Engineering Plasticity

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