Representative volume elements for discontinuous carbon fibre composites – Part 2: Determining the critical size

Abstract

This is the second part in a series of papers investigating the size of representative volume elements for discontinuous carbon fibre composites. An ‘embedded cell’ finite element approach, outlined in Part 1, has been used to determine critical RVE sizes for materials with increasing fibre lengths and fibre volume fractions. Convergence of the results for mechanical properties were seen at RVE edge lengths of four times the fibre length ( a/ L = 4), irrespective of the fibre volume fraction. The calculated Poisson’s ratios ( v 12 and v 21) were largely independent of the RVE size. The critical RVE size is seen to be dependent on deterministic size effects and statistical size effects. Deterministic size effects are dominant for RVE sizes smaller than a/ L = 4 because of the presence of bridging fibres. Statistical size effects beyond a/ L = 4 were seen to be principally dependant on the level of fibre homogeneity and the departure from isotropy within the RVE, and these aspects were evaluated. An analytical model has been used to extrapolate the variance data to understand the most computationally efficient way of determining the critical RVE size. This study confirmed that it is more efficient to test fewer larger models than many smaller models, for the same level of statistical confidence (95%).