Stress distribution rubber-toughened epoxy

We have used this model to investigate stress distributions in and around the rubber particle, or around a void, in a matrix of epoxy polymer. This chapter describes the modeling of stress concentrations in rubber-toughened epoxy and gives a simple model for predicting the fracture energy, Gc, of such a material. 

Stress Distributions in Rubber-Toughened Epoxy. The toughening mechanisms described in the introduction of this chapter are observed ahead of a crack, in a triaxial stress field. The simplest triaxial stress field that can be applied to the spherical cell is a pure hydrostatic stress. This stress field can be directly imposed by the application of stress, without prior knowledge of the material properties of the overall material. The shape of the deformed grid is automatically spherical, and this is the correct deformed shape. Pure hydrostatic stress was used for the detailed investigation of the stress distributions and the effect of rubber properties. 

Fond et al. [84] developed a numerical procedure to simulate a random distribution of voids in a definite volume. These simulations are limited with respect to a minimum distance between the pores equal to their radius. The detailed mathematical procedure to realize this simulation and to calculate the stress distribution by superposition of mechanical fields is described in [173] for rubber toughened systems and in [84] for macroporous epoxies. A typical result for the simulation of a three-dimensional void distribution is shown in Fig. 40, where a cube is subjected to uniaxial tension. The presence of voids induces stress concentrations which interact and it becomes possible to calculate the appearance of plasticity based on a von Mises stress criterion. 

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