Summary
It is shown that the components of a sixth rank anisotropy tensor are physically significant in representing the distortion observed in both the initial and subsequent yield surface for a polycrystalline material. This feature of anisotropy does not appear in the ellipsoidal surface given by previous theories in which second and fourth rank anisotropy tensors are employed. The number of tensor components, for a series function embodying tensor terms in ascending rank, reduces to a manageable number by the imposition of symmetry and coincidence between the axes of stress and principal orthotropic directions. The identification is made between the yield limits, as found from biaxial stress experiments and tensor components in composite sum form. A one-to-one correspondence is found from a further simplification through the assumption of incompressibility. This is confirmed experimentally for an orthotropic rolled copper and copper alloy sheet.
An examination is made of the physical significance of a translation tensor which appears in the subsequent yield function. It is shown that the components of this tensor can be directly identified with those of an internal stress tensor that is a consequence of the heterogenous slipped state in a deformed polycrystal.
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Rees, D.W.A. An examination of yield surface distortion and translation. Acta Mechanica 52, 15–40 (1984). https://doi.org/10.1007/BF01175962
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DOI: https://doi.org/10.1007/BF01175962