Meso-mechanical constitutive model for ratchetting of particle-reinforced metal matrix composites

Based on the Eshelby equivalent inclusion theory and Mori–Tanaka averaging method, a meso-mechanical cyclic elasto-plastic constitutive model is proposed to predict the ratchetting of particle-reinforced metal matrix composites. In the proposed model, a Hill-typed incremental formulation is used to simulate the elasto-plastic responses of the composites during cyclic loading with assumptions of elastic particle, elasto-plastic metal matrix and perfect interfacial bond between metal matrix and particles. A new nonlinear kinematic hardening rule extended from the Ohno–Abdel-Karim model [M. Abdel-Karim, N. Ohno, Kinematic hardening model suitable for ratchetting with steady-state, Int. J. Plasticity 16 (2000) 225–240] is employed to describe the ratchetting of metal matrix which dominates the ratchetting of the composites. With further assumption of spherical particles, the proposed meso-mechanical cyclic constitutive model is verified by comparing the predicted uniaxial ratchetting of SiCP/6061Al composites with corresponding experiments obtained at room temperature [G.Z. Kang, Uniaxial time-dependent ratchetting of SiCP/6061Al alloy composites at room and high temperature, Comp. Sci. Tech. 66 (2006) 1418–1430]. In the meantime, the effects of different tangent operators employed in the numerical implementation of the proposed model, i.e., continuum (or elasto-plastic) tangent operator Cep and algorithmic (or consistent) one Calg, on the predicted ratchetting are also discussed. It is concluded that the proposed model predicts the uniaxial ratchetting of SiCP/6061Al composites at room temperature reasonably.