates in the deformable element of the body in the form of a thermal component

In the mechanics of a deformable solid, irreversible work ω<sup>p</sup> and the power ω\_ <sup>p</sup> of deformations are associated with the stress-strain state of the body element by the

Joint consideration Eqs. (7) and (8) allows to establish a unique relationship

<sup>i</sup> ,ω\_ <sup>p</sup> <sup>¼</sup> <sup>σ</sup>iε\_ <sup>p</sup>

In accordance with the law of conservation and transformation of energy

<sup>d</sup>ω<sup>p</sup> <sup>¼</sup> <sup>σ</sup>id<sup>ε</sup> <sup>p</sup>

between the stress-strain and thermodynamic states of the body element

<sup>i</sup> is the rate of irreversible deformation.

!. Only a small part of the dissipation energy q accu-

ω<sup>p</sup> ¼ Δue þ q and ω\_ <sup>p</sup> ¼ u\_<sup>e</sup> þ q\_: (7)

! increasing its temperature (self-heating effect).

<sup>i</sup> : (8)

2.3 Thermodynamic analysis of interrelation between deformation and

=2kT : (2)

kT , (3)

kT , (4)

<sup>2</sup><sup>K</sup> , (6)

ð Þ� <sup>T</sup> βσ<sup>2</sup>

<sup>0</sup>, (5)

ð Þ σ0; T <sup>i</sup>

ð Þ σ0; T <sup>i</sup>

<sup>0</sup><sup>i</sup> þ ΔU″

dt <sup>¼</sup> <sup>B</sup> sinh ασ<sup>2</sup>

<sup>q</sup>\_ <sup>¼</sup> dq

here, A and B are the kinetic coefficient

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

> <sup>A</sup> <sup>¼</sup> <sup>2</sup>kT hV<sup>0</sup> ∑ n 1 U0 i

<sup>B</sup> <sup>¼</sup> <sup>2</sup>kT hV<sup>0</sup> ∑ n 1 U″

ð Þ� <sup>T</sup> βσ<sup>2</sup>

<sup>α</sup> <sup>¼</sup> <sup>γ</sup><sup>2</sup> <sup>σ</sup>V<sup>0</sup> <sup>6</sup><sup>G</sup> , <sup>β</sup> <sup>¼</sup> <sup>γ</sup><sup>2</sup>

absolute temperature; G, K is the shear and bulk elasticity modules.

<sup>0</sup><sup>i</sup> þ ΔU<sup>0</sup>

thermal effect q of plastic deformation.

ment due to heat exchange q

relation

37

where ε\_

p

of the internal energy ΔuT ¼ q� q

plastic deformation

U0 i

where U<sup>0</sup>

fracture

ð Þ¼ σ0; T U<sup>0</sup>

If you apply the basic concepts of plastic deformation of solids this theory for the analysis of the process of friction, it is possible to consider the method of triboergodynamics [4].

The major distinction of triboergodynamics from general ergodynamics of deformed solids is "scale factor" which exhibits itself in existence of critical friction volume. This volume determines the limit friction parameters and separate, in essence, the surface deformation from the traditional volume deformation.

In the most general case the triboergodynamics should be seen as structuralenergy interpretation of the friction process. In the framework of triboergodynamics the process of friction is considered as an evolutionary phenomenon of the contact friction (rubbing surfaces).

### 2. Short fundamentals of ergodynamic of deformed solids

### 2.1 Structural model of the material

The deformable body is considered as an open, multicomponent, essentially inhomogeneous and nonequilibrium system, representing a hierarchy of statistically uniformly distributed over the volume of metastable structural elements (defects and damages) of various (from macro- to micro-) levels. Some of these structural elements are virtual sources and sinks of elementary defects (vacancies, dislocations, etc.), others—obstacles to their movement.

The main parameters characterizing the structural state of the material are [2, 3]: γσ is the coefficient of overstress on interatomic bonds, characterizing the uneven distribution of external stresses <sup>σ</sup> on interatomic bonds <sup>σ</sup><sup>0</sup> γσ <sup>¼</sup> <sup>σ</sup><sup>0</sup> ð Þ <sup>=</sup><sup>σ</sup> <sup>≥</sup><sup>1</sup> ; ue is the density of latent (free) energy of defects and damages; v is the coefficient of unevenness of the distribution of latent energy in volume, representing the ratio between the density of latent energy in the local volume u<sup>0</sup> <sup>e</sup> to the average value ue <sup>ν</sup> <sup>¼</sup> <sup>u</sup><sup>0</sup> <sup>e</sup> =ue . The complex structural parameter <sup>k</sup> <sup>¼</sup> γσ=v<sup>0</sup>, <sup>5</sup> <sup>¼</sup> <sup>σ</sup> <sup>∗</sup> <sup>=</sup><sup>S</sup> <sup>∗</sup> characterizes the relationship between the theoretical σ <sup>∗</sup> and real S <sup>∗</sup> strength of a solid.

### 2.2 Physical model and structural-energy interpretation of the process

Macroscopic phenomena of plastic deformation and scattered destruction of the body element are a cooperation of a huge number of microscopic elementary acts of atomic and molecular rearrangements in the field of external (thermal, mechanical, electrical, etc.) forces activated by thermal energy fluctuations. The whole variety of mechanisms and structural levels of the process from the thermodynamic point of view is divided into two most characteristic groups—adaptive and dissipative (relaxation) type, which differ in physical nature and kinetic laws. The first group includes elementary acts that control the origin and accumulation of elementary defects in the deformable body (damageability). The integral characteristic of intensity of the specified processes is specific (referred to unit of volume) power of pumping of excess (latent) energy u\_<sup>e</sup>

$$
\dot{u}\_{\varepsilon} = \frac{du\_{\varepsilon}}{dt} = A \sinh\left[\left(a\sigma\_{i}^{2} - \nu \, u\_{\varepsilon}\right)/2kT\right].\tag{1}
$$

The second group includes mechanisms and elementary acts that control relaxation (dissipative) processes of plastic deformation. The integral

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

Such structural-energy interpretation of plastic deformation (friction of contact

If you apply the basic concepts of plastic deformation of solids this theory for the analysis of the process of friction, it is possible to consider the method of triboergo-

volumes) determines kinetic and competitive regularities of the process [1–3].

The major distinction of triboergodynamics from general ergodynamics of deformed solids is "scale factor" which exhibits itself in existence of critical friction volume. This volume determines the limit friction parameters and separate, in essence, the surface deformation from the traditional volume deformation.

In the most general case the triboergodynamics should be seen as structuralenergy interpretation of the friction process. In the framework of triboergodynamics the process of friction is considered as an evolutionary phenomenon of

The deformable body is considered as an open, multicomponent, essentially inhomogeneous and nonequilibrium system, representing a hierarchy of statistically uniformly distributed over the volume of metastable structural elements (defects and damages) of various (from macro- to micro-) levels. Some of these structural elements are virtual sources and sinks of elementary defects (vacancies, disloca-

The main parameters characterizing the structural state of the material are [2, 3]: γσ is the coefficient of overstress on interatomic bonds, characterizing the uneven distribution of external stresses <sup>σ</sup> on interatomic bonds <sup>σ</sup><sup>0</sup> γσ <sup>¼</sup> <sup>σ</sup><sup>0</sup> ð Þ <sup>=</sup><sup>σ</sup> <sup>≥</sup><sup>1</sup> ; ue is the density of latent (free) energy of defects and damages; v is the coefficient of unevenness of the distribution of latent energy in volume, representing the ratio

 . The complex structural parameter <sup>k</sup> <sup>¼</sup> γσ=v<sup>0</sup>, <sup>5</sup> <sup>¼</sup> <sup>σ</sup> <sup>∗</sup> <sup>=</sup><sup>S</sup> <sup>∗</sup> characterizes the relationship between the theoretical σ <sup>∗</sup> and real S <sup>∗</sup> strength of a solid.

Macroscopic phenomena of plastic deformation and scattered destruction of the body element are a cooperation of a huge number of microscopic elementary acts of atomic and molecular rearrangements in the field of external (thermal, mechanical, electrical, etc.) forces activated by thermal energy fluctuations. The whole variety of mechanisms and structural levels of the process from the thermodynamic point of view is divided into two most characteristic groups—adaptive and dissipative (relaxation) type, which differ in physical nature and kinetic laws. The first group includes elementary acts that control the origin and accumulation of elementary defects in the deformable body (damageability). The integral characteristic of intensity of the specified processes is specific (referred to unit of volume) power of

2.2 Physical model and structural-energy interpretation of the process

dt <sup>¼</sup> <sup>A</sup> sinh ασ<sup>2</sup>

relaxation (dissipative) processes of plastic deformation. The integral

The second group includes mechanisms and elementary acts that control

<sup>i</sup> � ν ue

=2kT : (1)

<sup>e</sup> to the average value

2. Short fundamentals of ergodynamic of deformed solids

dynamics [4].

Friction, Lubrication and Wear

ue <sup>ν</sup> <sup>¼</sup> <sup>u</sup><sup>0</sup>

36

<sup>e</sup> =ue

pumping of excess (latent) energy u\_<sup>e</sup>

<sup>u</sup>\_<sup>e</sup> <sup>¼</sup> due

the contact friction (rubbing surfaces).

2.1 Structural model of the material

tions, etc.), others—obstacles to their movement.

between the density of latent energy in the local volume u<sup>0</sup>

characteristic of these processes is the specific power of the thermal effect q\_ of plastic deformation

$$\dot{q} = \frac{dq}{dt} = B \sinh\left[\left(a\sigma\_i^2 + \nu \, u\_\epsilon\right)/2kT\right].\tag{2}$$

here, A and B are the kinetic coefficient

$$A = \frac{2kT}{hV\_0} \sum\_{1}^{n} U\_i'(\sigma\_0, T) \exp\left[-\frac{U'(\sigma\_0, T)\_i}{kT}\right],\tag{3}$$

$$B = \frac{2kT}{hV\_0} \sum\_{1}^{n} U\_i(\sigma\_0, T) \exp\left[-\frac{\boldsymbol{U}^\cdot(\sigma\_0, T)\_i}{kT}\right],\tag{4}$$

$$\boldsymbol{U}\_{i}^{\prime}(\sigma\_{0},T) = \boldsymbol{U}\_{0i}^{\prime} + \Delta \boldsymbol{U}^{\prime}(T) \pm \beta \sigma\_{0\prime}^{2} \, ^{\prime} \boldsymbol{U}\_{i}^{\prime}(\sigma\_{0},T) = \boldsymbol{U}\_{0i}^{\prime} + \Delta \boldsymbol{U}^{\prime}(T) \pm \beta \sigma\_{0\prime}^{2} \tag{5}$$

$$a = \frac{\chi^2\_{\sigma} V\_0}{\mathfrak{G}G}, \beta = \frac{\chi^2\_{\sigma} V\_0}{2\mathcal{K}},\tag{6}$$

where U<sup>0</sup> <sup>0</sup>i, <sup>U</sup>″0<sup>i</sup> is the activation energy of the formation and diffusion of the <sup>i</sup>th defect, respectively; σ0, σ<sup>i</sup> is the hydrostatic stress and stress intensity; V<sup>0</sup> is the atomic volume; k is the Boltzmann constant; h is the Planck constant; T is the absolute temperature; G, K is the shear and bulk elasticity modules.

### 2.3 Thermodynamic analysis of interrelation between deformation and fracture

From the thermodynamic point of view, the process of plastic deformation and destruction is characterized by the competition of two opposite, interrelated and simultaneously occurring trends in the body element—the growth of the latent energy density ue of various defects and damages arising and accumulating in the material due to the work of external forces ωр, and its reduction (release) due to relaxation processes occurring inside the deformable body element; in this case, the first trend is associated with the deformation hardening and material damage, the second-with the dynamic return and dissipation of strain energy, causing the thermal effect q of plastic deformation.

A significant part of the dissipation energy q is not retained in the deformable element of the body, passes through it as if in transit and dissipates in the environment due to heat exchange q !. Only a small part of the dissipation energy q accumulates in the deformable element of the body in the form of a thermal component of the internal energy ΔuT ¼ q� q ! increasing its temperature (self-heating effect).

In accordance with the law of conservation and transformation of energy

$$
\rho\_p = \Delta \mu\_\epsilon + q \quad \text{and} \quad \dot{\phi}\_p = \dot{\mu}\_\epsilon + \dot{q}. \tag{7}
$$

In the mechanics of a deformable solid, irreversible work ω<sup>p</sup> and the power ω\_ <sup>p</sup> of deformations are associated with the stress-strain state of the body element by the relation

$$
tau\_p = \sigma\_i d \varepsilon\_i^p,\\
\dot{\alpha}\_p = \sigma\_i \dot{\varepsilon}\_i^p. \tag{8}$$

where ε\_ p <sup>i</sup> is the rate of irreversible deformation.

Joint consideration Eqs. (7) and (8) allows to establish a unique relationship between the stress-strain and thermodynamic states of the body element

$$
\dot{\varepsilon}\_i^p = \frac{\dot{\alpha}\_p}{\sigma\_t} = \frac{1}{\sigma\_i} (\dot{u}\_\varepsilon + \dot{q}) = \dot{\varepsilon}\_i^\epsilon + \dot{\varepsilon}\_i^q. \tag{9}
$$

studies [1, 6], the critical value of the internal energy density u<sup>∗</sup> in the local macro-volume of the material responsible for destruction coincides well with the known thermodynamic characteristic of the material ΔHS is the enthalpy of

> T ðs

> > 0

here, TS is the melting temperature; cp is the heat capacity; LS is the latent heat

The present day analysis of sum total of modern friction investigations may be presented in the form of three theses (others are also possible) of essential property which are shared by many research workers as undoubt proof as to the most

(movement) of surfaces, localized at the points of contact tangent to them;

2. Friction is the process of converting (transforming) the energy of external mechanical motion into other types of energy, and mainly into thermal

3. Friction is a process of elastic-plastic deformation and fracture localized in

These three axioms may be regarded as initial friction axioms and called "zero"

In the capacity of axiomatic method of friction investigation of initial friction axioms [4] mentioned above the author thinks it expedient to use the method of ergodynamics of deformable solids [1–3] which are at present may be taken as axiomatic, that is, method which may be trusted owing to the theoretical, experi-

Taking into consideration that basic attribute of any system is a balance attribute then tribosystem framework should be determined by the framework of obeying, for example, energy balance friction. Then it follows that basic equation for

tribosystem is an energy balance equation characterizing movement within friction system in a generalized and quantitative way. Constituent parts of this balance must determine basic quantitative regulations of energy transformations (and move-

friction axioms as the starting-point of whence it is possible to develop logical

1. Friction is the phenomenon of resistance to the relative movement

cpdT þ Ls: (12)

u<sup>∗</sup> ¼ ΔHs ¼

melting, that is.,

of melting.

3.1 Friction

energy;

3. Triboergodynamic's method

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

3.1.1 Initial or zero axiom of friction

mental and practical substantiation.

ment) within the system.

39

3.1.2 Balanced and unitary attributes of friction

characteristic properties of generalized friction model:

thin surface layers of friction pair materials.

analysis of generalized engineering property for friction process.

Therefore, from the thermodynamic point of view, the total values of the work ω<sup>p</sup> and irreversible deformation ε p <sup>i</sup> and the rates of their change ω\_ <sup>p</sup>; ε\_ p i � � can be represented as the sum of two terms associated, respectively, with the deformation hardening and damage ε\_ e <sup>i</sup> ¼ u\_e=σ<sup>i</sup> � � and dynamic return ε\_ q <sup>i</sup> ¼ q\_=σ<sup>i</sup> � � controlling quasi-viscous flow of the body element.

This important conclusion is of fundamental importance in the analysis of the relationship between the processes of deformation and destruction of the body element. For damage and destruction of the body element is responsible only part of the plastic (irreversible) deformation ε<sup>e</sup> <sup>i</sup> controlled by microscopic processes associated with deformation hardening and accumulation of latent energy of defects and damages. A significant part of the irreversible deformation ε q <sup>i</sup> controlled by relaxation (dissipative) processes does not affect the damage and destruction of the body element, but only causes its quasi-viscous flow (stationary creep). The relationship between the work and the degree of irreversible deformation and their components varies within a very wide range and depends on the structure of the material and the conditions of its deformation [1].

### 2.4 Thermodynamic condition of local fracture

The parameter of damage (scattered destruction) is taken as the density of the internal energy u accumulated in the deformable volumes, determined by the sum of two components: potential (latent) ue and kinetic (thermal) uT that is

$$
\Delta \mathfrak{u} = \Delta \mathfrak{u}\_{\varepsilon} + \Delta \mathfrak{u}\_{T}, \dot{\mathfrak{u}} = \dot{\mathfrak{u}}\_{\varepsilon} + \dot{\mathfrak{u}}\_{T}. \tag{10}
$$

This energy is associated with the accumulation in the deformable element of the body of static ð Þ Δue and dynamic ð Þ ΔuT damages and distortions of the crystal lattice, therefore, is dangerous, responsible for the scattered destruction (damage). The element of the body is considered to be destroyed if at least one local micro-volume responsible for the destruction, the density of internal energy reaches a critical (limit) value u<sup>∗</sup> corresponding to the loss of crystal lattice stability "in a large." This point corresponds to the appearance in the local micro-volume of a crack of critical size (according to Griffiths-Orovan-Irvin) and a sharp localization of the process at the mouth (top) of the crack. The thermodynamic condition of local fracture is written as

$$\mu(\overline{r}\_\*, t\_\*) = \mu(\overline{r}\_\*, 0) + \int\_0^{t\_\*} \dot{\mu}(\overline{r}\_\*, t)dt = \mu\_\* = \text{const.} \tag{11}$$

here, u ð Þ r <sup>∗</sup> ; 0 is the density of internal energy in the local micro-volume of the material in the initial (before deformation t ¼ 0) state; u\_ ð Þ r <sup>∗</sup> ; t is the specific power of internal energy sources in the local volume responsible for the destruction; r <sup>∗</sup> is the parameter characterizing the coordinates x<sup>∗</sup> ; y <sup>∗</sup> ; z <sup>∗</sup> � � of the local volume responsible for the fracture.

