Micromechanical Analysis of the Viscoelastic Behaviour of Composites

Abstract

In two-phase materials such as fiber-reinforced composites, the effective behavior of the material is determined not only by the properties of the constituents, but also by their geometry and their arrangement in the composite — the microstructure of the material [1]. When calculating effective properties and local stress or strain fields, it is therefore important to consider the effect of modelling assumptions concerning the microstructure. In analytical approaches, the information on the composite’s microstructure is contained implicitely in certain model parameters. For example, in the Halpin-Tsai equations, the empirical fitting parameter is a function of the Poisson’s ratio and of the reinforcing phase’s geometry [2]. For analyses by finite elements (FE), the microstructure is defined explicitely by the FE mesh. A certain degree of idealization is necessary to keep the problem computationally tractable. This leads to the definition of a model material that is usually not representative of reality. On the other hand, a composite with a “random” fiber distribution is hard to define and a given distribution can be fairly arbitrary. A further difficulty lies in describing local concentrations of fibers or resin. However, certain models do describe experimental data better than others. This was shown by Adams and Tsai, who studied random fiber packings based on periodic arrays of possible fiber positions [1]. Coming closer to observed microstructures, Pyrz has explored ways to quantitatively describe the microstructure of unidirectional composites and the influence it can have on the material properties [3].