Stress Analysis of Surface-Mount Interconnections Due to Vibrational Loading

Recently, accelerated testing of surface mount interconnects under combined temperature and vibration environments has been recognized to be a necessary activity to ensure enhanced test-time compression. Successful use of vibration stresses requires a clear understanding of the correlation between vibrational damage and thermomechanical damage in surface mount solder joints. Hence, fatigue due to vibrational loading is important and accurate quantitative models are required to model effects due to vibrational fatigue. The proposed analysis in this paper contributes towards development of such quantitative models. This paper presents an approximate method to analyze stresses in surface mount solder joints subjected to vibration loading, using a generalized multidomain Rayleigh-Ritz approach (Ling and Dasgupta, 1995). The advantage of this approach is in its computational efficiency, compared to general-purpose finite element methods. Ling developed this approach in the context of thermomechanical stress analysis of solder joints. In this paper, the technique is modified and adapted for analyzing stresses caused by out-of-plane flexural dynamic modes of the printed wiring boards (PWBs). The analysis uses a two-step procedure where the local PWB curvatures are first estimated and the resulting deformations in the solder interconnect are then determined. The input boundary conditions for the first step are the bending moments in the PWB due to random vibrations. The stiffness of the interconnect assembly is then predicted using an energy method and curved-beam analysis. The bending moment and the computed stiffness of the interconnect assembly are then used to predict the local curvature of the PWB under any given surface-mount component by using an eigenfunction technique developed by Suhir (Suhir, 1988). In the second step of the analysis, the local curvature of the PWB is used as a boundary condition to predict the state of deformations, stresses, and strains in the solder joint using a modified version of the multidomain Rayleigh-Ritz approach. The overall method is applied to a specific example (J-lead solder joint) for illustrative purposes, and compared to finite element predictions for validation.