Three-parameter, elastic foundation model for analysis of adhesively bonded joints

Abstract

A novel three-parameter, elastic foundation model is proposed in this study to analyze interface stresses of adhesively bonded joints. The classical two-parameter, elastic foundation model of adhesive joints models the adhesive layer as a layer of normal and a layer of shear springs. This model does not satisfy the zero-shear-stress boundary conditions at the free edges of the adhesive layer due to the inherent flaw of the two-parameter, elastic foundation model, which violates the equilibrium condition of the adhesive layer. To eliminate this flaw, this study models the adhesive layer as two normal spring layers interconnected by a shear layer. This new three-parameter, elastic foundation model allows the peel stresses along the two adherend/adhesive interfaces of the joint to be different, and therefore, satisfies the equilibrium condition of the adhesive layer. This model regains the missing “degree of freedom” in the two-parameter, elastic foundation model of the adhesive layer by introducing the transverse displacement of the adhesive layer as a new independent parameter. Explicit closed-form expressions of interface stresses and beam forces are obtained. The new model not only satisfies all boundary conditions, but also predicts correctly which interface has the strongest stress concentration. The new model is verified by continuum models existing in the literature and finite element analysis. The new three-parameter, elastic foundation model provides an effective and efficient tool for analysis and design of general adhesive joints.