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
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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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 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