An Inelastic Analysis Methodology for Bonded Joints with Shear Deformable, Anisotropic Adherends

Abstract

The development of a one-dimensional analysis method for evaluating adhesively bonded joints composed of anisotropic adherends and adhesives that exhibit nonlinear material behavior is presented. The strain and resulting stress fields in a general, bonded joint overlap are determined by using a variable-step, finite-difference solution algorithm to iteratively solve a system of first-order differential equations. Applied loading is given as a system of combined extensional, bending, and shear loads that are applied to the edge of the joint overlap. Adherends are assumed to behave as linear, cylindrically-bent plates using classical laminated plate theory that includes the effects of first-order transverse shear deformation. This provides a capability for modeling differences in the transverse shear modulus between each adherend. Using a total plasticity theory and a modified von-Mises yield criterion, inelastic material behavior is modeled in the adhesive layer. Results for the proposed method are verified using the single-lap joint geometry against previous results from the literature and shown to be in excellent agreement. Convergence of the strain and stress fields determined using the finite-difference solver are described as a function of the number of evaluation points along the length of the joint. Additionally, design studies using the single-lap joint are presented that investigate the effects of changes to the joint overlap, adherend thickness, laminate stacking sequence of the adherend, adherend material properties, and adhesive material properties. Results from the design studies established a nonlinear relationship between changes in the bending and axial stiffness of the adherends due to laminate ply manipulations and a reduction in the inelastic adhesive strain and shear stress responses. Additionally, analyses performed on the bonded joint models that had a difference in the transverse shear stiffness between the upper and lower adherends displayed a minimal effect on the adhesive strain and stress responses.