A numerical prediction of failure probability under combined compression-shear loading for unidirectional fiber reinforced composites

Microbuckling (MB) is the dominant failure mode in unidirectional fiber reinforced polymers (FRPs) under predominantly compression loads. MB is highly sensitive to material imperfections and nonlinear material behavior. Material imperfections are spread in the form of fiber misalignment in the volume of the material. Because of high sensitivity of MB failure to the fiber misalignment, the MB strength shows uncertainty. It has been shown in the literature that the nature of the misalignment in FRPs is correlated random, where the misalignment of a fiber depends on the other fibers in its surroundings. To represent the misalignment in numerical models for the prediction of MB strength while preserving the spatial correlation information, the spectral representation method is employed in this investigation. For this purpose spectral densities were calculated for measured distributions of the fiber misalignment using computed tomography scans on specimens. This information was subsequently used to generate realistic distributions of the fiber misalignment in numerical modeling of FRPs for prediction of MB strength. Quantification of uncertainty in MB failure is essential for reliable design practices. Therefore, the current investigation aims for a probabilistic prediction of MB failure under axial compression and combined compression-shear loads. Different model series, each containing a large number of realizations, were developed based on spectral densities calculated from the measurements of the fiber misalignment from different specimens. The resulting distributions of strengths under the axial compression load case from these model series are compared and a suitable model series was chosen for further analysis. The stress-strain response under different combinations of combined compression-shear loads is discussed. A comparison of numerically predicted strengths against experimentally obtained results under the axial compression loads is included. Since the sizes of the model and the experimental specimen were different, this comparison was performed on the basis of a scaling law for the compression strength. Finally, the numerically determined probabilistic failure envelopes in stress and strain spaces are presented with lower percentiles of distributions of failure. The failure enveloped are also compared against classical failure criteria from the literature to highlight the limitations of the classical criteria.