Non-linear macroscopic response of fiber-reinforced composite materials due to initiation and propagation of interface cracks

In the present work the effects of micro-crack initiation and evolution under mixed mode loading conditions on the macroscopic response of elastic periodic composite materials, are investigated. To this end an innovative micro-mechanical approach based on homogenization techniques and adopting stress based failure criteria in conjunction with fracture mechanics concepts is presented, taking into account also the influence of unilateral frictionless contact between crack faces. The crack propagation process, including also the competition between progressive interface cracking and kinking out of the interface, is driven by the maximum energy release rate criterion adopted to predict incremental changes in crack path, whereas a generalized coupled stress-energy criterion is adopted to predict crack initiation under mixed mode conditions. A novel strategy for quasi-automatic simulation of arbitrary crack initiation and propagation in 2D finite element models has been implemented, accounting for mixed mode loading conditions and taking advantage of a generalized J-integral formulation. Numerical applications are developed with reference to a 2D model of a fiber-reinforced composite material with an initially undamaged inclusion/matrix interface. The capability of the proposed approach is shown by computing the composite nonlinear macroscopic response for prescribed uniaxial and shear macro-strain paths, assuming a crack initiation at the fiber/matrix interface. The effects of loading in the transverse fiber direction, inclusion size and fiber volume fraction, are also examined.