From stress concentrations between inclusions to probability of breakage: A two-dimensional peridynamic study of particle-embedded materials.

Abstract

Particle-embedded materials consist of a dispersed phase of particles in a sticking matrix. We used a bond-based peridynamics method to investigate their elastic properties, rupture, and probability of failure. We performed an extensive two-dimensional parametric study where particles are disk-shaped inclusions diluted into a pore-filling matrix. Both particle and matrix are considered to be brittle elastic with a perfectly bonded interface. The inclusion volume fraction φ and the inclusion matrix toughness ratio β (β≥1) were varied from 0.254-0.754 (jamming point) and 1.5-100.0, respectively. A total of 5000 uniaxial tensile tests up to failure were performed. We showed that the Halpin-Tsai model fits well all Young elastic moduli even for nearly in-contact particles. The stress distribution strongly depends on φ and β. As the highest stresses (at the origin of crack nucleation) occur between neighboring particles, we analyzed the average stress in gaps. We found that, regardless of the particle volume fraction, the yield stress is a power law of a grain-scaled stress concentration factor. We also investigated the probability of failure of the samples. We found that whatever φ and β, this probability follows a classical Weibull law. Finally, we showed that Weibull modulus, normalized by its value for infinitely rigid particles, is inversely proportional to a function of the stress concentration factor.