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A Symbolic-Numerical Algorithm for Material Parameter Identification
Abstract
The advanced yield criteria derived for describing plastic anisotropy in sheet metals during last decade provides higher accuracy and flexibility. These yield criteria are still not used extensively due to the complexities accrued: increasing number of material parameters (additional tests), a complex non-linear programming problem. The aim of the current study is to simplify the material parameters identification process. Symbolic-numerical algorithm for material parameters identification is treated. The algorithm proposed is based on reduction of the number of nonlinear relations included in material parameters identification problem. The error minimization algorithm based approach is employed. The global optimization is performed by use of hybrid genetic algorithm (GA). The formability analysis of the 6000 series aluminum alloy sheet AA6181-T4 is considered as a case study and used for testing the method proposed.
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Plastic anisotropy in numerical analysis of sheet metal forming operations can be described very efficiently by means of analytical yield functions. However, for an anisotropic sheet material acceptable calibration of an appropriate yield function requires numerous mechanical testing procedures involving different loading modes such as directional uniaxial tensile tests and an equibiaxial tensile or bulge test. Realization of the mentioned loading modes requires the usage of different testing devices that are not always available. Therefore, a calibration procedure for advanced yield functions involving only a single tensile test machine seems appealing. In the present article a calibration method involving three directional uniaxial tensile tests and two plane strain tensile tests is proposed. This calibration method is applied to the recently introduced yield function Yld2003 [H. Aretz, Applications of a new plane stress yield function to orthotropic steel and aluminium sheet alloys, Model. Simul. Mater. Sci. Eng. 12 (2004) 491–509; H. Aretz, A non-quadratic plane stress yield function for orthotropic sheet metals, J. Mater. Process. Technol. 168 (2005) 1–9] using different materials. The obtained results are compared to those obtained by using the conventional calibration based on uniaxial and equibiaxial test data. It is shown that for all considered materials the proposed calibration procedure gives satisfying results. Finally, for selected materials and with respect to the different calibration procedures sensitivity analyses concerning the predicted forming limit diagram (FLD) are carried out using the finite element based FLD simulation approach proposed by Lademo et al. [O.-G. Lademo, T. Berstad, O.S. Hopperstad, K.O. Pedersen, A numerical tool for forma-bility analysis of aluminium alloys. Part I. Theory, Steel Grips 2 (2004) 427-431; O.-G. Lademo, T. Berstad, O.S. Hopperstad, K.O. Pedersen, A numerical tool for formability analysis of aluminium alloys. Part II. Experimental validation, Steel Grips 2 (2004) 433–438].
The objective of the work presented here is to assess the performance of two non-quadratic yield functions for orthotropic sheet metals under plane stress conditions, namely Yld96 and BBC2000, on forming limit prediction. The similitude and the differences between both of them are discussed. The Newton–Raphson numerical method respectively the minimisation of an error-function has been used for the numerical identification of the Yld96 and BBC2000 coefficients. The necking phenomenon was modelled by using the Marciniack–Kuczinsky (M–K) theory. In the present study an aluminium alloy sheet metal AA5XXX is considered. Yield surface shapes, yield stress and r-value directionalities of Yld96 and BBC2000 were investigated and compared with the experimental data. A successful correlation is observed between the experimental FLDs and the computed limit strains when, the shape of yield locus is described by Yld96 criterion respectively BBC2000 criterion and the hardening law represented by Voce equation.