Effects of multiaxial cyclic loading conditions on the evolution of porous defects

Laboratoire de Mécanique des Solides, CNRS, UMR 7649, Ecole Polytechnique, 91128 Palaiseau, France

^a Corresponding author: e-mail: mbiakop@lms.polytechnique.fr

Abstract

Multiaxial loading conditions are one of the important parameters in estimating the lifetime of structure both in high and low cycle fatigue ([1 3]). In order to understand the coupling between the macroscopic multiaxial loading and the microscopic defects, we propose to investigate the evolution of an elasto-plastic porous material up to failure under low cycle fatigue conditions. The analysis is performed numerically, using finite elements, on a periodic 3D unit-cell under the assumption of finite strains and subjected to various stress triaxialities, translated as ratios between deviatoric, hydrostatic stress and Lode angles. The present discussion introduces several novel factors in the analysis: (i) 3D geometry in cyclic loading (ii) finite strains (iii) free evolving void shape (iiii) different hardening laws. That one of the important factors is the void shape and that its evolution during cyclic loading depends on its multiaxiality. Moreover, these factors will equally influence the apparent macroscopic hardening or softening of the material and the initiation of localized shear zones at the microscopic level. The Lode angle has a significant impact on the evolution of the aspect ratios and the ellipsoidicity of the pores, but has only a weak influence on the evolution of macroscopic variables such as the stress or the porosity. As a consequence, the results show that multiaxiality of the loading have an important on the evolution and growth of defects, pores in the present case problem, but are less important in the definition of the yield surface.