Analysis of displacement path dependence in mixed mode cohesive law

In the present work, a general theoretical analysis is presented and novel mathematical expressions are derived to obtain the cohesive law of adhesive joints under mixed-mode loading. It is theoretically stated that the mixed-mode truss-like cohesive laws, where the stress vector is forced to be parallel to the displacement vector, cannot adequately describe the fracture process when the displacement path is non-linear. Finally, an experimental proof is given to show that in a Mixed Mode Bending test the difference between the phase angles of the stress vector and displacement differential vector must be taken into account when the displacement path becomes nonlinear, so that the cohesive stress will no longer be a function only of the magnitude of the displacement.