Study of limit strains for FCC and BCC sheet metal using polycrystal plasticity

AbstractIn this research, we analyze forming-limit strains of FCC and BCC materials using a viscoplastic self-consistent polycrystal model (VPSC) in conjunction with the Marciniak–Kuczynski (MK) approach. In particular, our work is focused on the theoretical analysis and comparison between FCC and BCC crystal structures made by Inal et al. [Inal, K., Neale, K.W., Aboutajeddine, A., 2005. Forming limit comparison for FCC and BCC sheets, International Journal of Plasticity, 21, 1255–1266]. These authors performed their simulations based on a generalized Taylor-type polycrystal model (MK-FC), finding a remarkably low forming-limit curve for the FCC material and an extremely high forming-limit curve for the BCC material, in the biaxial stretching range. We verified that our predictions are similar to Inal’s results for both FCC and BCC materials when the MK-FC model is used. However, MK-VPSC calculations do not give such extreme values, and we believe that this theory predicts much more reliable results for both FCC and BCC crystallographic assumptions. We also found that localized necking depends on texture evolution in the vicinity of equi-biaxial stretching, through the sharpness of the predicted yield surface. Finally, it is shown that the MK-VPSC’s predictions are in good agreement with experimental data for AA5182-O and a DQ-type steel-sheet metal

Parameter identification method for a polycrystalline viscoplastic selfconsistent model based on analytical derivatives of the direct model equations

An inverse method for automatic identification of the parameters involved in a polycrystalline viscoplastic selfconsistent (VPSC) model is presented. The parameters of the constitutive viscoplastic law at the single-crystal level, i.e. the critical resolved shear stresses (CRSS) of slip and twinning and the micro-hardening coefficients, can be identified using experimental data at the polycrystal level, i.e. stress-strain curves and deformation-induced textures. The minimization problem is solved by means of a Gauss-Newton scheme and the sensitivity matrix is evaluated by analytical differentiation of the direct model equations. As a particular case, the optimization procedure for the Taylor full constraints (FC) formulation is also presented. The convergence and stability of the identification scheme are analysed using several validation tests for different deformation paths imposed to a polycrystal of hexagonal structure. As an example of application of this inverse method, the relative CRSS of the active deformation systems of a Zircaloy-4 sheet are identified, based on several textures measured for different reductions and rolling directions

Sensitivity of α-ZY4 high-temperature deformation textures to the β-quenched precipitate structure and to recrystallization: Application to hot extrusion

Hot extrusion of Zircaloy-4 tubes usually starts from β-quenched microstructures and induces strong textures. Individual crystallographic orientations were investigated by transmission electron microscopy using the electron backscatter pattern (EBSP) technique as well as Kikuchi patterns. Basal poles were found close to the tangential direction of the tubes in regions exhibiting fine and homogeneously distributed precipitates (FHDPs). In contrast, regions with large and isolated precipitates (LIPs) had more variable orientations. Laboratory plane strain compression tests were performed and the induced textures were compared with numerical simulations using a polycrystalline viscoplastic self-consistent model. The β-quenched material was modeled as a mixture of LIP and FHDP regions, each having a different set of slip system hardnesses, with a volume fraction depending on the previous thermal history. The model was subsequently applied to predict the texture evolution during extrusion with metadynamic recrystallization taking place thereafter. The calculation suggests that recrystallization modifies the orientation of those grains where 〈c+a〉 crystallographic slip has been significantly activated during deformation

Measurement of In-Grain Orientation Gradients by EBSD and Comparison with Finite Element Results

The characterization of In-grain orientation gradients by electron backscattering diffraction (EBSD) technique was studied. The study, based on finite element (FE) technique, involved the simulation of plane strain compression of the crystal grains. In regard to it, the construction of orientation distribution function (ODF) by superimposing spherical Gaussian distributions on the mean orientation of grains was also discussed

Structural reactivation in plate tectonics controlled by olivine crystal anisotropy

Reactivation of structures inherited from previous collisional or rifting events, especially lithospheric-scale faults, is a major feature of plate tectonics. Its expression ranges from continental break-up along ancient collisional belts to linear arrays of intraplate magmatism and seismicity. Here we use multiscale numerical models to show that this reactivation can result from an anisotropic mechanical behaviour of the lithospheric mantle due to an inherited preferred orientation of olivine crystals. We explicitly consider an evolving anisotropic viscosity controlled by the orientation of olivine crystals in the mantle. We find that strain is localized in domains where shear stresses on the inherited mantle fabric are high, and that this leads to shearing parallel to the inherited fabric. During rifting, structural reactivation induced by anisotropy results in oblique extension, followed by either normal extension or failure. Our results suggest that anisotropic viscosity in the lithospheric mantle controls the location and orientation of intraplate deformation zones that may evolve into new plate boundaries, and causes long-lived lithospheric-scale wrench faults, contributing to the toroidal component of plate motions on Earth. © 2009 Macmillan Publishers Limited. All rights reserved