On the concept of relative and plastic spins and its implications to large deformation theories. Part II: Anisotropic hardening plasticity

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Department of Mechanical Engineering-Engineering Mechanics


By resorting to both microscopic and macroscopic considerations, including the concept of single slip, dislocation stress, and a scale invariance argument we show that the notion and formalism of the "relative spin" introduced in Part I reduces to that of "plastic spin" previously recognized in the literature. The central feature of this reduction is the possibility of obtaining physically based constitutive equations for the plastic spin along with appropriate evolution equations for the dislocation or back stress. When these constitutive models are incorporated in the analysis of existing data on tension-torsion tests, we find satisfactory agreement between theory and experiment. In particular, a theoretical interpretation of the torsionally induced axial strain, as observed for example by Swift, Bailey et al., Hart and Chang, and others, is provided. Moreover, the recent experiments of Montheillet et al. on torsionally induced axial stresses are discussed in the light of the presently proposed models of large inelastic deformation inelasticity accounting for anisotropy and texture effects.

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© 1988 Springer-Verlag. Publisher’s version of record: https://doi.org/10.1007/BF01174626

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Acta Mechanica