**2. Experimental procedure**

The steels AISI 1010, 1030, 1040, 1050 and 50CrV4 were used in the study. The chemical compositions of these samples are given in Table 1. The specimens were in the form of cylinders of 9 *mm* diameter and 3 *mm* height.

The samples were prepared from non-heat treated and heat-treated steels. The heat treatment conditions are given in Table 2. The samples were ground with abrasive papers grading from 80 to 800 meshes and then polished with 0.3 *µm* diamonds. The hardness were measured by the Vickers hardness method in load of 98.0865 N (*HV*10). The average of measurements and the standard deviations were calculated. The average hardness values and standard derivations are given in Table 2. Wear experiment was carried out on the pinabrasion testing machine shown in Figure 2; tambour diameter *D*=118 *mm*, tambour rotation *n*=1000 *rpm* and abrasive wear set-up rate *V*=6.18 *ms-1*. In wear experiments, the 180, 125, 85, 70 and 50 *m* alumina (*Al2O3*) abrasive paper in sizes 100x1150 *mm* were used. For wear experiments, the apparatus in Figure 3 was mounted on the pin-abrasion testing machine. In order to fix the samples within apparatus in Figure 3, the cylindrical copper bars of 50 *mm* in length and 20 *mm* in diameter have been used. In order to prepare the specimens for abrasive wear test, holes of 9 *mm* in diameter and 1.5 *mm* in depth were milled on one end of the copper bars through which the specimen were replaced.


**Table 1.** The chemical compositions of experiment sample (wt. %) [19, 20]

where 

where 

70 and 50

*C*1 are constants.

relationship for metals as follows;

connected to abrasive particle size.

**2. Experimental procedure** 

cylinders of 9 *mm* diameter and 3 *mm* height.

the copper bars through which the specimen were replaced.

Khruschov [15] has studied experimentally the zone *I* in a stationary abrasive particle size using the non-heat treated steels and he found the relative wear resistance –hardness

is the relative wear resistance, *b* a constant coefficient and *H* the initial hardness.

0 and *H*0 are the relative wear resistance and hardness of annealed steel, and *C*0 and

Furthermore the following relationship has been determined to be in zone *II*, between the

There are numerous explanations in the literature to explain the abrasive grit size effect. However, most of them have been insufficient since they have not been able to explain the grit size effect encountered in all abrasive wear mechanisms (for example erosive wear) [15-18].

The focus of this study is to investigate the effect of abrasive particle size on abrasive wear resistance in zone *I*, *II* and to develop the equations of empirical abrasive wear resistance connected to abrasive particle size. Moreover, to search for the effects of relative wear resistance in zone *I*, *II* and to develop the equations of empirical relative wear resistance

The steels AISI 1010, 1030, 1040, 1050 and 50CrV4 were used in the study. The chemical compositions of these samples are given in Table 1. The specimens were in the form of

The samples were prepared from non-heat treated and heat-treated steels. The heat treatment conditions are given in Table 2. The samples were ground with abrasive papers grading from 80 to 800 meshes and then polished with 0.3 *µm* diamonds. The hardness were measured by the Vickers hardness method in load of 98.0865 N (*HV*10). The average of measurements and the standard deviations were calculated. The average hardness values and standard derivations are given in Table 2. Wear experiment was carried out on the pinabrasion testing machine shown in Figure 2; tambour diameter *D*=118 *mm*, tambour rotation *n*=1000 *rpm* and abrasive wear set-up rate *V*=6.18 *ms-1*. In wear experiments, the 180, 125, 85,

experiments, the apparatus in Figure 3 was mounted on the pin-abrasion testing machine. In order to fix the samples within apparatus in Figure 3, the cylindrical copper bars of 50 *mm* in length and 20 *mm* in diameter have been used. In order to prepare the specimens for abrasive wear test, holes of 9 *mm* in diameter and 1.5 *mm* in depth were milled on one end of

*m* alumina (*Al2O3*) abrasive paper in sizes 100x1150 *mm* were used. For wear

*bH* (4)

0 00 1 *CH CH* (5)

relative wear resistances of heat-treated steels and hardness;

 



Effect of Abrasive Particle Size on Abrasive Wear Resistance in Otomotive Steels 35

**Screw**

*LA* (6)

as:

**Rubber**

**Additional Mass II**

**Additional Mass I Additional Mass I** 

**Holder**

**Specimens**

On the other end, a hole of 14 *mm* in diameter and 25 *mm* in depth was drilled in order to balance the sample. An adhesive were applied to the samples and then the samples were attached into the holes milled on copper bars. Prior to the experiment, the samples were cleaned with alcohol and the mass of the sample were measured gravimetrically with 10-4 *mg* sensitivity. Then, they were assembled into the apparatus (Figure 3) mounted on the pinabrasion testing machine. Hard rubber dampers of 20 *mm* diameter and 10 *mm* thickness were put on the experiment sample to damp out the vibrations. Additional masses were fixed on the copper bars that were on top the rubber dampers. Abrasive wear experiments have been performed on each sample for 10 seconds under 0.13 *MPa* pressure and the experiment were repeated 5 times under the same conditions on each sample. At each repetition, the mass of the sample were determined gravimetrically and recorded. The wear volumes, *V*, were determined from the measured mass losses using the specific mass of the

samples. The linear wear rates, *W*, were computed using the following equation

section. In particular, we define the pressure wear resistance, <sup>1</sup> *WP*

*<sup>V</sup> <sup>W</sup>*

where *L* is the sliding distance of the experiment sample and *A* is the wear surface area of

In this section, we use the abrasive wear expressions and definitions given in nomenclature

**Abrasive Paper** 

**Screw**

the sample.

