On Gc, Jc and the characterisation of the mode-I fracture resistance in delamination or adhesive debonding

We focus on the mode-I quasi-static crack propagation in adhesive joints or composite laminates, where inelastic behaviour is due to damage on a relatively thin interface that can be effectively modelled with a cohesive-zone model (CZM). We studied the difference between the critical energy release rate, Gc, introduced in linear elastic fracture mechanics (LEFM), and the work of separation, Ω, i.e. the area under the traction-separation law of the CZM. This difference is given by the derivative, with respect to the crack length, of the energy dissipated ahead of the crack tip per unit of specimen width. For a steady-state crack propagation, in which that energy remains constant as the crack tip advances, this derivative vanishes and Ω=Gc. Thus, the difference between Ω and Gc depends on how far from steady-state the process is, and not on the size of the damage zone, unlike what is stated elsewhere in the literature. Therefore, even for very ductile interfaces, Gc=Ω for a double cantilever beam (DCB) loaded with moments and their difference is extremely small for a DCB loaded with forces. We also show that the proof that the critical value of the J integral, Jc, is equal to the nonlinear energy release rate is not valid for a non-homogeneous material. To compute Gc for a DCB, we use a method based on the introduction of an equivalent crack length, aeq, where the solution is a product of a closed-form part, which does not require the measurement of the actual crack length, and of a corrective factor where the knowledge of the actual crack length is required. However, we also show that this factor is close to unity and therefore has a very small effect on Gc.