Correction Factors to Biaxial Bending Strength of Thin Silicon Die in the Ball-on-Ring Test Due to Contact Nonlinearity Effect

The ball-on-ring test (BoR) in ASTM F394-78 is one of the standard tests for biaxial bending. However, from the literature, when the relatively thin silicon dies are tested, this test suffers from a contact-nonlinearity effect and thus results in overestimated maximum stress calculated by the theoretical solution. This study is to reexamine this issue experimentally, theoretically, and numerically by taking into account the specimen thickness effect on the maximum stresses and deflections. Then it proposes new correction factor equations to the linear theoretical solutions, based on the numerical fitting results of the geometric nonlinear finite element solutions. Those correction factor equations proposed in this study are material-property independent but specimen thickness-dependent. It has been proved that the BoR test using the conventional theory associated with the proposed correction factors can successfully determine the bending strength of the thin silicon dies, which mostly fails in the contact nonlinear region.