**3. Results and discussion** 

**Figure 3.** Apparatus for abrasive wear experiments [19, 20]

**Table 2.** Heat treatment and hardness values [19, 20]

**Figure 2.** The pin-abrasion testing machine [19, 20]

**Figure 3.** Apparatus for abrasive wear experiments [19, 20]

Materials Heat Treatment

**Table 2.** Heat treatment and hardness values [19, 20]

**Figure 2.** The pin-abrasion testing machine [19, 20]

AISI1050 Water quenched from 810-840 oC + tempered at 250 oC 6139±37 50CrV4 Water quenched from 830-850 oC + tempered at 250 oC 6845±25 AISI1030 Water quenched from 830-850 oC + tempered at 350 oC 4511±83 AISI1040 Water quenched from 820-850 oC + tempered at 350 oC 4884±26 AISI1050 Water quenched from 810-840 oC + tempered at 350 oC 5198±49 50CrV4 Water quenched from 830-850 oC + tempered at 350 oC 5492±29 AISI1030 Water quenched from 830-850 oC + tempered at 450 oC 3118±26 AISI1040 Water quenched from 820-850 oC + tempered at 450 oC 4550±49 AISI1050 Water quenched from 810-840 oC + tempered at 450 oC 4737±20 50CrV4 Water quenched from 830-850 oC + tempered at 450 oC 4805±39 AISI1030 Water quenched from 830-850 oC + tempered at 550 oC 3030±55 AISI1040 Water quenched from 820-850 oC + tempered at 550 oC 3324±29 AISI1050 Water quenched from 810-840 oC + tempered at 550 oC 3589±35 50CrV4 Water quenched from 830-850 oC + tempered at 550 oC 3727±64 AISI1030 Water quenched from 830-850 oC + tempered at 650 oC 1973±10 AISI1040 Water quenched from 820-850 oC + tempered at 650 oC 2059±25 AISI1050 Water quenched from 810-840 oC + tempered at 650 oC 2256±39 50CrV4 Water quenched from 830-850 oC + tempered at 650 oC 2902±34

Vickers hardness *HV*10 *(MPa)*

> On the other end, a hole of 14 *mm* in diameter and 25 *mm* in depth was drilled in order to balance the sample. An adhesive were applied to the samples and then the samples were attached into the holes milled on copper bars. Prior to the experiment, the samples were cleaned with alcohol and the mass of the sample were measured gravimetrically with 10-4 *mg* sensitivity. Then, they were assembled into the apparatus (Figure 3) mounted on the pinabrasion testing machine. Hard rubber dampers of 20 *mm* diameter and 10 *mm* thickness were put on the experiment sample to damp out the vibrations. Additional masses were fixed on the copper bars that were on top the rubber dampers. Abrasive wear experiments have been performed on each sample for 10 seconds under 0.13 *MPa* pressure and the experiment were repeated 5 times under the same conditions on each sample. At each repetition, the mass of the sample were determined gravimetrically and recorded. The wear volumes, *V*, were determined from the measured mass losses using the specific mass of the samples. The linear wear rates, *W*, were computed using the following equation

$$\mathcal{W} = \frac{V}{LA} \tag{6}$$

where *L* is the sliding distance of the experiment sample and *A* is the wear surface area of the sample.

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

In this section, we use the abrasive wear expressions and definitions given in nomenclature section. In particular, we define the pressure wear resistance, <sup>1</sup> *WP* as:

$$\mathcal{W}\_P^{-1} = \frac{P}{\mathcal{W}} \tag{7}$$

Effect of Abrasive Particle Size on Abrasive Wear Resistance in Otomotive Steels 37

125 9.8 0.111 0.99 85 12 0.083 0.99 70 13 0.077 0.99 50 15.5 0.065 1

> Coefficient of correlation *R*=0.99

*C*2 Wear coefficient *k=*1*/C*<sup>2</sup>

Coefficient of Correlation *R* 

Materials Abrasive

**Table 3.** Coefficient *C*2 and wear coefficient *k*[19]

seen Figure 5.