### 2.5 Thermodynamic criterion of fracture

In accordance with the structural-energy analogy of the process of mechanical destruction and melting of metals and alloys [5] and theoretical and experimental Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

studies [1, 6], the critical value of the internal energy density u<sup>∗</sup> in the local macro-volume of the material responsible for destruction coincides well with the known thermodynamic characteristic of the material ΔHS is the enthalpy of melting, that is.,

$$
\mu\_\* = \Delta H\_s = \int\_0^{T\_s} c\_p dT + L\_s.\tag{12}
$$

here, TS is the melting temperature; cp is the heat capacity; LS is the latent heat of melting.

### 3. Triboergodynamic's method

### 3.1 Friction

ε\_ p <sup>i</sup> <sup>¼</sup> <sup>ω</sup>\_ <sup>p</sup> σt ¼ 1 σi

e <sup>i</sup> ¼ u\_e=σ<sup>i</sup>

2.4 Thermodynamic condition of local fracture

uð Þ¼ r <sup>∗</sup> ; t <sup>∗</sup> uð Þþ r <sup>∗</sup> ; 0

the parameter characterizing the coordinates x<sup>∗</sup> ; y <sup>∗</sup> ; z <sup>∗</sup>

2.5 Thermodynamic criterion of fracture

responsible for the fracture.

38

damages. A significant part of the irreversible deformation ε

ω<sup>p</sup> and irreversible deformation ε

quasi-viscous flow of the body element.

the plastic (irreversible) deformation ε<sup>e</sup>

conditions of its deformation [1].

hardening and damage ε\_

Friction, Lubrication and Wear

u\_ ð Þ¼ <sup>e</sup> þ q\_ ε\_

Therefore, from the thermodynamic point of view, the total values of the work

represented as the sum of two terms associated, respectively, with the deformation

� � and dynamic return ε\_

This important conclusion is of fundamental importance in the analysis of the relationship between the processes of deformation and destruction of the body element. For damage and destruction of the body element is responsible only part of

ated with deformation hardening and accumulation of latent energy of defects and

tion (dissipative) processes does not affect the damage and destruction of the body element, but only causes its quasi-viscous flow (stationary creep). The relationship between the work and the degree of irreversible deformation and their components varies within a very wide range and depends on the structure of the material and the

The parameter of damage (scattered destruction) is taken as the density of the internal energy u accumulated in the deformable volumes, determined by the sum

This energy is associated with the accumulation in the deformable element of the body of static ð Þ Δue and dynamic ð Þ ΔuT damages and distortions of the crystal lattice, therefore, is dangerous, responsible for the scattered destruction (damage). The element of the body is considered to be destroyed if at least one local micro-volume responsible for the destruction, the density of internal energy reaches a critical (limit) value u<sup>∗</sup> corresponding to the loss of crystal lattice stability "in a large." This point corresponds to the appearance in the local micro-volume of a crack of critical size (according to Griffiths-Orovan-Irvin) and a sharp localization of the process at the mouth (top) of the crack. The thermodynamic condition of local fracture is written as

> t ð∗

> > 0

here, u ð Þ r <sup>∗</sup> ; 0 is the density of internal energy in the local micro-volume of the material in the initial (before deformation t ¼ 0) state; u\_ ð Þ r <sup>∗</sup> ; t is the specific power of internal energy sources in the local volume responsible for the destruction; r <sup>∗</sup> is

In accordance with the structural-energy analogy of the process of mechanical destruction and melting of metals and alloys [5] and theoretical and experimental

Δu ¼ Δue þ ΔuT, u\_ ¼ u\_<sup>e</sup> þ u\_T: (10)

u\_ð Þ r <sup>∗</sup> ; t dt ¼ u<sup>∗</sup> ¼ const: (11)

� � of the local volume

of two components: potential (latent) ue and kinetic (thermal) uT that is

p

e <sup>i</sup> þ ε\_ q

<sup>i</sup> and the rates of their change ω\_ <sup>p</sup>; ε\_

q <sup>i</sup> ¼ q\_=σ<sup>i</sup>

<sup>i</sup> controlled by microscopic processes associ-

q

<sup>i</sup> : (9)

� � controlling

p i � � can be

<sup>i</sup> controlled by relaxa-

### 3.1.1 Initial or zero axiom of friction

The present day analysis of sum total of modern friction investigations may be presented in the form of three theses (others are also possible) of essential property which are shared by many research workers as undoubt proof as to the most characteristic properties of generalized friction model:


These three axioms may be regarded as initial friction axioms and called "zero" friction axioms as the starting-point of whence it is possible to develop logical analysis of generalized engineering property for friction process.

In the capacity of axiomatic method of friction investigation of initial friction axioms [4] mentioned above the author thinks it expedient to use the method of ergodynamics of deformable solids [1–3] which are at present may be taken as axiomatic, that is, method which may be trusted owing to the theoretical, experimental and practical substantiation.

### 3.1.2 Balanced and unitary attributes of friction

Taking into consideration that basic attribute of any system is a balance attribute then tribosystem framework should be determined by the framework of obeying, for example, energy balance friction. Then it follows that basic equation for tribosystem is an energy balance equation characterizing movement within friction system in a generalized and quantitative way. Constituent parts of this balance must determine basic quantitative regulations of energy transformations (and movement) within the system.

Thus, tribosystem in the most generalized sense is quantitatively characterized by the energy balance equation. Most generalized quantitative regulatities of tribosystem behavior (states) are determined by magnitudes relations among constituencies of friction energy balance. These conditions may also be taken as friction axioms. In accordance with that it is possible to show justice of entropy balance equation and so of information and etc.

Taking into consideration the fact that the most characteristic magnitude of the most global balance principle is unit (whole), then, consequently, the basic parameters of tribosystem (friction), expressed as indexes of relations among balance constituents must also have criterion (limit) magnitudes equal to unit.

### 3.1.3 Common energy analysis of friction process

In the most general case the work of friction process WF is summed up from the work of elastic Welast <sup>F</sup> and plastic <sup>W</sup>plast <sup>F</sup> deformation and wear (failure) of contact volumes (Figure 2) and work for overcoming forces of viscous friction and failure of lubricant material Wlub:

$$\mathcal{W}\_F = \mathcal{W}\_F^{elast} + \mathcal{W}\_F^{plst} + \mathcal{W}\_{lubr} \tag{13}$$

The first part of the friction work is related to the change in the deformable (contact) volumes of materials of latent (potential) energy Δue<sup>1</sup> and Δue2. It is the energy of various elementary defects and damages arising and accumulating in deformable volumes. This energy is a unique and integral characteristic of submicroand microstructural changes that occur in plastically deformable volumes of materials

The second part of the friction work ω<sup>f</sup> is related to the processes of dynamic return, accompanied by the release of latent energy and the thermal effect q1, q<sup>2</sup> of friction. This energy is associated with the movement and destruction of various elementary defects of opposite signs, their exit to the surface, healing reversible

The relations between the components of the energy balance of the friction process Δue<sup>1</sup> and Δue2, as well as q<sup>1</sup> and q<sup>2</sup> vary widely and are determined by the physical and chemical properties of the materials that make up the friction pair,

In the most general case, Eqs. (18) and (19) should be presented (Figure 2)

where <sup>Δ</sup>Ue <sup>¼</sup> Vf <sup>Δ</sup>ue; <sup>U</sup>\_ <sup>e</sup> <sup>¼</sup> Vf <sup>u</sup>\_e; Vf is contact (deformed) volume of the

Solving Eqs. (20) and (21) with respect to the friction force F, we obtain

Fl <sup>¼</sup> <sup>Δ</sup>Ue<sup>1</sup> <sup>þ</sup> <sup>Δ</sup>Ue<sup>2</sup>

Fv <sup>¼</sup> <sup>U</sup>\_ <sup>e</sup><sup>1</sup> <sup>þ</sup> <sup>U</sup>\_ <sup>e</sup><sup>2</sup> v

<sup>μ</sup><sup>l</sup> <sup>¼</sup> <sup>Δ</sup>Ue<sup>1</sup> <sup>þ</sup> <sup>Δ</sup>Ue<sup>2</sup>

<sup>μ</sup><sup>v</sup> <sup>¼</sup> <sup>U</sup>\_ <sup>e</sup><sup>1</sup> <sup>þ</sup> <sup>U</sup>\_ <sup>e</sup><sup>2</sup>

Wf ¼ ΔUe þ Q ¼ ΔUe<sup>1</sup> þ ΔUe<sup>2</sup> þ ΔUT<sup>1</sup> þ ΔUT<sup>2</sup> þ Q

<sup>W</sup>\_ <sup>f</sup> <sup>¼</sup> <sup>U</sup>\_ <sup>e</sup> <sup>þ</sup> <sup>Q</sup>\_ <sup>¼</sup> <sup>U</sup>\_ <sup>e</sup><sup>1</sup> <sup>þ</sup> <sup>U</sup>\_ <sup>e</sup><sup>2</sup> <sup>þ</sup> <sup>U</sup>\_ <sup>T</sup><sup>1</sup> <sup>þ</sup> <sup>U</sup>\_ <sup>T</sup><sup>2</sup> <sup>þ</sup> \_

where l and v are the friction path and the slip velocity.

generalized equations for the coefficient of friction

coefficient μ (without lubrication) has view

Wf ¼ ΔUe þ Q ¼ ΔUe<sup>1</sup> þ ΔUe<sup>2</sup> þ Q<sup>1</sup> þ Q2, (20) <sup>W</sup>\_ <sup>f</sup> <sup>¼</sup> <sup>U</sup>\_ <sup>e</sup> <sup>þ</sup> <sup>Q</sup>\_ <sup>¼</sup> <sup>U</sup>\_ <sup>e</sup><sup>1</sup> <sup>þ</sup> <sup>U</sup>\_ <sup>e</sup><sup>2</sup> <sup>þ</sup> <sup>Q</sup>\_ <sup>1</sup> <sup>þ</sup> <sup>Q</sup>\_ <sup>2</sup>, (21)

<sup>l</sup> <sup>þ</sup> <sup>Q</sup><sup>1</sup> <sup>þ</sup> <sup>Q</sup><sup>2</sup>

Dividing both parts of the Eqs. (22) and (23) by the normal force N, we present

Nl <sup>þ</sup> <sup>Q</sup><sup>1</sup> <sup>þ</sup> <sup>Q</sup><sup>2</sup>

Nv <sup>þ</sup> <sup>Q</sup>\_ <sup>1</sup> <sup>þ</sup> <sup>Q</sup>\_ <sup>2</sup>

!), equations [8] for friction work Wf , frictional force F and friction

Thus, friction is generally described by the equation of energy balance and from the thermodynamic point of view [1–4] it is a competitive process of two (mentioned above) opposite, interrelated and simultaneously occurring in the deformable contacts trends. According to the energy balance scheme (Figure 1) for plastic deformation and fracture [1] presented above (relationships Δ u ¼ Δ ue þ Δ uT and

<sup>þ</sup> <sup>Q</sup>\_ <sup>1</sup> <sup>þ</sup> <sup>Q</sup>\_ <sup>2</sup>

<sup>l</sup> : (22)

<sup>v</sup> , (23)

Nl , (24)

Nv : (25)

! <sup>1</sup> þ Q !

Q ! <sup>1</sup> <sup>þ</sup> \_ Q ! <sup>2</sup>, (26)

<sup>2</sup>, (27)

[1, 2, 7]. It is a measure of deformation hardening and damage of materials.

submicroscopic discontinuities, etc.

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

materials of the friction pair.

q ¼ Δ uTþ q

41

generalized equations for the friction force

their structure and the conditions of the friction process.

taking into account the real (not unit) sizes of the tribocontacts.

For particular case of friction without lubrication (Wlub ffi 0) and in the conditions of stationary (developed) friction, when the work of elastic deformation may be neglected due to their insignificance, friction work WF will be determined mainly by the work of plastic deformation of surfaces (contact volumes) of shaft Wplast <sup>F</sup><sup>1</sup> and of bearing <sup>W</sup>plast <sup>F</sup><sup>2</sup> :

$$\mathcal{W}\_F = \mathcal{W}\_F^{plst} = \mathcal{W}\_{F1}^{plst} + \mathcal{W}\_{F2}^{plst}.\tag{14}$$

### 3.2 Structural-energy interpretation of friction process

It is known friction is characterized a product of frictional forces F by friction distance ℓ, that is., the work ω<sup>f</sup> , expended on overcoming frictional forces

$$a\_{\hat{f}} = F\ell,\tag{15}$$

$$
\Delta u\_f = \Delta u\_\epsilon + q,\tag{16}
$$

$$
\dot{a}\dot{a}\_f = \dot{u}\_e + \dot{q}.\tag{17}
$$

here, ω\_ <sup>f</sup> ¼ dω<sup>f</sup> =dt is a power of friction dissipation of energy; u\_<sup>e</sup> ¼ due=dt is the rate of storing latent energy in deformed (contact) volumes; q\_ ¼ dq=dt the power of thermal effect of plastic deformation (friction).

Since the contact volumes of both materials that make up the friction pair are deformed by friction (see Figure 2), Eqs. (16) and (17) should be written as

$$
\mu\_{\!\!\!f} = \Delta \mu\_{\epsilon 1} + \Delta \mu\_{\epsilon 2} + q\_1 + q\_2. \tag{18}
$$

$$
\dot{a}\_f = \dot{u}\_{\epsilon1} + \dot{u}\_{\epsilon2} + \dot{q}\_1 + \dot{q}\_2. \tag{19}
$$

These equations show, that from thermodynamic point of view, the work ω<sup>f</sup> of friction forces, (friction power ω\_ <sup>f</sup> ) is related to plastic deformation of the contact volumes. The work ω<sup>f</sup> may be divided conventionally into two specific parts.

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

Thus, tribosystem in the most generalized sense is quantitatively characterized

Taking into consideration the fact that the most characteristic magnitude of the most global balance principle is unit (whole), then, consequently, the basic parameters of tribosystem (friction), expressed as indexes of relations among balance

In the most general case the work of friction process WF is summed up from the

volumes (Figure 2) and work for overcoming forces of viscous friction and failure

<sup>F</sup> <sup>þ</sup> <sup>W</sup>plast

For particular case of friction without lubrication (Wlub ffi 0) and in the conditions of stationary (developed) friction, when the work of elastic deformation may be neglected due to their insignificance, friction work WF will be determined mainly by the work of plastic deformation of surfaces (contact volumes) of shaft

<sup>F</sup> <sup>¼</sup> <sup>W</sup>plast

It is known friction is characterized a product of frictional forces F by friction

here, ω\_ <sup>f</sup> ¼ dω<sup>f</sup> =dt is a power of friction dissipation of energy; u\_<sup>e</sup> ¼ due=dt is the rate of storing latent energy in deformed (contact) volumes; q\_ ¼ dq=dt the power of

Since the contact volumes of both materials that make up the friction pair are

These equations show, that from thermodynamic point of view, the work ω<sup>f</sup> of friction forces, (friction power ω\_ <sup>f</sup> ) is related to plastic deformation of the contact volumes. The work ω<sup>f</sup> may be divided conventionally into two specific parts.

deformed by friction (see Figure 2), Eqs. (16) and (17) should be written as

distance ℓ, that is., the work ω<sup>f</sup> , expended on overcoming frictional forces

<sup>F</sup><sup>1</sup> <sup>þ</sup> <sup>W</sup>plast

<sup>F</sup> deformation and wear (failure) of contact

ω<sup>f</sup> ¼ Fℓ, (15) ω<sup>f</sup> ¼ Δue þ q, (16)

ω\_ <sup>f</sup> ¼ u\_<sup>e</sup> þ q\_: (17)

ω<sup>f</sup> ¼ Δue<sup>1</sup> þ Δue<sup>2</sup> þ q<sup>1</sup> þ q2, (18)

ω\_ <sup>f</sup> ¼ u\_<sup>e</sup><sup>1</sup> þ u\_<sup>e</sup><sup>2</sup> þ q\_ <sup>1</sup> þ q\_ <sup>2</sup>: (19)

<sup>F</sup> þ Wlubr, (13)

<sup>F</sup><sup>2</sup> : (14)

by the energy balance equation. Most generalized quantitative regulatities of tribosystem behavior (states) are determined by magnitudes relations among constituencies of friction energy balance. These conditions may also be taken as friction axioms. In accordance with that it is possible to show justice of entropy balance

constituents must also have criterion (limit) magnitudes equal to unit.

equation and so of information and etc.

