Analysis of stresses in adhesive joints applicable to IC chips using symbolic manipulation and the numerical method

Abstract

In this study, a concentrated force is applied to both adherends bonded by an adhesive under pin-pin boundary conditions. First a mathematical model is derived with governing equations and boundary conditions. These complicated, and analytically problematic, coupled equations are solved numerically using symbolic manipulation and singular value decomposition (SVD). Also discussed are the effects of major factors, including the relative thickness of adherends, joint length and the action point of the concentrated force on the peel and shear stresses in the adhesive layer. This study identifies the conditions under which the upper adherend without breakage can be fully separated from the lower adherend. Particularly, it is found that the thickness of the lower adherend should be greater than ten times that of the adhesive layer but less than one-third that of the upper adherend, the adhesive layer should be relatively thin (h(a) <= 0.01 mm), and the adhesive joint should be relatively short (thickness to length ratio gamma(1) >= 0.08).