Book contents
- Frontmatter
- Contents
- Preface to the Fourth Edition
- 1 Stress and Strain
- 2 Plasticity
- 3 Strain Hardening
- 4 Plastic Instability
- 5 Temperature and Strain-Rate Dependence
- 6 Work Balance
- 7 Slab Analysis
- 8 Friction and Lubrication
- 9 Upper-Bound Analysis
- 10 Slip-Line Field Analysis
- 11 Deformation-Zone Geometry
- 12 Formability
- 13 Bending
- 14 Plastic Anisotropy
- 15 Cupping, Redrawing, and Ironing
- 16 Forming Limit Diagrams
- 17 Stamping
- 18 Hydroforming
- 19 Other Sheet Forming Operations
- 20 Formability Tests
- 21 Sheet Metal Properties
- Index
- References
10 - Slip-Line Field Analysis
Published online by Cambridge University Press: 05 June 2012
- Frontmatter
- Contents
- Preface to the Fourth Edition
- 1 Stress and Strain
- 2 Plasticity
- 3 Strain Hardening
- 4 Plastic Instability
- 5 Temperature and Strain-Rate Dependence
- 6 Work Balance
- 7 Slab Analysis
- 8 Friction and Lubrication
- 9 Upper-Bound Analysis
- 10 Slip-Line Field Analysis
- 11 Deformation-Zone Geometry
- 12 Formability
- 13 Bending
- 14 Plastic Anisotropy
- 15 Cupping, Redrawing, and Ironing
- 16 Forming Limit Diagrams
- 17 Stamping
- 18 Hydroforming
- 19 Other Sheet Forming Operations
- 20 Formability Tests
- 21 Sheet Metal Properties
- Index
- References
Summary
INTRODUCTION
Slip-line field theory is based on analysis of a deformation field that is both geometrically self-consistent and statically admissible. Slip lines are planes of maximum shear stress and are therefore oriented at 45° to the axes of principal stress. Basic assumptions are:
The material is isotropic and homogeneous.
The material is rigid-ideally plastic (i.e. no strain hardening).
Effects of temperature and strain rate are ignored.
Plane-strain deformation.
The shear stresses at interfaces are constant, usually frictionless or sticking friction.
Figure 10.1 shows the very simple slip line for indentation where the thickness, t, equals the width of the indenter, b. The maximum shear stress occurs on line DEB and CEA. The material in triangles DAE and CEB is rigid. As the indenters move closer together the field must change. However, for now, we are concerned with calculating the force when the geometry is 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 10.2 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 will be considered.
GOVERNING STRESS EQUATIONS
With plane-strain, all of the flow is in the x–y plane.
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- Information
- Metal FormingMechanics and Metallurgy, pp. 132 - 166Publisher: Cambridge University PressPrint publication year: 2011