A theory for plastic-bonded materials with a bimodal size distribution of filler particles

Abstract

Plastic-bonded materials are composites consisting of grains of filler material embedded in a polymeric matrix. A micromechanics model is proposed for investigating the mechanical behaviour of plastic-bonded materials having two disparate grain sizes. A hybrid theory is proposed to handle some aspects of the bimodal grain size distribution. Our model uses the first-order method of cells with an eight-cell representative volume element where one of the eight cells contains a large grain and the seven remaining cells contain a mixture of small grains embedded in the polymeric binder material. A Mori–Tanaka-based analysis is used to describe the small grain-binder mechanical response. The small grains in this analysis are assumed to be spherical and uniformly distributed in the binder. In this work, we use the explosive PBX 9501, in its unreacted state, as our test system. The explosive grain particle size distribution of PBX 9501 consists of two broad peaks centred at approximately 1 and 200 µm. The constitutive behaviour of the large explosive grains are assumed to be elastic-plastic and damage by way of micro-crack brittle fracture. Only linear elasticity of the small grains is considered. The rate and temperature dependence of the mechanical response of the polymer binder is accounted for by a generalized Maxwell viscoelasticity model. The theoretical uniaxial stress–strain response for PBX 9501 is reported for quasi-static and split Hopkinson pressure bar loading rates and compared to experimental measurements.