An analytic model for PTH/PWB stress due to three-dimensional forces generated by symmetric compliant-pins

Analytical models are presented, to address the deformations and stresses caused in PWBs by compliant-pins used for solder-less component-interconnection technologies. These models are proposed for rapid-assessment capabilities when designing such interconnect assemblies for reliability. This model is based on mechanistic understanding of the physics of the pin insertion process. Previous studies in the literature focused on analytic solutions for the in-plane (radial and tangential) forces generated in the PWB & PTH due to the compliant-pin. In this study, the approach is extended to three-dimensional solutions by approximately including the axial forces generated by friction during the compliant-pin insertion process. The solution is linear elastic and is based on Fourier series expansions of the contact forces generated by the compliant-pin. This approximate solution therefore is appropriate for rapid-assessment capabilities for parametric trade-off studies and design guidelines. Model parameters include PWB hole-diameter, PTH plating thickness, and the PTH and PWB material properties. The model can be used with any mirror-symmetric compliant-pin geometry and stiffness. The numerical predictions allow us to quantify the dependence of the stresses in the PWB on compliant-pin geometry and on the PTH construction.