Friction, Lubrication and Wear

3.1.3 Common energy analysis of friction process

<sup>F</sup> and plastic <sup>W</sup>plast

<sup>F</sup><sup>2</sup> :

thermal effect of plastic deformation (friction).

WF <sup>¼</sup> <sup>W</sup>elast

WF <sup>¼</sup> <sup>W</sup>plast

3.2 Structural-energy interpretation of friction process

work of elastic Welast

Wplast

40

of lubricant material Wlub:

<sup>F</sup><sup>1</sup> and of bearing <sup>W</sup>plast

The first part of the friction work is related to the change in the deformable (contact) volumes of materials of latent (potential) energy Δue<sup>1</sup> and Δue2. It is the energy of various elementary defects and damages arising and accumulating in deformable volumes. This energy is a unique and integral characteristic of submicroand microstructural changes that occur in plastically deformable volumes of materials [1, 2, 7]. It is a measure of deformation hardening and damage of materials.

The second part of the friction work ω<sup>f</sup> is related to the processes of dynamic return, accompanied by the release of latent energy and the thermal effect q1, q<sup>2</sup> of friction. This energy is associated with the movement and destruction of various elementary defects of opposite signs, their exit to the surface, healing reversible submicroscopic discontinuities, etc.

The relations between the components of the energy balance of the friction process Δue<sup>1</sup> and Δue2, as well as q<sup>1</sup> and q<sup>2</sup> vary widely and are determined by the physical and chemical properties of the materials that make up the friction pair, their structure and the conditions of the friction process.

In the most general case, Eqs. (18) and (19) should be presented (Figure 2) taking into account the real (not unit) sizes of the tribocontacts.

$$W\_f = \Delta U\_\varepsilon + Q = \Delta U\_{\varepsilon\_1} + \Delta U\_{\varepsilon\_2} + Q\_1 + Q\_2 \tag{20}$$

$$
\dot{W}\_f = \dot{U}\_\epsilon + \dot{Q} = \dot{U}\_{\epsilon\_1} + \dot{U}\_{\epsilon\_2} + \dot{Q}\_1 + \dot{Q}\_{\mathcal{D}} \tag{21}
$$

where <sup>Δ</sup>Ue <sup>¼</sup> Vf <sup>Δ</sup>ue; <sup>U</sup>\_ <sup>e</sup> <sup>¼</sup> Vf <sup>u</sup>\_e; Vf is contact (deformed) volume of the materials of the friction pair.

Solving Eqs. (20) and (21) with respect to the friction force F, we obtain generalized equations for the friction force

$$F\_l = \frac{\Delta U\_{e\_1} + \Delta U\_{e\_2}}{l} + \frac{Q\_1 + Q\_2}{l}.\tag{22}$$

$$F\_v = \frac{\dot{U}\_{e\_1} + \dot{U}\_{e\_2}}{v} + \frac{\dot{Q}\_1 + \dot{Q}\_2}{v},\tag{23}$$

where l and v are the friction path and the slip velocity.

Dividing both parts of the Eqs. (22) and (23) by the normal force N, we present generalized equations for the coefficient of friction

$$
\mu\_l = \frac{\Delta U\_{e1} + \Delta U\_{e2}}{Nl} + \frac{Q\_1 + Q\_2}{Nl},
\tag{24}
$$

$$
\mu\_v = \frac{\dot{U}\_{\epsilon\_1} + \dot{U}\_{\epsilon\_2}}{N\upsilon} + \frac{\dot{Q}\_1 + \dot{Q}\_2}{N\upsilon}. \tag{25}
$$

Thus, friction is generally described by the equation of energy balance and from the thermodynamic point of view [1–4] it is a competitive process of two (mentioned above) opposite, interrelated and simultaneously occurring in the deformable contacts trends. According to the energy balance scheme (Figure 1) for plastic deformation and fracture [1] presented above (relationships Δ u ¼ Δ ue þ Δ uT and q ¼ Δ uTþ q !), equations [8] for friction work Wf , frictional force F and friction coefficient μ (without lubrication) has view

$$W\_f = \Delta U\_\varepsilon + Q = \Delta U\_{\varepsilon\_1} + \Delta U\_{\varepsilon\_2} + \Delta U\_{T\_1} + \Delta U\_{T\_2} + \overrightarrow{Q}\_1 + \overrightarrow{Q}\_2 \tag{26}$$

$$
\dot{\boldsymbol{W}}\_f = \dot{\boldsymbol{U}}\_\varepsilon + \dot{\boldsymbol{Q}} = \dot{\boldsymbol{U}}\_{\varepsilon\_1} + \dot{\boldsymbol{U}}\_{\varepsilon\_2} + \dot{\boldsymbol{U}}\_{T\_1} + \dot{\boldsymbol{U}}\_{T\_2} + \dot{\boldsymbol{Q}}\_1 + \dot{\boldsymbol{Q}}\_{\mathcal{Q}} \tag{27}
$$

$$F\_l = \frac{\Delta U\_\epsilon}{l} + \frac{Q}{l} = \frac{\Delta U\_{e\_1} + \Delta U\_{e\_2}}{l} + \frac{Q\_1 + Q\_2}{l},\tag{28}$$

classified conventionally into two specific components with different kinetic behavior [3, 9]. The first component is associated with microscopic mechanisms of adaptive type and relates to the change of latent (potential) energy (Δ ue<sup>1</sup> , Δ ue<sup>2</sup> ) of various elementary defects and damages that are generated and accumulate in the deformable volumes of materials friction pair (Figure 1). This energy is a unique and integral characteristic of the submicro- and microstructural transformations that occur in plastically strained materials [1–3, 9]. It is a measure of deformation hardening and damage of materials. The second component is associated with microscopic mechanisms of dissipative type and related to dynamic recovery processes in which latent energy is released and heat effect of friction (q1, q2) take place. This energy is associated with the movement and destruction of various elementary defects of opposite signs, their exit to the surface, healing reversible submicroscopic discontinuities, etc. The ratios of the components Δ ue<sup>1</sup> and Δ ue<sup>2</sup> as well as q1, q<sup>2</sup> of the balance vary over a wide range, depending on the physical, chemical, and structural properties of the materials that comprise the friction cou-

Thus, the thermodynamic analysis of the plastic deformation and fracture of the solid volume at friction allows us to obtain generalized (two-term) dependences for the friction force F and the friction coefficient μ, which corresponds to the modern concepts of the dual nature of friction [10, 11]. It is a molecular mechanical Eq. (29) and deformation-adhesion Eq. (31) theories of friction. But, more correctly it is necessary to speak about adaptive-dissipative nature (model) of friction Eq. (30). As follows from the equations of the energy balance of friction Eqs. (26) and (27), the whole variety of manifestations of friction and wear can be conditionally reduced to at least two fundamentally different states. The first condition determines all types of damageability and wear, the second-the so-called condition of

The state of damageability and wear is characterized by the components of energy balance Eqs. (26) and (27), which are responsible for accumulation of internal energy Δ u ¼ Δ ue<sup>1</sup> þ Δ ue<sup>2</sup> þ Δ uT<sup>1</sup> þ Δ uT<sup>2</sup> in deformed volumes, that is, the process is irreversible [4, 8]. The "wearlessness" state is characterized by the components of the energy balance Eqs. (26) and (27), which are responsible for the dynamic dissipation (reversibility) of strain energy into elastic and structural dissi-

<sup>2</sup> of friction contact [4, 8].

In its turn, the first state may be classified depending on the relation between potential Δ ue and kinetic Δ uT components of internal energy. It is subdivided conventionally into mechanical damage and wear (due to so-called structure activation) and thermal damage and wear (due to thermal activation). For instance, let the thermal component of internal energy Δ uT be equal to zero (Δ uT ¼ 0) and the internal energy variation at damage and wear be defined only by variation of the potential Δ ueð Þ Δ u ¼ Δue component. Then, the mechanical damage and wear with brittle fracture of surfaces take place. On the contrary, if we have Δ ue ¼ 0 (Δ u ¼ Δ uT), then the thermal damage and wear with ductile fracture of surfaces take place. All the intermediate values of the components are associated with quasi-

In the most general case, taking into account a fundamental tribology's notion of the

In the special case, where the friction is localized into volume of the "third body"

Wf ¼ ΔUe<sup>1</sup> þ ΔUe<sup>2</sup> þ ΔUe<sup>3</sup> þ Q<sup>1</sup> þ Q<sup>2</sup> þ Q3: (32)

"third body" [10], the energy balance at dry friction Eq. (20) should be written as

ple and the friction process conditions [8].

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

"wearlessness" [7].

pated energy q

!¼ <sup>q</sup> ! <sup>1</sup> þ q !

(Figure 2) Eq. (32) develops into

43

brittle or quasi-ductile fracture of solids [4, 8].

$$F\_v = \frac{\dot{U}\_{e\_1} + \dot{U}\_{e\_2}}{v} + \frac{\dot{Q}\_1 + \dot{Q}\_2}{v} = F\_{mechanial} + F\_{mlocalar} \tag{29}$$

$$
\mu\_l = \frac{\Delta U\_{\epsilon\_1} + \Delta U\_{\epsilon\_2}}{Nl} + \frac{Q\_1 + Q\_2}{Nl} = \mu\_{\text{adapt}} + \mu\_{\text{dis}} = \mu\_{\text{adapt}} + \mu\_{T(\text{di})} + \mu\_{\stackrel{\sim}{Q(\text{di})}},\tag{30}
$$

$$
\mu\_v = \frac{\dot{U}\_{e\_1} + \dot{U}\_{e\_2}}{N\nu} + \frac{\dot{Q}\_1 + \dot{Q}\_2}{N\nu} = \mu\_{\text{deformation}} + \mu\_{\text{adhesion}}.\tag{31}
$$

where ΔUe ¼ Vf Δ ue; Q ¼ Vf q; Q ! ¼ Vf q !; <sup>U</sup>\_ <sup>e</sup> <sup>¼</sup> Vf <sup>u</sup>\_e; <sup>u</sup>\_<sup>e</sup> <sup>¼</sup> <sup>d</sup> ue=<sup>d</sup> <sup>t</sup> is the rate of latent energy density change in the contact volumes; Vf is a deformable volume of friction; μ is the coefficient of friction; μadapt is the adaptive coefficient of friction; <sup>μ</sup>T dis ð Þ and <sup>μ</sup><sup>Q</sup> ! ð Þ dis are the static and dynamic components of dissipative coefficient of friction; ΔUT is the thermal component of internal energy; N is the normal load; l is the friction distance; v is the sliding velocity. The latent energy density Δue is an integral parameter of tribostate and damageability (failure (Δu<sup>∗</sup> <sup>e</sup> )) of solids [1].

Thus, viewed thermodynamically, the work done by friction forces Wf (the friction power W\_ <sup>f</sup> ), the friction force F and the friction coefficient μ may be

Figure 1. Scheme of the energy balance for the plastic deformation (friction) of a solid [1–3].

### Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

Fl <sup>¼</sup> <sup>Δ</sup>Ue

Fv <sup>¼</sup> <sup>U</sup>\_ <sup>e</sup><sup>1</sup> <sup>þ</sup> <sup>U</sup>\_ <sup>e</sup><sup>2</sup> v

Nl <sup>þ</sup> <sup>Q</sup><sup>1</sup> <sup>þ</sup> <sup>Q</sup><sup>2</sup>

where ΔUe ¼ Vf Δ ue; Q ¼ Vf q; Q

<sup>μ</sup><sup>v</sup> <sup>¼</sup> <sup>U</sup>\_ <sup>e</sup><sup>1</sup> <sup>þ</sup> <sup>U</sup>\_ <sup>e</sup><sup>2</sup>

<sup>μ</sup><sup>l</sup> <sup>¼</sup> <sup>Δ</sup>Ue<sup>1</sup> <sup>þ</sup> <sup>Δ</sup>Ue<sup>2</sup>

Friction, Lubrication and Wear

!

<sup>μ</sup>T dis ð Þ and <sup>μ</sup><sup>Q</sup>

Figure 1.

42

<sup>l</sup> <sup>þ</sup> <sup>Q</sup>

<sup>l</sup> <sup>¼</sup> <sup>Δ</sup>Ue<sup>1</sup> <sup>þ</sup> <sup>Δ</sup>Ue<sup>2</sup>

<sup>þ</sup> <sup>Q</sup>\_ <sup>1</sup> <sup>þ</sup> <sup>Q</sup>\_ <sup>2</sup>

Nv <sup>þ</sup> <sup>Q</sup>\_ <sup>1</sup> <sup>þ</sup> <sup>Q</sup>\_ <sup>2</sup>

integral parameter of tribostate and damageability (failure (Δu<sup>∗</sup>

Scheme of the energy balance for the plastic deformation (friction) of a solid [1–3].

!

¼ Vf q

latent energy density change in the contact volumes; Vf is a deformable volume of friction; μ is the coefficient of friction; μadapt is the adaptive coefficient of friction;

friction; ΔUT is the thermal component of internal energy; N is the normal load; l is the friction distance; v is the sliding velocity. The latent energy density Δue is an

Thus, viewed thermodynamically, the work done by friction forces Wf (the friction power W\_ <sup>f</sup> ), the friction force F and the friction coefficient μ may be

<sup>l</sup> <sup>þ</sup> <sup>Q</sup><sup>1</sup> <sup>þ</sup> <sup>Q</sup><sup>2</sup>

Nl <sup>¼</sup> <sup>μ</sup>adapt <sup>þ</sup> <sup>μ</sup>dis <sup>¼</sup> <sup>μ</sup>adapt <sup>þ</sup> <sup>μ</sup>T dis ð Þ <sup>þ</sup> <sup>μ</sup><sup>Q</sup>

ð Þ dis are the static and dynamic components of dissipative coefficient of

<sup>v</sup> <sup>¼</sup> Fmechanical <sup>þ</sup> Fmolecular, (29)

Nv <sup>¼</sup> <sup>μ</sup>deformation <sup>þ</sup> <sup>μ</sup>adhesion, (31)

!; <sup>U</sup>\_ <sup>e</sup> <sup>¼</sup> Vf <sup>u</sup>\_e; <sup>u</sup>\_<sup>e</sup> <sup>¼</sup> <sup>d</sup> ue=<sup>d</sup> <sup>t</sup> is the rate of

<sup>l</sup> , (28)

!

<sup>e</sup> )) of solids [1].

ð Þ dis , (30)

classified conventionally into two specific components with different kinetic behavior [3, 9]. The first component is associated with microscopic mechanisms of adaptive type and relates to the change of latent (potential) energy (Δ ue<sup>1</sup> , Δ ue<sup>2</sup> ) of various elementary defects and damages that are generated and accumulate in the deformable volumes of materials friction pair (Figure 1). This energy is a unique and integral characteristic of the submicro- and microstructural transformations that occur in plastically strained materials [1–3, 9]. It is a measure of deformation hardening and damage of materials. The second component is associated with microscopic mechanisms of dissipative type and related to dynamic recovery processes in which latent energy is released and heat effect of friction (q1, q2) take place. This energy is associated with the movement and destruction of various elementary defects of opposite signs, their exit to the surface, healing reversible submicroscopic discontinuities, etc. The ratios of the components Δ ue<sup>1</sup> and Δ ue<sup>2</sup> as well as q1, q<sup>2</sup> of the balance vary over a wide range, depending on the physical, chemical, and structural properties of the materials that comprise the friction couple and the friction process conditions [8].

Thus, the thermodynamic analysis of the plastic deformation and fracture of the solid volume at friction allows us to obtain generalized (two-term) dependences for the friction force F and the friction coefficient μ, which corresponds to the modern concepts of the dual nature of friction [10, 11]. It is a molecular mechanical Eq. (29) and deformation-adhesion Eq. (31) theories of friction. But, more correctly it is necessary to speak about adaptive-dissipative nature (model) of friction Eq. (30).

As follows from the equations of the energy balance of friction Eqs. (26) and (27), the whole variety of manifestations of friction and wear can be conditionally reduced to at least two fundamentally different states. The first condition determines all types of damageability and wear, the second-the so-called condition of "wearlessness" [7].

The state of damageability and wear is characterized by the components of energy balance Eqs. (26) and (27), which are responsible for accumulation of internal energy Δ u ¼ Δ ue<sup>1</sup> þ Δ ue<sup>2</sup> þ Δ uT<sup>1</sup> þ Δ uT<sup>2</sup> in deformed volumes, that is, the process is irreversible [4, 8]. The "wearlessness" state is characterized by the components of the energy balance Eqs. (26) and (27), which are responsible for the dynamic dissipation (reversibility) of strain energy into elastic and structural dissipated energy q !¼ <sup>q</sup> ! <sup>1</sup> þ q ! <sup>2</sup> of friction contact [4, 8].

In its turn, the first state may be classified depending on the relation between potential Δ ue and kinetic Δ uT components of internal energy. It is subdivided conventionally into mechanical damage and wear (due to so-called structure activation) and thermal damage and wear (due to thermal activation). For instance, let the thermal component of internal energy Δ uT be equal to zero (Δ uT ¼ 0) and the internal energy variation at damage and wear be defined only by variation of the potential Δ ueð Þ Δ u ¼ Δue component. Then, the mechanical damage and wear with brittle fracture of surfaces take place. On the contrary, if we have Δ ue ¼ 0 (Δ u ¼ Δ uT), then the thermal damage and wear with ductile fracture of surfaces take place. All the intermediate values of the components are associated with quasibrittle or quasi-ductile fracture of solids [4, 8].

