A Three-Phase Shear-Lag Model for Longitudinal Cracking of a Ceramic Matrix Composite Ply With Thick Fiber Coatings

During progressive cracking of cross-ply ceramic matrix composites (CMCs), load is transferred from the fiber to the matrix in the longitudinal (0 deg) ply via shear through a compliant interphase layer, also referred to as the coating. In the material system of interest, this coating has significant thickness relative to the fiber diameter. The damage process in the cross-ply CMC is observed to be as follows: (1) elastic deformation, (2) cracking of the transverse plies, (3) matrix cracking within the longitudinal plies, (4) failure of longitudinal fibers, and (5) pullout of the cracked fibers from the matrix. In this paper, the focus is on the longitudinal (0 deg) ply. Existing shear-lag models do not fully represent either the stress transfer through the coating or the true accumulations of shear and normal stresses in the matrix. In the current study, a model is developed that takes into account both of these factors to provide a more accurate, analytical representation of the stress distribution and progressive damage accumulation in a longitudinal CMC ply.