# Method to Predict Performances of PCB Silicone Conformal Coating under Thermal Aging
## 3 Results
### Modelling Stress Build-up Associated with CTE Mismatch during Thermal Cycle Aging
Defining \(\xi=\frac{E_{s}\ \left(1-v_{a}^{2}\right)}{E_{a}\left(1-v_{a}^{2}\right)}\ \frac{x}{h_{a}}\), a dimensionless variable of the lateral position x (position x is multiplied by a factor function of both coating and substrate mechanical properties and coating thickness), the approximated shear stress distribution near the edge (valid for small \(\xi\) values, comprised between 0 and 2) takes the form:  
\[\tau_{x}\approx\ \frac{E_{s}\ \left(1-v_{a}^{2}\right)\Delta T\ (\alpha_{s}- \alpha_{a})}{(1-v_{a})(1-v_{s}^{2})}\ [(2\pi\ \xi)^{-\frac{1}{2}}-0.21938\ \xi^{\frac{1}{2}}+0.12698\ \xi^{\frac{1}{2}}\ ln\ (\xi)] \tag{6}\]  
When moving apart from the edge, the shear stress component decreases rapidly, and for \(\xi\) values > 5, an approximated value of shear stress spatial evolution is given by:  
\[\tau_{x}\approx\ \frac{E_{s}\ \left(1-v_{a}^{2}\right)\Delta T\ (\alpha_{s}- \alpha_{a})}{(1-v_{a})(1-v_{s}^{2})}\ [\ \frac{2}{\pi\xi^{2}}-4\ \frac{4}{\pi^{2}\xi^{3}}\ (1.2319-2\ln(\xi))] \tag{7}\]  
Analysis of the dimensionless variable \(\xi\), \(\xi\) takes large values very near the edge \(\frac{x}{h_{a}}\) when a large difference exists between [PERSON]'s modulus of the substrate and [PERSON]'s modulus of the coating, which is the case for the application studied in this paper. The evolution of \(\xi\) in the function of \(\frac{x}{h_{a}}\), the normalized distance from the edge is shown in Figure 6, using the mechanical properties of both the PCB substrate and conformal coating. A measured at 125 \({}^{\circ}\)C (Table 2). It is observed that we are outside the domain of validity of Equation (6) for \(\frac{x}{h_{a}}\) > 2.0 \(\times\)\(10^{-4}\) (a distance of 2.0 \(\times\)\(10^{-5}\) for a coating of 0.1 mm thickness), meaning that the high shear predicted by Equation (6) is very localized and decreases very rapidly when moving apart from the edge of the bi-layer sheet. Figure 7 shows the evolution of the shear stress in the function of distance from the edge, calculated for \(\xi\) values > 5 that corresponds to the domain of validity of the far edge approximated solution (7). A sharp stress decrease is observed, stress dropping to a value of 0.03 MPa at a distance equal to the hundredth of film thickness. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Performance** & **Unit** & **Coating A** & **Coating A** & **Coating B** & **Coating B** & **PCB** \\  & & **(\(-\)40 \({}^{\circ}\)C)** & **(125 \({}^{\circ}\)C)** & **(\(-\)40 \({}^{\circ}\)C)** & **(125 \({}^{\circ}\)C)** & **PCB** \\ \hline Density & Kg/m\({}^{3}\) & 1120 & 1120 & 980 & 980 & 1900 \\ Thermal Conductivity & W/(m-K) & 0.2 & 0.2 & 0.2 & 0.2 & 0.3 \\ Heat Capacity & J (Kg-K) & 1500 & 1500 & 1500 & 1500 & 1369 \\ CTE & 1/K & \(3.0\times 10^{-4}\) & \(3.0\times 10^{-4}\) & \(4.9\times 10^{-4}\) & \(4.9\times 10^{-4}\) & \(1.8\times 10^{-5}\) \\ Young’s Modulus E & MPa & 160.1 & 1.28 & 1.33 & 1.92 & 22000 \\ [PERSON]’s ratio \(\gamma\) & NA & 0.49 & 0.49 & 0.49 & 0.49 & 0.15 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Material properties input used for both the simplified model and the 2D FEA model. The large stress predicted by simplified Formula (7) results from the nearly full incompressible nature of the conformal coating. The plane of adhesion between the PCB and the coating restricts the free deformation of the coating required to conserve the volume, creating a local high shear stress. For comparison, solid mechanics equations are solved for a 2D geometry using a COMSOL FEA model (Figure 8). A multiphysics model (solid mechanics and thermal transfer) is built to have the stress induced in the coating coming from the CTE mismatch between the conformal coating and the PCB. The stress is assumed null at 20 \({}^{\circ}\)C, and the steady state stress that builds up when increasing temperature up to 125 \({}^{\circ}\)C is calculated.