Increasing crack growth resistance for through-thickness matrix cracking and its role in suppressing ply cracking in thin-ply laminates

A new analysis is proposed, and verified, to quantitively explain the recent experimental observations of a transition from unstable to slow, stable through-thickness crack growth in cross-ply laminates, as the ply thickness is decreased to 40 µm. The approach is prompted by the observed stable rise of crack opening under increasing applied strain in micromechanical model simulations. Estimates of the energy release rates associated with these crack opening profiles clearly indicate an increasing value of crack growth resistance with crack extension, i.e. an R-curve effect. To verify that the thickness dependence of the matrix crack growth behaviour can be attributed to an R-curve effect, the R-curves were independently determined by micromechanical modelling and employed to predict the progression of through-thickness cracking in constrained plies of various thicknesses. These predictions are shown to agree closely with the reported experimental observations. The benefit of this new approach is that only one simulation is required to generate the R-curve, instead of requiring separate simulations for each ply thickness, thus considerably reducing the computational burden. This is particularly valuable for parametric studies to investigate the dependence on various material properties. As an illustrative example, the effects of changing the fracture energy of the epoxy matrix and the volume fraction of fibres present in the composite were investigated, and simple linear relationships were identified for both the steady-state value of the crack-growth resistance and the crack extension required to reach the steady state. Such relationships can further reduce the computational cost of micromechanical modelling, especially when the relevant material properties may not be available from direct measurements but can be reasonably estimated, as for cryogenic applications