**4.3 Plastic deformation during asperity-asperity shear**

It was well known that, during the wear process, severe temperature fluctuations could result in major changes of mechanical properties. That was, during a higher temperature region, moduli and yield strength of metals could usually decrease, so the localized plasticity would increase and the welding could even occur if a critical temperature was reached [35]. It was found that, near the contact area of two asperities, the Al neck was deformed amorphously under very high stresses and temperatures. In this area, linear motion of debris along the sliding direction was transformed into thermally random atomic motions. Therefore, the higher the *V*I, the much higher the temperature profiles in the contact area became, so a thin and soft/liquid like layer may form. As a result, the deformed Al neck would behave like a viscous liquid under very high temperatures and stresses [36]. When at a very high *V*<sup>I</sup> (= 10*.*0 Å/ps), amorphous plasticity became the major deformation mechanism. However, at a very low *V*<sup>I</sup> (= 1*.*00 Å/ps) and other lower *T*I, *D*<sup>I</sup> and *O*I, in addition to amorphous deformation at the contact area, dislocation cores were identified by using the evaluation of the centrosymmetry parameter [10], so they were found to emit into the Al-substrate from the high temperature region (amorphous deformation region) along a favorable system 111 ð Þ <sup>101</sup> � �, see **Figure 3**.

#### **4.4 Thermal analysis**

if the *V*<sup>I</sup> was low while the *T*<sup>I</sup> was high, the Al neck would be deformed and elongated more, and the final fracture of the Al neck was more ductile.

*Tribology in Materials and Manufacturing - Wear, Friction and Lubrication*

*Three stages of MD simulation for asperity-asperity shear: (a) the LJ-tip contact; (b) the LJ-tip plowing; (c) the*

Outputs of the MD simulations indicated that the number of Al atoms removed from the Al-substrate (wear rate) varied from 262 to 3144, depending upon different factors in the MD simulations. Analyses for these data indicated that, increasing the *D*<sup>I</sup> and the *O*<sup>I</sup> would increase the wear rate mostly, increasing the *T*<sup>I</sup> would just slightly increase the wear rate, whereas raising the *V*<sup>I</sup> exhibited a weak inverse correlation with the wear rate. In details, (1) if the *D*<sup>I</sup> became stronger, two asperities would adhere together via solid–liquid welding in the contact area, and more bonding states would occur along with more heat generation to increase temperature profiles in the contact area. So, a stronger *D*<sup>I</sup> may result in more removal of Al atoms. Due to thermal diffusion, temperature profiles in other areas of two asperities were also increased; (2) if enlarging the *O*<sup>I</sup> which determined the contact area and hence controlled the volume of Al atoms being plowed by the LJ-tip, the deformation of the Al-substrate would increase. And then, it resulted in a higher wear rate. Komanduri *et al* also reported similar results in their studies [9]; (3) if increasing the *T*I, dislocations in the Al-substrate can move and glide more easily through the elevated temperature region, resulting in large plastic deformation, i.e., the transformation from the brittle fracture (a small Al necking) at lower temperatures to the ductile fracture at higher temperatures can be easily observed; (4) it has found that the *V*<sup>I</sup> would play a minor inverse correlation role in the wear rate. This could be due to the increase of strain rate along with the rise of the *V*I, which decreased the ductility of materials so that the wear process on the Al-substrate may undergo less plastic deformation before fracture. As discussed earlier, more plastic deformation at the stage of the LJ-tip plowing may enlarge the area of adhesion. Therefore, when less plastic deformation took place, fewer Al atoms were removed by the LJ-tip. Similar experiments on dry-sliding wear of Al-Si alloys indicated that the coefficient of wear in these alloy systems was highly dependent upon the disc speed: at a faster disc speed (0.356 m/s), the wear rate was found to be low or moderate; While at a slower speed (0.089 m/s), the wear rate increased dramatically [34]. So, it should be noticed that, in experiments when the *V*<sup>I</sup> increased, more asperity-asperity collisions could take place, whereas in our simulation, only two single asperities were simulated. Thus when comparing with experimental observations, one would have to consider both the damage per asperity and the increased

**4.2 Effects of four selected factors**

**Figure 2.**

*Al necking and fracture.*

number of two interacting asperities.

