Numerical Simulation of Fatigue Crack Growth in Microelectronics Solder Joints
K. Kaminishi, M. Iino, H. Bessho, M. Taneda

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 1, No. 1, pp. 107-110, 2000
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Keywords solder joints, life prediction, low cycle fatigue, finite element method
Abstract An FEA (finite element analysis) program employing a new scheme for crack growth analysis is developed and a prediction method for crack growth life is proposed. The FEA program consists of the subroutines for the automatic element re-generation using the Delaunay Triangulation technique, the element configuration in the near-tip region being provided by a super-element, elasto-inelastic stress analyses, prediction of crack extension path and calculation of fatigue life. The FEA results show that crack extension rate and path are controlled by a maximum opening stress range,$\Delta \sigma_{\theta \max}$, at a small radial distance of$r = d$, where$d$ is chosen to be a grain diameter's distance, 3.5$\mu m$, in solder material. The experimentally obtained crack extension rate is found to be related to$\Delta \sigma_{\theta \max}$ in FEA as$ da/dN = \beta\left[\Delta \sigma_{\theta \max} - \gamma\,\right]^\alpha$, where $\alpha=2.0$,$\beta= 4.5\times 10^{-9}$$mm^5\!/N^2$ and$\gamma = 98$$MPa$ are determined for all test conditions. The calculated values of crack extension life by the FEA using the above equation are in good agreement with the experimental ones and are independent of the joint types.
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