Engineering Plasticity

Engineering Plasticity

The Commonwealth and International Library: Structures and Solid Body Mechanics Division

1st Edition - January 1, 1969

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  • Author: C. R. Calladine
  • eBook ISBN: 9781483145754

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Description

Engineering Plasticity deals with certain features of the theory of plasticity that can be applied to engineering design. Topics covered range from specification of an ideal plastic material to the behavior of structures made of idealized elastic-plastic material, theorems of plastic theory, and rotating discs, along with torsion, indentation problems, and slip-line fields. This book consists of 12 chapters and begins by providing an engineering background for the theory of plasticity, with emphasis on the use of metals in structural engineering; the nature of physical theories; and the conceptual simplicity and power of plastic theory. The next chapter explains how to set up a model of the plastic behavior of metal for use in analysis and design of structures and forming processes, paying particular attention to the plastic deformation that occurs when a specimen of metal is stressed. Subsequent chapters focus on the behavior of a simple structure made of elastic-plastic material; theorems of plastic theory; rotating discs; and indentation problems. Torsion, slip-line fields, and circular plates under transverse loading are also discussed, together with wire-drawing and extrusion and the effects of changes in geometry on structure. This monograph is written primarily for engineering students.

Table of Contents


  • Preface

    I. Introduction

    1.1. Metals and Structural Engineering

    1.2. A Microscopic View

    1.3. The Theory of Plasticity

    1.4. The Nature of Physical Theories

    1.5. The Conceptual Simplicity and Power of Plastic Theory

    1.6. Uniqueness, Indeterminacy and Freedom

    1.7. Shortcomings

    II. Specification of an Ideal Plastic Material

    2.1. Observations on a Tension Test

    2.2. Behavior of Metals on the Atomic Scale

    2.3. Tension and Compression Tests

    2.4. Instability in the Tension Test

    2.5. Materials with Upper and Lower Yield Points

    2.6. The Bauschinger Effect

    2.7. The Yield Locus

    2.8. Yield Surface for Three-Dimensional Stress

    2.9. Symmetry of the C-Curve

    2.10. The Tresca Yield Condition

    2.11. Plastic Deformation

    2.12. The "Normality" Rule

    2.13. The Mises Yield Condition and Associated Flow Rule

    2.14. Tresca or Mises Yield Condition

    2.15. The Experiments of Taylor and Quinney

    2.16. Correlation between Tension and Shear Tests

    2.17. Perfectly Plastic Material

    III. Features of the Behavior of Structures Made of Idealized Elastic-Plastic Material

    3.1. Ideal Elastic-Plastic Material

    3.2. Equations of the Problem

    3.3. Ambiguity of σz

    3.4. Elastic-Plastic Deformation

    3.5. Behavior under Rising and Falling Pressure

    3.6. The Effect of Residual Stresses

    3.7. "Shakedown"

    3.8. A "Work" Calculation

    3.9. Summary

    IV. Theorems of Plastic Theory

    4.1. Lower and Upper Bounds on Collapse Loads

    4.2. The Lower-Bound ("Safe") Theorem

    4.3. Proof of the Lower-Bound Theorem

    4.4. Loads Other Than Point Loads

    4.5. The Upper-Bound Theorem

    4.6. Calculation of Dissipation of Energy

    4.7. Simpler Form of the Proofs

    4.8. Corollaries of the Bound Theorems

    4.9. Problems Solved in Terms of Stress Resultants

    V. Rotating Discs

    5.1. The Rotating Hoop

    5.2. The Flat Disc With No Central Hole

    5.3. A Physical Interpretation

    5.4. Discs With Central Holes

    5.5. Mechanisms of Collapse

    5.6. Discs with Edge Loading

    5.7. Analysis of Mass

    5.8. Discs of Variable Thickness

    5.9. Reinforcement of Central Holes

    VI. Torsion

    6.1. Torsion of Thin-Walled Tubes of Arbitrary Cross-Section

    6.2. Lower-Bound Analysis of Thick-Walled Tubes and Solid Cross-Sections

    6.3. The Sand-Hill Analogy

    6.4. Re-Entrant Corners

    6.5. Other Aspects of Plastic Torsion

    6.6. Combined Torsion and Tension

    6.7. Combined Torsion, Bending and Tension

    VII. Indentation Problems

    7.1. Upper-Bound Approach

    7.2. Lower-Bound

    7.5. A Simpler problem

    7.4. Experimental Confirmation: the Hardness Test

    7.5. Indentation of Finite Blocks of Plastic Material

    7.6. The Effects of Friction

    7.7. Compression of a Sheet between Broad Dies

    VIII. Introduction to Slip-Line Fields

    8.1. Equilibrium Equations

    8.2. Geometry of α, ß Nets

    8.3. Hyperbolic Equations

    8.4. Extension of α, ß Nets

    8.5. The Indentation Problem

    8.6. Choice of Approach: Slip Lines or Bound Theorems

    8.7. Notation

    IX. Circular Plates under Transverse Loading

    9.1. Validity of the Simple Plastic Theory

    9.2. Collapse of a Simply Supported Circular Plate

    9.3. Yield Locus for an Element of Plate

    9.4. Lower-Bound Analysis

    9.5. A Clamped Circular Slab: Lower-Bound Analysis

    9.6. Upper-Bound Calculations

    9.7. Modes of Deformation

    9.8. Reinforced Concrete Slabs

    9.9. Point Loads

    9.10. Experimental Behavior

    X. Metal-Forming Processes: Wire-Drawing and Extrusion

    10.1. Sheet Drawing

    10.2. A Simple Mode of Deformation

    10.3. Ideal Drawing

    10.4. Presentation of Results

    10.5. Drawing With Small Die Angles

    10.6. Sheet Drawing in the Presence of Friction

    10.7. Extrusion Through Square Dies

    10.8. Hydrostatic Extrusion

    10.9. Allowance for Work-Hardening

    10.10. Axisymmetric Wire-Drawing

    10.11. Diffuse Shear in Region B

    10.12. Evaluation of "Diffuse Shear" Work

    10.13. Optimum Die Angles

    10.14. Axisymmetric Extrusion for α = 90°

    XI. Effects of Changes in Geometry

    11.1. Three Broad Classes of Structural Behavior

    11.2. an Approach to Geometry-Change Effects in Plastic Deformation

    11.3. The Rate-Problem

    11.4. Geometry-Change Effects in Simple Structures

    11.5. Summary and Concluding Remarks

    XII. The Wider Scope of Plastic Theory and Design

    12.1. Inter-Relation with Other Aspects of Design

    12.2. The Role of Computers in Structural Design

    12.3. Application of Plastic Theory to Other Fields of Design

    Bibliography

    Appendix I. The Mohr Circle of Stress

    Appendix II. Virtual Work

    Appendix III. "Corresponding" Loads and Deflections

    Appendix IV. Proportional Loading

    Appendix V. Notation for Three-Dimensional Stress

    Appendix VI. Symbols, Units and Conversion Factors

    Answers To Problems

    Index

Product details

  • No. of pages: 332
  • Language: English
  • Copyright: © Pergamon 1969
  • Published: January 1, 1969
  • Imprint: Pergamon
  • eBook ISBN: 9781483145754

About the Author

C. R. Calladine

About the Editor

B. G. Neal

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