**306**

Thermal distributions from four different MD simulations are shown in **Figures 4** and **5**, which give insight into heat generation and heat transfer during asperity-asperity shear. Temperature profiles of the Al-substrate were calculated by using the following equation:

$$\frac{3}{2}n\,k\_BT\_i = \frac{1}{2}\sum\_k m\_k\mathbf{v}\_k^2,\tag{5}$$

where *mk*,*Ti* and *v<sup>k</sup>* were mass, temperature, and velocity for atom *i* and *k*, respectively. *kB* was the Boltzmann constant, and *n* was the number of atoms for the Al substrate and the LJ-tip within a sphere of about 27 Å in diamond at a point *i* considered [16]. For the moving LJ-tip and the Al atoms removed by the LJ-tip, the temperature profiles were calculated by

**Figure 3.** *Amorphous deformation of the Al neck and emission of dislocation cores in the Al-substrate.*

top of the Al-asperity (local melting) until they bonded to and transferred heat to

*Atomistic Simulation of Severely Adhesive Wear on a Rough Aluminum Substrate*

In these two Figures, the maximum local temperature and the temperature gradient were quite different: the heat generation was much faster than the heat diffusion under a very high *V*I, so the *V*<sup>I</sup> seemed to play a major role in generating the maximum local temperature. In addition, a higher local temperature may lead to a larger local softening of the Al-substrate, so the deformation was mostly limited to a narrow region, and hence materials were removed. It was noticed that the maximum local temperature was much higher than the starting temperature *T*I, so the *T*<sup>I</sup> seemed not to play a major role in removing the Al atoms. It should also be noticed that the maximum local temperature can briefly exceed the boiling point of the Al, and yet the local liquid was not boiling. The reason was that, the increase of

*Thermal analyses for two different MD simulations under* T*<sup>I</sup> = 100 K,* O*<sup>I</sup> = 3.5*a*0,* D*<sup>I</sup> = 1.00 eV, and*

**Figure 5** shows the temperature profiles for two selected systems: *T*<sup>I</sup> = 700 K, *O*<sup>I</sup> = 3*.*5 *a*0, *D*<sup>I</sup> = 1*.*00 eV, and *V*<sup>I</sup> = 1*.*00 Å/ps, 10.0 Å/ps, respectively. **Figure 6** shows the temperature profiles for two selected systems: *T*<sup>I</sup> = 100 K, *O*<sup>I</sup> = 3*.*5 *a*0, *D*<sup>I</sup> = 1*.*00 eV, and *V*<sup>I</sup> = 10*.*0 Å/ps, 1.00 Å/ps, respectively. In these two Figures, (1) at the contact stage of the LJ-tip, the local heating occurred as new atomic bonds formed in the contact area between two asperities. Thus for the LJ-tip, the temperature gradient was positive from the contact area to its top layers; while for the Alsubstrate, this positive gradient was found from the deformed Al neck to its far ends; (2) at the plowing stage of the LJ-tip, the heat diffused into the LJ-tip bulk from the contact area; while for the Al-asperity, the Al necking also produced more heat in the remnant surface where the Al necking root glided, so the heat diffused into the Al-substrate from the remnant surface, and hence increased the tempera-

the cooler LJ-tip.

*DOI: http://dx.doi.org/10.5772/intechopen.94025*

ture profiles there.

