Deformation and fracture of a particle-reinforced aluminum alloy composite: Part II. Modeling

In this article, the tensile and fracture properties of a discontinuously reinforced aluminum (DRA) alloy composite are modeled to determine the influence of constituent parameters on material behavior. Comparison of the elastic-modulus calculations to the experimental data suggest that the angular particles are more effective in load transfer than spherical particles, and that a unit cylinder geometry is a good representation of the particles under elastic conditions. This same geometry is used in the finite element-based elastic-plastic model of Bao et al., and reasonably good agreement is obtained between the experimental and predicted yield strengths. A fracture-mechanics model is proposed for predicting the elongation to failure. The model assumes the existence of particle cracks, and criticality is based on the strain required for matrix rupture between cracked particles. The damage criterion of Cockcroft and Latham is utilized, and model predictions are compared to data from different investigations. It is shown that the volume fraction of particles and the work-hardening coefficient of the matrix have a strong influence on the strain to failure. Fracture toughness modeling once again exposes the limitations of existing zero-degree crack-propagation models, such as that of Hahn and Rosenfield, which predict increased toughness with yield strength rather than a decrease, which is observed experimentally. A shear-failure model along a 45-deg direction is proposed for the higher-strength conditions, where concentrated slip bands were observed. The model exhibits the inverse toughness dependence on strength and better correlation to peak-aged (PA) data, but shows poorer agreement with underaged (UA) data. Thus, a transition from zero-degree propagation to 45-deg propagation with increasing strength is suggested. A simplified method for extracting particle stresses is illustrated and is used to estimate a Weibull modulus of 4.9 and a Weibull strength of 2450 MPa for the SiC particles of an average diameter of 10 μm.