Effective strength estimation of metal matrix composites by stress compensation method

• Extend the stress compensation method (SCM) for shakedown analysis of heterogeneous materials . • Estimate the effective strength of MMCs using SCM combined with computational homogenization method. • Propose the boundary conditions for stress-controlled and strain-controlled shakedown problems. • Reveal the discrepancy of shakedown boundaries determined by stress approach and strain approach. Shakedown theory has been widely used to evaluate the load-bearing capacity of elastic-plastic structures under cyclic load. The stress compensation method (SCM) shows good performance in the shakedown analysis of homogeneous materials in previous work. In this paper, the numerical procedure of the SCM is extended for shakedown analysis of metal matrix composites (MMCs) made of heterogeneous materials. To validate the applicability and accuracy of the extended SCM, the calculated results of the method are compared with those available in the literature and the results of step-by-step analyses. Based on the computational homogenization method, the effective strength of MMCs is determined through shakedown analysis on representative volume elements (RVEs). Two kinds of RVEs individually from periodic particle-reinforced metal matrix composite and continuous fiber-reinforced aluminum matrix composite are investigated. The shakedown boundaries under various combinations of thermal and mechanical loads are given. Both the ratchetting mechanism and reverse plasticity mechanism to determine the different regimes of the shakedown boundary are revealed. Additionally, we illustrate that both stress approach and strain approach are feasible for the shakedown analysis of MMCs . The boundary conditions for constructing the self-equilibrium stress fields for stress-controlled and strain-controlled shakedown problems are formulated. The corresponding shakedown boundaries are determined and compared. A discrepancy exists in the shakedown boundaries obtained under the two loading approaches. The discrepancy is strongly correlated with the macroscopic residual strain and macroscopic residual stress.