Dilatational viscoplasticity of polycrystalline solids with intergranular cavities

Abstract

We propose constitutive models for polycrystalline aggregates with intergranular cavities and test them against full-field numerical simulations. Such conditions are prevalent in many engineering applications and failure of metallic components (e.g. HIPing and other forming processes, spallation under dynamic loading conditions, etc.), where the dilatational effects associated with the presence of cavities must be accounted for, and standard polycrystalline models for incompressible plasticity are not appropriate. On the other hand, it is not clear that the use of porous plasticity models with isotropic matrix behavior is relevant, particularly, when large deformations can lead to significant texture evolution and therefore to strong matrix anisotropy. Of course, finite strains can also lead to significant changes in the porosity and pore shape, resulting in additional anisotropy development. In this work, we make use of 'variational linearcomparison' homogenization methods to develop constitutive models simultaneously accounting for texture of the matrix, porosity and average pore shape and orientation. The predictions of the models are compared with full-field numerical simulations based on fast Fourier transforms to study the influence of different microstructural features (e.g. overall porosity, texture of the matrix phase, single-crystal anisotropy, etc.) and type of loading (triaxiality) on the dilatational viscoplastic behavior of voided polycrystals. The results are also compared with the predictions of isotropic-matrix porous plasticity models to assess the effect of the possible matrix anisotropy in textured samples.

Fast fourier transform-based modeling for the determination of micromechanical fields in polycrystals

“…Among these applications, it is worth mentioning a recent study on dilatational plasticity of porous polycrystalline materials, 21 in which the effect of the crystallinity (and heterogeneity) of the material surrounding intergranular voids on the growth of such voids was for the first time assessed and quantified, and compared with homogenization approaches.…”

Modeling void growth in polycrystalline materials

“…On the other hand, classic self-consistent formulations [27][28][29][30], which are extensively used to estimate the viscoplastic response of fully dense polycrystals, have been recently extended to the case of voided polycrystals [31]. These new homogenization formulations, based on the variational theories of Ponte Castañ eda [32,33] and previous applications of the latter to cases of voids in a nonlinear matrix [34,35], are better suited to handle the strong mechanical contrast in the voided aggregate.…”

Bounding the plastic strength of polycrystalline solids by linear-comparison homogenization methods

“…Note that an outer bound on v P induces an upper bound on s 0 . The results presented below correspond to 200 crystal orientations (N = 200) prescribed according to a Sobol sequence Sobol (1967) in order to generate textures as close as possible to isotropy-see Lebensohn et al (2011). In any event, the exact same set of orientations were used for all computations so that comparisons between the different bounds are meaningful.…”

“…Given that these are materials with a strong heterogeneity contrast, the question arises as to whether larger differences between the non-relaxed and relaxed linear-comparison bounds will appear in the context of (two-phase) polycrystalline voided solids where the overall heterogeneity contrast is infinitely strong. Such bounds would help current efforts directed towards developing micromechanical models for voided polycrystals to incorporate texture effects in ductile-failure theories of engineering alloys-see Lebensohn et al (2011)-calculations are now underway and will be reported upon completion.…”

“…In addition, their results served to demonstrate the inconsistency of an 'incremental' theory of polycrystalline plasticity proposed by Hill (1965) and Hutchinson (1976), which was found to violate the bounds. More recently, Lebensohn et al (2011) have reported linearcomparison bounds for (two-phase) voided polycrystals and have shown that 'tangent' theories of polycrystalline plasticity such as those proposed by Molinari et al (1987), Lebensohn & Tomé (1993) and Bornert et al (2001) can also violate bounds. Idiart & Ponte Castañeda (2007a) have recently shown that the linearcomparison methods of deBotton & Ponte Castañeda (1995) and Ponte Castañeda & Suquet (1998) make implicit use of a relaxation in their linearization scheme which weakens the resulting bounds.…”