K. Inal and K. W. Neale

Faculty of Engineering,
University of Sherbrooke,
Sherbrooke, Quebec, Canada J1K 2R1,
E-mail: Kenneth. Neale@USherbrooke. ca


In this paper, applications of crystal plasticity theory to the numerical modelling of large strain plasticity phenomena are considered. In particular, instabilities and localized deformation phenomena for face-centred cubic (FCC) and body-centred cubic (BCC) polycrystals subjected to various deformation modes are investigated. In-house finite element analyses based on a rate-dependent crystal plasticity model have been developed to simulate the large strain behaviour for sheet specimens subjected to plane strain and plane stress deformation modes. In the formulation, the plastic deformation of an individual crystal is assumed to be due to crystallographic slip and simulations are performed using two approaches. In the first approach, each material point in the finite element analysis is considered to be a polycrystalline aggregate having a large number of FCC or BCC grains, and the Taylor theory of crystal plasticity is adopted to model the behaviour of the polycrystal. In the second approach, each grain is represented individually using one or more finite elements, and the constitutive response within each element is given by the single crystal constitutive model. Both approaches account for initial textures, as well as texture evolution during large plastic deformations. The numerical analyses incorporate parallel computing features. The results of simulations for the above-mentioned deformation modes are discussed, and in certain cases comparisons are made with experimental results for rolled aluminum sheet alloys and for draw quality steels.


The mechanical properties of a polycrystalline metal depend on many attributes of its microstructure; consequently, considerable efforts have been devoted to the study of micromechanics. These studies indicate that, among the factors which result in the plastic deformation of single crystals and polycrystals, crystallographic slip occurring by the migration across the slip planes of atomic defects, termed dislocations, is the dominant one.

Crystallographic slip induces lattice rotations, which result in a non-random distribution of the crystal orientations in polycrystals. The textures developed during forming processes are macroscopic averages of such non-random orientations. Research indicates that texture occurs in many metal forming processes such as drawing, extrusion, rolling and sheet metal forming. These textures not only have profound effects on the mechanical and thermal properties of metals, but also have great influence on subsequent fabrication processes as well as on the quality of the products. Thus, it is obvious that accurate simulations of large strain phenomena should consider initial texture and its evolution, as well as the anisotropy induced by the evolution of microstructure and microscopic properties.

To model processes such as texture evolution and its influence on deformation-induced anisotropy, micromechanically based models of plastic behaviour are required. In particular, constitutive relations formulated on the concepts of crystal plasticity must be adopted. Since Taylor’s pioneering work in 1938, the prediction of the deformation behaviour of polycrystalline solids from the response of their single crystal constituents has been the focus of many investigations. Thus, many crystal plasticity


M. Pandey et al. (eds), Advances in Engineering Structures, Mechanics & Construction, 583-593.

© 2006 Springer. Printed in the Netherlands.

models have been proposed or modified to simulate the behaviour of polycrystalline metals during plastic deformation from the response of their single crystal constituents.

The mathematical modelling of material behaviour is a very effective way of reducing time and costs involved in optimizing manufacturing processes. Indeed, numerous complex forming operations have been simulated using numerical methods in order to predict critical parameters. Up to the 1980’s, most applications involving numerical techniques such as the finite element method have been based on phenomenological constitutive models since microscopic models are significantly more demanding in terms of computational resources. However, the introduction of parallel computers has rendered metal forming modelling based on crystal plasticity feasible since they offer more computational power and storage than serial computer architectures. With proper parallelization techniques, realistic applications based on crystal plasticity can be performed on parallel supercomputers.

In this paper, applications of crystal plasticity theory to the numerical modelling of large strain plasticity phenomena are considered. Crystal plasticity theory is employed to model both FCC and BCC polycrystals where modelling of the polycrystalline aggregates is carried out at various scales. We first recapitulate the constitutive model. Then the parallel computing algorithms are briefly presented. In the last section we present two different applications where crystal plasticity theory is employed to simulate instabilities and localized deformation phenomena for FCC and BCC polycrystals subjected to plane strain tension and plane stress tension.