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6 - Slip-Line Field Theory

Published online by Cambridge University Press:  05 June 2013

William F. Hosford
Affiliation:
University of Michigan, Ann Arbor
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Summary

INTRODUCTION

Slip-line field analysis involves plane-strain deformation fields that are both geometrically self-consistent and statically admissible. Therefore, the results are exact solutions. Slip lines are really planes of maximum shear stress and are oriented at 45 degrees to the axes of principal stress. The basic assumptions are that the material is isotropic and homogeneous and rigid-ideally plastic (that is, no strain hardening and that shear stresses at interfaces are constant). Effects of temperature and strain rate are ignored.

Figure 6.1 shows a very simple slip-line field for indentation. In this case, the thickness, t, equals the width of the indenter, b and both are very much smaller than w. The maximum shear stress occurs on lines DEB and CEA. The material in triangles DEA and CEB is rigid. Although the field must change as the indenters move closer together, the force can be calculated for the geometry as shown. The stress, σy, must be zero because there is no restrain to lateral movement. The stress, σz, must be intermediate between σx and σy. Figure 6.2 shows the Mohr's circle for this condition. The compressive stress necessary for this indentation, σx = −2k. Few slip-line fields are composed of only straight lines. More complicated fields are considered throughout this chapter.

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Publisher: Cambridge University Press
Print publication year: 2013

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References

Hosford, W. F. and Caddell, R. M., Metal Forming: Mechanics and Metallurgy, 4th ed., Cambridge University Press (2011).CrossRefGoogle Scholar
Hill, R, The Mathematical Theory of Plasticity, Oxford University Press (1950).Google Scholar
Lüders, W, Dinglers Polytech., J. Stuttgart, 1860.Google Scholar
Johnson, W., Sowerby, R. and Haddow, J. B., Plane-Strain Slip Line Fields, American Elsevier, 1970.Google Scholar
Johnson, W. and Mellor, P. B., Engineering Plasticity, Van Nostrand Reinhold, 1973.Google Scholar
Körber, F., J. Inst. Metals v. 48. (1932) p. 317.
Prandl, L., Zeits. Angew. Math. Mech. v. 1., (1921).
Hencky, H., Zeits. Angew. Math. Mech. v. 1., (1921).
Prager, W., Trans. R. Inst. Tech., Stockholm, no. 5, (1953).
Green, A. P., J. Mech. Phys. Solids v.2, (1974).
Johnson, W., Sowrby, R. and Haddow, J. B., Plain-strain Slip-line Fields: Theory and Bibliography, American Elsevier (1970).Google Scholar
Johnson, W., Sowerby, R. and Venter, R. D., Plane-Strain Slip-line Fields for Metal Deformation Processes, Pergamon Press, (1982).Google Scholar
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  • Slip-Line Field Theory
  • William F. Hosford, University of Michigan, Ann Arbor
  • Book: Fundamentals of Engineering Plasticity
  • Online publication: 05 June 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9781139775373.007
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  • Slip-Line Field Theory
  • William F. Hosford, University of Michigan, Ann Arbor
  • Book: Fundamentals of Engineering Plasticity
  • Online publication: 05 June 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9781139775373.007
Available formats
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To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Slip-Line Field Theory
  • William F. Hosford, University of Michigan, Ann Arbor
  • Book: Fundamentals of Engineering Plasticity
  • Online publication: 05 June 2013
  • Chapter DOI: https://doi.org/10.1017/CBO9781139775373.007
Available formats
×