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Plane-Strain Slip-Line Fields for Metal-Deformation Processes
A Source Book and Bibliography
- 1st Edition - January 1, 1982
- Authors: W. Johnson, R. Sowerby, R. D. Venter
- Language: English
- Hardback ISBN:9 7 8 - 0 - 0 8 - 0 2 5 4 5 2 - 4
- Paperback ISBN:9 7 8 - 1 - 4 8 3 2 - 3 4 4 6 - 5
- eBook ISBN:9 7 8 - 1 - 4 8 3 2 - 7 8 4 9 - 0
Plane-Strain Slip-Line Fields for Metal-Deformation Processes: A Source Book and Bibliography provides information pertinent to the theory and application of plain-train slip… Read more
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Request a sales quotePlane-Strain Slip-Line Fields for Metal-Deformation Processes: A Source Book and Bibliography provides information pertinent to the theory and application of plain-train slip fields to metal-working problems. This book discusses the industrial importance of axial symmetry. Organized into seven chapters, this book begins with an overview of the oldest processes of metal forming, including forging, coining, hammering, drifting, cutting, or parting. This text then examines the basic aspects of the basic theory of classical plasticity. Other chapters consider the governing equations of the plane plastic flow of a rigid-perfectly plastic solid. This book discusses as well the methods for the solution of problems of plane plastic flow of a rigid-perfectly plastic solid. The final chapter deals with the application of the theory of plasticity to the quasi-static plane-strain deformation of an isotropic rigid-perfectly plastic, rate insensitive material. This book is a valuable resource for mechanical engineers, materials scientists, teachers, and research workers.
Chapter 1. Introduction
The Metal-Forming Process in History
Plane-Strain Slip-Line Fields: Historical Note
Physical Observations
(i) Surface Coatings
(ii) Surface Markings on the Metal
(iii) Grids or Nets of Lines
(iv) Heat Lines and Zones
(v) The Use of Plasticine and Wax
(vi) Measurement of Friction Coefficient
(vii) PVC : Chromoplasticity
(viii) Defects: Voids or Cavities, Cracks, De-Densification, Piping
(ix) Anisotropy
(X) Thermography
(xi) Load-Punch Travel Diagrams
(xii) Hardness Traverses
(xiii) Photoplasticity
(xiv) Photostress
(XV) Residual Stresses
(xvi) Photoelasticity
(xvii) Temperature-Sensitive Paints
(xviii) Thermocouples
(xix) Inserts
References
Chapter 2. General Plasticity Theory
Introduction
Strain Rate
Equilibrium and Virtual Work Equations
Surfaces of Stress Discontinuity
Surfaces of Velocity Discontinuity
Maximum Work Principle
Uniqueness
Extremum Principles
Summary
Tensor Calculus and Suffix Notation
Surfaces of Stress and Velocity Discontinuities
Plastic Potential and Flow Rule
Representative Stress and Representative Plastic Strain Increment
The Extremum Principles
References
Chapter 3. Basic Theory of Plane Plastic Flow
Introduction
Stress Equations
Velocity Equations
Hencky's First Theorem
Hencky's Second Theorem
Hodographs
Stress Plane
Requirements for a Complete Solution
References
Chapter 4. Application to Specific Problems
Introduction
Construction of Slip-Line Fields
Kinds of Slip-Line Fields
Stress Boundary Conditions
(i) Stress-Free Surface
(ii) Frictionless Interface
(iii) Interface with Coulomb Friction
(iv) Full Shearing along an Interface
Constructing the Hodograph
Solutions to Problems Using the Upper-Bound Method
References
Chapter 5. Applications to Specific Processes: Bibliography
Centered-Fan Fields
Pressure Vessels
Compression
(i) Perfectly Rough Parallel Dies
(ii) Perfectly Rough Inclined Dies
(iii) Frictionless Parallel Dies
(iv) Compression of Other than Slabs
