Constitutive Modeling of Polycrystalline Metals at Large Strains
In polycrystalline metals the major cause of the anisotropic plastic response is crystallographic texture resulting from the reorientation of the crystal lattices of grains during deformation. There have been considerable recent advances in the understand
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L. Anand, S. Balasubramanian and M. Kothari Massachusetts Institute of Technology, Cambridge, MA, USA
ABSTRACT In polycrystalline metals the major cause of the anisotropic plastic response is crystallographic texture resulting from the reorientation of the crystal lattices of grains during deformation. There have been considerable recent advances in the understanding of anisotropy due to crystallographic texturing, and a reasonably successful, physically-based elasto-viscoplasticity theory for the deformation of face- and bodycentered-cubic polycrystals deforming by crystallographic slip is now at hand. The constitutive equations in the theory are reviewed, and the implementation of these equations in a finite element program is described. The theory is able to predict the macroscopic anisotropic stress-strain response, shape changes and the evolution of crystallographic texture in complex deformation modes. Also, it is beginning to be applied to the analysis of deformation-processing problems. Applications to (i) the prediction of earing defects during quasi-static cup-drawing of an f.c.c. aluminum alloy, and (ii) the ovalization of pre-textured b.c.c. tantalum cylinders during dynamic Taylor cylinder-impact experiments are described.
C. Teodosiu (ed.), Large Plastic Deformation of Crystalline Aggregates © Springer-Verlag Wien 1997
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L. Anand, S. Balasubramanian and M. Kothari
1. INTRODUCTION
The purpose of this paper is (i) to review a set of constitutive equations for single and polycrystalline elasto-viscoplasticity which are capable of modeling the initial and evolving anisotropy in ductile metallic materials due to the evolution of crystallographic texture; (ii) to report on our implementation of the constitutive equations in a finite element program; and (iii) to report on applications of the computational capability to simulate (a) the classical quasi-static deformation processing operation of cup-drawing, and predict the formation of the important earing defects which develop during cup-drawing from an anisotropic sheet of an f.c.c. aluminum alloy; and (b) the ovalization of pre-textured b.c.c. tantalum cylinders during dynamic Taylor cylinder-impact tests. The work reported here has been carried out at M.I.T. by Anand in collaboration with his (former and current) doctoral students Curt Bronkhorst, Surya Kalidindi, Srihari Balasubramanian, and Manish Kothari. In writing this paper, we will quote freely from their recently published papers [1-8], and keep references to the related work of others in the literature at a minimal level; an extensive bibliography may be found in the references cited. The plan of the paper is as follows. In Section 2 we review the constitutive model for siqgle crystals. In this section, as in most recent work on crystal plasticity, we use a simplified power-law description for the shearing rates "y 0 on the slip systems (1)
In the equation above, T 0 is the resolved shear stress on the slip system, and s 0 (> 0) is the slip system deformation resistance. The parameter
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