Deformation Geometry for Materials Scientists

Deformation Geometry for Materials Scientists

International Series on Materials Science and Technology

1st Edition - January 1, 1973

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  • Author: C. N. Reid
  • eBook ISBN: 9781483159669

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Deformation Geometry for Materials Scientists presents the study of macroscopic geometry of deformation, particularly on crystalline solids. The book discusses a wide range of topics on the deformation of crystalline materials. The text discusses concepts on stress and strain on materials and tensile tests. Linear elastic and plastic deformations; and the macroscopic geometry mechanism of slip and deformation twinning are covered as well. Materials scientists, engineers, and students of materials science will find this book a great reference material.

Table of Contents

  • Preface

    1. The Concepts of Stress and Strain


    Inhomogeneous Stress

    The Stress Tensor

    Principal Axes

    Familiar Types of Stress State

    The Graphical Representation of Stress by the Mohr Circle

    True Stress and Engineering Stress


    Strain in Two Dimensions

    Strain in Three Dimensions

    The Strain Ellipsoid

    2. The Tensile Test

    Types of Tensile Test

    Types of Mechanical Response to Stress

    Features of the Tensile Test

    The Tensile Instability

    The Lüders Band—A Self-arresting Tensile Instability


    The Elastic Behavior of the Tensile Machine

    The Load Relaxation Test

    The Approach to a Steady-state Load-Extension Curve

    3. Linear Elastic Deformation

    Hooke's Law in Three Dimensions

    The Energy Stored in an Elastically Strained Body

    The Effect of Material Symmetry on the Elastic Constants

    The Bulk Modulus of Anisotropic Materials

    The Shear Modulus in Anisotropic Materials

    Specifying Elastic Anisotropy in Materials of Cubic and Hexagonal Symmetry

    4. Plastic Deformation of Isotropic Materials

    The State of Stress

    The Criterion for Yielding under a General State of Stress

    The Notion of an Effective Stress

    Stress-Strain Relations

    Tensile Instability under Biaxial Stresses

    5. The Geometry of Single and Duplex Slip

    What is Slip?

    The Initiation of Slip

    The Reorientation of Directions by Single Slip

    The Reorientation of Planes by Single Slip

    Single Slip in Response to a Tensile Force

    Single Slip in Response to a Compressive Force

    Single Slip in Crystals of Cubic Symmetry

    Slip on Two Systems—Duplex Slip

    Examples of Duplex Slip in Cubic Crystals

    6. Slip on More than Two Systems—multiple Slip

    Strains Produced by Slip

    Independent Slip Systems and the Effect of Cross-slip

    The Selection of Active Systems

    The State of Stress for Multiple Slip

    The Principle of Maximum Work

    Deformation of a Polycrystalline Aggregate

    Rigid Body Rotation During Slip

    7. Plastic Deformation of Crystals by Twinning

    The Definition of a Twinned Crystal

    The Origin of Twins

    The Geometry of Mechanical Twinning

    Experimental Identification of Twinning Elements

    Twinning on the Atomic Scale

    Nature's Choice of Twinning Elements

    The Sense of the Twinning Shear

    Transformation of Crystallographic Directions by Twinning

    Changes in Length Caused by Twinning




Product details

  • No. of pages: 220
  • Language: English
  • Copyright: © Pergamon 1973
  • Published: January 1, 1973
  • Imprint: Pergamon
  • eBook ISBN: 9781483159669

About the Author

C. N. Reid

About the Editor

W. S. Owen

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