0,00

by

0,04

0,08

Wear coefficient

*k*

0,12

0,16

0,20

particle size *d*, (*m*)

Non-heat treated steels 180 8 0.125 0.99

As seen in Figure 5, the dependence of wear coefficient *k* on the abrasive particle size *d* is consistent with previous works [5, 6, 10, 15, 16]. However, the results in Figure 5 shows that although wear coefficient *k* increases initially fast with increasing abrasive particle size *d*, the wear coefficient does not reach to a steady state value in terms of a critical particle size. Besides, as long as the abrasive particle size increases, the slope of the curve decreases as

*k*=9.2x10-3*d*

1/2

0 40 80 120 160 200

*m*)

*k d* 9.2 (10)

Abrasive particle size *d*, (

**Figure 5.** Variations of wear coefficient *k* of non-heat treated steels versus abrasive particle size [19]

From Figure 5, the relation between wear coefficient *k* and particle size *d* for zone *I* is given

where *P* is the applied pressure to the experiment sample, and *W* is the linear wear rate defined in (7).

#### **3.1. For non-heat treated steels**

The relationship between the pressure wear resistance, <sup>1</sup> *WP* , and hardness, *H*, of non-heat treated steels is illustrated in Figure 4. The following relationship can be deducted via curve fitting using the least square method in Figure 4;

$$\text{W}\_{\text{P}}^{-1} = \text{C}\_{2}\text{H} \tag{8}$$

where *C*2=*k* 1, and *k* is the wear coefficient.

Rewriting (8) in terms of wear coefficient, the following expression for pressure wear resistance is obtained

$$\mathcal{W}\_P^{-1} = \frac{H}{k} \tag{9}$$

In Table 3, the coefficients *C*2, *k* and *R* are given for non-heat-treated steels. The variation of wear coefficients *k* (Table 3) with abrasive particle size *d* for non-heat treated steels is seen in Figure 5.

**Figure 4.** Non-heat-treated steels pressure wear resistance versus Vickers hardness (Parameter: Abrasive particle size) [19]

Effect of Abrasive Particle Size on Abrasive Wear Resistance in Otomotive Steels 37


**Table 3.** Coefficient *C*2 and wear coefficient *k*[19]

36 Tribology in Engineering

defined in (7).

where *C*2=*k*

Figure 5.

resistance is obtained

**3.1. For non-heat treated steels** 

0

10

20

30

Pressure wear resistance

Abrasive particle size) [19]

*W*P-1, (*GPa*)

40

50

60

70

80

The relationship between the pressure wear resistance, <sup>1</sup> *WP*

Abrasive particle diameter *d*,

180 *m*  125 *m* 

85 *m*  70 *m*  50 *m* 

fitting using the least square method in Figure 4;

1, and *k* is the wear coefficient.

1 *P <sup>P</sup> <sup>W</sup> W*

where *P* is the applied pressure to the experiment sample, and *W* is the linear wear rate

treated steels is illustrated in Figure 4. The following relationship can be deducted via curve

<sup>1</sup> *W CH <sup>P</sup>* <sup>2</sup>

Rewriting (8) in terms of wear coefficient, the following expression for pressure wear

1 *P <sup>H</sup> <sup>W</sup> k*

In Table 3, the coefficients *C*2, *k* and *R* are given for non-heat-treated steels. The variation of wear coefficients *k* (Table 3) with abrasive particle size *d* for non-heat treated steels is seen in

0,0 0,5 1,0 1,5 2,0 2,5 3,0

Vickers hardness *HV*10, (*GPa*)

**Figure 4.** Non-heat-treated steels pressure wear resistance versus Vickers hardness (Parameter:

*1010 1030 1040 1050 50CrV4*

(7)

(8)

(9)

Applied pressure *P*=0.13 *MPa*

, and hardness, *H*, of non-heat

As seen in Figure 5, the dependence of wear coefficient *k* on the abrasive particle size *d* is consistent with previous works [5, 6, 10, 15, 16]. However, the results in Figure 5 shows that although wear coefficient *k* increases initially fast with increasing abrasive particle size *d*, the wear coefficient does not reach to a steady state value in terms of a critical particle size. Besides, as long as the abrasive particle size increases, the slope of the curve decreases as seen Figure 5.

**Figure 5.** Variations of wear coefficient *k* of non-heat treated steels versus abrasive particle size [19]

From Figure 5, the relation between wear coefficient *k* and particle size *d* for zone *I* is given by

$$k = 9.2 \sqrt{d} \tag{10}$$

where *d* is abrasive particle size.

If (10) is substituted in (9), the pressure wear resistance expression for zone *I* becomes

$$\left(W\_p^{-1}\right)\_{\text{ZoneI}} = \frac{H}{\mathfrak{P}.\mathfrak{Z}\sqrt{d}}\tag{11}$$

Effect of Abrasive Particle Size on Abrasive Wear Resistance in Otomotive Steels 39

(16)

(17)

*C*3 *C*4 Coefficient of

Applied pressure *P*=0.13 *MPa*

coefficient from Table 4, the

Correlation *R*

coefficient is not dependent on abrasive particle size it is understood

125 11700 2.6 0.98 85 16600 2.6 0.97 70 18200 2.6 0.96 50 28800 2.6 0.99

0 2 4 6 810

Vickers Hardnes *HV*10, (*GPa*)

