Modeling fatigue life of composite laminates: A statistical micro-mechanics approach

Modeling the stiffness degradation associated with intra-laminar damage is an essential aspect of many fatigue models for laminated polymer matrix composites. The present paper therefore investigates the effect of intra-laminar micro-cracks on the effective stiffness of unidirectional plies. Following a brief review of the damage mechanisms observed in laminates under fatigue loading as well as current approaches for fatigue modeling, a Monte-Carlo algorithm is employed to generate random arrangements of unidirectional carbon fibers embedded in a polymer matrix. The cross sections of these geometries are tessellated by means of Voronoi-cells and De/aunay-triangles to create potential crack paths and meshed using finite volume elements. The finite element models are then subjected to cyclic transverse strain via periodic boundary conditions. A multi-axial fatigue life criterion formulated on the micro-scale is used to model the damage process of the material in a simplified manner. For each simulated state, the effective stiffness properties of the composite are determined. Material behavior is then statistically analyzed for samples of random fiber arrangements containing different numbers of fibers. In general, the effective material behavior is monoclinic showing coupling between out of plane shear and transverse normal deformation. In the initial undamaged state, some but not all engineering stiffness parameters can be assumed to follow a normal distribution. As expected, a statistical size effect on the fatigue life to crack initiation can be demonstrated. For increasing severity of the simulated damage, a linear correlation is observed between most of the primary engineering stiffness parameters such as the elastic and shear moduli while this is not the case for many of the normal-shear coupling parameters.