Upper-bound anisotropic yield locus calculations assuming 〈111〉-pencil glide
TL;DR: In this paper, an upper-bound model which combines a least-shear analysis and Piehler's maximum virtual work analysis was proposed to determine axisymmetric deformation.
About: This article is published in International Journal of Mechanical Sciences.The article was published on 1980-01-01 and is currently open access. It has received 373 citations till now. The article focuses on the topics: Rotational symmetry & Yield (engineering).
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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.
1,374 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
TL;DR: In this article, two convex formulations are proposed to describe the anisotropic behavior of metals and alloys for a full stress state (3D) in general terms, and the type of input data recommended for the description of plastic anisotropy in sheet samples is discussed.
832 citations
TL;DR: In this article, a generalized phenomenological yield description is proposed to account for the behavior of the solute strengthened aluminum alloy sheets studied in this work and the experimental yield surfaces were found to be in good agreement with the polycrystal predictions for all materials and with the phenomenological predictions for most materials.
Abstract: In this work, yield surfaces were measured for binary aluminum-magnesium sheet samples which were fabricated by different processing paths to obtain different microstructures. The yielding behavior was measured using biaxial compression tests on cubic specimens made from laminated sheet samples. The yield surfaces were also predicted from a polycrystal model using crystallographic texture data as input and from a phenomenological yield function usually suitable for polycrystalline materials. The experimental yield surfaces were found to be in good agreement with the polycrystal predictions for all materials and with the phenomenological predictions for most materials. However, for samples processed with high cold rolling reduction prior to solution heat treatment, a significant difference was observed between the phenomenological and the experimental yield surfaces in the pure shear region. In this paper, a generalized phenomenological yield description is proposed to account for the behavior of the solute strengthened aluminum alloy sheets studied in this work. It is subsequently shown that this yield function is suitable for the description of the plastic behavior of any aluminum alloy sheet.
504 citations
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TL;DR: In this paper, a general relationship between stress and plastic strain in polycrystalline aggregate is derived for any metal in which individual crystals deform by slipping over preferred planes under a critical shear stress.
Abstract: Summary A general relationship between stress and plastic strain in a polycrystalline aggregate is derived for any metal in which individual crystals deform by slipping over preferred planes under a critical shear stress. Full account is taken of the non-uniform distortion due to mutual constraints between the grains of an aggregate. It is shown that a plastic potential exists which is identical with the yield function. Upper and lower bounds are obtained for an approximate calculation of this function for any applied system of combined stresses.
1,251 citations
TL;DR: In this paper, it was shown that the work-hardness of an isotropic aggregate of face-centred cubic crystals is a function only of the total plastic work if the grains hardened equally.
Abstract: Summary In continuation of a previous paper (Bishop and Hill 1951) it is conjectured that the work done in plastically deforming a polycrystal is approximately equal to that which would be done if the grains were free to deform equally. In conjunction with the principle of maximum plastic work, this enables the yield function of an aggregate to be calculated. This is done for an isotropic aggregate of face-centred cubic crystals, following a determination of the stresses needed to produce multi-slip. The theoretical yield criterion lies between those of Tresca and von Mises, in good agreement with observaton for copper and aluminum. It is shown further that the work-hardening of an aggregate would be a function only of the total plastic work if the grains hardened equally ; the departure from this functional relation is expressed explicitly in terms of the non-uniform hardening.
702 citations
633 citations
01 Dec 1971
TL;DR: In this article, the Taylor factor and the corresponding lattice rotations for tension or compression have been computed for grains of various orientations postulated to slip on arbitrary planes in 〈111〉 directions.
Abstract: Values of the Taylor factorM and the corresponding lattice rotations for tension or compression have been computed for grains of various orientations postulated to slip on arbitrary planes in 〈111〉 directions. The stresses in each grain were first obtained by numerically maximizing the work expression subject to the constraints of the pencil-glide yield expressions. The derived value of Mave = 2.733 is slightly lower than in the case of mixed {110}, {112}, and {l23} 〈111〉 slip and the computed rotations are in reasonable agreement with experiments on iron. In compression, 26 pct of the grains are predicted to rotate toward 〈100〉, although the 〈111〉 texture component develops faster. The computational method used can easily be applied to the determination of the mechanics of texture generation for arbitrary deformations.
196 citations
TL;DR: In this paper, the authors investigated the anomalous behavior of aluminium in uniaxial and biaxiaial tension and showed that anisotropic plasticity theory does not hold for all metals.
178 citations