**Figure 6.** Heat-treated steels pressure wear resistance versus Vickers hardness (Parameter: Abrasive

abrasive particle size *d*. The variation of *C*<sup>3</sup> coefficient is plotted versus abrasive particle size

that the abrasive particle size for heat-treated steels does not change the slope in zone *II* (Figure 6). The abrasive particle size affects the slopes in zone *I* and *II* (Figure 8). If *C*<sup>3</sup>

> <sup>1</sup> 1.4 2.6 *<sup>P</sup> ZoneII W H d*

 <sup>1</sup> 1 1.4 2.6 *ZoneII*

Heat treated steels 180 7750 2.6 0.98

*W H P d* 

Abrasive Particle Diameters *d*, Coefficients of correlation

*m R*=0.98

*m R*=0.98

*m R*=0.98

*m R*=0.99

*m R*=0.99

pressure wear resistance expression in zone *II* for the heat-treated steels becomes;

coefficient in (13) replaced with the value from Figure 7 and *C*<sup>4</sup>

*d* (Figure 7). Since *C*<sup>4</sup>

and the wear resistance becomes

**Table 4.** Coefficients *C*3 and *C*4 [20]

0

20

40

Pressure wear resistance

particle size) [20]

*W*P-1, (*GPa*)

60

80

100

Materials Abrasive particle size

*d*, (*m*)

180 

125 

85 

70 

50 

and the wear resistance is

$$\left(W^{-1}\right)\_{Zuel} = \frac{1}{9.2\sqrt{d}} \frac{H}{P} \tag{12}$$

The previous works [3, 5, 6] states that the wear coefficient *k* and/or the wear rate *W* are dependent on the particle size *d* for pure metals and non-heat treated steels, but they did not give the mathematical expressions for this. In this study situation, the equation (12) was derived for the relation between the wear coefficient *k* and the particle size *d* using a curve fitting technique based on least square approximation for non-heat treated steels. (12) is valid for ideal microcutting, according to Zum Garh [3].

#### **3.2. For heat treated steels**

The variation of pressure wear resistance of the heat-treated steels (water quenched, water quenched+ refrigerated at –25 oC, water quenched + tempered) with hardness is given in Figure 6. According to Figure 6, the general expression of pressure wear resistance in terms of hardness for heat-treated steels can be written as follows;

$$\left(\mathcal{W}\_P^{-1}\right)\_{\text{ZoneII}} = \mathbb{C}\_3 + \mathbb{C}\_4 \tag{13}$$

where *C*<sup>3</sup> and *C*4 are constants.

*C*<sup>3</sup> and *C*4 constants and coefficient of correlation *R* are given in Table 4 for heat-treated steels. (3) shows how the pressure wear resistance in zone *II* changes with the hardness. Let us define *C*<sup>3</sup> and *C*4 as follows:

$$C\_3 = \frac{2}{3k} H\_0 \tag{14}$$

$$C\_4 = \frac{1}{3k} \tag{15}$$

where *H*0 is defined in (3) as the hardness of annealed alloyed steel.

If we substitute for *C*<sup>3</sup> and *C*4 in (13), we obtain (3). According to (3), since the values of *H* and *Ho* are dependent on abrasive particle size *d*, both coefficients in (13) are dependent on abrasive particle size *d*. But our results (Table 4) show that *C*<sup>4</sup> coefficient is not dependent on abrasive particle size *d*. The variation of *C*<sup>3</sup> coefficient is plotted versus abrasive particle size *d* (Figure 7). Since *C*<sup>4</sup> coefficient is not dependent on abrasive particle size it is understood that the abrasive particle size for heat-treated steels does not change the slope in zone *II* (Figure 6). The abrasive particle size affects the slopes in zone *I* and *II* (Figure 8). If *C*<sup>3</sup> coefficient in (13) replaced with the value from Figure 7 and *C*<sup>4</sup> coefficient from Table 4, the pressure wear resistance expression in zone *II* for the heat-treated steels becomes;

$$\left(W\_p^{-1}\right)\_{ZomeII} = \frac{1.4}{d} + 2.6H \tag{16}$$

and the wear resistance becomes

38 Tribology in Engineering

where *d* is abrasive particle size.

and the wear resistance is

**3.2. For heat treated steels** 

where *C*<sup>3</sup> and *C*4 are constants.

us define *C*<sup>3</sup> and *C*4 as follows:

If (10) is substituted in (9), the pressure wear resistance expression for zone *I* becomes

9.2 *<sup>P</sup> ZoneI <sup>H</sup> <sup>W</sup>*

The previous works [3, 5, 6] states that the wear coefficient *k* and/or the wear rate *W* are dependent on the particle size *d* for pure metals and non-heat treated steels, but they did not give the mathematical expressions for this. In this study situation, the equation (12) was derived for the relation between the wear coefficient *k* and the particle size *d* using a curve fitting technique based on least square approximation for non-heat treated steels. (12) is

