Ductile rupture under cyclic loadings at high triaxiality: The influence of strain hardening and elasticity

Abstract

Previous works (Devaux et al., 1997; Cheng et al., 2017) have emphasized the effects of strain hardening and elasticity upon ductile rupture of metals under cyclic loading conditions. This work pursues the study and modelling of these two effects by distinct theoretical methods, each coupled with micromechanical finite element simulations of the behaviour of some “representative cell”. For the effect of strain hardening, we employ Morin et al. (2017)’s approach, based on the theory of sequential limit-analysis (Yang, 1993; Leu, 2007; Leblond et al., 2018). This approach is applied to various types of hardening of the metallic matrix: isotropic, linear kinematic, nonlinear kinematic with one or two kinematic variables (Armstrong and Frederick, 2007) , and even a simplified version of Chaboche (1991)’s model accounting for complex cyclic effects. Numerical micromechanical simulations of a hollow sphere made of elastic–plastic materials obeying the various hardening laws considered, and subjected to cyclic loadings at high triaxiality, fully confirm the predictions of the model developed, provided elasticity is made negligible by using an artificially high value of Young’s modulus. When a realistic value is employed, however, the agreement between theoretical predictions and numerical results is degraded, thus emphasizing again the importance of the effect of elasticity in cyclic ductile rupture. To deal with this effect we derive, apparently for the first time, an evolution equation of the porosity accounting for (compressible) elasticity. However, numerical micromechanical simulations reveal that simply using this new evolution law, while keeping all other aspects of the model unchanged, remains insufficient to get a good match of theoretical and numerical results. Such a match is achieved by introducing the ad hoc hypothesis that the yield criterion and flow rule derived from sequential analysis still apply in the presence of elasticity, but with some “effective porosity” slightly differing from the true one through some heuristic, adjustable factor.