**Figure 6.**

**309**

*(a)* **V***<sup>I</sup> = 1.00 Å/ps and (b)* **V***<sup>I</sup> = 10.0 Å/ps.*

**Figure 4.**

*(a). side view of the LJ-tip at the contact stage; (b) slide view of the LJ-tip at the plowing stage; (c) temperature profiles for a slice of the LJ-tip at the final stretching stage. (*T*<sup>I</sup> = 700 K,* O*<sup>I</sup> = 3.5* a*0,* D*<sup>I</sup> = 0.20 eV and* V*<sup>I</sup> = 10.0 Å/ps).*

**Figure 5.**

*Thermal analyses for two different MD simulations under* T*<sup>I</sup> = 700 K,* O*<sup>I</sup> = 3.5* a*0,* D*<sup>I</sup> = 1.00 eV, and (a)* **V***<sup>I</sup> = 1.00 Å/ps and (b)* **V***<sup>I</sup> = 10.0 Å/ps.*

$$\frac{3}{2}n\,k\_BT\_i = \frac{1}{2}\sum\_k m\_k(\mathbf{v}\_k - \mathbf{V}\_l)^2,\tag{6}$$

where *V<sup>I</sup>* was the impact velocity of the LJ-tip along the *x-*direction.

For examples, **Figure 4** shows three selected views of narrow slice for the LJ-tip during the MD simulations along with relevant temperature profiles. In **Figure 4(a)** and **(b)**, atoms in the first layer on the Al-asperity were found to follow almost same stacking sites as those L-J atoms being located at the top of the LJ-tip when two asperities came into bond together. And then in **Figure 4(c)**, the order of subsequent layers in the Al-asperity became more random in high temperature region (about 1200 � 1550 K): atoms in these layers moved randomly around the

*Atomistic Simulation of Severely Adhesive Wear on a Rough Aluminum Substrate DOI: http://dx.doi.org/10.5772/intechopen.94025*

top of the Al-asperity (local melting) until they bonded to and transferred heat to the cooler LJ-tip.

**Figure 5** shows the temperature profiles for two selected systems: *T*<sup>I</sup> = 700 K, *O*<sup>I</sup> = 3*.*5 *a*0, *D*<sup>I</sup> = 1*.*00 eV, and *V*<sup>I</sup> = 1*.*00 Å/ps, 10.0 Å/ps, respectively. **Figure 6** shows the temperature profiles for two selected systems: *T*<sup>I</sup> = 100 K, *O*<sup>I</sup> = 3*.*5 *a*0, *D*<sup>I</sup> = 1*.*00 eV, and *V*<sup>I</sup> = 10*.*0 Å/ps, 1.00 Å/ps, respectively. In these two Figures, (1) at the contact stage of the LJ-tip, the local heating occurred as new atomic bonds formed in the contact area between two asperities. Thus for the LJ-tip, the temperature gradient was positive from the contact area to its top layers; while for the Alsubstrate, this positive gradient was found from the deformed Al neck to its far ends; (2) at the plowing stage of the LJ-tip, the heat diffused into the LJ-tip bulk from the contact area; while for the Al-asperity, the Al necking also produced more heat in the remnant surface where the Al necking root glided, so the heat diffused into the Al-substrate from the remnant surface, and hence increased the temperature profiles there.

In these two Figures, the maximum local temperature and the temperature gradient were quite different: the heat generation was much faster than the heat diffusion under a very high *V*I, so the *V*<sup>I</sup> seemed to play a major role in generating the maximum local temperature. In addition, a higher local temperature may lead to a larger local softening of the Al-substrate, so the deformation was mostly limited to a narrow region, and hence materials were removed. It was noticed that the maximum local temperature was much higher than the starting temperature *T*I, so the *T*<sup>I</sup> seemed not to play a major role in removing the Al atoms. It should also be noticed that the maximum local temperature can briefly exceed the boiling point of the Al, and yet the local liquid was not boiling. The reason was that, the increase of

#### **Figure 6.**

*Thermal analyses for two different MD simulations under* T*<sup>I</sup> = 100 K,* O*<sup>I</sup> = 3.5*a*0,* D*<sup>I</sup> = 1.00 eV, and (a)* **V***<sup>I</sup> = 1.00 Å/ps and (b)* **V***<sup>I</sup> = 10.0 Å/ps.*

