Stress-function variational method for stress analysis of bonded joints under mechanical and thermal loads

Abstract

High interfacial stresses near the ends of adherends are responsible for debonding failure of bonded joints used extensively in structural engineering and microelectronics packaging. This paper proposes a stress-function variational method for determination of the interfacial stresses in a single-sided strap joint subjected to mechanical and thermal loads. During the process, two interfacial shear and normal (peeling) stress functions are introduced, and the planar stresses of adherends of the joints are expressed in terms of the stress functions according to the static equilibrium equations. Two coupled governing ordinary differential equations (ODEs) of the stress functions are obtained through minimizing the complementary strain energy of the joints and solved explicitly in terms of eigenfunctions. The stress field of the joints based on this method can satisfy all the traction boundary conditions (BCs), especially the shear-free condition near the adherend ends. Compared to results based on finite element method (FEM) and other analytic methods in the literature, the present variational method is capable of predicting highly accurate interfacial stresses. Dependencies of the interfacial stresses upon the adherend geometries, moduli and temperature are examined. Results gained in this study are applicable to scaling analysis of joint strength and examination of solutions given by other methods. The present formalism can be extended conveniently to mechanical and thermomechanical stress analysis of other bonded structures such as adhesively bonded joints, composite joints, and recently developed flexible electronics, among others.