Localized Effects in Periodic Elastoplastic Composites

A method is applied for the study of the field distributions in metal matrix fiber reinforced composites with periodic microstructure in which localized damage exists in the form of complete or partial fiber loss and crack. In addition, the behavior of ceramic/metal periodically layered composites with a single broken ceramic layer is determined. The pro-posed analysis is based on continuum damage mechanics considerations, and the method of solution combines three distinct approaches. In the first one, referred to as the representative cell method, the periodic composite domain is reduced, in conjunction with the discrete Fourier transform to a finite domain problem of a single representative cell. This method has been previously applied on linear thermoelastic, smart and electrostrictive composites, but is presently extended and applied on elastoplastic composites (presently deformation and incremental plasticity). In the second approach, the appropriate far-field boundary conditions in the transform domain are applied in conjunction with the high-fidelity generalized method of cells micromechanical model for the prediction of the macroscopic behavior of the inelastic composite. The third approach consists of the application of the inelastic higher-order theory for the computation of the elastoplastic field in the transform domain. An inverse transform provides the actual field. The effect of damage is included in the analysis in the form of eigenstresses which are a priori unknown. Hence an iterative procedure is employed to obtain a convergent solution. The proposed method is verified by a comparison with an analytical solution, and several applications illustrate the applicability of the method for metal matrix composites with localized damage in the form of a crack or fiber loss.