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ABSTRACTIn the work presented in this paper, several strain rate potentials are examined in order to analyze their ability to model the initial stress and strain anisotropy of several orthotropic sheet materials. Classical quadratic and more advanced non-quadratic strain rate potentials are investigated in the case of FCC and BCC polycrystals. Different identifications procedures are proposed, which are taking into account the crystallographic texture and/or a set of mechanical test data in the determination of the material parameters.
In this paper, anisotropic strain rate potentials based on linear transformations of the plastic strain rate tensor were reviewed in general terms. This type of constitutive models is suitable for application in forming simulations, particularly for finite element analysis and design codes based on rigid plasticity. Convex formulations were proposed to describe the anisotropic behavior of materials for a full 3-D plastic strain rate state (5 independent components for incompressible plasticity). The 4 th order tensors containing the plastic anisotropy coefficients for orthotropic symmetry were specified. The method recommended for the determination of the coefficients using experimental mechanical data for sheet materials was discussed. The formulations were shown to be suitable for the constitutive modeling of FCC and BCC cubic materials. Moreover, these proposed strain rate potentials, called Srp2004-18p and Srp2006-18p, led to a description of plastic anisotropy, which was similar to that provided by a generalized stress potential proposed recently, Yld2004-18p. This suggests that these strain rate potentials are pseudo-conjugate of Yld2004-18.
For numerical simulation of sheet metal forming, more and more advanced phenomenological functions are used to model the anisotropic yielding. The latter can be described by an adjustment of the coefficients of the yield function or the strain rate potential to the polycrystalline yield surface determined using crystal plasticity and X-ray measurements. Several strain rate potentials were examined by the present authors and compared in order to analyse their ability to model the anisotropic behaviour of materials using the methods described above to determine the material parameters. Following that, a specific elastic-plastic time integration scheme was developed and the strain rate potentials were implemented in the FE code. Comparison of the previously investigated potentials is continued in this paper in terms of numerical predictions of cup drawing, for different bcc and fcc materials. The identification procedure is shown to have an important impact on the accuracy of the FE predictions.
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