Model for evolution of quasi-static transverse cracking in multiple plies of multidirectional polymer composite laminates

Quasi-static damage in multidirectional polymer composite (PMC) laminates developing during manufacturing and quasi-static loading degrades the modulus and strength. A model to predict simultaneous evolution of quasi-static transverse cracking in multiple plies and its effect on modulus of multidirectional PMCs is presented. A 3-D variational analysis formulating the in-plane and out-of-plane stresses of the plies in occurrence of multiple cracking has been developed to work within a lamination theory-based model framework. The stress state in the plies is determined using the lamination theory during an incremental change in loading. The strain energy, determined using this stress state, is compared to strain energy-based failure criteria to determine if a ply cracks after the increment. If crack is predicted, crack density of the ply is updated and the variational analysis is used to determine the perturbation in ply stresses due to cracking. The new stress state is used to determine the laminate modulus after cracking and the ply stresses for the next increment. This procedure is repeated to determine the crack evolution and modulus until reaching the desired load. Model predictions compare very well with experimental results for a [±θm/90n]s laminate at two elevated test temperatures of 80 °C and 180 °C.