Thermal stresses in a layered electrical assembly joined with solder are computed with plane strain, generalized plane strain, and three-dimensional (3D) finite element models to assess the accuracy of the two-dimensional (2D) modeling assumptions. Cases in which the solder is treated as an elastic and as a creeping material are considered. Comparison of the various solutions shows that, away from the corners, the generalized plane strain model produces residual stresses that are identical to those computed with the 3D model. Although the generalized plane strain model cannot capture corner stresses, the maximum stresses computed with this 2D model are, for the mesh discretization used, within 12 percent of the corner stresses computed with the 3D model when the solder is modeled elastically and within 5 percent when the solder is modeled as a creeping material. Plane strain is not a valid assumption for predicting thermal stresses, especially when creep of the solder is modeled. The effect of cooling rate on the residual stresses computed with creep models is illustrated.
Greens's functions for an anisotropic elliptic inclusion under generalized plane strain deformations
