Introduction to Engineering Plasticity

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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. Key Features A number of examples are presented in chapters eight and nine to illustrate the applications of the slip-line field theory, and lower and upper bound theorems Table of Contents 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 a and ß-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.