Optimal dual actuator loading configurations for extracting mixed-mode cohesive relations from interacting beams

Cohesive zone models are often used in analyses of interfacial fracture where the damage process zones are relatively large and can be described by proper traction-separation relations. Successful implementation of the cohesive zone modeling depends upon the veracity of the interfacial traction-separation relations used to represent the interactions across the interface. To extract the generally mixed-mode traction-separation relations experimentally, we compare various loading conditions for simultaneous extraction of the normal and shear interactions using laminated beam specimens subjected to asymmetric end loading. We develop a mixed-mode double cantilever beam model with linear normal and shear interactions between the contact surfaces of the beams. Four different loading conditions are considered by controlling the end forces, end displacements, end moments, or end rotations. The model is validated by finite element simulations. Rotation control is found to be the optimal loading configuration, based on a condition number that reflects desirable experimental characteristics for extracting the traction-separation relations. By applying uneven end rotations, the whole range of mode-mix with combined normal and shear interactions can be extracted, while ensuring stable crack growth.