## Mechanical metallurgy |

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Page 54

Chapter 3 ELEMENTS OF THE

beyond which Hooke's law is no longer valid. The mathematical description of the

...

Chapter 3 ELEMENTS OF THE

**THEORY**OF PLASTICITY 3-1. Introduction The**theory**of plasticity deals with the behavior of materials in the region of strainbeyond which Hooke's law is no longer valid. The mathematical description of the

...

Page 65

Octahedral Shear Stress and Shear Strain The octahedral stresses are a

particular set of stress functions which are important in the

They are the stresses acting on the faces of a three-dimensional octahedron

which has the ...

Octahedral Shear Stress and Shear Strain The octahedral stresses are a

particular set of stress functions which are important in the

**theory**of plasticity.They are the stresses acting on the faces of a three-dimensional octahedron

which has the ...

Page 68

Mathematical

Deformation

stress to the strain rate, or the velocity of strain. Deformation

averaging ...

Mathematical

**theories**of plasticity can be divided roughly into two types.Deformation

**theories**relate the stress to the strain, while flow**theories**relate thestress to the strain rate, or the velocity of strain. Deformation

**theories**utilize anaveraging ...

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### Contents

Introduction | 3 |

Stress and Strain Relationships for Elastic Behavior | 17 |

Elements of the Theory of Plasticity | 54 |

Copyright | |

21 other sections not shown

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### Common terms and phrases

alloys angle annealing ASTM axis behavior bending billet brittle fracture Burgers vector cent compressive constant crack creep rate cycles decrease determined diameter direction dislocation line distribution drawing ductile edge dislocation effect elastic equation extrusion factor failure fatigue limit flow curve flow stress force forging forming friction given grain boundaries hardness high-temperature increase indentation lattice length load longitudinal mandrel martensite material maximum measured mechanical metallurgical Metals Park method modulus notch obtained occurs orientation particles plastic deformation pressure principal stresses Proc produced properties punch quenched radius ratio region relationship residual stresses rolling screw dislocations shear stress sheet shown in Fig shows single crystals slip plane Society for Metals specimen steel strain energy strain hardening strain rate stress-strain curve structure surface temper tensile strength tensile stress tension theory thickness tion torsion Trans transition temperature tube usually yield strength yield stress