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Shear, principal, and equivalent strains in equal-channel angular deformation

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An Erratum to this article was published on 01 February 2002

Abstract

The shear and principal strains involved in equal channel angular deformation (ECAD) were analyzed using a variety of methods. A general expression for the total shear strain calculated by integrating infinitesimal strain increments gave the same result as that from simple geometric considerations. The magnitude and direction of the accumulated principal strains were calculated based on a geometric and a matrix algebra method, respectively. For an intersecting angle of π/2, the maximum normal strain is 0.881 in the direction at π/8 (22.5 deg) from the longitudinal direction of the material in the exit channel. The direction of the maximum principal strain should be used as the direction of grain elongation. Since the principal direction of strain rotates during ECAD, the total shear strain and principal strains so calculated do not have the same meaning as those in a strain tensor. Consequently, the “equivalent” strain based on the second invariant of a strain tensor is no longer an invariant. Indeed, the equivalent strains calculated using the total shear strain and that using the total principal strains differed as the intensity of deformation increased. The method based on matrix algebra is potentially useful in mathematical analysis and computer calculation of ECAD.

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Authors and Affiliations

  1. the Department of Mechanical and Manufacturing Engineering, University of Melbourne, 3010, Victoria, Australia

    K. Xia (Senior Lecturer)

  2. the School of Metallurgical Engineering, Xi’an University of Architecture and Technology, 710055, Xi’an, People’s Republic of China

    J. Wang (Professor and Deputy Dean)

Authors
  1. K. Xia
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  2. J. Wang
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An erratum to this article is available at http://dx.doi.org/10.1007/s11661-002-0107-4.

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Xia, K., Wang, J. Shear, principal, and equivalent strains in equal-channel angular deformation. Metall Mater Trans A 32, 2639–2647 (2001). https://doi.org/10.1007/s11661-001-0054-5

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  • DOI: https://doi.org/10.1007/s11661-001-0054-5

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