engleski

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 study 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 = Jc for a double cantilever beam (DCB) loaded with moments and their difference is extremely small for a DCB loaded with forces. For a flat R-curve (constant Ω over the interface), it is possible to derive close-form expressions for Ω, which are equal to the critical value of the J integral, Jc. For a rising R-curve simulated by a CZM with variable Ω, we show that neither Jc nor Gc are equal to the value of Ω at the current crack tip, but both of them are close to it even for very ductile interfaces. More generally, we show that the proof that Jc is equal to the non- linear 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, a_eq, 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. Hence, the closed-form part of the solution can be used as a very accurate and ‘industry friendly’ data reduction scheme because it does not require the measurement of end rotations, needed for Jc, and of the crack length, required in all current standards. For a DCB loaded with forces or moments, formulae for the fracture resistance based on Euler-Bernoulli’s and Timoshenko’s beam theories have been derived and their results compared. For the latter, we derive closed-form formulae for the evaluation of a_eq and Jc, which are not available in the literature. All our arguments are supported by analyses of the results of a wide range of ‘virtual experiments’, in which accurate numerical simulations are conducted on DCB specimens used in real experiments.

DCB test ; mode-I delamination ; data-reduction schemes ; fracture toughness ; crack-length measurement ; cohesive-zone models

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