3 2

*(a)* **V***<sup>I</sup> = 1.00 Å/ps and (b)* **V***<sup>I</sup> = 10.0 Å/ps.*

**Figure 4.**

**Figure 5.**

**308**

V*<sup>I</sup> = 10.0 Å/ps).*

*n kBTi* <sup>¼</sup> <sup>1</sup>

2 X *k*

*Thermal analyses for two different MD simulations under* T*<sup>I</sup> = 700 K,* O*<sup>I</sup> = 3.5* a*0,* D*<sup>I</sup> = 1.00 eV, and*

where *V<sup>I</sup>* was the impact velocity of the LJ-tip along the *x-*direction.

For examples, **Figure 4** shows three selected views of narrow slice for the LJ-tip during the MD simulations along with relevant temperature profiles. In **Figure 4(a)** and **(b)**, atoms in the first layer on the Al-asperity were found to follow almost same stacking sites as those L-J atoms being located at the top of the LJ-tip when two asperities came into bond together. And then in **Figure 4(c)**, the order of subsequent layers in the Al-asperity became more random in high temperature region (about 1200 � 1550 K): atoms in these layers moved randomly around the

*(a). side view of the LJ-tip at the contact stage; (b) slide view of the LJ-tip at the plowing stage; (c) temperature profiles for a slice of the LJ-tip at the final stretching stage. (*T*<sup>I</sup> = 700 K,* O*<sup>I</sup> = 3.5* a*0,* D*<sup>I</sup> = 0.20 eV and*

*Tribology in Materials and Manufacturing - Wear, Friction and Lubrication*

*mk*ð Þ v*<sup>k</sup>* � V*<sup>I</sup>*

2

, (6)

temperature was very brief (about 10–100 ps), while the activation energy for atoms to jump into the gas phase was much higher (approximately the cohesive energy), so the kinetics prevented any significant amount of evaporation from occurring.

### **4.5 Statistical analysis**

Seventeen outputs for the MD simulations are listed in **Table 4**. The goal of the statistical analysis by the DOE is to determine the "best fit" equation to describe the wear rate as a function of four simulation variables (inter-asperity bonding, geometry overlap, impact velocity and starting temperature). It was assumed that the effect of each variable is additive, and there is no interaction between each of two variables (no cross term). So, this simplest model may work very well for the DOE analysis [16]. However, because the wear rate varied over a large range (the ratio of wear rate from its maximum to minimum was about 12), the wear rate must by transformed by using a natural log. Therefore, the equation for the wear rate in terms of the selected four factors was expressed as follows

*Wear* ¼ exp 5½ � *:*08 þ 0*:*000639 � *A* � 0*:*03 � *B* þ 0*:*42 � *C* þ 0*:*93 � *D* , (7)

It is more useful to describe the wear rate using the normalized variables (vari-

ables are normalized to a scale from �1 to +1, the low and high levels for each variable) because the magnitude of *A*, *B*, *C* and *D* coefficients allows one to easily

*ANOVA for those selected factorial models provided by the design expert™ software.*

**Source Sum of square DF Mean square F values**

*Atomistic Simulation of Severely Adhesive Wear on a Rough Aluminum Substrate*

Model 6.33 4 1.58 34.44 < 0.0001 *A* 0.47 1 0.47 10.30 0.0075 *B* 0.30 1 0.30 6.61 0.0245 *C* 3.09 1 3.09 67.29 < 0.0001 *D* 2.46 1 2.46 53.56 < 0.0001

Through using the normalized variables, Eq. (7) can be rewritten as follows

*Wear* ¼ exp 6½ � *:*80 þ 0*:*19 � *A* � 0*:*12 � *B* þ 0*:*42 � *C* þ 0*:*37 � *D :* (8)

In Eq. (8), coefficient magnitudes of variables indicated that *A* (= +0.19) term had a small effect, *B* (= �0.12) term had a minor inverse correlation, while *C* (= +0.42) and *D* (= +0.37) terms had major effects on the wear rate. That was, the inter-asperity bonding (*D*) and the geometry overlap (*C*) had much more effects on the wear rate than the starting temperature (*A*) and the impact velocity (*B*).

