Multi-particle modelling for the prediction of delamination in multi-layered materials

To approach the three-dimensional stress state in multi-layered composites, a laminate theory which considers a kinematic field per layer (particle) is used. Thus, interlaminar stresses are naturally introduced to carry out the equilibrium conditions of the plies. These stresses have a physical meaning and represent the exact out-of-plane 3D stresses calculated at the interface between two layers. These simplified models are able to provide finite interfacial stresses, even at the free edge of a structure. The first part of the paper describes the model and shows its validation by means of a comparison with finite element calculations. The model can involve inelastic strain fields in the layers and fields of displacement discontinuities at the interfaces. These inelastic fields, such as interface sliding, are assumed to be known by the user. The second part proposes some relevant criteria able to predict delamination initiation in some angle-ply laminates based on the model results. The laminates considered here are elementary cross-plies ±( θ n ) s with θ < 30° to avoid more complicated phenomena as fiber rotation, transverse cracking or other non-linearity. The three criteria proposed herein integrate naturally interface stresses, and have been confronted to experimental results in mode III, for a ±( θ n ) s. The first criterion is based on the calculation of the maximum interfacial shear stresses. The second criterion is based on the analytical calculation of the strain energy release rates in a delaminated multi-layer. The third criterion is based on an experimental observation: a critical interface sliding value seems to govern delamination onset during tensile tests. Two plastic models were proposed for relating the interface sliding with the interfacial stresses: perfect plasticity and plasticity with a linear softening. Brittle linear elastic (criteria 1 and 2) and plastic analyses both provide accurate predictions. A more detailed study of this presumptive contradictory assertion is lastly led.