A novel traction–separation law for the prediction of the mixed mode response of ductile adhesive joints

A new traction–separation law that represents the constitutive relation of a ductile adhesive material in Mode I and Mode II is developed and introduced in interface elements for the finite element analysis of adhesive joints, within the framework of Cohesive Zone Modeling (CZM) techniques. The proposed law is based on the embedded process zone approach and is formulated to address the mixed-mode loading and fracture of adhesively bonded joints.

This law is first used for the description of the pure Mode I (opening) and pure Mode II (sliding) loading and fracture and then it is integrated into a developed mixed-mode model in order to account for the dependence of the separate pure mode laws. The traction increasing part of the law is described by an exponential function, whereas the softening part is described by a linear decrease.

Prediction of damage initiation is established through the nominal quadratic stress criterion, whereas the damage propagation is established through the linear energetic criterion. Experimental results from steel-to-steel single lap and Double Strap Joint configurations have been utilized for the validation of the proposed law and mixed-mode model.

Comparisons are also provided from finite element analyses with the already known trapezoidal law and with the PRP (Park–Paulino–Roesler) model. The proposed law adequately captures the elastoplastic behaviour of the tested adhesive joints, in terms of their global response. Additionally, the strength of the tested joints is predicted with great accuracy.