In this work, a severely adhesive wear was investigated by simulating asperityasperity shear between a fast moving rigid LJ-tip toward an Al-asperity. Molecular dynamics simulations were conducted for 17 different combinations of four variables: the starting temperature, the relative velocity, the geometry overlap and the inter-asperity bonding between two asperities. It was found that the wear process occurred in three stages: the contact, the plowing, and the necking/fracture on the aluminum substrate. Thermal analyses indicated that the heat generated during the MD simulations stemmed from the adhesive reaction in the contact area between two asperities, and then in the remnant surface on the Al residual substrate where the Al necking root glided. Bond formation and mechanical deformation during asperity-asperity shear may result in large increases of local temperature in the contact area (1200 � 2500 K), so the primary mechanism of deformation on the Al-substrate was due to amorphous plasticity and local melting. Generations and motions of dislocation cores were observed under milder conditions where little melting occurred. A method: *The 2<sup>4</sup> full factorial design* in the Design Of Experiment was adopted in analyzing effects of those four variables (factors) on the wear process. Analysis results indicated that, the inter-asperity bonding and the geometry overlap between two asperities would play much more important roles in the

wear process than the starting temperature and the impact velocity.

determine the relative importance of each variable.

Residual 0.55 12 0.046

Core Total 6.88 16 *Please note:* A *—* T*I;* B *—* **V***I;* C *—* O*I;* D *—* D*I.*

*DOI: http://dx.doi.org/10.5772/intechopen.94025*

**5. Conclusions**

**311**

*Prob > F*

**Table 5.**

where the *Wear* (wear rate) was the number of Al atoms removed by the LJ-tip, *A* was the starting temperature (K), *B* was the impact velocity (Å/ps), *C* was the geometry overlap (Å), and *D* was the inter-asperity bonding (eV). Please note, Eq. (7) applied an exponential formula to describing the wear rate because of the large variation in the wear rate (see the detailed analyses of variance for the selected factors in **Table 5**).


#### **Table 4.**

*Seventeen combinations of the MD simulations for the DOE analyses.*

*Atomistic Simulation of Severely Adhesive Wear on a Rough Aluminum Substrate DOI: http://dx.doi.org/10.5772/intechopen.94025*


#### **Table 5.**

temperature was very brief (about 10–100 ps), while the activation energy for atoms to jump into the gas phase was much higher (approximately the cohesive energy), so the kinetics prevented any significant amount of evaporation from

*Tribology in Materials and Manufacturing - Wear, Friction and Lubrication*

Seventeen outputs for the MD simulations are listed in **Table 4**. The goal of the statistical analysis by the DOE is to determine the "best fit" equation to describe the wear rate as a function of four simulation variables (inter-asperity bonding, geometry overlap, impact velocity and starting temperature). It was assumed that the effect of each variable is additive, and there is no interaction between each of two variables (no cross term). So, this simplest model may work very well for the DOE analysis [16]. However, because the wear rate varied over a large range (the ratio of wear rate from its maximum to minimum was about 12), the wear rate must by transformed by using a natural log. Therefore, the equation for the wear rate in

*Wear* ¼ exp 5½ � *:*08 þ 0*:*000639 � *A* � 0*:*03 � *B* þ 0*:*42 � *C* þ 0*:*93 � *D* , (7)

*T***<sup>I</sup> (K),** *A***-term** *V***<sup>I</sup> (Å/ps),** *B***-term** *O***<sup>I</sup> (Å),** *C***-term** *D***<sup>I</sup> (eV),** *D***-term Wear rate (atom number)**

