Engineering Plasticity
The Commonwealth and International Library: Structures and Solid Body Mechanics Division
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Engineering 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.
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 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
Product details
- No. of pages: 332
- Language: English
- Copyright: © Pergamon 1969
- Published: January 1, 1969
- Imprint: Pergamon
- eBook ISBN: 9781483139876