Keywords: uniaxial compression, crystal plasticity finite element method, true strain, true stress.

The deformation of polycrystalline is determined by the deformation of a single crystal. The best way of dealing with the polycrystalline deformation behaviour is to apply the proprieties of single crystal to the polycrystalline by the statistical method. If the arrangement is disorderly and unsystematic without any obvious textures, the deformations of polycrystalline can be obtained by averaging the deformation of the single crystal. If there are some tendencies that the single crystal in the polycrystalline materials arranges along a certain direction, the properties of polycrystalline can be obtained by the weighted average. In the polycystic constitutive model, the plastic deformation of polycrystalline can be obtained from the average of single crystal plastic deformation. A rate dependent crystal plasticity constitutive model [1] with respect to latent hardening in the finite element (FE) analysis is developed to simulate the compression - upsetting of pure aluminium. To compare the influence of the different finite element models on the simulation results, the Taylor-Type and finite element polycrystalline models are respectively employed in the finite element software ABAQUS to simulate the development of the deformation texture using rate dependent crystal constitutive equations. In order to obtain the random uniform equiaxed grains, the samples of the electron backscatter diffraction (EBSD) were prepared with the method of Mao [2] and Raabe et al. [3], the pure aluminum samples had been forged three times on the three orthogonal dimensions with the deformations of 25%, 15% and 5% respectively. The samples were annealed at 500°C. All the initial data from the experiments were input into the UMAT subroutine of the ABAQUS software to simulate the uniaxial compression (upsetting) of the aluminium plate [4]. With an increase of true strain, the crystal can rotate, and form the silk textures easily. Therefore, the predicted and experimental silk textures tend to be sharper and stronger accordingly. The results from the two polycrystalline models are both close to the experimental results. There is only one kind of silk texture (<110> texture) formed during the uniaxial compression, and the silk axes locate in the centre of the pole figure. At the same time, it is certain that there is a minority of crystals distribute along the <110> and <113> axes. However, with the same true strain, the stress values from the two modelling results are lower than those from the experimental results. Comparison with the deformation contouring map of the pure aluminium at the different strains, the finite element polycrystalline model can predict the drum deformation of pure aluminium accurately during the uniaxial compression. Whereas the deformation from the Taylor-type model is very even without any drum deformation. The reason is that the Taylor-type model has a much lower deformation flow stress than that of the finite element model. The slip systems can be activated more easily than those of the finite element model.

1

S.R. Kalidindi, L. Anand, "Crystallographic Texture Evolution in Bulk Deformation Processing of FCC Metals", Journal of the Mechanics and Physics of Solids, 40(3), 537-569, 1992. doi:10.1016/0022-5096(92)80003-9

2

W. Mao, "Quantitative Investigation of Rolling Texture in Aluminum Plate", Journal of University of Science and Technology Beijing, 12(1), 3236-3238, 1990 (in Chinese).

3

D. Rabbe, Z. Zhao, W. Mao, "On the Dependence of In-Grain Subdivision and Deformation Texture of Aluminum on Grain Interaction", Acta Mater, 50 (17), 4379-4394, 2002. doi:10.1016/S1359-6454(02)00276-8

4

"ABAQUS/Standard user's manual", Hibbitt, Karlsson & Sorensen, Inc, 2002.

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