Predictive modelling of the mechanical properties of rubber-toughened epoxy

Abstract

Introduction Single-phase epoxy polymers are usually relatively brittle materials and are frequently toughened by the incorporation of a rubbery phase [1]. Two important toughening mechanisms have been identified for such two-phase materials, which consist of a rubbery phase dispersed in a matrix of a cross-linked polymer. The first is localized shear yielding, or shear banding, which occurs between rubbery particles at an angle of approximately + 45 ° to the direction of the maximum principal tensile stress [1-3]. Due to the large number of particles involved, the volume of thermoset matrix material which can undergo plastic yielding is effectively increased compared to the single-phase polymer. Consequently, far more irreversible energy dissipation is involved and the toughness of the material is improved. The second mechanism is the internal cavitation, or interfacial debonding, of the rubber particles, which then enables the subsequent growth of these voids by plastic deformation of the epoxy matrix [1-4, 5]. This irreversible hole-growth process of the epoxy matrix also dissipates energy, and so contributes to the enhanced fracture toughness. Recently, attempts [4, 5] have been made to model the toughening mechanisms and this work has clearly demonstrated the importance of establishing a sound finite element analysis representation of the effects of the rubbery phase on the properties of the rubber-toughened polymer. Indeed, this is the aim of the present work, and some most interesting initial results are the subject of the present letter. Predictive modelling of particulate-filled composite materials has frequently been based on the assumption that the material consists of a collection of cylinders, each containing a sphere at its centre [4, 6, 7]. The size of the cylinders as a function of the overall volume fraction can be deduced from assuming a uniform array [4, 6], or assuming a random array [7]. Such analysis is relatively straightforward since the constraints required to model the interactions of surrounding particles may be simply applied by forcing the sides of the cylinder to remain straight. However, this material model is inherently inaccurate since it does not reflect the overall isotropy of the material. The more accurate material model used in the present work is a collection of spheres, each consist-