Analytical Solutions for Stress Concentrations near a Fiber Break in Unidirectional Elastoplastic Composites

摘要

In this study, 3D analytical solutions of stress profiles are obtained for the fibers adjacent to a broken fiber in unidirectional composites with interfacial slip and matrix yielding. To this end, a hexagonal fiber-array model containing a broken fiber is considered in order to derive differential equations based on a shear lag model. By using this model, it is shown that all releYant material parameters are consolidated into a nondimensional characteristic length. The governing differential equations are then analytically solved under the condition that uniform axial deformation prevails in the second and third nearest-neighbor fibers, respectively. The resulting two analytical solutions are verified by numerically solving the governing equations more generally. The analytical solutions are, moreover, compared with the detailed 3D finite element computations reported recently.