Shakedown analysis of fibre-reinforced copper matrix composites by direct and incremental approaches

Plastic failure caused by variable loads is a critical design concern for fibre-reinforced metal matrix composites when the matrix is very soft. Shakedown analysis provides a quantitative prediction regarding the safe loading domain. In this article, shakedown analysis of fibre-reinforced copper composites is presented. For a comparative study both the FEM-based direct method and the incremental method were applied, which were based on the shakedown theorem combined with an optimisation process and FEM cyclic plasticity simulations, respectively. In addition to unidirectional lamina, a cross-ply laminate was also investigated using three dimensional unit cell models subjected to bi-axial loads. The shakedown predictions obtained from the two theoretically independent approaches showed a nice agreement each other for both lamina and laminate. Effects of loading condition, fibre volume fraction, unit cell architecture and plastic hardening laws are discussed. The trend of the lamina shakedown behaviour was interpreted in terms of the Mori–Tanaka mean field theory.