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Fundamentals of Engineering Plasticity by William F.,Hosford

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6 Slip-Line Field Theory

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 lines1 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 ...

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