 1.00 1.50 *a*<sup>0</sup> 0.20 409 1.00 1.50 *a*<sup>0</sup> 0.20 453 10.0 1.50 *a*<sup>0</sup> 0.20 262 10.0 1.50 *a*<sup>0</sup> 0.20 292 1.00 3.50 *a*<sup>0</sup> 0.20 947 1.00 3.50 *a*<sup>0</sup> 0.20 1231 10.0 3.50 *a*<sup>0</sup> 0.20 842 10.0 3.50 *a*<sup>0</sup> 0.20 982 1.00 1.50 *a*<sup>0</sup> 1.00 711 1.00 1.50 *a*<sup>0</sup> 1.00 1433 10.0 1.50 *a*<sup>0</sup> 1.00 694 10.0 1.50 *a*<sup>0</sup> 1.00 933 1.00 3.50 *a*<sup>0</sup> 1.00 1346 1.00 3.50 *a*<sup>0</sup> 1.00 3144 10.0 3.50 *a*<sup>0</sup> 1.00 1402 10.0 3.50 *a*<sup>0</sup> 1.00 1855 5.00 2.50 *a*<sup>0</sup> 0.50 1244

where the *Wear* (wear rate) was the number of Al atoms removed by the LJ-tip, *A* was the starting temperature (K), *B* was the impact velocity (Å/ps), *C* was the geometry overlap (Å), and *D* was the inter-asperity bonding (eV). Please note, Eq. (7) applied an exponential formula to describing the wear rate because of the large variation in the wear rate (see the detailed analyses of variance for the selected

terms of the selected four factors was expressed as follows

*Seventeen combinations of the MD simulations for the DOE analyses.*

occurring.

**4.5 Statistical analysis**

factors in **Table 5**).

**Table 4.**

**310**

*ANOVA for those selected factorial models provided by the design expert™ software.*

It is more useful to describe the wear rate using the normalized variables (variables are normalized to a scale from �1 to +1, the low and high levels for each variable) because the magnitude of *A*, *B*, *C* and *D* coefficients allows one to easily determine the relative importance of each variable.

Through using the normalized variables, Eq. (7) can be rewritten as follows

$$Wear = \exp\left[6.80 + 0.19 \times A - 0.12 \times B + 0.42 \times C + 0.37 \times D\right]. \tag{8}$$

In Eq. (8), coefficient magnitudes of variables indicated that *A* (= +0.19) term had a small effect, *B* (= �0.12) term had a minor inverse correlation, while *C* (= +0.42) and *D* (= +0.37) terms had major effects on the wear rate. That was, the inter-asperity bonding (*D*) and the geometry overlap (*C*) had much more effects on the wear rate than the starting temperature (*A*) and the impact velocity (*B*).

### **5. Conclusions**

In this work, a severely adhesive wear was investigated by simulating asperityasperity shear between a fast moving rigid LJ-tip toward an Al-asperity. Molecular dynamics simulations were conducted for 17 different combinations of four variables: the starting temperature, the relative velocity, the geometry overlap and the inter-asperity bonding between two asperities. It was found that the wear process occurred in three stages: the contact, the plowing, and the necking/fracture on the aluminum substrate. Thermal analyses indicated that the heat generated during the MD simulations stemmed from the adhesive reaction in the contact area between two asperities, and then in the remnant surface on the Al residual substrate where the Al necking root glided. Bond formation and mechanical deformation during asperity-asperity shear may result in large increases of local temperature in the contact area (1200 � 2500 K), so the primary mechanism of deformation on the Al-substrate was due to amorphous plasticity and local melting. Generations and motions of dislocation cores were observed under milder conditions where little melting occurred. A method: *The 2<sup>4</sup> full factorial design* in the Design Of Experiment was adopted in analyzing effects of those four variables (factors) on the wear process. Analysis results indicated that, the inter-asperity bonding and the geometry overlap between two asperities would play much more important roles in the wear process than the starting temperature and the impact velocity.
