Numerical study and theoretical modelling of void growth in porous ductile materials subjected to cyclic loadings

•Numerical simulations of porous cells evidence a « ratcheting » of the porosity under cyclic loadings.•Gurson's model does not reproduce such an effect, due to an oversimplified description of strain hardening.•An improved variant of this model is proposed and shown to better reproduce the results of the simulations.

Experiments have shown that in porous ductile materials, cyclic loadings lead to lower fracture strains than monotone ones. The effect has been tentatively ascribed to a continued increase of the mean porosity during each cycle with the number of cycles (“ratcheting of the porosity”). In this work, we first perform finite-element-based micromechanical simulations of elementary hollow cells. These cells are initially spherical, contain an initially spherical void and are loaded cyclically through conditions of homogeneous boundary strain rate; the triaxiality is held constant throughout in absolute value. These simulations fully confirm the interpretation of the reduced fracture strains under cyclic loadings just mentioned. The modelling of the ratcheting of the porosity is then discussed. Gurson (1977)'s classical model is shown not to be able to predict such an effect, the evolution of the porosity being stabilized right from the first semi-cycle. The so-called LPD model due to Leblond et al. (1995), an improved variant of Gurson (1977)'s model with a more refined description of strain hardening, makes a better job but fails to accurately reproduce the results of the micromechanical simulations. One explanation of the discrepancy is the assumption of positively proportional straining made in this model, which is basically inadequate for cyclic loadings. An improved version of the LPD model is introduced; this version discards this assumption, at the expense of introduction and radial discretization of an underlying spherical “microcell” at each material point. It is not significantly more computationally expensive than the old one and permits a satisfactory reproduction of the results of the micromechanical simulations. This paves the way to simulations of ductile rupture under cyclic loadings within the framework of Gurson-like models.