# 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  
The large CTE mismatch between silicone coatings and electronics components requires the accurate calculation of stress at equilibrium at both low and high temperatures, the change in temperature concerning the temperature of coating application creating either a negative or positive lateral differential displacement. The state-of-the-art method consists in solving solid mechanics equations using an FEA tool. However, this method is not necessarily the most appropriate for a first material selection because:  
* FEA modeling requires an accurate identification of the material elastic model: most silicone materials show a stress-strain nonlinear dependence, requiring multiple test piece geometries (uniaxial testing, pure shear, bi-axial testing) to accurately describe mechanical behavior, particularly when having stress-strain dependence showing saddle point that requires high order nonlinear models. Those measurements are particularly complex with very rigid material, having low deformation capabilities;
* Silicone compounds are nearly incompressible; therefore, high local stress builds up near the interface between the substrate and the coating and particularly close to composite edges, demanding a high grid density to obtain a mesh-independent solution. This point is discussed later in the paper. PCB architectures vary significantly from case to case; therefore, it makes sense to compare performances of conformal coating, starting with simpler geometry, i.e., an assembly substrate/coating. To identify which coating properties to focus on in the development of a soft silicone conformal coating, it is convenient to have analytical solutions obtained, making simplification assumptions valid for those coatings. Analysis of the function solution of solid mechanics equations provides intuition on the most important parameter impacting coating durability and how those parameters vary in improving coating performances. The calculation of the tensile stress developing in a bi-layer thin sheet has been studied since the 1970s, and simplified formulas have been proposed using plane stress assumption [22]. Considering the generalized Hooke's law modified to include a strain contribution associated with thermal dilatation and assuming that all stress components along sheet thickness are null (referred to as z direction in Figure 5), i.e., \(\Delta\sigma_{z}=\Delta\tau_{yz}=\Delta\tau_{xz}=0\) (the plane stress assumption), the relation linking the tensile stress and the tensile strain in a thin sheet is given by:  
\[\Delta\;\epsilon_{x}=\frac{\Delta\sigma_{x}}{E}\;(1-v)+\alpha\;\Delta\;T\; \text{and}\;\Delta\;\epsilon_{x}=\Delta\;\epsilon_{y} \tag{2}\]  
With \(\Delta\;\epsilon_{x}\), \(\Delta\;\epsilon_{y}\) the elongation along the x and y direction associated with thermal dilation, \(\Delta\sigma_{x}\), the thermal stress associated with elongation \(\Delta\;\epsilon_{x}\), \(v\) the Poisson ratio, and \(\alpha\) the thermal dilation coefficient. The next step consists of coupling Equation (2) built for both the substrate and the coating to create a bi-layer material. A condition to guarantee model consistency is to impose that the deformation in both the substrate and the coating are equal at the junction between the two layers, i.e., \(\left[\Delta\;\epsilon_{x}\right]_{a}=\left[\Delta\;\epsilon_{x}\right]_{s}\) where subscripts \(a\) and \(s\) correspond to coating and substrate, respectively. To eliminate the stress in the substrate from Equation (2) and have the stress in the coating be the sole unknown, we know that at equilibrium, the sum of forces is null:  
\[h_{a}\left[\Delta\sigma_{x}\right]_{a}+h_{s}\left[\Delta\sigma_{x}\right]_{s}=0 \tag{3}\]  
with \(h_{a}\) and \(h_{s}\), the thicknesses of the coating and the substrate.