A theory of the yielding and plastic flow of anisotropic metals
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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.read more
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Overview of constitutive laws, kinematics, homogenization and multiscale methods in crystal plasticity finite-element modeling: Theory, experiments, applications
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Plane stress yield function for aluminum alloy sheets—part 1: theory
Frédéric Barlat,Frédéric Barlat,J.C. Brem,Jeong W. Yoon,Jeong W. Yoon,Kwansoo Chung,Re Dick,D.J. Lege,Farhang Pourboghrat,Shi-Hoon Choi,E. Chu +10 more
TL;DR: In this article, a plane stress yield function that well describes the anisotropic behavior of sheet metals, in particular, aluminum alloy sheets, was proposed, which was introduced in the formulation using two linear transformations on the Cauchy stress tensor.
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Plastic behavior and stretchability of sheet metals. Part I: A yield function for orthotropic sheets under plane stress conditions
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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.
References
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The Mathematical Theory of Elasticity.
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The Plastic Distortion of Metals
TL;DR: The plasticity of metals has been the subject of many recent papers as discussed by the authors, but, owing to the complexity of the subject, there is but little agreement between different researches and attempts to extract simple generalisations from the very complex phenomena have been made chiefly in two directions: engineers have used test bars of certain specially simple form, such as uniform round bars which they have subjected to twisting or tension, and they have found the effect on their test of varying physical conditions.
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Rectilinear Locomotion in Snakes
TL;DR: Rectilinear movement is quite impossible for such snakes as Coluber, which have the skin on the venter firmly attached, but it is characteristic of Bitis, Crotalus, and other thick-bodied venomous snakes when they are prowling.
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