Engineering Plasticity

PrefaceI. 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. ShortcomingsII. 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 MaterialIII. 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 sz 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. SummaryIV. 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 ResultantsV. 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 HolesVI. 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 TensionVII. 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 DiesVIII. Introduction to Slip-Line Fields 8.1. Equilibrium Equations 8.2. Geometry of a, ß Nets 8.3. Hyperbolic Equations 8.4. Extension of a, ß Nets 8.5. The Indentation Problem 8.6. Choice of Approach: Slip Lines or Bound Theorems 8.7. NotationIX. 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 BehaviorX. 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.