Stress concentrations around multiple fiber breaks in an elastic matrix with local yielding or debonding using quadratic influence superposition

Abstract

A new computational technique, called the quadratic influence superposition (QIS) technique, is developed to study the stresses around arbitrary arrays of fiber breaks in a unidirectional composite loaded in simple tension, and consisting of elastic fibers in a matrix, which is either elastic-perfectly plastic or which can debond at the interface leaving residual friction. The method involves extending a recently developed break influence superposition (BIS) technique, where to model the behavior of damaged (yielded or debonded) matrix elements, we use special compensating shear stress profiles and develop the corresponding influence functions. The QIS technique appears to be at least an order of magnitude more efficient than other numerical schemes as the computation time is tied mainly to the amount of damage, and it is more accurate than a simpler version of this technique developed earlier. In illustrative examples, the method determines the Mode I fiber and matrix stress distributions around a “center crack” consisting of up to 31 contiguous fiber breaks. Incremental treatment is needed to establish the extent of the inelastic regions and the results, which achieve excellent agreement with exact shear lag analyses, clearly show that QIS calculated these correctly. Results show that the extent of the matrix damage region increases approximately linearly with applied load and nonlinearly with the number of breaks. The stress concentrations and overload profiles along nearby unbroken fibers are altered as compared to the fully elastic case with magnitudes reduced but length scales increased.