Quantitative Dependence of the Effective Modulus of Particle Reinforced Composites on Partially Debonding Damage

Abstract

BACKGROUND Interfacial deboding may be one of the main damage modes, and largely influence the mechanical performance of the composites. Developing a simple method for accurately predicting the effect of this damage is in keen demand in the domains of both science and engineering. To realize this objective, quantitative characterization of the relationship between the effective material properties and the damage degree should be a prerequisite. Zhao et al. [1] proposed a fictitious inclusion method, and used the volume of the inclusion directly beneath the interfacial cracks as a measure of damage degree. However, the final prediction by this definition made a large difference against the corresponding FE results. Liu et al. [2] adopted the ratio between the projected damaged area in a certain direction and the original interface area to determine the damage variables. Wada [3-4] conducted a systematic analysis of damage variables ranging from 0 to 1, and picked out optimum damage variables for each debonding angle. The change of load carrying capacity of the damaged particles was also studied by FEM. Zheng et al. [5] made use of FEM to examine the influence of debonding angle on the stiffness of the composite. Cho et al. [6] proposed a novel FE model to study the load carrying capacity of a broken particle, and this method can be equally applied to study the influence of partially debonding. So far, the accuracy of these damage variables has never been clearly addressed yet. Since most of FEM analysis were based on a unit cell model, so a big obstacle in the process of verifying these damage variables is the absence of appropriate equivalent medium model. Fortunately, Jiang et al. [7-8] developed a micromechanics model for composites with regularly distributed particles, and thus the validity of the damage variables can be fully examined. A micromechanics method is employed for particle reinforced composite (PRC) with partially debonding damage, and to establish quantitative dependence of the effective modulus on the damage. FEM is also used to study the stress field and implore the inherent damage mechanism. METHODS Particles with elastic stiffness Cp are randomly located in the matrix with stiffness Cm. The terms for particle, matrix and PRC are represented by symbols with the subscripts ‘p’, ‘m’ and an upper bar, respectively. Additionally, tensors and vectors are denoted by bold face letters. Based on Kachanov’s concept of effective stress [9], Chow and Wang [10] proposed a damage effect tensor M(di) to account for the reduction of elastic stiffness of materials at three principal directions, here d1 , d2 and d3 are the damage variables at three principal axes. Defining the effective compliance tensor Dp as T pp =⋅ ⋅