Modeling of void growth in ductile solids: effects of stress triaxiality and initial porosity

Abstract

The effects of stress triaxiality and initial porosity on void growth and coalescence are studied in this paper. The representative material volume (RMV) is modeled by two approaches: (1) a unit cell containing a discrete, spherical void at its center, and (2) a unit cell having the same void volume fraction and obeying the Gurson–Tvergaard constitutive relation. The macroscopic stress–strain response and the void growth and coalescence behavior of the voided cell are obtained from detailed finite element analyses and the results show strong dependencies on stress triaxiality and the initial void volume fraction. The micromechanics parameters of the GT model, q 1 and q 2, are calibrated to minimize the differences between the predicted void growth rate and macroscopic stress–strain relation by the GT model and the corresponding finite element results of the voided RMV. The calibrated values of q 1 and q 2 as functions of the stress triaxiality and the initial porosity are obtained for an idealized material under the axi-symmetric condition. Furthermore, discussions are made on the description of the triaxial stress state of the RMV. It is found that the effect of stress triaxiality on void growth and coalescence cannot be uniquely described by the stress triaxiality factor, defined as the ratio of the hydrostatic stress and the effective stress, alone. Multiple stress states with different principal stress ratios ρ 1(= Σ 1/ Σ 2) and ρ 2(= Σ 3/ Σ 2) can result in the same stress triaxiality ratio, and the macroscopic stress–strain response and the void growth and coalescence behavior of the voided RMV are different for each stress state. In order to characterize the effects of stress triaxiality on void growth and the macroscopic stress–strain behavior of the RMV, the principal stress ratios must be specified and consequently, the q-parameters of the GT model should be expressed as functions of ρ 1 and ρ 2.