Three-dimensional (3-D) finite element analyses have been performed for square assemblies, each with a homogeneous component attached to a homogeneous substrate by an areal array of solder joints to test the assumption of replacing the square geometry of the component, substrate, and joint array by equivalent circular disks. Three different square assemblies, namely a Plastic Ball Grid Array (PBGA), a Ceramic Ball Grid Array (CBGA), and a Flip-Chip package have been considered for comparing the maximum shearing displacement, obtained from the 3-D numerical model, with the analytical estimate, which is based on an axisymmetric model. Comparison of the analytical and the finite element results indicates excellent agreement in estimating maximum shearing displacement, provided that the array stiffness is sufficiently smaller than the Young’s moduli of the component and substrate materials. These convincing comparison results indicate that the analytical approach may in some applications provide a useful alternative to the more expensive and time-consuming finite element method.

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