Time evolution of stress redistribution around multiple fiber breaks in a composite with viscous and viscoelastic matrices

We develop an efficient computational technique, called viscous break interaction (VBI), to determine the time evolution of fiber and matrix stresses around a large, arbitrary array of fiber breaks in a unidirectional composite with a matrix that creeps. The matrix is assumed to be linearly viscoelastic or viscous in shear following a power-law in time (creep exponent 0 ~< a ~< 1), and interface debonding or slip is not permitted. Such a law is applicable to polymeric matrices over a wide range of temperatures or to a viscous, glassy interphase in a ceramic composite with elongated microstructure. Specifically, we consider an infinitely large, 2-D composite lamina in the shear-lag framework of Hedgepeth, and the multiple break formulation is built on weighted superposition using influence functions based on the response to an isolated break. We apply the method to problems involving large transverse cracks (i.e., aligned, contiguous breaks), fully bridged cracks, and arrays of interacting, longitudinally staggered breaks. In each case we calculate the time evolution of stress concentrations and displacements of individual fibers. In comparing cracks vs spatially staggered breaks, the results reveal interesting contrasts in the time variation of both peak fiber stress concentrations and break opening displacements. In the latter case, we see behavior consistent with the three stages of creep, and show how the local fiber tensile stresses can rise (and subsequently even fall) at rates depending on various microstructural length scales. The motivation for developing VBI is to provide the computational framework for modeling the statistical features of the lifetime of composites in creep-rupture resulting from an accumulation of many fiber breaks and ultimately localization and collapse. © 1998 Elsevier Science Ltd. All rights reserved