Reducing Computational Cost and Allowing Automatic Remeshing in FEM Models of Metal Forming Coupled With Polycrystal Plasticity

Reprinted with permission from AIP Conf. Proc May 17, 2007 Volume 908, pp. 387-392 MATERIALS PROCESSING AND DESIGN; Modeling, Simulation and Applications; NUMIFORM '07; Proceedings of the 9th International Conference on Numerical Methods in Industrial Forming Processes; doi:10.1063/1.2740842. Copyright 2007 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of PhysicsInternational audienceThe paper proposes an original use of the Lagrangian particles concept for finite element computation of microstructure evolution in metal forming. The method amounts to distributing incomplete representations of the microstructure among the integration points of the mesh while a complete microstructure is associated with each Lagrangian particle. This decreases the computation time and enables the transport of microstructural variables when remeshing. While the method is presented for any kind of discretized microstructure, it is applied here to the prediction of mechanical anisotropy induced by crystallographic texture. In this specific case, the numerical predictions are validated against experiment by considering compression of a textured aluminium alloy (AA7175). The model accuracy is assessed with respect to mechanical anisotropy but texture evolution is also considered

Coupling the thermal and mechanical fields to metallurgical evolutions within a finite element description of a forming process

Finite element formulations are commonly used to predict stress, strain and temperature fields in metal forming. As these models have now gained robustness, an increasing attention is placed on the metallurgical evolutions associated with the thermal and mechanical fields. A finite element can be associated to a microstructure, and the microstructure description allows the modeling of a constitutive behavior, using conventional homogenization theories. These theories can be further refined with the help of finite element calculations describing the material structure at multiple scales. The paper concentrates on numerical strategies than can be developed to couple finite element formulations to metallurgical models of two kinds: those predicting crystallographic textures and mechanical anisotropy, and those dealing with phase changes controlled by diffusion. Multiscale finite element models describing key features of metallic structures are also discussed, within a digital material framework. © 2005 Elsevier B.V. All rights reserved

Reducing computational cost and allowing automatic remeshing in FEM models of metal forming coupled with polycrystal plasticity

The paper proposes an original use of the Lagrangian particles concept for finite element computation of microstructure evolution in metal forming. The method amounts to distributing incomplete representations of the microstructure among the integration points of the mesh while a complete microstructure is associated with each Lagrangian particle. This decreases the computation time and enables the transport of microstructural variables when remeshing. While the method is presented for any kind of discretized microstructure, it is applied here to the prediction of mechanical anisotropy induced by crystallographic texture. In this specific case, the numerical predictions are validated against experiment by considering compression of a textured aluminium alloy (AA7175). The model accuracy is assessed with respect to mechanical anisotropy but texture evolution is also considered. © 2007 American Institute of Physics

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