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High interfacial stresses near the edges of bonded joints are responsible for their debonding failure. This paper reports a new semianalytic stress-function variational approach to the interfacial stresses of a bonded joint, which is made of a straight tension bar covered with a reinforcing patch and subjected to mechanical loads and/or uniform change of temperature. The process introduces two interfacial shear and normal stress functions, which are correlated via the approximately same radius of curvature of the slender adherends. All the stress components in the joint are expressed in terms of the interfacial stress functions based on the classic Euler-Bernoulli beam theory and equilibrium equations of elasticity. Deformation compatibility of the joint is satisfied by minimizing the complementary strain energy, which leads to a fourth-order ordinary differential equation (ODE) of the interfacial shear stress function. The interfacial shear and normal stresses are determined explicitly and compared with those given by the elementary beam theory and FEM, respectively. The results gained in this study are applicable to scaling analysis of joint strength and optimization of structural design of joints. The present formalism can be extended conveniently to the mechanical stress and thermal stress analysis of various bonded structures, including adhesively bonded joints, composite joints, and recently developed flexible electronics. [ABSTRACT FROM AUTHOR]

Abstract: High interfacial stresses at the free edges of adherends are responsible for the debonding failure of adhesively bonded joints (ABJs). In this paper, a general stress-function variational method is formulated to determinate the interfacial shear and normal (peeling) stresses in ABJs in high accuracy. By extending authors’ prior work in stress analysis of bonded joints (Wu and Jenson, 2011), all the planar stress components in the adherends and adhesive layer of an ABJ are expressed in terms of four unknown interfacial stress functions, which are introduced at the upper and lower surfaces of the adhesive layer. A set of governing ordinary differential equations (ODEs) of the four interfacial stress functions is obtained via minimizing the complimentary strain energy of the ABJ, which is further solved by using eigenfunctions. The obtained semi-analytic stress field can satisfy all the traction boundary conditions (BCs) of the ABJ, especially the stress continuity across the bonding lines and the shear-free condition at the ends of adherends and adhesive layer. As an example, the stress field in an adhesively single-sided strap joint is determined by the present method, whose numerical accuracy and reliability are validated by finite element method (FEM) and compared to existing models in the literature. Parameter studies are performed to examine the dependencies of the interfacial stresses of the exemplified ABJ upon the geometries, moduli and temperature change of the adherends and adhesive layer, respectively. The present method is applicable for scaling analysis of joint strength, optimal design of ABJs, etc. [Copyright &y& Elsevier]