Coupled stress and energy criterion for multiple matrix cracking in cross-ply composite laminates

Transverse cracking, i.e. matrix cracking in the off-axis plies of the laminate, is widely recognized as the first damage mode to appear in continuous fibre-reinforced composite laminates subjected to in-plane loading. Since transverse cracking has a great influence on the subsequent damage steps such as delaminations or oblique cracks, it is important to be able to predict its onset and growth accurately. In this paper, it is proposed to use a combination of the Coupled Criterion of Finite Fracture Mechanics (FFM) and the Equivalent Constraint Model (ECM) to predict the evolution of crack density with increasing applied load. Two formulations - a discrete formulation and a continuous formulation - are developed for the energy criterion within the Coupled Criterion. Some dependences between the two formulations are proved, which justifies the good agreement found by the models based on continuous formulations presented by other authors despite the inherent discrete nature of the phenomenon. Dependence of the failure load predicted by the Coupled Criterion on the layer thickness ratio and brittleness number (a structural parameter that characterizes a combination of the stiffness, strength, fracture toughness and the thickness of the cracked ply of the laminate) is examined and discussed for carbon/epoxy and glass/epoxy laminates. Finally, a comparison against experimental results shows a good agreement.