Establishing size effects in discontinuous fibre composites using 2D finite element analysis

Size effects are observed within discontinuous fibre composites, such that the material properties change with the specimen volume. Representative volume elements (RVEs) are commonly used to simulate random fibre architectures for finite element analysis of discontinuous fibre composites. A series of simplified 2D RVE models have been created and studied in this paper, in order to determine the relationship between the critical RVE size and fibre length and volume fraction. All models are subjected to periodic boundary conditions, but average properties are extracted from an inner region offset from the model boundary by a distance equivalent to two fibre lengths. According to Saint–Venant’s principle, this offset removes the uncertainty associated with the approximate boundary conditions. A statistical stopping criterion has been adopted to determine the number of realisations required to achieve a representative set of elastic properties for each fibre architecture. The critical RVE side length is shown to be approximately four times the fibre length when considering convergence of the tensile and shear stiffnesses for the range of fibre lengths and volume fractions studied.

► An RSA model is used to create meso-scale discontinuous fibre architectures.
► Saint–Venant’s principle has been adopted to enable periodic boundary conditions to be used.
► The critical decay length for approximate boundary conditions is two times the fibre length.
► The critical RVE size is four times the fibre length.