The cracked lap shear specimen revisited—a closed form solution

Abstract

This paper revisits the cracked lap shear specimen and reports a closed form solution to determine three fracture parameters, the energy release rate, the fracture mode mixity, and the fracture efficiency parameter. The solution is based on a beam-column approach pioneered by Goland and Reissner. Because of the geometrically nonlinear nature of this specimen, it is found that the fracture parameters are functions of five independent nondimensional parameters. The closed form solution reported in this paper provides a simple and useful tool to design the cracked lap shear specimen and to understand the behavior of this test geometry. The results in this paper suggest that to design a specimen with an energy release rate less dependent on the crack length, the adherend thickness should be small compared to the specimen length, and the thicker or stiffer adherend should be used as the strap. For a specimen of unequal adherend thickness, using the thicker adherend as the strap would significantly reduce the likelihood of yielding in the adherend. Compared with the finite element analyses found in the literature, the closed form solution shows good agreement in energy release rates, but less satisfactory agreement in fracture mode mixities. Finally, the closed form solution is used to give a reasonable explanation of anomalous debond behavior in a series of fatigue experiment using the cracked lap shear specimen.