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# Engineering Plasticity

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

- 1st Edition - January 1, 1969
- Author: C. R. Calladine
- Editor: B. G. Neal
- Language: English
- Paperback ISBN:9 7 8 - 0 - 0 8 - 0 1 3 9 6 9 - 2
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 3 9 8 7 - 6

Engineering Plasticity focuses on certain features of the theory of plasticity that are particularly appropriate to engineering design. Topics covered range from specification of… Read more

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Request a sales quoteEngineering Plasticity focuses on certain features of the theory of plasticity that are particularly appropriate 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. Torsion, indentation problems, and slip-line fields are also discussed. 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 and the nature of physical theories. The reader is then introduced to the general problem of 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 explore 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 considered, along with wire-drawing and extrusion and the effects of changes in geometry on structure. This monograph is intended for students of engineering.

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 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 winh 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 Approach

7.3. 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

- No. of pages: 332
- Language: English
- Edition: 1
- Published: January 1, 1969
- Imprint: Pergamon
- Paperback ISBN: 9780080139692
- eBook ISBN: 9781483139876