crystalline plasticity

Continuum crystal plasticity theory aims at establishing a continuum mechanical framework accounting for the result of complex dislocation glide, multiplication and interaction processes at work in plastically deformed metals.

It encompasses a large class of now wide–spread models accounting for the anisotropic deformation of metal single crystals. Its roots are to be found in the works of Taylor, but the complete finite deformation framework is due to the successive contributions of Bilby, Kröner, Teodosiu, Rice and finally Mandel (1973). It is the appropriate framework to simulate the deformation of single crystal specimens under complex loading conditions (tension, shear, torsion, channel die, etc). Crystal plasticity can be used also to derive the behavior of metal polycrystals from the behavior of individual grains. Such models are now available at two levels. The most predictive version consists in considering sets of interacting grains with a sufficient

description of the transgranular behaviour which delivers three classes of information: the overall response of the considered material volume that may be close to the wanted effective behavior of the polycrystal, the mean stress and strain for grains having similar crystal orientations, and, finally, the complete heterogeneous stress/strain distribution inside individual grains. The results are obtained through considerable computational effort. 

The estimations provided by the Taylor or self–consistent schemes can capture the initial and strain–induced anisotropy of polycrystal behavior from the knowledge of single crystal behavior and material texture described by the orientation distribution function. Such models are now very efficient regarding computation time and quality of prediction, so that they can be used for industrial purposes like prediction of texture evolution in metal forming. They can even be included in finite element simulations.

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