A 3D ductile constitutive mixed-mode model of cohesive elements for the finite element analysis of adhesive joints

In this paper, a new traction–separation law is developed that represents the constitutive relation of ductile adhesive materials in Modes I, II, and III. The proposed traction–separation laws model the elastic, plastic, and failure material response of a ductile adhesive layer. Initially, the independent-mode proposed laws (loading and fracture in Modes I, II, and III) are mathematically described and then introduced in a developed formulation that simulates the interdependency of the mixed-mode coupled laws. Under mixed-mode conditions, damage initiation is predicted with the quadratic stress criterion and damage propagation with the linear energetic fracture criterion. For verification and validation purposes of the proposed laws and mixed-mode model, steel adherends have been adhesively bonded with a structural ductile adhesive material in order to fabricate a series of single and double strap adhesive joint configurations. The specimens have been tested under uni-axial quasi-static load and the respective force and displacement loading history have been recorded. Corresponding numerical and experimental results have been compared for each joint case, respectively. Additionally, the developed stress fields (peel, in-plane, and out-of-plane shear) are presented as they evolve during the loading of both joint cases.