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Paper 264

Calibration of a Distortional Hardening Model of Plasticity

J. Plešek1, Z. Hrubý1, S. Parma1, H.P. Feigenbaum2 and Y.F. Dafalias3
1Institute of Thermomechanics, Academy of Sciences of the Czech Republic, Prague
2Department of Mechanical Engineering, Northern Arizona University, Flagstaff, USA
3Department of Civil and Environmental Engineering, University of California at Davis, USA

Keywords: directional distortional hardening, metal plasticity, yield surface.

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Distortion of yield surfaces as a result of strain hardening was observed in numerous experiments with various types of metals. In the stress space, the subsequent yield surfaces are highly curved in the direction of loading and flattened in the opposite direction. Following several attempts at modelling such behaviour in the past, promising approaches have been proposed recently. Feigenbaum and Dafalias developed the Armstrong-Frederick hardening rule by constructing directional terms involving the inner product of the backstress with local normal tensors, which gave rise to two models [1,2].

The model studied in this paper, suitable for metal plasticity, represents probably the simplest form of constitutive equations listing only five additional material parameters. Despite the simplicity of this model can capture reasonably well all the essential features of a yield surface distortion. Four of the constants enter the Armstrong-Frederick type evolution equations with recall memory terms for backstress and the isotropic variable. The fifth parameter controls directional multiplier, which, motivated by the AF rule, consists of the inner product of the stress tensor with backstress.

The usual problem arises with the identification of parameters governing internal variables. Apart from thermodynamic constraints, conditions on maintaining convexity of distorted surfaces should be met, as noted by Plesek et al. [3], so that the convergence of return mapping numerical integrators was guaranteed.

The availability of fitting procedures is often a decisive factor in practice. Reduction of constitutive equations to one variable form leads to an algebro-differential system difficult to solve. This, of course, hinders finding a proper way to identify material parameters from tensile or torsion tests. The present paper, nevertheless, shows that a closed form solution exists and may be used for calibration purposes. The idea of computing asymptotic states for cyclically loaded specimens is another asset and indeed, the ensuing equations are much more simpler. Revealing insight into the process of calibration may be gained by sensitivity analysis. In this work, the analysis was carried out numerically and the optimum loading modes selected.


H.P. Feigenbaum, Y.F. Dafalias, "Directional distortional hardening in metal plasticity whithin thermodynamics", Int. J. Solids Struct., 44, 7526-7542, 2007.
H.P. Feigenbaum, Y.F. Dafalias, "Simple model for directional distortional hardening in metal plasticity whithin thermodynamics", J. Eng. Mech., 134, 730-738, 2008.
J. Plešek, H.P. Feigenbaum, Y.F. Dafalias, "Convexity of yield surface with directional distortional hardening rules", J. Eng. Mech., 136, 477-484, 2010.