Abstract
The rate-independent Schmid assumption for a metal crystal results in a yield surface that is faceted with sharp corners. Regularized yield surfaces round off the corners and can be convenient in computational implementations. To assess the error by doing so, the coefficients of regularized yield surfaces are calibrated to exactly interpolate certain points on the facets of the perfect Schmid yield surface, while the different stress predictions in the corners are taken as the error estimate. Calibrations are discussed for slip systems commonly activated for bcc and fcc metals. It is found that the quality of calibrations of the ideal rate-independent behavior requires very large yield-surface exponents. However, the rounding of the corners of the yield surface can be regarded as an improved approximation accounting for the instant, thermal strain-rate sensitivity, which is directly related to the yield-surface exponent. Distortion of the crystal yield surface during latent hardening is also discussed, including Bauschinger behavior or pseudo slip systems for twinning, for which the forward and backward of the slip system are distinguished.
Highlights
A robust and general formulation with a yield surface for crystal plasticity can conveniently be applied in a framework similar to the continuum-plasticity framework for finite-element calculations, e.g., including elasticity and using a return-mapping algorithm
The regularized yield surface corresponds exactly to a self-similar iso-value of the rate of plastic work of the flow potential for the viscoplastic power-law formulation. This solution again corresponds to a Taylor ambiguity solution for the selection of active slip systems, namely the limit of vanishing strain-rate sensitivity, which showed that this solution corresponds to the one which can approximately, but not exactly, can be obtained applying singular-value decomposition or quadratic programming
The results show that the approximation ξs = 1 holds for n larger than ≈ 50, which is the case for ferritic steels at room temperature and below
Summary
A robust and general formulation with a yield surface for crystal plasticity can conveniently be applied in a framework similar to the continuum-plasticity framework for finite-element calculations, e.g., including elasticity and using a return-mapping algorithm. The regularized yield surface corresponds exactly to a self-similar iso-value of the rate of plastic work of the flow potential for the viscoplastic power-law formulation This solution again corresponds to a Taylor ambiguity solution for the selection of active slip systems, namely the limit of vanishing strain-rate sensitivity (see [10]), which showed that this solution corresponds to the one which can approximately, but not exactly, can be obtained applying singular-value decomposition or quadratic programming. The framework discussed in this article, enables formulation of models with latent hardening and several sets of active slip systems This allows yield-surface distortions as predicted by models dealing with strain-path changes related to Bauschinger and cross-hardening effects, e.g., [17,18,19,20].
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