Introduction to Engineering Plasticity covers the mathematical theories of plasticity that are based on hypotheses and assumptions to represent the experimental observations as generalized mathematical formulations. Following a brief introduction in the first chapter, the next three chapters of the book deal with stress and strain tensors, and stress-strain relationships followed by yield criteria and their experimental verifications in chapter five. Associated flow rules and plastic stress-strain relationships are also derived in this chapter. Chapters six and seven present the concepts of plastic anisotropy and plastic instability. The slip-line field theory as applied to plane strain problems of rigid, perfectly plastic materials is presented in chapter eight and the limit theorem is elaborated in chapter nine.
G. K. Lal / N. Venkata Reddy.: Department of Mechanical Engineering Indian Institute of Technology Kanpur, Kanpur
Preface / Plastic Behaviour: Introduction / Flow Curve / Mechanism of Plastic Deformation / Stress: Stress at a Point / Stress Circle / Stress Invariants / Deviatoric Stress / Equilibrium Equations / Strain: Strain at a Point/ Physical Interpretation of Strain Components / Compatibility of Strain / Strain Invariants / Strain Deviator Tensor / Stress-Strain Relations: Introduction / Elastic Stress-Strain Relations / Plastic Stress-Strain Relations / Elastic-Plastic Stress-Strain Relations / Yield and Flow: Yield Condition / von Mises Yield Criterion / Tresca Yield Criterion / Hill Yield Criterion / Experimental Verification of Yield Criteria / Plastic Anisotropy: Introduction / Anisotropic Yield Criterion / Flow Rule / Generalised Stress and Generalised Strain Increment / Plastic Instability: Introduction / First Necking Condition / Second Necking Condition / Instability under Complex State of Stress / Evaluation of Critical Sub-tangent / Slip-line Field Theory: Introduction / Plane Strain / ? and ?-lines / Stress Equations / Velocity Equations / Hencky's First Theorem / Hencky's Second Theorem / Velocity Discontinuities / Stress Discontinuities / Stress Boundary Conditions / Construction of Slip-line Fields / Construction of Hodograph / Applications of Slip-line Field Technique / Indentation of a Semi-infinite Mass by a Frictionless Wedge shaped Punch/ Plane Strain Compression with Perfectly Rough Platens / Drawing of Rectangular Strip with Frictionless Tapered Die / Limit Theorem: Introduction / Principle of Virtual Work / Principle of Maximum Plastic Work / Lower Bound Theorem / Applications / Upper Bound Theorem / Applications / Review Questions / Bibliography / Index.
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