Monte Carlo simulation with energy-based matrix and transverse crack growth model for cross-ply ceramic matrix composites under static tensile behavior

A simulation model was developed to represent the initial pseudo-ductile behavior of the stress - strain relationship and the multiple matrix and transverse crack growth processes in cross-ply ceramic matrix composites (CMCs), accounting for the interaction of the 0 degrees and 90 degrees layers owing to matrix and transverse cracks at arbitrary positions. The model incorporates formulations of the stress distribution, fiber-matrix interface slip length, and energy changes before and after matrix and transverse crack formation. The multiple matrix and transverse crack growth were simulated using the Monte Carlo method, which represents random crack growth. Numerical simulations were conducted on three types of cross-ply laminates. The simulated results for the matrix crack density - strain relationship are in good agreement with the experimental results. The analytical results of the transverse crack density - strain relationship generally followed the test trend; however, they were overestimated in comparison to the test results. This discrepancy may be attributed to two mechanisms. For the [02/904]S analysis, perpendicular cracks in the tensile direction were assumed, whereas diagonal cracks were visualized in the experiment. In the [0/90]3S analysis, we could not account for the stress levels in the 902 layer on the stacking symmetry plane being lower than those in the 901 layer positioned away from the stacking symmetry plane. The simulated results for the stress - strain relationship aligned with the experimental results up to approximately 0.3% strain.