The variation of pressure wear resistance of the heat-treated steels (water quenched, water quenched+ refrigerated at –25 oC, water quenched + tempered) with hardness is given in Figure 6. According to Figure 6, the general expression of pressure wear resistance in terms

*<sup>P</sup>* 3 4 *ZoneII*

*C*<sup>3</sup> and *C*4 constants and coefficient of correlation *R* are given in Table 4 for heat-treated steels. (3) shows how the pressure wear resistance in zone *II* changes with the hardness. Let

> 3 0 2 3 *C H*

> > 1 3

4

If we substitute for *C*<sup>3</sup> and *C*4 in (13), we obtain (3). According to (3), since the values of *H* and *Ho* are dependent on abrasive particle size *d*, both coefficients in (13) are dependent on

*C*

where *H*0 is defined in (3) as the hardness of annealed alloyed steel.

abrasive particle size *d*. But our results (Table 4) show that *C*<sup>4</sup>

<sup>1</sup>

 <sup>1</sup> <sup>1</sup> *ZoneI* 9.2 *<sup>H</sup> <sup>W</sup>*

*d*

*d P*

(11)

(12)

*W CC* (13)

*<sup>k</sup>* (14)

*<sup>k</sup>* (15)

coefficient is not dependent on

<sup>1</sup>

valid for ideal microcutting, according to Zum Garh [3].

of hardness for heat-treated steels can be written as follows;

$$\left(\left(\boldsymbol{W}^{-1}\right)\_{ZomeII} = \frac{1}{P} \left(\frac{1.4}{d} + 2.6H\right) \tag{17}$$


**Table 4.** Coefficients *C*3 and *C*4 [20]

**Figure 6.** Heat-treated steels pressure wear resistance versus Vickers hardness (Parameter: Abrasive particle size) [20]

Effect of Abrasive Particle Size on Abrasive Wear Resistance in Otomotive Steels 41

<sup>4</sup> *ex H* 6 10 (18)

=6x10-1*H*

Aplied pressure *P*=0.13 *MPa*

Coefficient of correlation *R*=0.99

due to the heat-treatment of the material [14, 15, 16]. After heat-treatment the hardness of the material changes. According to the abrasive wear mechanism of heat-treated steels, abrasive particle cuts more chips than wear groove volume [1-3]. Abrasive particle produces chip via micro cutting and micro cracking mechanisms. It was concluded that the difference in the wear resistance of heat-treated and non-heat treated steels arises from micro cracking

The variations of the pressure wear resistances of non-heat-treated and heat-treated steels with the hardness are shown in Figure 8. As seen in Figure 8, the pressure wear resistances

From Figure 9, the dependence of the relative wear resistance on hardness for non-heat

The relative wear resistance of non-heat-treated steels does not depend on abrasive particle size. This result is supported with the results calculated by equation (4) which was proposed

0,0 0,5 1,0 1,5 2,0 2,5 3,0

Vickers hardness *HV*10, (*GPa*)

**Figure 9.** Non-heat-treated steels relative rear resistance versus Vickers hardness (Parameter: Abrasive

of non-heat-treated and heat-treated steels are dependent on abrasive particle size.

mechanism in heat-treated steels during abrasive wear.

**3.3. Relative wear resistance for non heat treated** 

treated steels can be expressed as

0,0

particle size) [19]

0,5

1,0

1,5

Relative wear resistance

2,0

2,5

3,0

Abrasive particle diameters *d*,

180 *m* 125 *m*

85 *m* 70 *m* 50 *m*

by Khruschov [15].

**Figure 7.** Constant *C*3 of heat-treated steels versus abrasive particle size *d* [20]

**Figure 8.** Non-heat treated and heat treated steels pressure wear resistance versus Vickers hardness (Parameter: Abrasive particle size) [19, 20]

In previous works, the abrasive wear resistances of heat-treated steels were found to be different than that of non-heat treated steels. Researchers concluded that this difference was due to the heat-treatment of the material [14, 15, 16]. After heat-treatment the hardness of the material changes. According to the abrasive wear mechanism of heat-treated steels, abrasive particle cuts more chips than wear groove volume [1-3]. Abrasive particle produces chip via micro cutting and micro cracking mechanisms. It was concluded that the difference in the wear resistance of heat-treated and non-heat treated steels arises from micro cracking mechanism in heat-treated steels during abrasive wear.

The variations of the pressure wear resistances of non-heat-treated and heat-treated steels with the hardness are shown in Figure 8. As seen in Figure 8, the pressure wear resistances of non-heat-treated and heat-treated steels are dependent on abrasive particle size.