In the most general case, taking into account a fundamental tribology's notion of the "third body" [10], the energy balance at dry friction Eq. (20) should be written as

$$W\_f = \Delta U\_{\epsilon 1} + \Delta U\_{\epsilon 2} + \Delta U\_{\epsilon 3} + Q\_1 + Q\_2 + Q\_3. \tag{32}$$

In the special case, where the friction is localized into volume of the "third body" (Figure 2) Eq. (32) develops into

$$W\_f = \Delta U\_{\epsilon 3} + \overrightarrow{Q}\_3. \tag{33}$$

of the laws of change of the accumulated latent energy of deformation by the

3.4 Generalized experimental friction curves

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

Figure 3.

Figure 4.

45

3—medium; 4—considerable).

Experimental results of Conti [13].

contacting volumes of the solid, that is, change of Amontons coefficient of friction [12].

The dependences obtained for the friction coefficient μ are in agreement with experimental curves μ ¼ μð Þ N; v (Figures 3–5). Analyzing various experimental friction curves using the Eqs. (20)–(31) of friction energy balance, it was concluded

Generalized friction experiments in I.V. Kragelsky's interpretation [10]: sliding velocity (load: 1—small; 2 and

here, ΔUe<sup>3</sup> ¼ V3Δue3.

### 3.3 Energy interpretation of the friction coefficient by Amonton (Leonardo da Vinci)

According to the main conclusion of the thermodynamic theory of strength [1], as a structural parameter should not take the entire value of the accumulated plastic deformation, but only its part associated with the deformation hardening, which is uniquely and integrally determined by the density of the potential component of the internal energy (i.e., the density Δ ue of the so-called latent energy) of various defects and damages accumulated in the plastically deformable volumes of the material. With this in mind, if we neglect the heat effect Q of friction, one will infer from the thermodynamic analysis of friction of Eqs. (24) and (25) that the Amonton (Leonardo da Vinci) friction coefficient is

$$
\mu = \frac{\Delta U\_\epsilon}{\mu^\* N l} = \frac{F}{N}; F = \frac{\Delta U\_\epsilon}{l}; Q \cong \mathbf{0}, \mu^\* \,\,=\mathbf{1}.\tag{34}
$$

Consequently, the coefficient of friction has a very deep physical sense. On the one hand, it is the parameter which generally characterizes the resistance of relative displacement (movement) of surfaces, for it reflects the portion of energy, which "is done by friction away" as accumulated latent energy ΔUe, by relation to parameter of external forces work μ<sup>∗</sup> Nl (energy of external relative movement) [12]. On the other hand, it is the generalized characteristic of damage, for it is defined of the latent energy density Δ ue as integral characteristic of the structure defectiveness measure, because this energy is the generalized parameter of damage. Here too, coefficient of friction generally reflects the structural order (disorder) of deforming contact volume, since the parameter ΔUe ¼ ΔueVf is defined of the energy of defects and damages of different types, that are accumulated into contact volumes Vf solids [12].

Thus, the coefficient of friction is a true and generalized parameter of the state of the tribosystem. It follows a very important conclusion that the analysis of the regularities of the evolution of the states of tribosystems is, first of all, the analysis

Figure 2. Conditional scheme of friction contact [4].

Wf ¼ ΔUe<sup>3</sup> þ Q

According to the main conclusion of the thermodynamic theory of strength [1], as a structural parameter should not take the entire value of the accumulated plastic deformation, but only its part associated with the deformation hardening, which is uniquely and integrally determined by the density of the potential component of the internal energy (i.e., the density Δ ue of the so-called latent energy) of various defects and damages accumulated in the plastically deformable volumes of the material. With this in mind, if we neglect the heat effect Q of friction, one will infer from the thermodynamic analysis of friction of Eqs. (24) and (25) that the Amonton

<sup>N</sup> ; F <sup>¼</sup> <sup>Δ</sup>Ue

one hand, it is the parameter which generally characterizes the resistance of relative displacement (movement) of surfaces, for it reflects the portion of energy, which "is done by friction away" as accumulated latent energy ΔUe, by relation to parameter of external forces work μ<sup>∗</sup> Nl (energy of external relative movement) [12]. On the other hand, it is the generalized characteristic of damage, for it is defined of the latent energy density Δ ue as integral characteristic of the structure defectiveness measure, because this energy is the generalized parameter of damage. Here too, coefficient of friction generally reflects the structural order (disorder) of deforming contact volume, since the parameter ΔUe ¼ ΔueVf is defined of the energy of defects and damages of different types, that are accumulated into contact volumes

Consequently, the coefficient of friction has a very deep physical sense. On the

Thus, the coefficient of friction is a true and generalized parameter of the state of the tribosystem. It follows a very important conclusion that the analysis of the regularities of the evolution of the states of tribosystems is, first of all, the analysis

3.3 Energy interpretation of the friction coefficient by Amonton

here, ΔUe<sup>3</sup> ¼ V3Δue3.

Friction, Lubrication and Wear

(Leonardo da Vinci)

Vf solids [12].

Figure 2.

44

Conditional scheme of friction contact [4].

(Leonardo da Vinci) friction coefficient is

<sup>μ</sup> <sup>¼</sup> <sup>Δ</sup>Ue

<sup>μ</sup><sup>∗</sup> Nl <sup>¼</sup> <sup>F</sup>

!

<sup>3</sup>: (33)

<sup>l</sup> ; Q ffi <sup>0</sup>, <sup>μ</sup><sup>∗</sup> <sup>¼</sup> <sup>1</sup>: (34)

of the laws of change of the accumulated latent energy of deformation by the contacting volumes of the solid, that is, change of Amontons coefficient of friction [12].

### 3.4 Generalized experimental friction curves

The dependences obtained for the friction coefficient μ are in agreement with experimental curves μ ¼ μð Þ N; v (Figures 3–5). Analyzing various experimental friction curves using the Eqs. (20)–(31) of friction energy balance, it was concluded

Figure 3. Experimental results of Conti [13].

Figure 4.

Generalized friction experiments in I.V. Kragelsky's interpretation [10]: sliding velocity (load: 1—small; 2 and 3—medium; 4—considerable).

experimental friction curves that reflect the evolution (the change in the friction

We propose an energetic interpretation of the experimental friction curves μ ¼ μð Þ N; v (Figure 6). According to our concept [4, 15, 16], the ascending portion of the friction coefficient curve μ is mainly controlled by processes associated with the accumulation of latent energy ΔUe in various structural defects and damages. Here the increase in μ is due to the increasing density of latent (potential) energy Δ ue and the increasing adaptive friction volume Vf . The descending portion of the friction curve is mainly controlled by processes associated with the release and

latent energy density within the friction volume Vf or (which is virtually the same)

So, in Figure 6 you can see the following conditionally marked points and areas: 0-1—the area of static friction and strain hardening; 1—the point of the limit strain hardening; 1-2—excess energy pumping area; 2—point of adhesion (seizure) and transition of external friction into internal (point of critical instability); area of formation of dissipative structures (formation of temperature fluctuation in the friction volume); 3—the point of minimum compatibility (maximum frictionness); 1-2-3—area of self-organization; 3-4—compatibility area; 4—point of wearlessness

The ideal evolution of the friction contact is symmetric. The friction process begins and ends in areas of elastic behavior. Between them is the plastic maximum (super activated state) as a condition of self-organization and adaptation. In the most general case, the regularities of evolution (adaptation) of tribosystems can be represented as two-stage (Figure 6). At the first stage (0–2) of the evolution of

potential energy of structure defects. This is an elementary tribosystem, that is., an elementary and self-sufficient energy transformer. In the first stage, the latent

stage, contact is evolutionarily developed due to structural transformation. At this stage, a wide spectrum of compatible friction structures (Figure 6) can be formed depending on the nature of the environment. The second stage (2–4) can be con-

tribosystem) conditionally to the adaptive Vadapt and dissipative Vdis friction volumes (Figure 7). The end point (point 4) of this stage of evolution is characterized

The above volumes mentioned characterize different regularities of energy conversion of external mechanical motion at friction. Adaptive volume Vadapt

This is the smallest volume of friction that has accumulated the maximum

sidered as a structural transformation of the critical friction volume V <sup>∗</sup>

by the complete transformation of the critical adaptive friction volume V <sup>∗</sup>

. Here the decrease in μ is due to the decrease in

e

) and to the increase

<sup>f</sup> of friction (point 2).

<sup>f</sup> (elementary

adapt into

<sup>e</sup> within the critical friction

<sup>f</sup> is constant in the second stage of evolution. At this

!

!<sup>∗</sup> <sup>¼</sup> <sup>u</sup><sup>∗</sup> e .

The evolution of the tribosystem is presented in the form of a diagram (Figure 6) and has an adaptive-dissipative character Eqs. (29)–(34) and reflects the competitive (dialectical) nature of friction. The evolutionary curve has a number of fundamental points (1–5) of transition states of the tribosystem, which are strictly subject to the balance principle of friction. Between these points there are the most characteristic areas of behavior of the tribosystem. These areas reflect the most

to the decrease of the adaptive friction volume Vadapt ue <sup>¼</sup> <sup>u</sup><sup>∗</sup>

general properties of nonlinear dynamics of friction evolution.

(abnormally low friction); 5—thermal adhesion point.

the friction contact, it tends to form a critical volume V <sup>∗</sup>

energy density Δue increases to a limit value Δu<sup>∗</sup>

volume V <sup>∗</sup>

f .

the dissipative V <sup>∗</sup>

47

The volume of friction V <sup>∗</sup>

dis one.

coefficient) of tribosystem.

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

dissipation of energy Q ¼ ΔUTþ Q

of the dissipative volume Vdis q

Figure 5. Experimental results of Watanabe for a pair of friction—nylon 6—steel [14].

Figure 6. Structural-energy diagram of the evolution of friction surfaces [4, 16–18].

[4] that the experimental friction curves (Figures 3–5) of the type a μ ¼ μð Þ N; v are generalized experimental friction curves and reflect the general (for all materials and friction pairs) laws of evolution (changes in the friction coefficient) of tribosystems.

### 3.5 Structural-energy regularities of rubbing surfaces evolution

An analysis of modern experimental data using Eqs. (20)–(31) has shown that the experimental friction curves of type μ ¼ μð Þ N; v are the generalized

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

experimental friction curves that reflect the evolution (the change in the friction coefficient) of tribosystem.

We propose an energetic interpretation of the experimental friction curves μ ¼ μð Þ N; v (Figure 6). According to our concept [4, 15, 16], the ascending portion of the friction coefficient curve μ is mainly controlled by processes associated with the accumulation of latent energy ΔUe in various structural defects and damages. Here the increase in μ is due to the increasing density of latent (potential) energy Δ ue and the increasing adaptive friction volume Vf . The descending portion of the friction curve is mainly controlled by processes associated with the release and dissipation of energy Q ¼ ΔUTþ Q ! . Here the decrease in μ is due to the decrease in latent energy density within the friction volume Vf or (which is virtually the same) to the decrease of the adaptive friction volume Vadapt ue <sup>¼</sup> <sup>u</sup><sup>∗</sup> e ) and to the increase

of the dissipative volume Vdis q !<sup>∗</sup> <sup>¼</sup> <sup>u</sup><sup>∗</sup> e .

The evolution of the tribosystem is presented in the form of a diagram (Figure 6) and has an adaptive-dissipative character Eqs. (29)–(34) and reflects the competitive (dialectical) nature of friction. The evolutionary curve has a number of fundamental points (1–5) of transition states of the tribosystem, which are strictly subject to the balance principle of friction. Between these points there are the most characteristic areas of behavior of the tribosystem. These areas reflect the most general properties of nonlinear dynamics of friction evolution.

So, in Figure 6 you can see the following conditionally marked points and areas: 0-1—the area of static friction and strain hardening; 1—the point of the limit strain hardening; 1-2—excess energy pumping area; 2—point of adhesion (seizure) and transition of external friction into internal (point of critical instability); area of formation of dissipative structures (formation of temperature fluctuation in the friction volume); 3—the point of minimum compatibility (maximum frictionness); 1-2-3—area of self-organization; 3-4—compatibility area; 4—point of wearlessness (abnormally low friction); 5—thermal adhesion point.

The ideal evolution of the friction contact is symmetric. The friction process begins and ends in areas of elastic behavior. Between them is the plastic maximum (super activated state) as a condition of self-organization and adaptation. In the most general case, the regularities of evolution (adaptation) of tribosystems can be represented as two-stage (Figure 6). At the first stage (0–2) of the evolution of the friction contact, it tends to form a critical volume V<sup>∗</sup> <sup>f</sup> of friction (point 2). This is the smallest volume of friction that has accumulated the maximum potential energy of structure defects. This is an elementary tribosystem, that is., an elementary and self-sufficient energy transformer. In the first stage, the latent energy density Δue increases to a limit value Δu<sup>∗</sup> <sup>e</sup> within the critical friction volume V <sup>∗</sup> f .

The volume of friction V <sup>∗</sup> <sup>f</sup> is constant in the second stage of evolution. At this stage, contact is evolutionarily developed due to structural transformation. At this stage, a wide spectrum of compatible friction structures (Figure 6) can be formed depending on the nature of the environment. The second stage (2–4) can be considered as a structural transformation of the critical friction volume V <sup>∗</sup> <sup>f</sup> (elementary tribosystem) conditionally to the adaptive Vadapt and dissipative Vdis friction volumes (Figure 7). The end point (point 4) of this stage of evolution is characterized by the complete transformation of the critical adaptive friction volume V <sup>∗</sup> adapt into the dissipative V <sup>∗</sup> dis one.

The above volumes mentioned characterize different regularities of energy conversion of external mechanical motion at friction. Adaptive volume Vadapt

[4] that the experimental friction curves (Figures 3–5) of the type a μ ¼ μð Þ N; v are generalized experimental friction curves and reflect the general (for all materials and friction pairs) laws of evolution (changes in the friction coefficient) of

An analysis of modern experimental data using Eqs. (20)–(31) has shown that

3.5 Structural-energy regularities of rubbing surfaces evolution

Structural-energy diagram of the evolution of friction surfaces [4, 16–18].

Experimental results of Watanabe for a pair of friction—nylon 6—steel [14].

the experimental friction curves of type μ ¼ μð Þ N; v are the generalized

tribosystems.

46

Figure 6.

Figure 5.

Friction, Lubrication and Wear

It is shown [4] that the value of the minimum adaptive friction volume Vmin

corresponding to the zero value of the plastic friction component μadapt is not zero, but is equal to the size of a certain minimum structural element of the deformable

3.6 The idea of a mechanical (nano) quantum of dissipative friction structures

The result of ideal elementary tribosystem (contact) evolution is forming of unique nanostructure—a mechanical (nano) quantum. Strict ideas about mechanical quantum obtained [4, 18] considering for point 4 of the friction evolution

disNlf <sup>¼</sup> <sup>V</sup> <sup>∗</sup>

This equation is a special case of the solution of the equations of energy balance

of compatible friction volume; T is the characteristic temperature of compatible

contact friction volume; lf is the linear dimension of elementary contact. Accordingly, under the conditions of maximum compatibility (point 4), when the tribosystem implements a complete evolutionary cycle of adaptation with the formation of the most perfect, dissipative structure, its (structure) behavior is subject to the equation of state of a quasi-ideal solid, that is, it should be assumed that the interactions between the elements of this structure are minimized—the state of ideal elasticity in dynamics. Eq. (28), taking into account the Planck-Boltzmann formula S ¼ k lnW and the real number of atomic oscillators Nf in the volume of the elementary tribosystem (contact) V <sup>∗</sup>

is given to the form explaining the regularities of friction in terms of the

<sup>¼</sup> kTNf ln <sup>W</sup> Nlf

> <sup>¼</sup> <sup>1</sup> � SQ ! T Nlf

Nlf

The tribosystem always tends to some optimal state characterized, that is, to the

The number of thermodynamic state probability W equal to 20, 08553696… was interpreted [4, 12–15] as the smallest number of linear, atomic oscillators in one of

to the state of almost absolute elastic friction—abnormally low friction (safe deformation threshold). Accordingly, the number of atomic oscillators in this volume is

It is the universal size (volume) of mechanical quantum [4, 7, 16–18].

where k is the Boltzmann constant; W is the probability of state; SU is the

The analysis and solution of these equations [4, 16–18] allows to show the principle of the constancy of the magnitude of the probability (the state's parameter (order)) W of the tribological system) for the entire range of compatible friction,

<sup>μ</sup>diss <sup>¼</sup> SQ ! Nlf

most probable state W<sup>0</sup> ¼ Nf lnW for the given friction conditions.

the three directions of the minimum adaptive friction volume Vmin

<sup>μ</sup>adapt <sup>¼</sup> <sup>1</sup> � <sup>μ</sup>diss <sup>¼</sup> <sup>1</sup> � kTNf ln <sup>W</sup>

configuration entropy of friction (contact) volume.

namely ln <sup>W</sup> <sup>¼</sup> 3, and <sup>W</sup> <sup>¼</sup> e3 <sup>¼</sup> <sup>20</sup>, <sup>08553696</sup>….

VQ <sup>¼</sup> <sup>e</sup><sup>3</sup> ð Þ<sup>3</sup> <sup>¼</sup> ð Þ <sup>20</sup>; <sup>08553695</sup>… <sup>3</sup> <sup>¼</sup> <sup>8103</sup>, <sup>083969</sup>….

