Analysis of adhesive-bonded single-lap joint with an interfacial crack and a void

We use the first-order shear deformation plate theory (FSDT) to analyze stresses in two layers bonded together with an adhesive as recommended by the ASTM D3165 standard, except that we also include a void within the adhesive. Depending upon the number of notches and voids, the specimen is divided into several regions. Assuming that a plane strain state of deformation prevails in the specimen, we write the balance of forces and moments for each section and impose the continuity of displacements, forces and moments at the interfaces between the adjoining sections. By taking the Laplace transform of the resulting ordinary differential equations we get a system of simultaneous linear algebraic equations that can be easily solved. The inverse transform of the solution of the algebraic equations provides stresses and displacements in the adhesive and the substrates, which are found to agree well with those obtained by the finite element method (FEM). It is also found that the order of the stress singularity at the corner of the free surface of the adhesive and the substrate, and the strain energy release rate computed from the solution of the problem with the FSDT agree well with those determined from the solution of the problem by the FEM. We note that the computational effort required to analyze the problem with the FSDT is considerably less than that needed to solve the problem by the FEM.