A micromechanical damage model for effective elastoplastic behavior of partially debonded ductile matrix composites

Abstract

A micromechanical damage model considering progressive partial debonding is presented to investigate the effective elastoplastic-damage behavior of partially debonded particle reinforced ductile matrix composites (PRDMCs). The effective, evolutionary elastoplastic-damage responses of three-phase composites, consisting of perfectly bonded spherical particles, partially debonded particles and a ductile matrix, are micromechanically derived on the basis of the ensemble-volume averaging procedure and the first-order effects of eigenstrains. The effects of random dispersion of particles are accommodated. Further, the evolutionary partial debonding mechanism is governed by the internal stresses of spherical particles and the statistical behavior of the interfacial strength. Specifically, following Zhao and Weng (1996), a partially debonded elastic spherical isotropic inclusion is replaced by an equivalent, transversely isotropic yet perfectly bonded elastic spherical inclusion. The Weibull's probabilistic function is employed to describe the varying probability of progressive partial particle debonding. The proposed effective yield criterion, together with the assumed overall associative plastic flow rule and the hardening law, forms the analytical framework for the estimation of the effective elastoplastic-damage behavior of ductile matrix composites. Finally, the present predictions are compared with the predictions based on Ju and Lee's (2000) complete particle debonding model, other existing numerical predictions, and available experimental data. It is observed that the effects of partially debonded particles on the stress–strain responses are significant when the damage evolution becomes rapid.

Introduction

Considerable work has been published in the literature on damage in particle-reinforced ductile matrix composites (PRDMCs). We refer to Dvorak (1991), Levy and Papazian (1991), Soboyejo et al. (1994), and Zhao and Weng, 1995, Zhao and Weng, 1996, Zhao and Weng, 1997 for a literature review. Several failure mechanisms have been observed, such as the interfacial debonding between the matrix and inclusions (Lewis et al., 1993; Whitehouse and Clyne, 1993, Whitehouse and Clyne, 1995), the particle cracking (Lloyd, 1991), and the ductile plastic failure in the matrix (Lewandowski and Liu, 1989; Llorca et al., 1991). The mechanism of failure apparently depends on many factors, such as the interfacial strength, the strength of reinforcements, the manufacturing process, and the matrix aging condition (Lewandowski and Liu, 1989).

In recent years, Ju and Chen (1994a) and Ju and Tseng, 1996, Ju and Tseng, 1997 developed micromechanical formulations to predict effective elastoplastic behavior of two-phase metal matrix composites with random particle locations and under general loading histories. They considered the first-order and the second-order stress perturbations of elastic particles on the ductile matrix, and the second-order relationship between the far-field stress $\text{σ}{}^0$ and the ensemble-volume averaged stress $\text{σ}\text{̄}$ on the basis of Ju and Chen (1994b, 1994c). On the other hand, Tohgo and Weng (1994) and Zhao and Weng (1995) proposed progressive interfacial complete debonding models for PRDMCs under triaxial tension. They used Weibull (1951) probability distribution function to describe the probability of complete interfacial particle debonding. It was postulated that the debonding of particles was controlled by the internal stresses of particles and the interfacial strength parameter. Further, Zhao and Weng (1996, 1997) derived effective elastic moduli and elastoplastic responses of partially debonded composites using fictitious, perfectly bonded transversely isotropic “equivalent” particles. Very recently, Ju and Lee (2000) proposed an elastoplastic-damage formulation based on a micromechanical framework and the ensemble-volume averaging approach for PRDMCs considering complete interfacial particle debonding. In particular, the authors predicted the overall elastoplastic behavior and damage evolution in three-phase PRDMCs based on the mechanical properties of constituent phases, particle volume fractions, random spatial inclusion distributions, micro-geometry of particles and probabilistic micromechanics.

The primary objective of the present paper is to extend the framework of Ju and Lee (2000) to assess the effects of partially debonded particle interfaces on the overall elastoplastic-damage behavior. The partial interfacial debonding mechanism in a PRDMC is displayed in Fig. 1. Specifically, when a PRDMC is subjected to a uniaxial tensile loading, the particles may partially debond on the top and bottom interfaces normal to the applied loading direction. The resulting partially debonded particles will lose their load-carrying capacity along the loading direction, but will still be able to transmit stresses to the matrix in the transverse direction through the bonded portion of the interfaces. In addition, the particles are assumed to be elastic spheres randomly dispersed in the matrix, and the ductile matrix behaves elastoplastically under uniaxial loading/unloading histories. All particles are assumed to be nonintersecting and initially embedded firmly in the matrix with perfect interfaces. It is further assumed that the partial interfacial debonding is governed by the average internal stress of a particle and the probabilistic Weibull's parameter of the particle–matrix interfacial strength.

This paper is organized as follows. In Section 2, we consider a transversely isotropic and perfectly bonded fictitious particle which is “equivalent” to a partially debonded isotropic particle. The effective elastic moduli of three-phase composites with perfectly bonded and partially debonded particles are micromechanically derived. In Section 3, the effective yield criterion and overall elastoplastic-damage characterization of three-phase composites are micromechanically constructed according to the ensemble-volume averaging procedure and the first-order eigenstrain effects owing to the randomly dispersed, perfectly bonded or partially debonded spherical particles. An evolutionary probabilistic interfacial partial particle debonding model is presented in Section 4 in accordance with the Weibull's function. The proposed probabilistic and progressive elastoplastic-damage formulation is applied to the uniaxial tensile loading in Section 5. Finally, to illustrate the potential applicability of the proposed method, the present predictions are compared with Ju and Lee's (2000) and Zhao and Weng's (1996) analytical predictions, and available experimental data in Section 6.