<sup>f</sup> u<sup>∗</sup> <sup>e</sup> <sup>¼</sup> <sup>V</sup> <sup>∗</sup> <sup>f</sup> q !

dis. Here S

!

diagram the equation of a quasi-ideal solid:

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

evolution of systems:

49

Q ! <sup>∗</sup>

of friction Eq. (29), at <sup>μ</sup>adapt <sup>¼</sup> 0 and <sup>μ</sup>dis <sup>¼</sup> <sup>1</sup> <sup>¼</sup> <sup>μ</sup><sup>∗</sup>

¼ S !

<sup>Q</sup> <sup>T</sup> <sup>¼</sup> <sup>μ</sup><sup>∗</sup>

solid.

adapt

<sup>∗</sup> : (36)

<sup>Q</sup> is the inertial entropy

, (37)

, (38)

adapt corresponding

<sup>¼</sup> SUT Nlf

f ,

Figure 7.

The model of the energy evolution of the contact friction volume at points 1–5 of the diagram (Figure 6) [4].

is associated with irreversible absorption of strain energy. In this volume, there is an accumulation of latent deformation energy Δue and centers of destruction are born. The dissipative volume Vdis is able to reversibly transform (dissipate) the energy of the outer movements. In this volume, there is no accumulation of latent deformation energy due to the flow of reversible elastic-viscoplastic deformation.

Theoretical and calculated estimates [4, 16, 18] have shown that the dissipative friction volume performs a reversible elastic transformation of the energy of external mechanical motion with a density q ! <sup>∗</sup> equal to the critical density <sup>u</sup><sup>∗</sup>

<sup>e</sup> of the latent energy. The culmination of the evolution of the tribosystem is its final and limiting state of point 4—the state of abnormally low friction and wearlessness (maximum efficient).

A schematic evolution of the contact volume of friction in diagram's points 1–5 is presented in Figure 7.

Calculations show [4] that with the ideal evolution of the tribosystem, the adaptive (Amonton) coefficient of friction μadapt at point 2 of the diagram drops sharply, reaching at point 4 the elastic coefficient of friction μelast. For point 4 of compatibility area 3-4, an equation of energy balance Eq. (30) should be put in the following way:

$$
\mu\_{\text{adapt}} = \mu^\* - \mu\_{\text{dis}} = \mathbb{1} - \mu\_{\text{dis}} = \mu\_{\text{plant}} = \mathbb{0} = \mu\_{\text{elast}}; \mu^\* = \mathbb{1}, \mathbb{0}. \tag{35}
$$

Thus, we have at point 4 of the ideal evolution of the contact friction volume the condition of perfectly elastic-viscous-plastic deformation. This actually shows the Eq. (35), that is, the coefficient of friction of Amonton μadapt, being, in fact, a plastic coefficient of friction μplast has a minimum value equal to zero. Consequently, plastic friction becomes elastic with the coefficient μelast of friction. This means that the plastic deformation of the contact friction volume is realized with the maximum dynamic dissipation (Q ! ¼ max) of the accumulated latent energy. Therefore, the amount of accumulated energy at point 4 is zero (ΔUe ¼ 0). This fact proves the ideal state with the full evolution of the contact volume. From the physical point of view, this state can be explained by the complete dissipating of the energy ΔU <sup>∗</sup> e accumulated at point 2, along the newly formed structures of point 4 in the form of elastic energy of interaction between them (energy Q ! <sup>∗</sup> of dynamic dissipation). Here μdis ¼ 1, 0. The structural elements themselves are defectlessness—μadapt ¼ 0, and friction is elastic—μ ¼ μelast.

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

It is shown [4] that the value of the minimum adaptive friction volume Vmin adapt corresponding to the zero value of the plastic friction component μadapt is not zero, but is equal to the size of a certain minimum structural element of the deformable solid.

### 3.6 The idea of a mechanical (nano) quantum of dissipative friction structures

The result of ideal elementary tribosystem (contact) evolution is forming of unique nanostructure—a mechanical (nano) quantum. Strict ideas about mechanical quantum obtained [4, 18] considering for point 4 of the friction evolution diagram the equation of a quasi-ideal solid:

$$
\overrightarrow{\dot{Q}}^{\*} = \overrightarrow{\mathcal{S}}\_{Q} T = \mu\_{\text{di}}^{\*} \text{N} \\
\text{l}\_{f} = \text{V}\_{f}^{\*} \text{u}\_{\epsilon}^{\*} = \text{V}\_{f}^{\*} \overrightarrow{\dot{q}}\_{\*} \text{ .} \tag{36}
$$

This equation is a special case of the solution of the equations of energy balance of friction Eq. (29), at <sup>μ</sup>adapt <sup>¼</sup> 0 and <sup>μ</sup>dis <sup>¼</sup> <sup>1</sup> <sup>¼</sup> <sup>μ</sup><sup>∗</sup> dis. Here S ! <sup>Q</sup> is the inertial entropy of compatible friction volume; T is the characteristic temperature of compatible contact friction volume; lf is the linear dimension of elementary contact.

Accordingly, under the conditions of maximum compatibility (point 4), when the tribosystem implements a complete evolutionary cycle of adaptation with the formation of the most perfect, dissipative structure, its (structure) behavior is subject to the equation of state of a quasi-ideal solid, that is, it should be assumed that the interactions between the elements of this structure are minimized—the state of ideal elasticity in dynamics. Eq. (28), taking into account the Planck-Boltzmann formula S ¼ k lnW and the real number of atomic oscillators Nf in the volume of the elementary tribosystem (contact) V <sup>∗</sup> f , is given to the form explaining the regularities of friction in terms of the evolution of systems:

$$
\mu\_{\rm diss} = \frac{\overrightarrow{S\_Q}}{Nl\_f} = \frac{kT \mathbf{N}\_f \ln \mathbf{W}}{Nl\_f},
\tag{37}
$$

$$
\mu\_{\text{adapt}} = \mathbf{1} - \mu\_{\text{dis}} = \mathbf{1} - \frac{kTN\_f \ln W}{Nl\_f} = \mathbf{1} - \frac{\overline{S}\_Q}{Nl\_f} \frac{T}{Nl\_f} = \frac{S\_U T}{Nl\_f},\tag{38}
$$

where k is the Boltzmann constant; W is the probability of state; SU is the configuration entropy of friction (contact) volume.

The tribosystem always tends to some optimal state characterized, that is, to the most probable state W<sup>0</sup> ¼ Nf lnW for the given friction conditions.

The analysis and solution of these equations [4, 16–18] allows to show the principle of the constancy of the magnitude of the probability (the state's parameter (order)) W of the tribological system) for the entire range of compatible friction, namely ln <sup>W</sup> <sup>¼</sup> 3, and <sup>W</sup> <sup>¼</sup> e3 <sup>¼</sup> <sup>20</sup>, <sup>08553696</sup>….

The number of thermodynamic state probability W equal to 20, 08553696… was interpreted [4, 12–15] as the smallest number of linear, atomic oscillators in one of the three directions of the minimum adaptive friction volume Vmin adapt corresponding to the state of almost absolute elastic friction—abnormally low friction (safe deformation threshold). Accordingly, the number of atomic oscillators in this volume is VQ <sup>¼</sup> <sup>e</sup><sup>3</sup> ð Þ<sup>3</sup> <sup>¼</sup> ð Þ <sup>20</sup>; <sup>08553695</sup>… <sup>3</sup> <sup>¼</sup> <sup>8103</sup>, <sup>083969</sup>….

It is the universal size (volume) of mechanical quantum [4, 7, 16–18].

is associated with irreversible absorption of strain energy. In this volume, there is an accumulation of latent deformation energy Δue and centers of destruction are born. The dissipative volume Vdis is able to reversibly transform (dissipate) the energy of the outer movements. In this volume, there is no accumulation of latent deformation energy due to the flow of reversible elastic-viscoplastic deformation. Theoretical and calculated estimates [4, 16, 18] have shown that the dissipative friction volume performs a reversible elastic transformation of the energy of external

The model of the energy evolution of the contact friction volume at points 1–5 of the diagram (Figure 6) [4].

! <sup>∗</sup> equal to the critical density <sup>u</sup><sup>∗</sup>

The culmination of the evolution of the tribosystem is its final and limiting state of point 4—the state of abnormally low friction and wearlessness (maximum efficient). A schematic evolution of the contact volume of friction in diagram's points 1–5 is

<sup>μ</sup>adapt <sup>¼</sup> <sup>μ</sup><sup>∗</sup> � <sup>μ</sup>dis <sup>¼</sup> <sup>1</sup> � <sup>μ</sup>dis <sup>¼</sup> <sup>μ</sup>plast <sup>¼</sup> <sup>0</sup> <sup>¼</sup> <sup>μ</sup>elast; <sup>μ</sup><sup>∗</sup> <sup>¼</sup> <sup>1</sup>, <sup>0</sup>: (35)

¼ max) of the accumulated latent energy. Therefore, the

! <sup>∗</sup>

Thus, we have at point 4 of the ideal evolution of the contact friction volume the condition of perfectly elastic-viscous-plastic deformation. This actually shows the Eq. (35), that is, the coefficient of friction of Amonton μadapt, being, in fact, a plastic coefficient of friction μplast has a minimum value equal to zero. Consequently, plastic friction becomes elastic with the coefficient μelast of friction. This means that the plastic deformation of the contact friction volume is realized with the maximum

amount of accumulated energy at point 4 is zero (ΔUe ¼ 0). This fact proves the ideal state with the full evolution of the contact volume. From the physical point of view, this state can be explained by the complete dissipating of the energy ΔU <sup>∗</sup>

accumulated at point 2, along the newly formed structures of point 4 in the form of

Here μdis ¼ 1, 0. The structural elements themselves are defectlessness—μadapt ¼ 0,

Calculations show [4] that with the ideal evolution of the tribosystem, the adaptive (Amonton) coefficient of friction μadapt at point 2 of the diagram drops sharply, reaching at point 4 the elastic coefficient of friction μelast. For point 4 of compatibility area 3-4, an equation of energy balance Eq. (30) should be put in the

<sup>e</sup> of the latent energy.

e

of dynamic dissipation).

mechanical motion with a density q

Friction, Lubrication and Wear

presented in Figure 7.

dynamic dissipation (Q

48

and friction is elastic—μ ¼ μelast.

!

elastic energy of interaction between them (energy Q

following way:

Figure 7.

### Friction, Lubrication and Wear

On the other hand, taking the meaning of Boltzmann entropy S, we obtain a universal friction constant Rf ¼ kNf [4, 16–18], which in physical sense characterizes the "energy size" of the elementary tribosystem (TS) containing under ideal conditions the same number of atomic oscillators Nf (mechanical quanta NQ ):

$$R\_f = k \cdot N\_f = k \cdot W^3 \cdot N\_Q = R\_{MQ} \cdot N\_{Q}, \frac{J}{grade \cdot TS}, \tag{39}$$

$$R\_{MQ} = k \cdot W^{\beta}, \frac{J}{grade \cdot MQ},\tag{40}$$

where RMQ is the universal constant of deformation at friction.

As follows from the calculations [4], the size of the minimum adaptive friction volume Vmin adapt coincides in its magnitude with the size of the submicroscopic zone at the mouth of the crack, which for metals is equal 4ð Þ� :::<sup>9</sup> <sup>10</sup>�<sup>6</sup> mm, that is, with the size of the critical volume responsible for the fracture. Thus, the size of the minimum adaptive friction volume Vmin adapt ¼ Velast can be represented as the size of some mechanical "quantum".

This mechanical quantum is the minimum number of atoms capable of providing a configuration of their distribution (structure), which has the property of reversibly absorb and dissipate (return) the energy of external mechanical motion (action). It also represents the smallest structural formation under plastic deformation and is formed during the transition of the tribosystem (deformable volume) through the extremely activated (critical) state (Figure 6) due to the development of self-organizational processes of adaptation of the tribosystem. The mutual rotational-oscillatory motion of these mechanical quanta relative to each other inside the elementary tribosystem (contact) determines the state of the most perfect dissipative structure of friction. Actually, this state is described by the equation of state of a quasi-ideal solid Eq. (36), the state when the interaction between the elements of the structure (mechanical quanta) is minimized-the state of the ideal elasticity of the quasi-viscous flow. The calculated coefficient of friction between the quanta is approximately 10�<sup>8</sup> [4, 16–18].

The conclusion that the mechanical quantum is the smallest structural formation under plastic deformation (friction) is confirmed by the calculation. If we compare the values of the elastic modules E to the atomic (true) elasticity Er, we obtain values equal to 60, where the number 60 ¼ 3W can be interpreted as a characteristic of the volume elasticity of one mechanical quantum—the minimum adaptive friction volume Vmin adapt. Calculation of the parameter W ffi 20 ¼ E=3Er for different metals and steels gives an average value of 20, 77 (Table 1); ΔHS ¼ 3Er is the enthalpy of melting.

It is concluded [4, 16–18] that for all materials, under the conditions of the ideal evolution of the tribosystem, the number of atoms Nf (mechanical quanta (MQ)) in the volume of one elementary tribosystem (TS) is constant. Thus, we can talk about the amount of matter equal in mass to one elementary tribosystem and to one mechanical quantum.

newly formed (on the mechanism of self-organization in the vicinity of the critical state) structural elements-mechanical quanta (dynamic oscillators), which implement the most complete rotational-oscillatory behavior relative to each other in the volume of the elementary tribosystem. At the same time, the resistance to their relative interaction is minimal-elastic and corresponds to the elasticity of ideal atomic (thermodynamically equilibrium) interactions at the level

Metals and steels <sup>E</sup> � <sup>10</sup>�3, MPa <sup>u</sup><sup>∗</sup>

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

e

Cr 235.4 8.5 27.69 Mg 44.4 1.9 23.37 Ag 79.0 3.7 21.35 Au 78.7 4.0 19.67 Co 200.1 10.6 18.88 Fe 211.4 9.9 21.35 Ta 184.4 10.6 17.39 Ti 105.9 6.7 15.8 Nb 104.0 9.2 11.3 Zr 95.6 5.7 16.77 Mo 316.9 12.0 26.4 W 392.4 14.4 27.25 Ni 201.1 9.4 21.39 Iron 210.9 10.1 20.88 20 200.1 9.5 21.06 1Kh13 206.0 8.9 23.14 3Kh13 218.8 9.2 23.78 Kh18N9T 199.1 9.4 21.19 Kh18M9 199.1 9.6 20.74 30Kh 214.1 10.2 20.99 30N3 207.5 10.3 20.11 40 209.4 9.7 21.58 30G2 207.2 10.0 20.72 30KhGN3 208.0 10.2 20.4 G13 204.0 10.0 20.4 50S2G 196.2 10.3 19.05 U8 198.0 10.3 19.22 U12 198.0 10.4 19.04

� �ΔHS � <sup>10</sup>�3, MJ/m3 <sup>E</sup>=3Er

The universal constants of the mechanical quantum and the elementary tribosystem (material point) determine both the quantum model of surface

of electronic shells.

ΔHS ¼ 3Er, E=3Er ¼ 20:77.

Parameter estimation for different metals and steels [4].

damping:

51

Table 1.

### 3.7 The synergy of the tribosystem and the optimality states

Mechanical quantum is a dynamic oscillator of dissipative friction structures. The ideal, quasi-elastic state of contact at its full evolution is the effect of the most complete energy dissipation of external mechanical motion on the


### Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

On the other hand, taking the meaning of Boltzmann entropy S, we obtain a

universal friction constant Rf ¼ kNf [4, 16–18], which in physical sense characterizes the "energy size" of the elementary tribosystem (TS) containing under ideal conditions the same number of atomic oscillators Nf (mechanical

RMQ <sup>¼</sup> <sup>k</sup> � <sup>W</sup><sup>3</sup>

where RMQ is the universal constant of deformation at friction.

Rf <sup>¼</sup> <sup>k</sup> � Nf <sup>¼</sup> <sup>k</sup> � <sup>W</sup><sup>3</sup> � NQ <sup>¼</sup> RMQ � NQ , <sup>J</sup>

, <sup>J</sup>

adapt coincides in its magnitude with the size of the submicroscopic zone at

As follows from the calculations [4], the size of the minimum adaptive friction

the mouth of the crack, which for metals is equal 4ð Þ� :::<sup>9</sup> <sup>10</sup>�<sup>6</sup> mm, that is, with the size of the critical volume responsible for the fracture. Thus, the size of the mini-

This mechanical quantum is the minimum number of atoms capable of providing a configuration of their distribution (structure), which has the property of reversibly absorb and dissipate (return) the energy of external mechanical motion (action). It also represents the smallest structural formation under plastic deformation and is formed during the transition of the tribosystem (deformable volume) through the extremely activated (critical) state (Figure 6) due to the development of self-organizational processes of adaptation of the tribosystem. The mutual rotational-oscillatory motion of these mechanical quanta relative to each other inside the elementary tribosystem (contact) determines the state of the most perfect dissipative structure of friction. Actually, this state is described by the equation of state of a quasi-ideal solid Eq. (36), the state when the interaction between the elements of the structure (mechanical quanta) is minimized-the state of the ideal elasticity of the quasi-viscous flow. The calculated coefficient of friction between

The conclusion that the mechanical quantum is the smallest structural formation under plastic deformation (friction) is confirmed by the calculation. If we compare the values of the elastic modules E to the atomic (true) elasticity Er, we obtain values equal to 60, where the number 60 ¼ 3W can be interpreted as a characteristic of the volume elasticity of one mechanical quantum—the minimum adaptive

It is concluded [4, 16–18] that for all materials, under the conditions of the ideal evolution of the tribosystem, the number of atoms Nf (mechanical quanta (MQ)) in the volume of one elementary tribosystem (TS) is constant. Thus, we can talk about the amount of matter equal in mass to one elementary tribosystem and to one

metals and steels gives an average value of 20, 77 (Table 1); ΔHS ¼ 3Er is the

3.7 The synergy of the tribosystem and the optimality states

Mechanical quantum is a dynamic oscillator of dissipative friction

structures. The ideal, quasi-elastic state of contact at its full evolution is the effect of the most complete energy dissipation of external mechanical motion on the

adapt. Calculation of the parameter W ffi 20 ¼ E=3Er for different

grade � TS , (39)

grade � MQ , (40)

adapt ¼ Velast can be represented as the size of some

quanta NQ ):

Friction, Lubrication and Wear

volume Vmin

mum adaptive friction volume Vmin

the quanta is approximately 10�<sup>8</sup> [4, 16–18].

mechanical "quantum".

friction volume Vmin

enthalpy of melting.

mechanical quantum.

