Fracture of parallel elements

Abstract

A new approach to modeling of progressive damage of interphases in random particulate composites is proposed. In the model the interphases are represented by layers of springs whose stiffness parameters change as a result of damage associated with gradually increasing loading. Consequently, due to local degradation of the interphase, variation of these parameters over the inhomogeneity surface becomes progressively non-uniform. This, in turn, causes the effective properties of the composite to become increasingly anisotropic. To describe the effects of interphase damage on the overall properties of the composite three ideas proposed in the past with the authors’ participation are utilized. One is the Method of Conditional Moments (MCM), a statistical homogenization technique developed in the past to analyze the effective properties of random composites without interphases. The second idea is the recently introduced notion of Energy Equivalent Inhomogeneity (EEI), which replaces the original inhomogeneities and their interphases with uniform inhomogeneities; the notion of EEI allows methods devised to examine composites without interphases (such as MCM) to analyze composites with interphases. The most important, and novel in application to problems considered in this work, is the third idea concerning the statistical interphase damage model. In the proposed approach local micro-damage of interphases is modelled by an increasing fraction of randomly distributed destructed springs in the spring layers surrounding the inhomogeneities of the composite. The model assumes that the local interphase micro-strength at the points located on the surface of different inhomogeneities and specified by the same spherical coordinates is described by one-point Weibull distribution function. In view of the strong nonlinearity of the problem, an incremental/iterative scheme is used in practical evaluation of effective properties. The approach is illustrated considering unidirectional and triaxial stretching of a composite.