Prediction of yield surfaces of textured sheet metals
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INTRODUCTION
THE yield surface defines the critical stress levels for plastic yielding, and it often serves as a plastic potential for the plastic strain increment according to the associated flow rule. For finite-element analysis of forming operations, the yield surface and the stress-strain curve are important material property data. The constitutive equations that have been proposed to describe the plastic yielding of isotropic and anisotropic materials are divided into two approaches: crystallographic and phenomenological. In the crystallographic approach, the material is assumed to be a polycrystal consisting of many single crystals (grains). Plastic flow is assumed to occur only by crystallographic slip on given slip systems within each crystal.[1] The yield stress, normalized by the critical resolved shear stress, is derived from polycrystal plasticity calculations as an averaged behavior over the total number of single crystals. This approach can be used to take crystallographic texture evolution into account during forming operations. In the phenomenological approach, the plastic behavior of metals is assumed to be well described by an analytical yield function. Hill’s 1948 yield function is certainly the most popular for describing the plastic behavior of anisotropic materials such as rolled sheets.[2] However, Hill’s yield function cannot account for the so-called anomalous behavior of aluminum alloys.[3] Hill proposed a nonquadratic yield function that can be used to improve the yielding description for aluminum alloys.[4,5] Hosford introduced an isotropic yield function based on the results of polycrystal calculations.[6] Other nonquadratic yield functions that describe plastic anisotropy were proposed by Barlat and Lian[7] and Barlat et al.[8,9] The purpose of this study is to compare the effects of texture components typical of aluminum alloy sheets on yield stresses and R-values predicted from the Taylor– S.H. CHOI, Postdoctoral Fellow, J.H. CHO, Graduate Student, and K.H. OH, Professor, are with the Division of Materials Science and Engineering and Research Institute for Advanced Materials, Seoul National University, Seoul 151-742, Korea. F. BARLAT, Technical Specialist, is with the Material Mechanics and Microstructure Center, Alcoa Technical Center, Alcoa Center, PA 15069-0001. K. CHUNG, Professor, is with the Department of Fiber and Polymer Science, Seoul National University. J.W. KWON, Senior Research Engineer, is with the Institute for Advanced Engineering, Kyonggi-do 449-020, Korea. Manuscript submitted December 5, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS A
Bishop–Hill (TBH) polycrystal model[10,11,12] and the phenomenological yield function approach. The six texture components investigated here were cube, Goss, copper, brass, S, and rotated cube, as these components are typically observed in aluminum alloys. The calculated values were used to determined the coefficients of the phenomenological yield functions. The phenomenological yield functions proposed by Hill in 1948, by Barlat e
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