Material-tailored adhesively bonded multilayers: A theoretical analysis

Multimaterial multilayered systems such as bonded/welded joints, adhesive anchors, electronic assemblies, coatings and micro- and nano-scale fiber reinforced composites, often exhibit interfacial failure during service as they experience steep stress gradients at the interfaces. In this study, a theoretical framework for the stress analysis of material-tailored adhesively bonded multilayers is presented. Single-lap joints (SLJs) even under tensile loading undergo large lateral defection and rotation as a result of non-collinear load-path, giving rise to stress concentrations near the free edges whereas the resulting stresses in SLJs with compliance-tailored adherends are influenced by the net effect of reduced bending moment and reduction in bending stiffness of the joint. Using Euler-Bernoulli and Timoshenko beam bending theories, shear force (SF) and bending moment (BM) along the overlap length of the adherend-tailored SLJs are evaluated. Subsequently, using SF and BM obtained above as boundary conditions, a force-based sandwich model for an unbalanced joint within the context of 2D elastostatics is formulated to predict adhesive stresses. The model predictions are validated by finite element results and are found to be in good agreement. Reduction in adhesive shear and peel stress concentrations of about 46% and 42%, respectively, was observed for joints with compliance-tailored adherends at sub-critical bondlength (l=0.2lcr) relative to baseline joints, where lcr is the minimum bondlength required for a baseline joint to enable shear-dominated load transfer. At critical bondlength, i.e., l=lcr (250 mm for the parameters considered here), 89% and 68% reduction in adhesive shear and peel stress concentrations, respectively, was observed. Furthermore, the model is extended to evaluate the combined effect of compliance-tailoring of both adhesive and adherend and found reduction in adhesive shear and peel stress concentrations of about 90% and 74% respectively at l=lcr. The results of this study provide guidelines for the design of material-tailored multilayers and can be readily extended to study effect of anisotropic tailoring of adherends as the formulation allows for the variation of adherend's modulus in both longitudinal and transverse directions.