Simulating Grain Growth in a Deformed Polycrystal by Coupled Finite-Element and Microstructure Evolution Modeling
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INTRODUCTION
MANY metals forming processes involve combinations of deformation and heating to produce specific shapes and properties. Deforming a metal not only changes its shape, but can also change its microstructure (e.g., via the introduction of dislocations). In general, heating a metal promotes the evolution of its microstructure (e.g., via grain growth), and this process can be greatly affected by prior (or concurrent) deformation. Thus, not only the shape but also the properties of a formed metal part can be tailored by controlling its mechanical and thermal treatment. Deformation can influence microstructural evolution in a variety of ways, but perhaps those most pertinent to the processing of single-phase metals are recrystallization and strain-induced boundary migration (SIBM).[1] Recrystallization involves the nucleation and growth of (virtually) dislocation-free grains from the deformation substructure that forms when dislocations organize into subcells or subgrains. Strain-induced boundary migration occurs when differences in stored deformation energy (elastic or plastic) across a grain boundary drive the interface to move in a manner that is unlike that due to interface curvature. Deformation[2] and microstructural evolution[3–7] have been subjects of theoretical and computational C.C. BATTAILE, G.W. WELLMAN, T.E. BUCHHEIT, and E.A. HOLM, Members of Technical Staff, are with the Sandia National Laboratories, Albuquerque, NM 87111, USA. Contact e-mail: [email protected] W.A. COUNTS, Postdoctoral Fellow, is with the Max-Planck-Institut fu¨r Eisenforschung GmbH, Du¨sseldorf, Germany. Manuscript submitted December 13, 2006. Article published online September 13, 2007. METALLURGICAL AND MATERIALS TRANSACTIONS A
study for many years. Efforts have been made to couple the two,[8–10] but the complexity of this task makes a robust implementation difficult. In this article, we present an approach for simulating SIBM with twoway feedback between the deformation state and the microstructureÕs evolution. Deformation is simulated using the finite-element method (FEM) and boundary migration by interface tracking. The implementation and results are presented for a linear anisotropic elastic material and for elastic-plastic Cu using a rate-dependent plastic hardening model. (In the purely elastic case, Cu elastic constants are used for consistency.) The two approaches are compared and discussed. II.
METHOD
Strain-induced boundary migration is simulated using finite-element analysis (FEA) for deformation and interface tracking for boundary migration. The FEA approach provides microstructure- and texture-dependent mechanical state information, including local stresses and (estimates of) dislocation densities. These mechanical state data are used, along with the local interface curvature obtained from the interface geometries, to parameterize the driving ‘‘forces’’ for boundary motion needed by the interface tracking model. In this section, the deformation and migration models are discussed separately, and the procedure used
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