Delamination modeling at the inter-ply scale in unidirectional composite laminates
Résumé
Composite materials such as carbon/epoxy laminates made of unidirectional plies are nowadays widely used in the aeronautic industry due to their good specific mechanical properties. However, they still suffer of early delamination when subjected to low velocity impact for example. For that, toughened materials have been developed to improve the properties related to delamination. One solution among others has been to incorporate polyamide particles in the inter-ply region [1, 2]. Under macroscopic loading conditions of mode II type, this solution gives good results, while for mode I the toughening effect is not always achieved. A model developed at the inter-ply scale would be interesting to clarify the link between macroscopic loading conditions and local dissipative mechanisms and therefore develop robust toughening solutions. Delamination consists in crack propagation between two plies. Typical delamination tests aim to achieve pure-mode macroscopic loading conditions and to quantify the energy dissipated by crack propagation. The generalization of these results to more complex loading conditions is not straightforward, as the link between the macroscopic mode and the local dissipation mechanisms is not simple (see for example [3]). The relation between matrix properties and macroscopic delamination has been studied experimentally by [4]. In mode I, the crack mainly goes out of the inter-ply zone to the weakest link which is the fiber/matrix interface. In mode II, the crack is formed from successive hackles leading to a large process zone. The simulation of such a macroscopic crack therefore needs for the micro simulation to go further than the first micro crack. Some plasticity is accompanying this mechanism. In epoxy matrices, the size of the plastic zone ahead of a crack tip can be roughly estimated to 10 microns to 20 microns which is then the optimal thickness of the inter-ply region to ensure maximum dissipation. Note that in general, this plastic zone is confined by the surrounding plies which are very stiff in the fiber’s directions. The purpose of this paper is to discuss the models available to describe and simulate properly the physics of degradation in the inter-ply region. For that, available models in Abaqus are studied and their limits discussed especially regarding localization and scale transition representativity. To overcome the difficulty to represent correctly dissipated energies during cracking, a phase-field model [5] has been developed in the framework of a thermo-mechanical coupled problem. This leads to a very simple implementation in Abaqus. Several classical representative examples are treated (DCB and CLS testing configurations) to illustrate this approach.