50

### Table 1.

Parameter estimation for different metals and steels [4].

newly formed (on the mechanism of self-organization in the vicinity of the critical state) structural elements-mechanical quanta (dynamic oscillators), which implement the most complete rotational-oscillatory behavior relative to each other in the volume of the elementary tribosystem. At the same time, the resistance to their relative interaction is minimal-elastic and corresponds to the elasticity of ideal atomic (thermodynamically equilibrium) interactions at the level of electronic shells.

The universal constants of the mechanical quantum and the elementary tribosystem (material point) determine both the quantum model of surface damping:

Friction, Lubrication and Wear

$$\mu\_{dis} = \frac{\Re\_{MQ} T n\_i}{N l\_f} = \frac{U\_{1Q} n\_i}{U\_{1Q} n\_\*} = \frac{n\_i}{n\_\*} = \mathbb{1} - \mu\_{adapt}; \quad \mu\_{adap} = \mathbb{1} - \frac{n\_i}{n\_\*} = \frac{n\_{det}}{n\_\*}, \tag{41}$$

taking into account the quanta of destruction ndest (irreversible component of the process) and the quanta of damping ni (reversible, elastic component (fatigue number)), and the probabilistic model of the evolution of the tribosystem to the most ordered state:

$$
\mu\_{\text{adapt}} = \mathbf{1} - \mu\_{\text{dis}} = \mathbf{1} - \frac{\mathbf{R}\_f T \ln W\_i}{N l\_f} = \mathbf{1} - \frac{\ln W\_i}{\ln W\_\*}.\tag{42}
$$

Calculations have shown [4, 8] the number NQ of such mechanical "quanta"

Therefore, the smaller the coefficient of friction μadapt (the greater the coefficient μdis) of the tribosystem, the higher its fatigue endurance (durability), as a greater number of mechanical quanta involved in the process of damping (elastic return) of the energy of the external mechanical motion (impact), and consequently the smaller the number of quanta associated with the fracture (accumulation of latent energy of defects and damage of the limit value). In the limit, the tribosystem is characterized by the effect of "wearlessness" (abnormally low friction), corresponding to the state of almost complete thermodynamic reversibility of the friction (deformation) process. Here, all mechanical quanta, with the exception of one, reversible elastic transform (damp out) the energy of external mechanical movement. By analogy with classical quantum theory, we can say that in this case the system (tribosystem) is in the ground state (here, as if all mechanical quanta are directed against the field)—tribosystem cannot give energy to any other system (environment) simply because it (tribosystem) and does not accumulate energy in this state. In this case, the tribosystem is in almost perfect balance with the envi-

The principle of mechanical quantum determines nanoquantum levels of all

The model [4] of the moving critical (equilibrium) friction volume (Figure 9) is

<sup>n</sup>нnv <sup>¼</sup> <sup>W</sup>\_ fi

H lf � Lv lf

: (44)

Here, the instantaneous value of the friction work <sup>W</sup>\_ fi is connected with the friction work W\_ <sup>f</sup> per unit time, taking into account the uniform distribution of contacts (micro-shocks) in the longitudinal nv and transverse n<sup>н</sup> directions of the

friction parameters of compatible (optimal) tribosystems and other.

considered for the analysis of wear problems.

Scheme to the calculation of wear parameters of friction [4].

<sup>W</sup>\_ <sup>f</sup> <sup>¼</sup> <sup>W</sup>\_ fi

4. The model for the evaluation of wear of compatible friction

<sup>n</sup> <sup>¼</sup> <sup>W</sup>\_ fi

<sup>f</sup> <sup>¼</sup> <sup>V</sup> <sup>∗</sup>

dis to be

(subtribosystems) within the elementary tribosystem's volume V <sup>∗</sup>

<sup>0</sup>:<sup>63</sup> � <sup>10</sup><sup>8</sup> which is close to the safe number <sup>n</sup><sup>∗</sup> of fatigue cycles.

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

ronment.

friction surface:

Figure 9.

53

where 3RMQ T ¼ U1<sup>Q</sup> is the energy of one mechanical quantum; Wi and W <sup>∗</sup> is the current and limit probabilities of states of compatible tribosystems.

According to the model of quantum damping of surfaces under friction in the conditions of the most complete evolution (adaptation) of the elementary tribosystem, all mechanical quanta except one, elastically and reversibly transform the energy of external action (mechanical motion). One mechanical quantum of radiation (ffi 8103 atoms)—there is a minimum loss (the essence of wearlessness (the ideal damping properties) or the standard of wear).

The linear size of a mechanical quantum is equal to the diameter of a spherical ideal crystal with atomic roughness [4, 7]:

$$D\_{\rm MQ} = \text{2} \cdot \text{W} \cdot \overline{d}\_a \cdot \left(\text{3/4} \cdot \pi\right)^{\circ\_3} = \text{7, 17/nm.} \tag{43}$$

here, da is the average atomic diameter, for metals; <sup>W</sup> <sup>¼</sup> e3 is the mechanical quantum state parameter [4].

The mechanical quantum (Figure 8) itself should be considered as an elementary nanostructure of a metal solid.

Figure 8. Model of an ideal crystal of elementary nanostructure of friction contact (8103 atomic cubical cells) [4, 16–18].

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

<sup>μ</sup>dis <sup>¼</sup> <sup>3</sup>RMQ Tni Nlf

Friction, Lubrication and Wear

most ordered state:

<sup>¼</sup> <sup>U</sup>1<sup>Q</sup> ni U1<sup>Q</sup> n<sup>∗</sup> ¼ ni n∗ <sup>¼</sup> <sup>1</sup> � <sup>μ</sup>adapt; <sup>μ</sup>adapt <sup>¼</sup> <sup>1</sup> � ni

taking into account the quanta of destruction ndest (irreversible component of the

Nlf

where 3RMQ T ¼ U1<sup>Q</sup> is the energy of one mechanical quantum; Wi and W <sup>∗</sup> is

According to the model of quantum damping of surfaces under friction in the

tribosystem, all mechanical quanta except one, elastically and reversibly transform the energy of external action (mechanical motion). One mechanical quantum of radiation (ffi 8103 atoms)—there is a minimum loss (the essence of wearlessness

The linear size of a mechanical quantum is equal to the diameter of a spherical

here, da is the average atomic diameter, for metals; <sup>W</sup> <sup>¼</sup> e3 is the mechanical

The mechanical quantum (Figure 8) itself should be considered as an elemen-

Model of an ideal crystal of elementary nanostructure of friction contact (8103 atomic cubical cells)

DMQ <sup>¼</sup> <sup>2</sup> � <sup>W</sup> � da � ð Þ <sup>3</sup>=<sup>4</sup> � <sup>π</sup> <sup>1</sup>=<sup>3</sup> <sup>¼</sup> <sup>7</sup>, <sup>177</sup>nm: (43)

process) and the quanta of damping ni (reversible, elastic component (fatigue number)), and the probabilistic model of the evolution of the tribosystem to the

<sup>μ</sup>adapt <sup>¼</sup> <sup>1</sup> � <sup>μ</sup>dis <sup>¼</sup> <sup>1</sup> � RfT ln Wi

the current and limit probabilities of states of compatible tribosystems.

(the ideal damping properties) or the standard of wear).

ideal crystal with atomic roughness [4, 7]:

quantum state parameter [4].

Figure 8.

[4, 16–18].

52

tary nanostructure of a metal solid.

conditions of the most complete evolution (adaptation) of the elementary

n∗

<sup>¼</sup> <sup>1</sup> � ln Wi ln W <sup>∗</sup> <sup>¼</sup> ndest n∗

, (41)

: (42)

Calculations have shown [4, 8] the number NQ of such mechanical "quanta" (subtribosystems) within the elementary tribosystem's volume V <sup>∗</sup> <sup>f</sup> <sup>¼</sup> <sup>V</sup> <sup>∗</sup> dis to be <sup>0</sup>:<sup>63</sup> � <sup>10</sup><sup>8</sup> which is close to the safe number <sup>n</sup><sup>∗</sup> of fatigue cycles.

Therefore, the smaller the coefficient of friction μadapt (the greater the coefficient μdis) of the tribosystem, the higher its fatigue endurance (durability), as a greater number of mechanical quanta involved in the process of damping (elastic return) of the energy of the external mechanical motion (impact), and consequently the smaller the number of quanta associated with the fracture (accumulation of latent energy of defects and damage of the limit value). In the limit, the tribosystem is characterized by the effect of "wearlessness" (abnormally low friction), corresponding to the state of almost complete thermodynamic reversibility of the friction (deformation) process. Here, all mechanical quanta, with the exception of one, reversible elastic transform (damp out) the energy of external mechanical movement. By analogy with classical quantum theory, we can say that in this case the system (tribosystem) is in the ground state (here, as if all mechanical quanta are directed against the field)—tribosystem cannot give energy to any other system (environment) simply because it (tribosystem) and does not accumulate energy in this state. In this case, the tribosystem is in almost perfect balance with the environment.

The principle of mechanical quantum determines nanoquantum levels of all friction parameters of compatible (optimal) tribosystems and other.

### 4. The model for the evaluation of wear of compatible friction

The model [4] of the moving critical (equilibrium) friction volume (Figure 9) is considered for the analysis of wear problems.

Here, the instantaneous value of the friction work <sup>W</sup>\_ fi is connected with the friction work W\_ <sup>f</sup> per unit time, taking into account the uniform distribution of contacts (micro-shocks) in the longitudinal nv and transverse n<sup>н</sup> directions of the friction surface:

$$
\dot{\mathcal{W}}\_f = \dot{\mathcal{W}}\_{f\_i} n = \dot{\mathcal{W}}\_{f\_i} n\_n n\_v = \dot{\mathcal{W}}\_{f\_i} \frac{H}{l\_f} \cdot \frac{L\_v}{l\_f} \,. \tag{44}
$$

Figure 9. Scheme to the calculation of wear parameters of friction [4].

Accordingly, we have a number of ratios for power, force and coefficient of friction

$$
\dot{\mathcal{W}}\_f^\* = \dot{\mathcal{W}}\_{f\_i}^\* \cdot \boldsymbol{\pi} = \boldsymbol{V}\_f^\* \cdot \Delta \boldsymbol{u}\_e^\* \cdot \boldsymbol{\pi} = \boldsymbol{V}\_{f\_H}^\* \cdot \Delta \boldsymbol{u}\_e^\* \cdot \boldsymbol{\pi}\_{\boldsymbol{\nu}} \tag{45}
$$

$$F^\* = \frac{\dot{W}\_f^\*}{v} = \frac{V\_f^\* \cdot \Delta u\_e^\* \cdot n}{l\_f \cdot n\_v} = \frac{V\_{f\_H}^\* \cdot \Delta u\_e^\*}{l\_f},\tag{46}$$

$$
\mu^{\*} = \frac{\dot{W}\_{T}^{\*}}{N^{\*} \cdot \upsilon} = \frac{V\_{f}^{\*} \cdot \Delta u\_{\epsilon}^{\*} \cdot \upsilon}{N^{\*} \cdot \upsilon} = \frac{V\_{f\_{H}}^{\*} \cdot \Delta u\_{\epsilon}^{\*}}{N^{\*} \cdot \upsilon}. \tag{47}
$$

Here V <sup>∗</sup> <sup>f</sup> <sup>H</sup> <sup>¼</sup> <sup>V</sup> <sup>∗</sup> <sup>f</sup> � nH (Figure 9); <sup>W</sup><sup>i</sup> <sup>∗</sup> <sup>T</sup> is the instantaneous (contact) the value of the friction work; <sup>n</sup> <sup>¼</sup> <sup>V</sup><sup>t</sup> f Vf <sup>¼</sup> nv � nH is the ratio of the volume of friction <sup>V</sup><sup>t</sup> <sup>f</sup> deformable per unit time t to the instantaneous volume of friction Vf ; nv, nH is the number of micro-shocks in the sliding direction of the sample per unit time and in the transverse direction.

Eq. (47), performed to the form of the <sup>μ</sup><sup>∗</sup> <sup>¼</sup> hr�Δu<sup>∗</sup> e pr�lf <sup>¼</sup> ha�Δu<sup>∗</sup> e pa�<sup>B</sup> , represents the basic equation of wear for compatible friction region:

$$
\pi\_r = \frac{h\_r}{l\_f} \Delta u\_\epsilon^\* = I\_r \Delta u\_\epsilon^\*,\tag{48}
$$

When working gear engagement, for each revolution of the wheel (gear), each roughness (material point) of the active surface of the tooth is loaded once, with a minimum loss (wear) in one mechanical (nano) quantum. Since the critical volume of friction (elementary tribosystem) contains 0:<sup>63</sup> � <sup>10</sup><sup>8</sup> mechanical quantum, the number of loads (wheel revolutions), equal to the critical number of loading cycles —63 millions, leads to fatigue wear (loss) of the material layer of unit thickness h<sup>∗</sup> . Linear wear <sup>h</sup><sup>∗</sup> of the gear wheel is equal to the diameter QTS <sup>¼</sup> <sup>2</sup>:<sup>85</sup> � <sup>10</sup>�<sup>6</sup> m of the

Model of active tooth surface of a gear wheel with equilibrium roughness of spherical shape [4].

wear. Accordingly, it is clear that the constructive limit criterion of wear of the tooth of the gear is equal to the limit of wear when the bending strength of the tooth is violated. For example, this is approximately 0.3 modulus of the tooth of the gear. Consequently, the elementary nanostructure of deformable solids should be considered as the wear standard and used to optimize the operating time of real

5.2 Evaluation of the capacity for work of bearings of internal combustion

limit linear wear of the bearing which is equal to <sup>h</sup><sup>∗</sup> <sup>¼</sup> <sup>0</sup>:1 mm. We know the linear size of the elementary tribosystem—DTS <sup>¼</sup> <sup>2</sup>:85 mkm <sup>¼</sup> <sup>2</sup>:<sup>85</sup> � <sup>10</sup>�<sup>6</sup><sup>m</sup> [19]. For each revolution of the shaft one elementary tribosystem (equilibrium, run-in contact) loses one mechanical quantum. The number of revolutions required for the wear of one elementary tribosystem is equal to the number of mechanical quanta in this

Let's take an engine with an average shaft rotation—<sup>n</sup> <sup>¼</sup> 1500 min‐<sup>1</sup>

Now we can determine the wear time of one elementary tribosystem:

<sup>1500</sup> <sup>¼</sup> <sup>42</sup>, 000 min <sup>¼</sup> <sup>42</sup>, <sup>000</sup>

tribosystem, that is, it is nMQ <sup>¼</sup> <sup>0</sup>:<sup>63</sup> � <sup>10</sup><sup>8</sup> revolutions.

<sup>f</sup> (Figure 10) [19]. This is a physical criterion of

<sup>60</sup> <sup>¼</sup> 700 hour <sup>¼</sup> <sup>700</sup>

. Take the

<sup>24</sup> <sup>¼</sup> <sup>29</sup>, 166 day

(50)

equilibrium friction volume V <sup>∗</sup>

engines

Figure 10.

tTS <sup>¼</sup> nMQ

55

<sup>¼</sup> <sup>29</sup>, <sup>166</sup>

<sup>n</sup> <sup>¼</sup> <sup>0</sup>:<sup>63</sup> � <sup>108</sup>

<sup>365</sup> <sup>¼</sup> <sup>0</sup>:0799 year:

highly loaded Hertzian friction systems.

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

$$
\pi\_d = \frac{h\_d}{B} \Delta u\_e^\* = I\_d \Delta u\_e^\*. \tag{49}
$$

here, Ir, Ia is the linear wear rate, related to the real and nominal areas of contact; B, H is the sample sizes in the slide and the longitudinal directions.

### 5. Nano quantum models of the maximum capacity for work of the tribosystem

### 5.1 The principle of calculating the wear of gears

All parameters of compatible (optimal) friction should be in nanoquant levels, which are commensurate with the parameters of one mechanical quantum standard of wear.

