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Macroscopic effects of micro-shear banding in plasticity of metals

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Summary

Mathematical idealization of a micro-shear bands system by means of the theory of singular surfaces of order one, related to a physical model of shear strain-rate produced by active micro-shear bands and a certain averaging procedure over the representative volume element, is studied. Theoretical description of small elastic and large plastic deformations within the framework of a two-surface plasticity model, with the internal yield surface connected to kinematic hardening anisotropy and the external surface related to micro-shear banding, is proposed. The idea of the multiple potential surfaces forming a vertex on the smooth external surface is applied to display the connection with the geometric pattern of micro-shear bands. A new physical insight is given into the linear and nonlinear flow laws, in rates of deformation and stress, known in the theory of plasticity.

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Author notes

  1. R. B. Pęcherski

    Present address: Center of Mechanics, Institute of Fundamental Technological Research, Polish Academy of Sciences, Swietokrzyska 21, PL-00-049, Warsaw, Poland

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    1. R. B. Pęcherski
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    Dedicated to E. Stein on the occasion of his 65th birthday

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    Pęcherski, R.B. Macroscopic effects of micro-shear banding in plasticity of metals. Acta Mechanica 131, 203–224 (1998). https://doi.org/10.1007/BF01177225

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    • DOI: https://doi.org/10.1007/BF01177225

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