# Interplay Between Wear and Thermal Expansion in 6082 Aluminum: A Simulation and Experimental Study
## 2 Materials and Methods
### Thermal Model
#### 2.3.1 Thermal Contact Definition  
The contact behavior in the solid mechanism model was exported to the heat transfer model to determine the heat source using frictional dissipation. The thermal contact was defined by Equations (2)-(7). \[-\mathbf{n}_{\text{dst}}\cdot\mathbf{q}_{\text{dst}}=-h(T_{\text{sct}}-T_{ \text{dst}})+rQ_{\text{b}} \tag{2}\]  
Equation (2) represents the heat flux balance at the destination surface (dst); for the disc, \(\mathbf{n}_{\text{dst}}\) is the unit normal vector at the destination surface, \(\mathbf{q}_{\text{dst}}\) is the heat flux vector at the destination surface, \(h\) is the heat transfer coefficient, \(T_{\text{sct}}\) and \(T_{\text{dst}}\) are the temperatures at the scatter (source) and destination surfaces, respectively, \(r\) is a reflection coefficient, and \(Q_{\text{b}}\) is the heat source term. The left side of the equation represents the heat flux leaving the destination surface. The right side combines the convective heat transfer due to the temperature difference between the source and destination surfaces and a portion of the heat source term, which is adjusted by the reflection coefficient \(r\). \[-\mathbf{n}_{\text{src}}\cdot\mathbf{q}_{\text{src}}=-h(T_{\text{sct}}-T_{ \text{src}})+(1-r)Q_{\text{b}} \tag{3}\]  
Equation (3) represents the heat flux balance at the source surface (src); for the pin, \(\mathbf{n}_{\text{src}}\) is the unit normal vector at the source surface, \(\mathbf{q}_{\text{src}}\) is the heat flux vector at the source surface, and \(T_{\text{src}}\) is the temperature at the source surface. Similar to the first equation, the left side represents the heat flux leaving the source surface. The right side includes the convective heat transfer due to the temperature difference between the source and destination surfaces and the remaining portion of the heat source term (adjusted by \(1-r\)). \[r=\frac{1}{1+\xi},\quad\xi=\sqrt{\frac{\rho_{\text{src}}c_{\text{p,cr}}(k_{ \text{src}}\mathbf{n}_{\text{src}})\cdot\mathbf{n}_{\text{src}}}{\rho_{ \text{dst}}c_{\text{p,dst}}(k_{\text{dst}}\mathbf{n}_{\text{dst}})\cdot \mathbf{n}_{\text{dst}}}} \tag{4}\]  
Equation (4) defines the reflection coefficient \(r\) based on the relative thermal properties of the source and destination materials. \(r\) is the reflection coefficient. The parameter \(\xi\) involves the densities, specific heat capacities, and thermal conductivities of the two surfaces; \(\xi\) is a dimensionless parameter that depends on the properties of the source and destination materials, \(\rho\) is the density, \(c_{\text{p}}\) is the specific heat capacity, and \(k\) is the thermal conductivity. \[h_{\rm c}=1.25k_{\rm contact}\frac{m_{\rm assp}}{\sigma_{\rm asst}}\bigg{(}\frac{p} {H_{\rm c}}\bigg{)}^{0.95} \tag{5}\]  
Equation (5) estimates the contact heat transfer coefficient based on the contact mechanics and material properties at the interface. \(h_{\rm c}\) is the contact heat transfer coefficient, \(k_{\rm contact}\) is the effective thermal conductivity at the contact interface, \(m_{\rm assp}\) is the mean asperity slope (0.6), \(\sigma_{\rm asst}\) is the standard deviation of the asperity heights (3.181 \(\upmu\)m), \(p\) is the contact pressure, and \(H_{\rm c}\) is the hardness of the softer material. \[\frac{2}{k_{\rm contact}}=\frac{1}{(k_{\rm src}\mathbf{n}_{\rm src})\cdot \mathbf{n}_{\rm src}}+\frac{1}{(k_{\rm dst}\mathbf{n}_{\rm dst})\cdot\mathbf{ n}_{\rm dst}} \tag{6}\]  
Equation (6) calculates the effective thermal conductivity \(k_{\rm contact}\) at the contact interface based on the thermal conductivities of the source and destination materials. \[h=h_{\rm c}+h_{\rm g}+h_{\rm r} \tag{7}\]  
Equation (7) sums the contributions of different mechanisms (contact conductance, gap conductance, and radiation) to the overall heat transfer coefficient.