Improved ball-on-elastic-pad and ball-on-hole tests for silicon die strength

For determining die strength, there are a couple of tests available in the literature, such as three-point and four-point bending, ball breaker, ball-on-the-ring, ring-on-the-ring, and recently proposed ball-on-elastic-pad (BoEP) and ball-on-the-hole (BoH) tests. It's well known that the test data reduction with theoretical formulations is more convenient and useful than that with numerical simulation results. However, those theoretical formulations have to be validated either by numerical simulation or experiments, before their applications. The objective of this study is to reevaluate and thus improve the existing BoEP and BoH tests for die strength using Hertzian contact theory, plate theories and finite element method (FEM). In this paper, the FEM analysis with "contact element" successfully has been verified with Hertzian contact theory and further proved that Hertzian contact theory can be employed to estimate the contact area for calculating die strength in both methods. The results indicate that the consistency between the theoretical formulation and FEM simulation for both tests exist only at the relatively large radius of ball and high applied loading, because the feasibility of the theoretical formulations requires large contact radius(> 0.06 mm) or area. For the BoEP test, the elastic moduli of elastic pad and ball have no obvious effect on the difference of maximum die stress between theoretical and FEM results. The theoretical solutions associated with contact radius determined by Hertzian contact theory are successfully proved for improving BoEP and BoH tests for die strength determination, and for better accuracy of die strength the ball with radius ranging from 2 mm to 4 mm is suggested.