Tài liệu Unified Plastic Constitutive Laws of Deformation doc

Unified

Plastic

Constitutive

Laws of

Deformation

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I

Unified Constitutive

Laws of

Plastic Deformation

Edited by

A. S. Krausz and K. Krausz

Department of Mechanical Engineering

University of Ottawa

Ontario, Canada

Academic Press

San Diego New York Boston London Sydney Tokyo Toronto

This book is printed on acid-free paper. Q

Copyright 9 1996 by ACADEMIC PRESS, INC.

All Rights Reserved.

No part of this publication may be reproduced or transmitted in any form or by any

means, electronic or mechanical, including photocopy, recording, or any information

storage and retrieval system, without permission in writing from the publisher.

Academic Press, Inc.

A Division of Harcourt Brace & Company

525 B Street, Suite 1900, San Diego, California 92101-4495

United Kingdom Edition published by

Academic Press Limited

24-28 Oval Road, London NW1 7DX

Library of Congress Cataloging-in-Publication Data

Unified constitutive laws of plastic deformation / edited by A.S.

Krausz, K. Krausz.

p. cm.

Includes index.

ISBN 0-12-425970-7 (alk. paper)

1. Deformations (Mechanic)--Mathematical models. 2. Plasticity-

-Mathematical models. 3. Dislocations in crystals--Mathematical

models. I. Krausz, K.

TA417.6.U57 1996

620.1' 123--dc20 96-2097

CIP

PRINTED IN THE UNITED STATES OF AMERICA

96 97 98 99 00 01 MM 9 8 7 6 5 4 3 2 1

Contents

Contributors ix

Preface xi

~l Unified Cyclic Viscoplastic Constitutive Equations:

Development, Capabilities, and Thermodynamic

Framework

J. L. Chaboche

List of Symbols 1

I. Introduction 2

II. A Cyclic Viscoplastic Constitutive Law 4

III. Capabilities of the Constitutive Model 20

IV. Thermoviscoplasticity 33

V. Conclusion 61

References 63

Dislocation-Density-Related Constitutive Modeling

Yuri Estrin

I. Introduction 69

II. One-Internal-Variable Model 72

III. Two-Internal-Variable Model 91

IV. Conclusion 103

References 104

~1 Constitutive Laws for High-Temperature Creep and

Creep Fracture

R. W. Evans and B. Wilshire

Contents

I. Introduction 108

II. Traditional Approaches to Creep and Creep

Fracture 109

III. The 0 Projection Concept 117

IV. Analysis of Tensile Creep Data 123

V. Creep under Multiaxial Stress States 132

VI. Creep under Nonsteady Loading Conditions

VII. Conclusions 150

References 151

143

~]1 Improvements in the MATMOD Equations

for Modeling Solute Effects and

Yield-Surface Distortion

Gregory A. Henshall, Donald E. Helling, and Alan K. Miller

I. Introduction 153

II. Modeling Yield-Surface Distortions 160

III. Simulating Solute Effects through Short Range

Back Stresses 189

IV. Using the Models 214

V. Summary 221

References 224

The Constitutive Law of Deformation Kinetics

A. S. Krausz and K. Krausz

I. Introduction 229

II. The Kinetics Equation 234

III. The State Equations 247

IV. Measurement and Analysis of the Charac￾teristic Microstructural Quantities 256

V. Comments and Summary 270

References 277

A Small-Strain Viscoplasticity Theory Based

on Overstress

Erhard Krempl

I. Introduction 282

II. Viscoplasticity Theory Based on Overstress 282

III. Discussion 294

References 316

Contents ~

VII

Anisotropic and Inhomogeneous Plastic

Deformation of Polycrystalline Solids

J. Ning and E. C. Aifantis

I. Introduction 319

II. Constitutive Relations for a Single Crystallite

III. Texture Effects and the Orientation

Distribution Function 322

IV. Texture Tensor and Average Procedures 324

V. Texture Effect on the Plastic Flow and Yield

VI. Inhomogeneous Plastic Deformation 332

References 339

321

327

~~l Modeling the Role of Dislocation Substructure

during Class M and Exponential Creep

S. V. Raj, I. S. Iskovitz, and A. D. Freed

List of Symbols 344

I. Introduction 347

II. Class M and Exponential Creep in Single￾Phase Materials 355

III. Substructure Formation in NaC1 Single

Crystals in the Class M and Exponential

Creep Regimes 371

IV. Microstructural Stability 403

V. Nix-Gibeling One-Dimensional Two-Phase

Creep Model 411

VI. Development of a Multiphase Three-Dimensional

Creep Model 419

VII. Summary 428

Appendix 428

References 430

~~l Comments and Summary

K. Krausz and A. S. Krausz

Index 451

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Contributors

Numbers in parentheses indicate the pages on which the authors' contributions begin.

