Multiscale modeling of plasticity based on embedding the viscoplastic self-consistent formulation in implicit finite elements Javier Segurado a , Ricardo A. Lebensohn b,⇑ , Javier LLorca a , Carlos N. Tomé b a Madrid Institute for Advanced Studies of Materials (IMDEA Materials Institute), Department of Materials Science, Polytechnic University of Madrid, C/Profesor Aranguren s/n, 28040 Madrid, Spain b Materials Science and Technology Division, Los Alamos National Laboratory, MS G755, Los Alamos, NM 87845, USA article info Article history: Received 5 April 2011 Received in final revised form 11 July 2011 Available online 22 July 2011 Keywords: B. Polycrystalline material B. Anisotropic material B. Crystal plasticity A. Microstructures C. Finite elements abstract 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 visco- plastic behavior is used to provide a texture-sensitive constitutive response of each mate- rial 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) formu- lation 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 dom- inant texture component with respect to the bending plane. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction The formulation of multiscale frameworks for modeling and simulation of plastic deformation of polycrystalline materials is a very active field of research, representing at the same time a challenging material science and computational problem and a relevant development for engineering applications. The main goal is to simultaneously account for the strength of the actual deformation mechanisms active at single-crystal level, the polycrystalline character of the aggregate microstructure and its evolution with deformation, and the specific boundary conditions applied to a polycrystalline specimen. 0749-6419/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijplas.2011.07.002 ⇑ Corresponding author. Tel.: +1 505 665 3035; fax: +1 505 667 8021. E-mail addresses: jsegurado@mater.upm.es (J. Segurado), lebenso@lanl.gov (R.A. Lebensohn), javier.llorca@imdea.org (J. LLorca), tome@lanl.gov (C.N. Tomé). International Journal of Plasticity 28 (2012) 124–140 Contents lists available at ScienceDirect International Journal of Plasticity journal homepage: www.elsevier.com/locate/ijplas