A model of grain fragmentation based on lattice curvature La ´szlo ´ S. To ´th a, * , Yuri Estrin b,c , Rimma Lapovok b , Chengfan Gu b a Laboratoire de Physique et Me ´canique des Mate ´riaux, Universite ´ Paul Verlaine Metz, Metz, France b ARC Centre of Excellence for Design in Light Metals, Department of Materials Engineering, Monash University, Clayton, Victoria 3800, Australia c CSIRO Division of Materials Science and Engineering, Clayton, Victoria, Australia Received 13 August 2009; received in revised form 10 November 2009; accepted 14 November 2009 Available online 7 December 2009 Abstract A new model is proposed that aims to capture within a single modelling frame all the main microstructural features of a severe plastic deformation process. These are: evolution of the grain size distribution, misorientation distribution, crystallographic texture and the strain-hardening of the material. The model is based on the lattice curvature that develops in all deformed grains. The basic assumption is that lattice rotation within an individual grain is impeded near the grain boundaries by the constraining effects of the neighbouring grains, which gives rise to lattice curvature. On that basis, a fragmentation scheme is developed which is integrated in the Taylor visco- plastic polycrystal model. Dislocation density evolution is traced for each grain, which includes the contribution of geometrically nec- essary dislocations associated with lattice curvature. The model is applied to equal-channel angular pressing. The role of texture development is shown to be an important element in the grain fragmentation process. Results of this modelling give fairly precise pre- dictions of grain size and grain misorientation distribution. The crystallographic textures are well reproduced and the strength of the material is also reliably predicted based on the modelling of dislocation density evolution coupled with texture development. Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Grain fragmentation; Severe plastic deformation; Texture development; Strain-hardening; Misorientation distribution 1. Introduction Grain refinement by plastic deformation is a potent way of improving the mechanical properties of metallic materials. In a recent stream of research articles, extreme grain refine- ment down to micron and sub-micron range by severe plastic deformation (SPD) has been reported. Recent overviews of the area can be found in Refs. [1,2]. Most popular techniques of grain refinement by severe plastic deformation are equal- channel angular pressing, high pressure torsion and accumu- lated roll bonding, but further SPD-based processing routes are also emerging. While experimental work in this area has produced a significant body of knowledge with regard to microstructure and properties of SPD processed materials, the mechanisms of grain refinement, which is crucial for the property improvement, are far from being unravelled. Important work of the RISØ group [3,4] has led to a compre- hensive classification of the grain structures produced by deformation to large strains, but again the underlying mech- anisms are not fully understood. Previous work on SPD- induced microstructures [5,6] suggests that a dislocation cell structure formed within a grain can be considered as a pre- cursor of the eventual grain structure. Pantleon [7] and Estrin et al. [8] quantified the notion that fine granularity is attained through gradual accumulation of misorientations across the dislocation cell boundaries with progressing straining. Their calculations of the increase of dislocation cell misorientations are consistent with the observed level of misorientations associated with the incidental grain boundaries (in the terminology of Pantleon and Hansen [3]), but cannot account for the occurrence of a very signifi- cant fraction of large-angle grain boundaries found experi- mentally, e.g. for equal-channel angular pressing (ECAP). The current situation with modelling SPD processing can be characterized as follows. Whereas the existing 1359-6454/$36.00 Ó 2009 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2009.11.020 * Corresponding author. Tel.: +33 387547238; fax: +33 387315366. E-mail address: toth@univ-metz.fr (L.S. To ´ th). www.elsevier.com/locate/actamat Available online at www.sciencedirect.com Acta Materialia 58 (2010) 1782–1794