E. C. Aifantis (319), Center for Mechanics of Materials and Instabilities, Michigan

Technological University, Houghton, Michigan 49931 and Aristotle University

of Thessaloniki, Thessaloniki 54006, Greece

J. L. Chaboche (1), MECAMAT, ONERA, 92320 Chatillon, France

Yuri Estrin (69), Department of Mechanical and Materials Engineering, The Uni￾versity of Western Australia, Nedlands, Western Australia 6907, Australia

R. W. Evans (107), Interdisciplinary Research Centre in Materials for High Per￾formance Applications, Department of Materials Engineering, University of

Wales, Swansea SA2 8PP, United Kingdom

A. D. Freed (343), Lewis Research Center, National Aeronautics and Space Ad￾ministration, Cleveland, Ohio 44135

Donald E. Helling (153), Hughes Aircraft, E1 Segundo, California 90245

Gregory A. Henshall (153), Lawrence Livermore National Laboratory, University

of California, Livermore, California 94551

!. S. Iskovitz (343), Ohio Aerospace Institute, Cleveland, Ohio 44135

A. S. Krausz (229, 443), University of Ottawa, Ottawa, Ontario, Canada K1N 6N5

K. Krausz (229, 443), University of Ottawa, Ottawa, Ontario, Canada K1N 6N5

Erhard Krempl (281), Mechanics of Materials Laboratory, Rensselaer Polytechnic

Institute, Troy, New York 12180

Alan K. Miller (153), Lockheed-Martin Missles and Space, Palo Alto, California

94304

J. Ning (319), Center for Mechanics of Materials and Instabilities, Michigan Tech￾nological University, Houghton, Michigan 49931

S. V. Raj (343), Lewis Research Center, National Aeronautics and Space Admin￾istration, Cleveland, Ohio 44135

B. Wilshire (107), Interdisciplinary Research Centre in Materials for High Per￾formance Applications, Department of Materials Engineering, University of

Wales, Swansea SA2 8PP, United Kingdom

ix

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Preface

The constitutive law of plastic deformation expresses the effects of material

behavior and properties for stress analysis in the design of manufacturing tech￾nology and product service behavior, for materials testing, and for the maintenance

of structural and machine components.

The book represents the state of the art, but the editors do not rule out other

concepts of constitutive laws. There are many different facets of the same problem

and as many answers; the right one is the one that gives the most practical solution,

the one that best serves the specific problem. The selection of the best solution

can be ensured with a complex procedure that involves analysis of material cost,

performance characteristics other than plastic deformation, marketing concerns,

financial decisions, etc. No single book can give a full presentation of all of these

issues or guidance that addresses all of these concerns. In this volume, we focus

on the technical aspects of the constitutive laws of plastic deformation.

During fabrication the major manufacturing processes subject the workpiece to

plastic deformation. Examples of these processes are forging, coining, extrusion,

metal cutting, bending, and deep drawing. During service many structural and

machine components are subjected to plastic deformation: pressure tubes and

turbine blades creep; the service lifetime of springs is affected by stress relaxation,

which in turn is controlled by plastic deformation, and thus fatigue is controlled by

it; and crack growth is associated with plastic deformation. In addition, many other

service conditions require an understanding of plastic deformation (Figure A).

Efficient maintenance and materials testing depend on information derived from

the constitutive laws. All of these activities are carried out with the assistance

of computers and depend ultimately on the understanding and ingenuity of the

design and operating engineer. The end result of these activities is to achieve

cost efficiency while ensuring a marketable, competitive product. Within the

bounds of this book the authors present their understanding of the constitutive

laws and the application of these laws to this purpose. It is clear from these

chapters that further work must be done; plastic deformation is a very complicated

process.

xi

xii Preface

The manufacturing process and product performance diagrams give a condensed

schematic of the design aspects. The dark boxes indicate aspects that are served by the constitu￾tive law of plastic deformation.

Constitutive laws serve to enhance our understanding of the mechanisms that

control plastic deformation, as well as the need to represent behaviors and processes

for the development of improved material characteristics--to tailor them for better

performance. Clearly, there are a variety of causes to serve, and a variety of

constitutive laws are needed. These laws do not contradict each other when they

are developed within the principles of the other engineering sciences: these laws

must be economical for the purpose that they serve. For instance, it would be

wrong to base the design of bridges on the effects of atomic interaction energies

and the applied forces acting on these atoms however true it may be that these

control plastic deformation. This approach would be inappropriate, extremely

uneconomical---extremely wrong. On the other hand, consideration of the effects

of the microstructure obviously requires representation of the microscopic and

submicroscopic conditions of the structure and the processes that occur at these

levels. These concepts are very much embedded in science and engineering.

It is well known that in the design of structures and machine elements, linear

elasticity is usually considered, but in the design for fluctuating loads, where

energy absorption is critical, the nonlinear hysteresis effect must be considered.

Nature is one, but it has many facets to be examined and the one chosen must give

the optimum condition for the specific purpose. It is in this context that we present

the contributions to this volume.

Preface xiii

The editors express their thanks to D. Grayson, J. Bunce, and D. Ungar of

Academic Press for their kind and competent assistance in the preparation of this

book. It has been a pleasure working with them. Much appreciation is due to

the authors of the chapters for their contributions--their collaboration made our

editing job easy.

K. Krausz

A. S. Krausz

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