Stress near apex of dissimilar material with bilinear behavior

This study presents an analytical solution for the asymptotic stress field near the apex of a wedge composed of dissimilar materials exhibiting elastic and/or plastic deformation that can be described by a bilinear material model. Under the same assumptions, previous investigations resulted in eigenvalue differential equations that were not amenable to analytical integration. The present formulation avoids the numerical integration of such equations. After establishing its validity, the corner of the junction formed between a solder ball and a substrate was considered in order the study the effect of the hardening parameter on the strength of the singular stress field. Also, this formulation provides the exact form of the displacement field, which permits the construction of a global element to capture the correct strength of the singular stress field in regions with material and geometric discontinuities.