Multiscale modeling of plasticity based on embedding the viscoplastic self-consistent formulation in implicit finite elements

• Published in: International journal of plasticity 2012, Vol.28 (1), p.124-140
• Main Authors: Segurado, Javier, Lebensohn, Ricardo A., LLorca, Javier, Tomé, Carlos N.
• Format: Article
• Language: English
• Subjects: A. Microstructures; B. Anisotropic material; B. Crystal plasticity; B. Polycrystalline material; C. Finite elements; Computer simulation; Condensed matter: structure, mechanical and thermal properties; Deformation; Deformation and plasticity (including yield, ductility, and superplasticity); Exact sciences and technology; Finite element method; Fundamental areas of phenomenology (including applications); Inelasticity (thermoplasticity, viscoplasticity...); Mathematical analysis; Mathematical models; Mechanical and acoustical properties of condensed matter; Mechanical properties of solids; Physics; Polycrystals; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Surface layer; Texture
• ISSN: 0749-6419; 1879-2154
• DOI: 10.1016/j.ijplas.2011.07.002

► The widely-used VPSC model is embedded in ABAQUS Standard. ► Each FE integration point is represented by a polycrystal with evolving texture. ► The constitutive response is that of an elasto-viscoplastic polycrystalline material. ► Benchmarks and applications are used to illustrate the proposed multiscale approach. This paper is concerned with the multiscale simulation of plastic deformation of metallic specimens using physically-based models that take into account their polycrystalline microstructure and the directionality of deformation mechanisms acting at single-crystal level. A polycrystal model based on self-consistent homogenization of single-crystal viscoplastic behavior is used to provide a texture-sensitive constitutive response of each material point, within a boundary problem solved with finite elements (FE) at the macroscale. The resulting constitutive behavior is that of an elasto-viscoplastic material, implemented in the implicit FE code ABAQUS. The widely-used viscoplastic selfconsistent (VPSC) formulation for polycrystal deformation has been implemented inside a user-defined material (UMAT) subroutine, providing the relationship between stress and plastic strain-rate response. Each integration point of the FE model is considered as a polycrystal with a given initial texture that evolves with deformation. The viscoplastic compliance tensor computed internally in the polycrystal model is in turn used for the minimization of a suitable-designed residual, as well as in the construction of the elasto-viscoplastic tangent stiffness matrix required by the implicit FE scheme. Uniaxial tension and simple shear of an FCC polycrystal have been used to benchmark the accuracy of the proposed implicit scheme and the correct treatment of rotations for prediction of texture evolution. In addition, two applications are presented to illustrate the potential of the multiscale strategy: a simulation of rolling of an FCC plate, in which the model predicts the development of different textures through the thickness of the plate; and the deformation under 4-point bending of textured HCP bars, in which the model captures the dimensional changes associated with different orientations of the dominant texture component with respect to the bending plane.