Probabilistic strength based matrix crack evolution model in multi-directional composite laminates under fatigue loading

A model to predict the matrix crack evolution in multi-directional (MD) polymer matrix composite laminates under in-plane fatigue loading is presented in the current work. Unlike matrix crack evolution under static loading, the matrix cracks in off-axis plies do not form tunneling cracks under fatigue loading; rather, they initiate and grow with increasing load cycles. A probabilistic strength based criterion for matrix crack initiation in off-axis plies based on a Weibull distribution for in situ ply strength variation has been used. An oblique co-ordinate based shear lag analysis has been used to estimate the stresses in the cracked laminate. Smith Watson Topper (SWT) parameter has been used to model the number of cycles to initiate the first matrix crack, and log-normal probability distribution has been used to handle the scatter in crack initiation life. The matrix crack growth rate has been modeled using Paris law based on mixed mode effective stress intensity factor. Using the crack initiation curve and strength degradation based on Palmgren-Miner damage rule, new crack initiation has been simulated. Few parameters needed for the threshold stress intensity and saturation crack spacing have been identified from a reference stress data of cross-ply laminate. The crack density evolution has been simulated for cross-ply and MD-laminates under various constant amplitude in-plane fatigue stress levels. The matrix crack density evolution and its stiffness degradation predictions with the number of cycles have been compared with existing experimental values. A good correlation is found to exist between the experimental data and predictions for both cross-ply and MD-laminates.