Operation of all heavily loaded tribosystems should be considered from the standpoint of the ideal evolution of tribosystems. This is a perfect condition contact friction is the true indicator of the state of the tribosystem for practical examples of tribology. This is the standard of maximum efficiency of the tribosystem—abnormally low friction and wearlessness.

A typical example of wear (destruction) of real tribosystems on the model of mechanical quantum is the work of gears (for example, reducers) and systems of wheel-rail and other, in which the elementary particle of wear (pitting) is wear equal to one mechanical quantum. Imagine the engagement of a pair of teeth involute profile on the field of the length of the active line of engagement (Figure 10) as the model of smooth surfaces with uniformly distributed equilibrium roughnesses after run-in (elementary tribosystems, which are analogues of the material point of mechanics). Engagement of a pair of teeth corresponds to the theoretical principle of running two cylinders under the conditions of Hertz elasticplastic contact. The materials of the teeth work at the limit of the fatigue threshold, which corresponds to the minimum loss (pitting) of the contact volume (elementary tribosystem) in the form of a single mechanical quantum.

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

Accordingly, we have a number of ratios for power, force and coefficient of

<sup>f</sup> � <sup>Δ</sup>u<sup>∗</sup>

<sup>f</sup> � <sup>Δ</sup>u<sup>∗</sup>

lf � nv

<sup>f</sup> � <sup>Δ</sup>u<sup>∗</sup>

able per unit time t to the instantaneous volume of friction Vf ; nv, nH is the number of micro-shocks in the sliding direction of the sample per unit time and in the

<sup>e</sup> � <sup>n</sup> <sup>¼</sup> <sup>V</sup> <sup>∗</sup>

¼ V ∗

<sup>e</sup> � n

<sup>e</sup> � n <sup>N</sup> <sup>∗</sup> � <sup>v</sup> <sup>¼</sup> <sup>V</sup> <sup>∗</sup>

Vf <sup>¼</sup> nv � nH is the ratio of the volume of friction <sup>V</sup><sup>t</sup>

<sup>e</sup> <sup>¼</sup> IrΔu<sup>∗</sup>

<sup>e</sup> <sup>¼</sup> IaΔu<sup>∗</sup>

e pr�lf <sup>¼</sup> ha�Δu<sup>∗</sup>

<sup>f</sup> <sup>H</sup> � <sup>Δ</sup>u<sup>∗</sup>

<sup>f</sup> <sup>H</sup> � <sup>Δ</sup>u<sup>∗</sup> e

> <sup>f</sup> <sup>H</sup> � <sup>Δ</sup>u<sup>∗</sup> e

<sup>T</sup> is the instantaneous (contact) the value of

e

lf

<sup>e</sup> � nv, (45)

, (46)

pa�<sup>B</sup> , represents the basic

<sup>e</sup> , (48)

<sup>e</sup> : (49)

<sup>f</sup> deform-

<sup>N</sup> <sup>∗</sup> � <sup>v</sup> : (47)

friction

Here V <sup>∗</sup>

<sup>f</sup> <sup>H</sup> <sup>¼</sup> <sup>V</sup> <sup>∗</sup>

Friction, Lubrication and Wear

the friction work; <sup>n</sup> <sup>¼</sup> <sup>V</sup><sup>t</sup>

transverse direction.

tribosystem

standard of wear.

54

W\_ <sup>∗</sup>

<sup>f</sup> <sup>¼</sup> <sup>W</sup>\_ <sup>∗</sup>

<sup>F</sup> <sup>∗</sup> <sup>¼</sup> <sup>W</sup>\_ <sup>∗</sup> f <sup>v</sup> <sup>¼</sup> <sup>V</sup> <sup>∗</sup>

<sup>μ</sup><sup>∗</sup> <sup>¼</sup> <sup>W</sup>\_ <sup>∗</sup>

f

equation of wear for compatible friction region:

5.1 The principle of calculating the wear of gears

tribosystem—abnormally low friction and wearlessness.

tary tribosystem) in the form of a single mechanical quantum.

<sup>f</sup> � nH (Figure 9); <sup>W</sup><sup>i</sup> <sup>∗</sup>

Eq. (47), performed to the form of the <sup>μ</sup><sup>∗</sup> <sup>¼</sup> hr�Δu<sup>∗</sup>

<sup>τ</sup><sup>r</sup> <sup>¼</sup> hr lf Δu<sup>∗</sup>

<sup>τ</sup><sup>a</sup> <sup>¼</sup> ha B Δu<sup>∗</sup>

here, Ir, Ia is the linear wear rate, related to the real and nominal areas of contact; B, H is the sample sizes in the slide and the longitudinal directions.

5. Nano quantum models of the maximum capacity for work of the

All parameters of compatible (optimal) friction should be in nanoquant levels, which are commensurate with the parameters of one mechanical quantum—

Operation of all heavily loaded tribosystems should be considered from the standpoint of the ideal evolution of tribosystems. This is a perfect condition contact friction is the true indicator of the state of the tribosystem for practical examples of tribology. This is the standard of maximum efficiency of the

A typical example of wear (destruction) of real tribosystems on the model of mechanical quantum is the work of gears (for example, reducers) and systems of wheel-rail and other, in which the elementary particle of wear (pitting) is wear equal to one mechanical quantum. Imagine the engagement of a pair of teeth involute profile on the field of the length of the active line of engagement

(Figure 10) as the model of smooth surfaces with uniformly distributed equilibrium roughnesses after run-in (elementary tribosystems, which are analogues of the material point of mechanics). Engagement of a pair of teeth corresponds to the theoretical principle of running two cylinders under the conditions of Hertz elasticplastic contact. The materials of the teeth work at the limit of the fatigue threshold, which corresponds to the minimum loss (pitting) of the contact volume (elemen-

T <sup>N</sup> <sup>∗</sup> � <sup>v</sup> <sup>¼</sup> <sup>V</sup> <sup>∗</sup>

fi � <sup>n</sup> <sup>¼</sup> <sup>V</sup> <sup>∗</sup>

When working gear engagement, for each revolution of the wheel (gear), each roughness (material point) of the active surface of the tooth is loaded once, with a minimum loss (wear) in one mechanical (nano) quantum. Since the critical volume of friction (elementary tribosystem) contains 0:<sup>63</sup> � <sup>10</sup><sup>8</sup> mechanical quantum, the number of loads (wheel revolutions), equal to the critical number of loading cycles —63 millions, leads to fatigue wear (loss) of the material layer of unit thickness h<sup>∗</sup> . Linear wear <sup>h</sup><sup>∗</sup> of the gear wheel is equal to the diameter QTS <sup>¼</sup> <sup>2</sup>:<sup>85</sup> � <sup>10</sup>�<sup>6</sup> m of the equilibrium friction volume V <sup>∗</sup> <sup>f</sup> (Figure 10) [19]. This is a physical criterion of wear. Accordingly, it is clear that the constructive limit criterion of wear of the tooth of the gear is equal to the limit of wear when the bending strength of the tooth is violated. For example, this is approximately 0.3 modulus of the tooth of the gear.

Consequently, the elementary nanostructure of deformable solids should be considered as the wear standard and used to optimize the operating time of real highly loaded Hertzian friction systems.

### 5.2 Evaluation of the capacity for work of bearings of internal combustion engines

Let's take an engine with an average shaft rotation—<sup>n</sup> <sup>¼</sup> 1500 min‐<sup>1</sup> . Take the limit linear wear of the bearing which is equal to <sup>h</sup><sup>∗</sup> <sup>¼</sup> <sup>0</sup>:1 mm. We know the linear size of the elementary tribosystem—DTS <sup>¼</sup> <sup>2</sup>:85 mkm <sup>¼</sup> <sup>2</sup>:<sup>85</sup> � <sup>10</sup>�<sup>6</sup><sup>m</sup> [19]. For each revolution of the shaft one elementary tribosystem (equilibrium, run-in contact) loses one mechanical quantum. The number of revolutions required for the wear of one elementary tribosystem is equal to the number of mechanical quanta in this tribosystem, that is, it is nMQ <sup>¼</sup> <sup>0</sup>:<sup>63</sup> � <sup>10</sup><sup>8</sup> revolutions.

Now we can determine the wear time of one elementary tribosystem:

$$\begin{split} t\_{\text{TS}} &= \frac{n\_{\text{MQ}}}{n} = \frac{0.63 \cdot 10^8}{1500} = 42,000 \text{ min} = \frac{42,000}{60} = 700 \text{ hour} = \frac{700}{24} = 29,166 \text{ day} \\ &= \frac{29,166}{365} = 0.0799 \text{ year}. \end{split}$$

Now let's define the number of layers of elementary tribosystems into linear wear—0:1 mm:

$$\sigma\_{h^{\*}} = \frac{h^{\*}}{D\_{\rm TS}} = \frac{1 \cdot 10^{-4}}{2.85 \cdot 10^{-6}} = 0.35 \cdot 10^{2} = 35.0$$

Now, let's define the time of wear of shaft-bearing system with the ultimate linear given wear—h<sup>∗</sup> <sup>¼</sup> <sup>0</sup>:1 mm, namely:

$$t\_{\rm motor} = t\_{\rm TS} \cdot a\_h \cdot = 0.0799 \cdot 35 = 2,7968 \text{ year.} \tag{52}$$

Finally, we have 2, 7968 years of continuous work at ultimate load.

For this result we have the wear rate—i ¼ 4 nm=h. For example, this fits well with the data for the engine wear rate—i ¼ 5 nm=h specified by Prof. F. Franek [20].

If we work 8 hours per day, then we will get the following result:

$$\text{2,7968} \cdot \text{3} = \text{8.39 year.}\tag{53}$$

from each other; (2) layer, which has a low coefficient of internal friction; (3) layer, which has a high capacity for work, that is, very small wear; and (4) layer, which

Now you need to determine a value for the coefficient of friction of this selforganized solid lubricant and compare it with the coefficient of friction, for exam-

It is known that the hydrodynamic lubrication when the stationary condition

For nanoquantum self-organized solid lubricant friction coefficient will be

1. It is known [4, 15] that between the nanoquanta coefficient of friction is

Conditional scheme for equilibrium elementary tribosystem, structured mechanical quanta. At length of this

(Figure 11) has coefficients of friction μ down to 0:005÷0:001 values.

may be seen as a solid lubricant.

Notional scheme of hydrodynamic lubrication.

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

Figure 11.

Figure 12.

57

calculated in the following order:

equal to <sup>μ</sup>MQ <sup>¼</sup> <sup>1</sup>:<sup>587</sup> � <sup>10</sup>�8.

tribosystem there are 397 mechanical quantums.

ple, the most effective, or hydrodynamic lubrication.

This is a real result for modern cars. If we work less than 8 hours a day, then the duration will increase significantly.

### 5.3 The principle of critical wheel rolling speed

The limit of this speed is determined by the principle of filling the entire nominal friction area of the sliding system with elementary tribosystems damping the process. Above this speed of movement of the vehicle there will be a complete unloading of the tribosystem, the separation of the wheel from the rail surface, since the principle of minimum resistance to movement (the principle of one elementary tribosystem or the principle of irreversibility) will be violated. In this case, all mechanical quanta in the elementary tribosystem will repel the wheel. There will be no quantum activating the process of maintaining the system in an excited state.

The calculation will be made in the following order [21]. The elementary nominal size of the contact area is known. By definition [4], nTS <sup>∗</sup> <sup>¼</sup> <sup>0</sup>:<sup>63</sup> � <sup>10</sup><sup>8</sup> elementary tribosystems can be placed and operate on the elementary nominal contact area. Each elementary tribosystem (for the model of spherical roughness) has a size <sup>D</sup>1TS <sup>¼</sup> <sup>2</sup>:<sup>85</sup> � <sup>10</sup>�<sup>6</sup> <sup>m</sup> [19] and is capable of providing a rolling path of the wheel in the elementary act of rolling on the length of this tribosystem.

Thus, if all elementary tribosystems work in a unit of time on the entire nominal contact area, then the path traversed by the wheel in a unit of time is equal to

$$L\_{\rm{2TS}} = D\_{\rm{1TS}} \cdot n\_{\rm{TS}}^{\*} = 2.85 \cdot 10^{-6} \cdot 0.63 \cdot 10^{8} = 179.55 \, m. \tag{54}$$

Consequently, the critical speed of wheel rolling is equal

$$\mathbf{v}\_{\*} = L\_{\rm 2TS} \cdot \mathbf{3600} = \mathbf{646} \text{, } \mathbf{38} \text{ km/h.} \tag{55}$$

This result is close to modern speed of 574:8 km=h (TGV, France).

### 5.4 Self-organized nanoquantum solid lubricant

Information above allows us to consider new self-organized surface layer as follows: (1) the layer that separates the two original surfaces (alloys) of friction Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

Now let's define the number of layers of elementary tribosystems into linear

Now, let's define the time of wear of shaft-bearing system with the ultimate

This is a real result for modern cars. If we work less than 8 hours a day, then the

The limit of this speed is determined by the principle of filling the entire nominal friction area of the sliding system with elementary tribosystems damping the process. Above this speed of movement of the vehicle there will be a complete unloading of the tribosystem, the separation of the wheel from the rail surface, since the principle of minimum resistance to movement (the principle of one elementary tribosystem or the principle of irreversibility) will be violated. In this case, all mechanical quanta in the elementary tribosystem will repel the wheel. There will be no quantum activating the process of maintaining the system in an

The calculation will be made in the following order [21]. The elementary nomi-

Thus, if all elementary tribosystems work in a unit of time on the entire nominal

TS <sup>¼</sup> <sup>2</sup>:<sup>85</sup> � <sup>10</sup>�<sup>6</sup> � <sup>0</sup>:<sup>63</sup> � <sup>10</sup><sup>8</sup> <sup>¼</sup> <sup>179</sup>:<sup>55</sup> <sup>m</sup>: (54)

v<sup>∗</sup> ¼ LΣTS � 3600 ¼ 646, 38 km=h: (55)

tribosystems can be placed and operate on the elementary nominal contact area. Each elementary tribosystem (for the model of spherical roughness) has a size <sup>D</sup>1TS <sup>¼</sup> <sup>2</sup>:<sup>85</sup> � <sup>10</sup>�<sup>6</sup> <sup>m</sup> [19] and is capable of providing a rolling path of the wheel in

contact area, then the path traversed by the wheel in a unit of time is equal to

This result is close to modern speed of 574:8 km=h (TGV, France).

Information above allows us to consider new self-organized surface layer as follows: (1) the layer that separates the two original surfaces (alloys) of friction

<sup>2</sup>:<sup>85</sup> � <sup>10</sup>�<sup>6</sup> <sup>¼</sup> <sup>0</sup>:<sup>35</sup> � <sup>10</sup><sup>2</sup> <sup>¼</sup> <sup>35</sup>: (51)

2, 7968 � 3 ¼ 8:39 year: (53)

<sup>∗</sup> <sup>¼</sup> <sup>0</sup>:<sup>63</sup> � <sup>10</sup><sup>8</sup> elementary

tmotor ¼ tTS � ah<sup>∗</sup> ¼ 0:0799 � 35 ¼ 2, 7968 year: (52)

<sup>¼</sup> <sup>1</sup> � <sup>10</sup>�<sup>4</sup>

Finally, we have 2, 7968 years of continuous work at ultimate load. For this result we have the wear rate—i ¼ 4 nm=h. For example, this fits

well with the data for the engine wear rate—i ¼ 5 nm=h specified by

If we work 8 hours per day, then we will get the following result:

ah<sup>∗</sup> <sup>¼</sup> <sup>h</sup><sup>∗</sup> DTS

linear given wear—h<sup>∗</sup> <sup>¼</sup> <sup>0</sup>:1 mm, namely:

duration will increase significantly.

5.3 The principle of critical wheel rolling speed

nal size of the contact area is known. By definition [4], nTS

the elementary act of rolling on the length of this tribosystem.

Consequently, the critical speed of wheel rolling is equal

<sup>L</sup>ΣTS <sup>¼</sup> <sup>D</sup>1TS � <sup>n</sup><sup>∗</sup>

5.4 Self-organized nanoquantum solid lubricant

wear—0:1 mm:

Friction, Lubrication and Wear

Prof. F. Franek [20].

excited state.

56

Figure 11. Notional scheme of hydrodynamic lubrication.

from each other; (2) layer, which has a low coefficient of internal friction; (3) layer, which has a high capacity for work, that is, very small wear; and (4) layer, which may be seen as a solid lubricant.

Now you need to determine a value for the coefficient of friction of this selforganized solid lubricant and compare it with the coefficient of friction, for example, the most effective, or hydrodynamic lubrication.

It is known that the hydrodynamic lubrication when the stationary condition (Figure 11) has coefficients of friction μ down to 0:005÷0:001 values.

For nanoquantum self-organized solid lubricant friction coefficient will be calculated in the following order:

1. It is known [4, 15] that between the nanoquanta coefficient of friction is equal to <sup>μ</sup>MQ <sup>¼</sup> <sup>1</sup>:<sup>587</sup> � <sup>10</sup>�8.

