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Hill yield criterion
About: Hill yield criterion is a research topic. Over the lifetime, 254 publications have been published within this topic receiving 11161 citations.
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TL;DR: In this article, a theory is suggested which describes the yielding and plastic flow of an anisotropic metal on a macroscopic scale and associated relations are then found between the stress and strain-increment tensors.
Abstract: A theory is suggested which describes, on a macroscopic scale, the yielding and plastic flow of an anisotropic metal. The type of anisotropy considered is that resulting from preferred orientation. A yield criterion is postulated on general grounds which is similar in form to the Huber-Mises criterion for isotropic metals, but which contains six parameters specifying the state of anisotropy. By using von Mises' concept (1928) of a plastic potential, associated relations are then found between the stress and strain-increment tensors. The theory is applied to experiments of Korber & Hoff (1928) on the necking under uniaxial tension of thin strips cut from rolled sheet. It is shown, in full agreement with experimental data, that there are generally two, equally possible, necking directions whose orientation depends on the angle between the strip axis and the rolling direction. As a second example, pure torsion of a thin-walled cylinder is analyzed. With increasing twist anisotropy is developed. In accordance with recent observations by Swift (1947), the theory predicts changes in length of the cylinder. The theory is also applied to determine the earing positions in cups deep-drawn from rolled sheet.
3,426 citations
TL;DR: In this article, a yield function that describes the behavior of orthortropic sheets, metals exhibiting planar anisotropy and subjected to plane stress conditions is proposed, which is shown to give a reasonable approximation to plastic potentials calculated with the Taylor/Bishop and Hill theory of polycrystalline plasticity for plane stress states.
1,083 citations
TL;DR: In this paper, a new six-component yield surface description for orthotropic materials is developed, which has the advantage of being relatively simple mathematically and yet is consistent with yield surfaces computed with polycrystal plasticity models.
940 citations
01 Jan 1979
TL;DR: In this paper, the authors considered the plasticity of metal polycrystals with preferred orientations from a phenomenological standpoint and proved the existence of a work-equivalent function of the tensor strain-rate over any yield surface.
Abstract: The plasticity of metal polycrystals with preferred orientations is considered from a phenomenological standpoint. Some new general theorems are proved, in particular the existence of a work-equivalent function of the tensor strain-rate over any yield surface. The status of the classical theory of plastic anisotropy is re-appraised in the light of recent experiments, which are themselves critically reviewed. A new type of yield function is proposed to account for the so-called anomalous behaviour of some materials.
699 citations
TL;DR: In this article, a macroscopic orthotropic yield criterion, which can describe both the anisotropy of a material and the yielding asymmetry between tension and compression, is introduced.
650 citations