An Adhesive Bonded Single Lap Joint Model

This paper investigates the mechanical behavior of lap joints by modeling adhesive damage and fracture using the cohesive crack technique. To improve predictive accuracy, the study adopts a linear softening law for the adhesive shear traction-separation response and neglects peeling effects. The main goal is to derive closed-form solutions for the mechanical behavior of lap joints under monotonic loading, reassess traditional failure criteria, and develop a framework linking failure mechanisms to joint length. For short joints, where the adhesive shear traction distribution is nearly uniform, joint strength can be accurately estimated using the average stress method. In contrast, for very long joints, the tractions become highly localized, making the Griffith energy-based fracture criterion a more suitable predictor of failure. The model further shows that a crack in the adhesive layer can only nucleate and propagate when the joint bonded length exceeds a critical value $L^{\ast }$, which is specific to each adhesive-adherend system. These theoretical results are validated through two-dimensional finite element simulations, which confirm the accuracy and predictive power of the proposed approach.