### Figure 12.

Conditional scheme for equilibrium elementary tribosystem, structured mechanical quanta. At length of this tribosystem there are 397 mechanical quantums.


$$n\_{MQ}^{\prime} = \frac{D\_{TS}}{D\_{MQ}} = \frac{2.85 \cdot 10^{-6}}{7.177 \cdot 10^{-9}} = 397. \tag{56}$$

5. Let's define the coefficient of friction for a single equilibrium critical volume of friction (elementary tribosystem), the length of which is 397 mechanical

6. Let's take the average friction surface wavelength equal to LW ffi <sup>1</sup> � <sup>10</sup>�3m.

Now define a number of elementary tribosystems on this wave length (Figure 13)

<sup>¼</sup> <sup>1</sup> � <sup>10</sup>�<sup>3</sup>

As a result, we have a full conformity (Figure 14) of friction coefficient values

1. Structural-energy analysis of the friction process allows us to consider the

evolution of the tribosystem (contact) has an adaptive-dissipative character.

3. The coefficient of friction has an energy interpretation that reveals its deep

2. From the equations of the energy balance of friction it follows that the

4. Experimental friction curves of μ ¼ μð Þ N; v type may be examined as

5. Structural-energy diagram of the evolution of rubbing surfaces (friction

contact) interprets the general regularities of transformation and dissipation

6. In the process of evolution of the friction contact, an elementary tribosystem is formed as a self-sufficient energy transformer under friction. This elementary tribosystem (critical friction volume) can be considered as an

7. The most complete evolution of the tribosystem has a symmetrical form—the

tribosystem), a unique nanostructure (tribosubsystem) is formed; the basis of this nanostructure is a mechanical (nano) quantum and the friction contact (material point of mechanics) consists of about 0:<sup>63</sup> � <sup>10</sup><sup>8</sup> such nano quanta.

9. We can consider the mechanical quantum as the smallest structural form of a

8. With the most complete evolution of the friction contact (elementary

material solid and as the structural standard of material solid.

7. Now define friction coefficient at a wavelength of friction surface

for hydrodynamic lubrication—0:005÷0:001 and solid lubricant—0:0022. Thus, it is fair to talk about nanoquantum self-organized solid lubrication.

MQ <sup>¼</sup> <sup>1</sup>:<sup>587</sup> � <sup>10</sup>�<sup>8</sup> � <sup>397</sup> <sup>¼</sup> <sup>0</sup>:<sup>63</sup> � <sup>10</sup>�<sup>5</sup>

<sup>μ</sup><sup>W</sup> <sup>¼</sup> <sup>μ</sup>TS � nTS <sup>¼</sup> <sup>0</sup>:<sup>63</sup> � <sup>10</sup>�<sup>5</sup> � <sup>351</sup> <sup>¼</sup> <sup>0</sup>:<sup>0022</sup> (59)

<sup>2</sup>:<sup>85</sup> � <sup>10</sup>�<sup>6</sup> <sup>¼</sup> <sup>351</sup>: (58)

: (57)

quantums (Figure 12).

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

6. Conclusions

59

physical sense.

of energy during friction.

μTS ¼ μMQ � n<sup>0</sup>

nTS <sup>¼</sup> LW DTS

friction process as an evolutionary process.

generalized friction experimental curves.

analogue of the material point of mechanics.

friction process begins and ends in the elastic region.

### Figure 13.

Notional scheme of friction on the wavelength, structured elementary tribosystems. At the surface friction wavelength is 351 elementary tribosystems.

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

5. Let's define the coefficient of friction for a single equilibrium critical volume of friction (elementary tribosystem), the length of which is 397 mechanical quantums (Figure 12).

$$
\mu\_{\rm TS} = \mu\_{\rm MQ} \cdot n\_{\rm MQ}' = 1.587 \cdot 10^{-8} \cdot 397 = 0.63 \cdot 10^{-5}.\tag{57}
$$

6. Let's take the average friction surface wavelength equal to LW ffi <sup>1</sup> � <sup>10</sup>�3m.

Now define a number of elementary tribosystems on this wave length (Figure 13)

$$m\_{\rm TS} = \frac{L\_W}{D\_{\rm TS}} = \frac{1 \cdot 10^{-3}}{2.85 \cdot 10^{-6}} = 351. \tag{58}$$

7. Now define friction coefficient at a wavelength of friction surface

$$
\mu\_W = \mu\_{\rm TS} \cdot n\_{\rm TS} = 0.63 \cdot 10^{-5} \cdot \text{351} = 0.0022 \tag{59}
$$

As a result, we have a full conformity (Figure 14) of friction coefficient values for hydrodynamic lubrication—0:005÷0:001 and solid lubricant—0:0022.

Thus, it is fair to talk about nanoquantum self-organized solid lubrication.

### 6. Conclusions

2. It is known [19] that the size of the critical volume of frictional contact

3. Let's picture an elementary tribosystem in the plane as a circle with a

Notional scheme of friction on the wavelength, structured elementary tribosystems. At the surface friction

Notional scheme of self-organized nanoquantum contact with unsteady hydrodynamic lubrication.

<sup>¼</sup> <sup>2</sup>:<sup>85</sup> � <sup>10</sup>�<sup>6</sup>

MQ on a length

<sup>7</sup>:<sup>177</sup> � <sup>10</sup>�<sup>9</sup> <sup>¼</sup> <sup>397</sup>: (56)

(elementary tribosystem) is equal to DTS <sup>¼</sup> <sup>2</sup>:<sup>85</sup> � <sup>10</sup>�<sup>6</sup> <sup>m</sup>.

4. Next, let's define the number of mechanical (nano) quanta n<sup>0</sup>

diameter of DTS ¼ 2:85 mkm (Figure 12).

Friction, Lubrication and Wear

DTS of elementary tribosystem (Figure 12):

MQ <sup>¼</sup> DTS DMQ

n0

Figure 13.

Figure 14.

58

wavelength is 351 elementary tribosystems.


10. The mechanical quantum is precisely an asymptotically stable attractor of the limit cycle type for a deformable solid body (at friction).

References

(In Russian)

pp. 883-889

Russian)

61

p. 416. (In Russian)

[1] Fedorov VV. Thermodynamic Aspects of Strength and Fracture of Solids. Tashkent: Science; 1979. p. 168.

1985. p. 186. (In Russian)

[2] Fedorov VV. Kinetics of Damage and Fracture of Solids. Tashkent: Science;

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

Vol. 174. 2017. p. 012012. DOI: 10.1088/

[11] Bowden FP, Tabor D. The Friction and Lubrication of Solids. Oxford: Oxford University Press; 2001. p. 424

[12] Fedorov SV. Energy balance of friction and friction coefficient in energetical interpretation. Tribology in

[13] Conti P. Sulla Resistenza di Attrito. Vol. II. Royal Akademia dei Lencei; 1875

[14] Lancaster IK. Basic mechanisms of friction and wear of polymers. Plastics and Polymers. 1973;41:296-306

[15] Fedorov SV. Energy model of sliding friction coefficient and generalized regularities of tribosystems evolution. In: Proceeding of the International Colloquium Tribology-Industrial and Automotive Lubrication; 11-13 January 2014; TAE. Available from: www.tae.de

[16] Fedorov SV. The friction coefficient and its relation to the contact fatigue characteristics of materials. Industrial

Laboratory. 1995;61(1):41-49

Congress (V WTC 2013); 8-13 September 2013; Turino, Italy; 2013.

[18] Fedorov SV. The mechanical quantum of dissipative friction structures is the elementary

ISBN 9788890818509

[17] Fedorov SV. Generalized energy model of sliding friction coefficient and regularities of tribosystem evolution. In: Proceedings of the V World Tribology

Industry. 2015;37(3):380-389

[10] Kragelskii IV, Dobychin MN, Kombalov VS. Friction and Wear Calculation Methods. Moscow: Mechanical Engineering; 1977. p. 526.

1757-899X/174/1/012012

(In Russian)

info@tae.de

[3] Fedorov VV. Ergodynamic concept of failure. In: Strength of Materials, Translated from Russian. Vol. 23/8. New

York: Consultants Bureau; 1991.

[4] Fedorov SV. The Foundations of Triboergodynamics and Physico-Chemical Prerequisits of Compatibility Theory. Kaliningrad: Kaliningrad State Technical University Press; 2003.

[5] Ivanova VS. Synergetics: Strength and Destruction of Metallic Materials. Moscow: Science; 1992. p. 160. (In

Erkenntnisse aus heutigen Sicht. In: 1st Arnold Tross Kolloquium. Germany:

constructive (limiting) criterions of gear wheels wear. In: Proceedings of the 9th International Conference on Tribology (Balkantrib'17); IOP Publishing IOP Conf. Series: Materials Science and Engineering. Vol. 295. 2018. p. 012038. DOI: 10.1088/1757-899X/295/1/012038

[6] Fleischer G. Die Tross'schen

Hamburg; 2005. pp. 215-242

[7] Fedorov SV. Physical and

[8] Fedorov SV. Nano-structural

in Industry. 2018;40(/2):225-238

[9] Fedorov SV. Structural-energetic regularities of tribocontact evolution. In: Proceedings of the 13th International Conference on Tribology, ROTRIB'16 IOP Publishing. IOP Conf. Series: Materials Science and Engineering.

standard of friction and wear. Tribology


### Author details

Sergey Fedorov Kaliningrad State Technical University, Kaliningrad, Russia

\*Address all correspondence to: fedorov@klgtu.ru

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Structural-Energy Interpretation of the Friction DOI: http://dx.doi.org/10.5772/intechopen.86123

### References

10. The mechanical quantum is precisely an asymptotically stable attractor of the

11. All parameters of compatibility (optimal) friction have to be in quanta levels —commensurable with the parameters of the one mechanical quantum.

12. Interaction between nanoquantums is nature the net elasticity. The value of the

13. Exploitation of gear wheels and other heavy-loaded tribosystems (Hertzian contact) are subjected to model of nano-quantum damping, when one mechanical quantum is the standard of contact structure and wear.

limit cycle type for a deformable solid body (at friction).

coefficient of friction between mechanical quanta has order

<sup>μ</sup>MQ <sup>¼</sup> <sup>1</sup>:<sup>587</sup> � <sup>10</sup>�8.

Friction, Lubrication and Wear

Author details

Sergey Fedorov

60

Kaliningrad State Technical University, Kaliningrad, Russia

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

\*Address all correspondence to: fedorov@klgtu.ru

provided the original work is properly cited.

[1] Fedorov VV. Thermodynamic Aspects of Strength and Fracture of Solids. Tashkent: Science; 1979. p. 168. (In Russian)

[2] Fedorov VV. Kinetics of Damage and Fracture of Solids. Tashkent: Science; 1985. p. 186. (In Russian)

[3] Fedorov VV. Ergodynamic concept of failure. In: Strength of Materials, Translated from Russian. Vol. 23/8. New York: Consultants Bureau; 1991. pp. 883-889

[4] Fedorov SV. The Foundations of Triboergodynamics and Physico-Chemical Prerequisits of Compatibility Theory. Kaliningrad: Kaliningrad State Technical University Press; 2003. p. 416. (In Russian)

[5] Ivanova VS. Synergetics: Strength and Destruction of Metallic Materials. Moscow: Science; 1992. p. 160. (In Russian)

[6] Fleischer G. Die Tross'schen Erkenntnisse aus heutigen Sicht. In: 1st Arnold Tross Kolloquium. Germany: Hamburg; 2005. pp. 215-242

[7] Fedorov SV. Physical and constructive (limiting) criterions of gear wheels wear. In: Proceedings of the 9th International Conference on Tribology (Balkantrib'17); IOP Publishing IOP Conf. Series: Materials Science and Engineering. Vol. 295. 2018. p. 012038. DOI: 10.1088/1757-899X/295/1/012038

[8] Fedorov SV. Nano-structural standard of friction and wear. Tribology in Industry. 2018;40(/2):225-238

[9] Fedorov SV. Structural-energetic regularities of tribocontact evolution. In: Proceedings of the 13th International Conference on Tribology, ROTRIB'16 IOP Publishing. IOP Conf. Series: Materials Science and Engineering.

Vol. 174. 2017. p. 012012. DOI: 10.1088/ 1757-899X/174/1/012012

[10] Kragelskii IV, Dobychin MN, Kombalov VS. Friction and Wear Calculation Methods. Moscow: Mechanical Engineering; 1977. p. 526. (In Russian)

[11] Bowden FP, Tabor D. The Friction and Lubrication of Solids. Oxford: Oxford University Press; 2001. p. 424

[12] Fedorov SV. Energy balance of friction and friction coefficient in energetical interpretation. Tribology in Industry. 2015;37(3):380-389

[13] Conti P. Sulla Resistenza di Attrito. Vol. II. Royal Akademia dei Lencei; 1875

[14] Lancaster IK. Basic mechanisms of friction and wear of polymers. Plastics and Polymers. 1973;41:296-306

[15] Fedorov SV. Energy model of sliding friction coefficient and generalized regularities of tribosystems evolution. In: Proceeding of the International Colloquium Tribology-Industrial and Automotive Lubrication; 11-13 January 2014; TAE. Available from: www.tae.de info@tae.de

[16] Fedorov SV. The friction coefficient and its relation to the contact fatigue characteristics of materials. Industrial Laboratory. 1995;61(1):41-49

[17] Fedorov SV. Generalized energy model of sliding friction coefficient and regularities of tribosystem evolution. In: Proceedings of the V World Tribology Congress (V WTC 2013); 8-13 September 2013; Turino, Italy; 2013. ISBN 9788890818509

[18] Fedorov SV. The mechanical quantum of dissipative friction structures is the elementary

tribonanostructure. In: Proceedings of the IV World Tribology Congress (IV WTC 2009); 13-19 September 2009; Kyoto, Japan: 2009. p. 926

[19] Fedorov SV. Calculation of the true friction volume. Friction & Lubrication in Machines and Mechanisms. 2010;5: 3-7. (In Russian)

[20] Franek F, Wopelka T, Jech M. Onboard applicable high-resolution wear measurement technique for internal combustion engines. In: Proceedings of the International Conference BALTTRIB'2011; 30-31 October; Kaunas. Luthuania: 2011. pp. 196-201

[21] Fedorov SV. Energetical nature of the wheel elastic rolling. In: Proceedings of the 7th International Conference (Contact Mechanics and Wear Of Rail/ Wheel Systems); 24-27 September 2006; Brisbane, Australia. Vol. 1. 2006. pp. 105-114

**63**

**Chapter 4**

**Abstract**

Thin Films: Study of the Influence

Modes on the Volume of Wear and

The purpose of this work is to study the influence of the micro-abrasive wear modes on the behaviors of the volume of wear (*V*) and of the coefficient of friction (*μ*) of thin films submitted to micro-abrasive wear. Experiments were conducted with thin films of TiN, TiAlN, TiN/TiAlN, TiHfC, ZrN, and TiZrN, using a ball of AISI 52100 steel and abrasive slurries prepared with black silicon carbide (SiC) particles and glycerine. The results show that the abrasive slurry concentration affected the microabrasive wear modes ("grooving abrasion" or "rolling abrasion") and, consequently, the magnitude of the volume of wear and of the coefficient of friction, as described: (i) a low value of abrasive slurry concentration generated "grooving abrasion," which was related to a relatively low volume of wear and high coefficient of friction, and (ii) a high value of abrasive slurry concentration generated "rolling abrasion," which was

related to a relatively high volume of wear and low coefficient of friction.

the called "wear craters" on the surface of the tested material.

of wear (*k*), and coefficient of friction (*μ*) of thin films [2, 6–10].

**Keywords:** micro-abrasive wear, grooving abrasion, rolling abrasion, thin films,

The micro-abrasive wear test by rotating ball ("ball-cratering wear test") is an important method adopted to study the micro-abrasive wear behavior of metallic, polymeric, and ceramic materials. **Figure 1** presents a schematic diagram of the principle of this micro-abrasive wear test, in which a rotating ball is forced against the tested specimen in the presence of an abrasive slurry, generating, consequently,

Initially, the development of the ball-cratering wear test aimed to measure the thickness of thin films (**Figure 2a** and **b**) [1], which can be made using the equations detailed in Ref. [2]. Because of the technical features, this type of microabrasive wear test has been applied to study the tribological behavior of different materials [3–5], for example, in the analysis of the volume of wear (*V*), coefficient

As a function of the abrasive slurry concentration, two micro-abrasive wear modes can be usually observed on the surface of the worn crater: "grooving abrasion" is observed when the abrasive particles slide on the surface, whereas "rolling abrasion" results from abrasive particles rolling on the specimen's surface.

of the Micro-Abrasive Wear

Coefficient of Friction

*Ronaldo Câmara Cozza*

volume of wear, coefficient of friction

**1. Introduction**

### **Chapter 4**

tribonanostructure. In: Proceedings of the IV World Tribology Congress (IV WTC 2009); 13-19 September 2009;

[19] Fedorov SV. Calculation of the true friction volume. Friction & Lubrication in Machines and Mechanisms. 2010;5:

[20] Franek F, Wopelka T, Jech M. Onboard applicable high-resolution wear measurement technique for internal combustion engines. In: Proceedings of

[21] Fedorov SV. Energetical nature of the wheel elastic rolling. In: Proceedings of the 7th International Conference (Contact Mechanics and Wear Of Rail/ Wheel Systems); 24-27 September 2006; Brisbane, Australia. Vol. 1. 2006.

the International Conference BALTTRIB'2011; 30-31 October; Kaunas. Luthuania: 2011. pp. 196-201

Kyoto, Japan: 2009. p. 926

Friction, Lubrication and Wear

3-7. (In Russian)

pp. 105-114

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