#### **3.3. Relative wear resistance for non heat treated**

40 Tribology in Engineering

0

0

(Parameter: Abrasive particle size) [19, 20]

20

40

Pressure wear resistance

*W*P-1, (*GPa*)

60

Zone *I*

180 

125 

85 

70 

50 

80

100

5

10

Costant of

*C*3x103

15

20

25

30

0 40 80 120 160 200

0 2 4 6 810

Zone *II*

Vickers Hardnes *HV*10, (*GPa*)

**Figure 8.** Non-heat treated and heat treated steels pressure wear resistance versus Vickers hardness

In previous works, the abrasive wear resistances of heat-treated steels were found to be different than that of non-heat treated steels. Researchers concluded that this difference was

Abrasive Particle Size *d*, (

Abrasive particle diameter *d*, Correlation Coefficent

*m R*=0.99

*m R*=0.99

*m R*=0.99

*m R*=0.99

*m R*=1

**Figure 7.** Constant *C*3 of heat-treated steels versus abrasive particle size *d* [20]

*C*3 =1400 *d* -1

*m*)

> Applied presure *P*=0.13 *MPa*

Coefficient of correlation *R*=0.98

> From Figure 9, the dependence of the relative wear resistance on hardness for non-heat treated steels can be expressed as

$$e = 6 \text{x}10^{-4}H \tag{18}$$

The relative wear resistance of non-heat-treated steels does not depend on abrasive particle size. This result is supported with the results calculated by equation (4) which was proposed by Khruschov [15].

**Figure 9.** Non-heat-treated steels relative rear resistance versus Vickers hardness (Parameter: Abrasive particle size) [19]

#### **3.4. Relative wear resistance for heat treated steels**

The variation of pressure wear resistance of the heat-treated steels (water quenched, water quenched+ refrigerated at –25 *<sup>o</sup> C*, water quenched + tempered) with hardness has been shown in Figure 10. As seen in Figure 10, the relative wear resistance in steel shows different slopes depending on abrasive particle size. The relative wear resistance equations in zone *II* for the heat-treated steels can be written in general as follows;

$$
\mathfrak{a} = \mathsf{A}\_o + \mathsf{B}\_o \mathsf{H} \tag{19}
$$

Effect of Abrasive Particle Size on Abrasive Wear Resistance in Otomotive Steels 43

<sup>0</sup> *B xd* 1.42 10 (23)

125 0.76 16 85 0.87 13 70 0.9 11.5 50 1.158 10.1

(24)

, is independent on abrasive particle size *d* in zone *I* while

Coefficients of correlation

*R*=0.99

*R*=0.97

*m*)

*m*) *A*0 *B*0 10-5

0

8

16

Coefficient of

*B*0x105

24

32

40

, of the non-heat-

3

Heat treated steels 180 0.62 19.2

If *A*<sup>0</sup> and *B*0 constants in (19) replaced with the expressions given in (22) and (23), the relative

<sup>3</sup> 8 10 <sup>3</sup> 1.42 10 *<sup>x</sup> x dH*

treated and heat-treated steels are shown graphically in Figure 12. As seen in Figure 12 and

0 40 80 120 160 200

*B0* =1.42 *d* 1/2

Abrasive Particle Size *d*, (

**Figure 11.** Coefficients *A*0 and *B*0 of heat-treated steels versus abrasive particle size *d* [19, 20]

*A0* =8 *d* -1/2 Materials Abrasive particle size *d*, (

wear resistance expression in zone *II* for the heat-treated steels becomes;

The hardness *H*, of abraded material versus the relative wear resistances

*d*

**Table 5.** Coefficients *A*0 and *B*0 [20]

(18), the relative wear resistance

0,0

0,3

0,6

Coefficient of

*A*<sup>0</sup>

0,9

1,2

1,5

it is dependent on *d* in zone *II* (see (24)).

where *A*0 and *B*0 are constant coefficients.

**Figure 10.** Heat-treated steels relative wear resistance versus Vickers hardness (Parameter: Abrasive particle size) [19, 20]

The experimental results for *A*<sup>0</sup> and *B*<sup>0</sup> constants, and coefficient of correlation *R* are given in Table 5 for heat-treated steels. (5) shows how the relative wear resistance in zone *II* changes with the hardness. Let us define *A*0 and *B*0 as follows;

$$A\_0 = \left(\varepsilon\_o - \mathbb{C}\_o H\_\odot\right) \tag{20}$$

$$B\_0 = \mathbb{C}\_1\tag{21}$$

The variation of *A0* and *B0* constants are plotted versus abrasive particle size *d* (Figure 11). The following equation are obtained using least square approximation method,

$$A\_0 = \frac{8\varkappa 10^{-3}}{\sqrt{d}}\tag{22}$$

Effect of Abrasive Particle Size on Abrasive Wear Resistance in Otomotive Steels 43

$$B\_0 = 1.42x10^{-3} \sqrt{d} \tag{23}$$


**Table 5.** Coefficients *A*0 and *B*0 [20]

42 Tribology in Engineering

quenched+ refrigerated at –25 *<sup>o</sup>*

where *A*0 and *B*0 are constant coefficients.

