Dilatational viscoplasticity of polycrystalline solids with intergranular cavities

M. I. IDIART; R. A. LEBENSOHN; P. PONTE CASTAÑEDA

Barcelona

Conferencia; International Conference on Computational Modeling of Fracture and Failure of Materials and Structures; 2011

International Center for Numerical Methods in Engineering

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 (e.g. dynamic loading of polycrystalline materials, forming aggregates with initial porosity), where the dilatational effects associated with the presence of voids 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 are relevant, particularly, when large deformations can lead to significant texture evolution leading 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 the “second-order linear-comparison” homogenization methods to develop constitutive models simultaneously accounting for texture of the matrix, porosity and average pore shape and orientation. The predictions of the model are compared with full-field numerical simulations based on Fast Fourier transforms to study the influence of different microstructural features (e.g. overall porosity, void shape, texture of the material 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. Numerical simulations and theoretical predictions both indicate that the effective response of untextured voided solids is relatively insensitive to the crystallinity of the polycrystalline matrix, even when crystal symmetry and strain-rate sensitivity are low. By contrast, the effective response of strongly textured voided solids was found to be quite sensitive to matrix crystallinity when crystal symmetry and strain-rate sensitivity are both sufficiently low. In this case, standard models based on isotropic-matrix theories are inadequate and polycrystalline theories like the ones presented in this work should be employed. In this connection, it is emphasized that even if crystal structure exhibits many geometrical symmetries (e.g., FCC and BCC crystals), local processes like strain hardening may introduce a strong anisotropy in the crystal's response upon large deformations, further restricting the range of validity of isotropic-matrix models.