Strain localization in rate sensitive porous ductile materials

Ductile failure by the onset of strain localization in rate sensitive porous materials is investigated using a linear perturbation stability analysis. A micromechanics-based constitutive model accounting for inhomogeneous yielding at the micro-scale, due to plastic strain concentration in the inter-void ligaments, is used. Strain and strain rate hardening of the material is accounted for using a phenomenological viscoplastic extension of the model. Unlike in earlier studies employing a rate-dependent model, an analytical closed form expression for the critical value of the hardening modulus at the onset of localization is derived. The predicted shape of the failure locus under proportional loading is shown to be consistent with known results in the literature for the loading path dependence of ductile failure. The model predicted failure loci are validated by comparison with mesoscopic unit cell model simulations of void growth in a viscoplastic power law hardening material. It is shown that the failure strains predicted by the model as a function of the hardening parameters are in good agreement with the strains to the onset of elastic unloading in the cell model simulations, signifying the onset of void coalescence at the micro-scale.