180 

125 

85 

70 

50 

with the hardness. Let us define *A*0 and *B*0 as follows;

0

particle size) [19, 20]

1

2

Relative wear resistance

3

4

5

**3.4. Relative wear resistance for heat treated steels** 

for the heat-treated steels can be written in general as follows;

The variation of pressure wear resistance of the heat-treated steels (water quenched, water

shown in Figure 10. As seen in Figure 10, the relative wear resistance in steel shows different slopes depending on abrasive particle size. The relative wear resistance equations in zone *II*

*Ao o*

0 2 4 6 810

Vickers Hardness *HV*10, (*GPa*)

**Figure 10.** Heat-treated steels relative wear resistance versus Vickers hardness (Parameter: Abrasive

The experimental results for *A*<sup>0</sup> and *B*<sup>0</sup> constants, and coefficient of correlation *R* are given in Table 5 for heat-treated steels. (5) shows how the relative wear resistance in zone *II* changes

> *A CH* <sup>0</sup> *o oO*

The variation of *A0* and *B0* constants are plotted versus abrasive particle size *d* (Figure 11).

3

*d* 

The following equation are obtained using least square approximation method,

0 8 10 *<sup>x</sup> <sup>A</sup>*

Abrasive Particle Diameters *d*, Coefficients of correlation

*m R*=0.97

*m R*=0.99

*m R*=0.99

*m R*=0.99

*m R*=0.98

*C*, water quenched + tempered) with hardness has been

*B H* (19)

Applied pressure *P*=0.13 *MPa*

(20)

0 1 *B C* (21)

(22)

If *A*<sup>0</sup> and *B*0 constants in (19) replaced with the expressions given in (22) and (23), the relative wear resistance expression in zone *II* for the heat-treated steels becomes;

$$
\varepsilon = \frac{8\,\mathrm{x}\,10^{-3}}{\sqrt{d}} + 1.42\,\mathrm{x}\,10^{-3}\sqrt{d}H \tag{24}
$$

The hardness *H*, of abraded material versus the relative wear resistances , of the non-heattreated and heat-treated steels are shown graphically in Figure 12. As seen in Figure 12 and (18), the relative wear resistance , is independent on abrasive particle size *d* in zone *I* while it is dependent on *d* in zone *II* (see (24)).

**Figure 11.** Coefficients *A*0 and *B*0 of heat-treated steels versus abrasive particle size *d* [19, 20]

Effect of Abrasive Particle Size on Abrasive Wear Resistance in Otomotive Steels 45

Heat-treated steels have lower resistance to wear than non heat-treated steels of the

same hardness.

: Wear Rate (Linear wear intensity)

: Pressure Wear Resistance (*MPa*)

: Wear Resistance of reference material

mechanism steels, Wear of Material pp: 585-593, 1987

Metals, Wear, 55(1979) 163-190.

*Mersin University, Engineering Faculty, Department of Mechanical Engineering, Ciftlikkoy,* 

[1] Sevim. I., "Effect of Abrasive Particle Size on Wear Resistance for Abrasive Wear of Steels". Ph.D. Thesis, İ.T.Ü. Institute of Science and Technology, İstanbul, 1998 [2] Rabinowicz E., A., "Friction and wear of materials" Wiley, New York, pp: 168, 1965 [3] Zum Gahr.K.H." Microstructure and Wear of Materials". Elsevier Science, 1987

[4] Hakkirigawa. K., and Li, Z., Z., The effect of hardness on the transition of abrasive wear

[5] Sin, H., Saka, N., and Suh, P., Abrasive Wear Mechanisms and The Grit Size Effect of

[6] Misra, M., and Finnie, I., Some observations on two-body abrasive wear, Wear, 68(1981)

[7] Avient., W., E., Goddard, J., and Wilman, H., An Experimental Study of Friction and wear during Abrasion of Metals, Proc. R. Soc. (London), Ser. A, 256 (1960) 159-179. [8] Mulhearn, T., O., and Samuels, L., E., The Abrasion of Metals: A Model of The Process.

: Wear Resistance

: Relative Wear Resistance

: Wear Resistance of sample

**Nomenclature** 

*G*

**Author details** 

Ibrahim Sevim

*Mersin, Turkey* 

**5. References** 

pp:41-56.

Wear 5(1962) 478-498

1 1 *n r*

*V G <sup>W</sup> LA LA* 

<sup>1</sup> *LA <sup>W</sup> G*

 

1 *P LA W P*

*W W* 

<sup>1</sup> *Wn*

<sup>1</sup> *Wr*

**Figure 12.** Non-heat treated and heat treated steels relative wear resistance versus Vickers hardness (Parameter: Abrasive particle size) [19, 20]

## **4. Conclusion**

The results showed that the wear resistance of non-heat treated and heat-treated steels are functions of the abrasive particle size. From the results, an empirical mathematical wear resistance model and an empirical mathematical relative wear resistance , as a function of abrasive particle size *d* were derived [18-20].


behavior of hardness *H* and relative wear resistance is dependent on the terms of <sup>1</sup> *d*

and *d* as given in equation (24).

 Heat-treated steels have lower resistance to wear than non heat-treated steels of the same hardness.

