A matrix failure criterion independent of empirical parameters for brittle fiber-reinforced composites

Based on Hashin's fracture plane assumption, a matrix failure criterion for brittle fiber-reinforced composites is proposed. The failure function is expressed as a quadratic polynomial of the stress components on the fracture plane. The unknown coefficients in the failure criterion are only calibrated by the three basic strengths of unidirectional composites, i.e., the transverse tensile strength, transverse compressive strength, and longitudinal shear strength, thus overcoming the limitation of requiring empirical parameters in most previous matrix failure criteria. Especially, under plane stress states (${\sigma }_{22},{\tau }_{21}$), an analytical solution for the fracture angle of unidirectional composites can be provided. The prediction results of the proposed criterion are consistent with a large number of experimental data, confirming its applicability. In addition, the study establishes the relationship among the three transverse basic strengths ($Y_t$, $Y_c$ and $S_{23}$). It can be used to predict $S_{23}$ which is difficult to measure experimentally.