Stress profiles and energy release rates around fiber breaks in a lamina with propagating zones of matrix yielding and debonding

We examine the stress profiles and initiation and propagation of interfacial damage around fiber breaks along a fiber within a planar lamina. The lamina contains a large number of equi-spaced fibers of the same stiffness, embedded in a matrix. The matrix is initially elastic, but can yield plastically, and at a critical matrix shear strain can debond from the fiber and slide frictionally. The coexistence of these three zones is motivated by experimental observations on idealized, epoxy-matrix microcomposites. We use our recently developed quadratic influence superposition (QIS) technique to calculate: (1) stress and strain profiles in the fibers and matrix, (2) the extent of the yield and debond zones, and (3) the energy release rate in propagating the damage under increasing applied load. We investigate the effects of fiber spacing, interfacial shear strength, matrix yield shear stress, critical debond shear strain, and frictional sliding stress. Results show that the growth of the yield and debond zones and the total energy release rate depend strongly on the inter-fiber spacing and on a combination of these material properties. Insight is provided into: (a) the inverse relationship between extent of debonding and the fiber spacing, (b) variations in the fiber stress profiles as a result of coexisting elastic, yield, and debond zones, and (c) interfacial parameters which give rise to stable longitudinal damage growth. For breaks arbitrarily spaced along a fiber, we obtain asymmetries in the lengths of the yield and debond zones around each break and corresponding alterations in the axial fiber tensile-stress profiles from the corresponding elastic case. A key result is that the total energy release rate varies strongly with the fiber spacing, thus suggesting that this quantity, as measured say from a single-fiber-composite test, is not an intrinsic quantity governing damage growth around a fiber break in a fibrous composite. Details of local geometry, fiber and matrix stresses and displacements are important. By such modeling one can assess trade-offs in toughness versus strength in large composites involving sequential statistical fiber fracture.