#### **Nomenclature**

44 Tribology in Engineering

0,0

(Parameter: Abrasive particle size) [19, 20]

abrasive particle size *d* were derived [18-20].

size *d* (equation (17)). The relative wear resistance

**4. Conclusion** 

0,5

1,0

1,5

Relative wear resistance

2,0

2,5

3,0

Abrasive Particle Diameters, *d*

Zone *I* Zone *II*

180 *m* 125 *m*

85 *m* 70 *m* 50 *m*

0 2 4 6 810

Applied Pressure *P*=0.13 *MPa*

But, relative wear resistance

is dependent on the terms of <sup>1</sup>

and hardness *H* related linearly for non-heat treated steels

, as a function of

for

*d*

Vickers Hardness *HV*10, (*GPa*)

**Figure 12.** Non-heat treated and heat treated steels relative wear resistance versus Vickers hardness

The results showed that the wear resistance of non-heat treated and heat-treated steels are functions of the abrasive particle size. From the results, an empirical mathematical wear

 There is a linear relationship between the abrasive wear resistance *W*-1 and hardness *H*, depending on abrasive particle size *d*, for non-heat treated steels. The relationship between wear coefficient *k* and abrasive particle size *d* is a parabolic as seen in equation (10). The wear resistance *W*-1 is inversely proportional with the square root of particle

 The relationships for the heat-treated steels between the abrasive wear resistance and hardness *H*, show positive intercepts on the ordinate, depending on abrasive particle

as it can be seen in equation (18), abrasive particle size does not effect the relationship

the heat-treated steels is dependent on abrasive particle size *d*, and the relationships for the heat-treated steels show positive intercepts on the ordinate. The proportionality

resistance model and an empirical mathematical relative wear resistance

size *d*, for non-heat treated steels as seen in equation (12).

between hardness *H* and relative wear resistance

behavior of hardness *H* and relative wear resistance

and *d* as given in equation (24).

$$\begin{array}{lcl}\hline \text{W} = \frac{V}{LA} = \frac{G}{\rho LA} & : \text{Wear Rate (Linear wear intensity)}\\\\ \text{} & W^{-1} = \frac{\rho LA}{G} & : \text{Wear Resistance} \\\\ \text{} & W\_p^{-1} = P \frac{\rho LA}{G} & : \text{Pressure Wear Resistance (MPa)}\\\\ \text{} & \varepsilon = \frac{W\_n^{-1}}{W\_r^{-1}} & : \text{Relative Wear Resistance} \\\\ & \vdots & \vdots & \vdots \\\\ & W\_n^{-1} & : \text{Wear Resistance of sample} \\\\ & \vdots & \vdots & \vdots \\\\ & \vdots & \vdots & \vdots \\\\ & \end{array}$$

#### **Author details**

#### Ibrahim Sevim

*Mersin University, Engineering Faculty, Department of Mechanical Engineering, Ciftlikkoy, Mersin, Turkey* 

#### **5. References**


[9] Rabinowicz, E. and Mutis, A., Effect of Abrasive Particle Size on Wear. Wear, 8(1965) 381-390

**Chapter 4** 

© 2013 Kulczycki and Kajdas, licensee InTech. This is an open access chapter 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.

© 2013 Kulczycki and Kajdas, licensee InTech. This is a paper 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.

**A New Attempt to Better Understand** 

Andrzej Kulczycki and Czesław Kajdas

http://dx.doi.org/10.5772/54503

**1. Introduction** 

Additional information is available at the end of the chapter

relationship is described by Arrehnius equation

**Arrehnius Equation and Its Activation Energy** 

Activation energy (Ea) is strictly combined with kinetics of chemical reactions. The

where k is the rate coefficient, A is a constant, R is the universal gas constant, and T is the temperature (in Kelvin); R has the value of 8.314 x 10-3 kJ mol-1K-1, Ea is the amount of energy required to ensure that a reaction happens. Common sense is that at higher temperatures, the probability of two molecules colliding is higher. Accordingly, a given reaction rate is higher and the reaction proceeds faster and, the effect of temperature on reaction rates is calculated using the Arrhenius equation. Further reaction rate enhancement is promoted by catalysis. Catalysis is the phenomenon of a catalyst in action. Catalyst is a material that increases the rate of chemical reaction, and for equilibrium reactions it increases the rate at which a chemical system approaches equilibrium, without being consumed in the process [1]. It is applied in small amounts relative to the reactants. Chemical kinetics, based on Arrhenius equation assumes that catalysts lower the activation energy (Ea) and the presence of catalyst results higher reaction rate at the same temperature. In chemical kinetics Ea is the height of the potential barrier separating the products and reactants. Catalytic reactions have a lower Ea than those of the thermally activated. This fact enables a chemical reaction not only to proceed faster but also at a lower temperature than otherwise possible. The solid heterogeneous catalyst mechanism that would lower activation energy is still under discussion. It is known that the effect of catalysts is intrinsically connected to the material surface states. However, the connection of catalysts material states to their action is not yet fully clear and specific stimulators of this action are unknown. Few years ago [2] a new approach to Ea was proposed and a first indirect confirmation was made [3]. Dante et al. [4]

k = Aexp(-Ea/RT) (1)