Indentation of a Semi-Infinite Medium
Cutting
Sheet Drawing
Extrusion and Extrusion Forging
(i) Inverted Extrusion
(ii) Extrusion Forging
(iii) Grid Distortion
(iv) Energy-Dissipation Rate
Piercing
Forging
Orthogonal Machining
Swaging
Yielding of Notched Bars in Tension
Crack Initiation and Fracture
Bending
(i) Cantilevers Under Concentrated Loading
(ii) Pure Bending of Notched Bars
Rolling
Blanking and Shearing
Bibliography
Books
Bibliographies and Reviews
Theory
General
Pressure Vessels
Compression
Indenting
Cutting
Drawing
Extrusion
Piercing
Forging
Machining
Notched Bars Pulled in Tension
Crack Initiation and Fracture
Bending
Rolling
Blanking, Shearing and Surface Asperities
Chapter 6. Matrix-Operator Methods for Solving Plane-Strain Slip-Line Field Problems
Introduction
Governing Equations in Slip-Line-Field Theory
(i) Radii of Curvature
(ii) Moving Coordinates
(iii) Velocity Equations
Series Expansion for Radii of Curvature
(i) Definitions: Radius of Curvature, Base Point, Intrinsic Direction
(ii) Hencky's Second Theorem
(iii) Series Representation of the Radius of Curvature
(iv) Series Representation of a Circular arc
(v) Generalized Radius of Curvature at a Point
Centered Fans and Regular Nets
(i) Centered Fans
(ii) Regular Nets
(iii) Construction on the Concave Side of the Base Line
Matrix Operators
(i) Reversion Operator, R
(ii) Operators P and Q: the Centered Fan: the Regular Net
(iii) Shift Operator, S
(iv) Numerical Application of the Operators Rφ and Sφ
(v) Frictionless Boundary Operator, T
(vi) Straight Rough Doundary Operator, G
(vii) Stress-Free Surface Boundary Operator, F
(viii) Matrix Operator Identities
(ix) Matrix Operator Subroutines
Determination of the Coordinates of Slip Lines
Determination of Forces Acting on a Slip Line
Method of solution
(i) Direct-Type Solutions
(ii) Indirect-Type Solutions
Application of the Matrix Operator Method to the Solution of Direct-Type Problems
(i) Extrusion/Drawing through a Frictionless Wedge-Shaped Die
(ii) Extrusion at High Reduction
(iii) Symmetrical and Asymmetrical Piercing Examples
(iv) Slip-Line Fields for Drawing and Wall-Ironing
Application of the Matrix Operator Method to the Solution of Indirect-Type Problems
(i) Range of Slip-Line-Field Solutions for Extrusion/Drawing through Frictionless Wedge-Shaped Dies
(ii) Drawing through Rough Wedge-Shaped Dies
(iii) Slip-Line-Field Solutions for the Hot Rolling of Strip
Summary
Summary of Matrix Operators
References
Appendix 1
Matrix Operators
Appendix 2
Mikhlin and Cartesian Coordinates of a Slip Line
Determination of Expressions for the Mikhlin Coordinates
Appendix 3
Computer Listing for Indentation Problem
Appendix 4
The Determination of the Forces Acting on a Slip Line: Subroutine SLFORC
Chapter 7. Plasticity Problems for Other than Plane-Strain Conditions
Introduction
The Method of Characteristics for Other than Plane Strain Processes
(i) Plane Stress
(ii) Axial Symmetry
(iii) Soils
Anisotropy
(i) Crystallographic Approach
(ii) Macroscopic Theories of Anisotropy
Slip-Line Fields for Anisotropie Materials
Analogies with Metal-Working Operations
(i) Minimum Weight Frames
(ii) The Transverse Plastic Bending of Rigid-Perfectly Plastic Plates
(iii) The Force-Plane Diagram for Plane-Strain Slip-Line Fields
References
Appendices
5. Suffix Notation and the Summation Convention
6. Characteristics of Partial Differential Equations
7. Centered-Fan Fields : Nodal Points
Additional References
Author Index
Subject Index
- No. of pages: 376
- Language: English
- Edition: 1
- Published: January 1, 1982
- Imprint: Pergamon
- Hardback ISBN: 9780080254524
- Paperback ISBN: 9781483234465
- eBook ISBN: 9781483278490