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Experimental Mechanics

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15.06.2020 | Research paper

On the New Shear Constraint for Plane-Stress Orthotropic Plasticity Modeling of Sheet Metals

verfasst von: W. Tong, M. Alharbi, J. Sheng

Erschienen in: Experimental Mechanics | Ausgabe 7/2020

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Abstract

Background

A shear constraint was very recently proposed by Abedini et al. (Int. J. Solids and Structures 151: 118–134 2018) to evaluate and calibrate advanced non-quadratic anisotropic yield criteria and to eliminate what they called non-physical numerical artifacts in those criteria.

Objective

This investigation points out that such a shear constraint is in fact unnecessary for plane-stress orthotropic plasticity in general.

Methods

Using the well-known Hill’s 1948 quadratic and Gotoh’s 1977 quartic yield functions for orthotropic sheet metals in plane stress, it is shown analytically that pure shear stressing and pure shear straining loading conditions are not equivalent except for very special cases. By conducting a series of shearing experiments on an aluminum sheet metal, the actual test results are shown not to provide any unequivocal supporting evidence at all to the newly proposed shear constraint.

Results

The so-called non-physical numerical artifacts of the non-equivalence in pure shear stressing and pure shear straining of a sheet metal are in fact the intrinsic features of an anisotropic material in general.

Conclusions

The newly proposed shear constraint should thus not be accepted to be universally applicable at all for anisotropic plasticity modeling of sheet metals. Such a proposed constraint itself shall be regarded as a provisional simplifying assumption of reduced anisotropy only for some particular sheet metals under consideration.

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Per the 2D coordinate transformation of stress tensor, one has \( \sigma _{x} = \sigma _{1} \text {cos}^{2}\theta +\sigma _{2} \sin \limits ^{2}\theta \), \( \sigma _{y} = \sigma _{1} \sin \limits ^{2}\theta +\sigma _{2} \text {cos}^{2}\theta \), \( \tau _{xy} =(\sigma _{1}-\sigma _{2})\sin \limits \theta \text {cos}\theta \).

So for simplicity, the superscript ‘p’ will be dropped in the rest of the manuscript for components of plastic strain increments

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Titel: On the New Shear Constraint for Plane-Stress Orthotropic Plasticity Modeling of Sheet Metals
verfasst von: W. Tong
M. Alharbi
J. Sheng
Publikationsdatum: 15.06.2020
Verlag: Springer US
Erschienen in: Experimental Mechanics / Ausgabe 7/2020
Print ISSN: 0014-4851
Elektronische ISSN: 1741-2765
DOI: https://doi.org/10.1007/s11340-020-00596-3

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Abstract

Background

Objective

Methods

Results

Conclusions

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