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Fundamentals of Engineering Plasticity by William F.,Hosford

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7 Anisotropic Plasticity

Although materials are frequently assumed to be isotropic, they rarely are. The two main causes of anisotropy are preferred orientations of grains (crystallographic texture) and mechanical fibering, which reflect the elongation and alignment of microstructural features such as inclusions and grain boundaries. Anisotropy of plastic behavior is almost entirely caused by the presence of preferred orientations.

Hill's 1948 Anisotropic Theory

In 1948, Hill [1, 2] proposed the first quantitative treatment of plastic anisotropy. He considered materials with three orthogonal axes of anisotropy, x, y, and z about which there is a two-fold symmetry of properties. Therefore, the yz, zx, and xy planes are planes of mirror symmetry. ...

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