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Mechanical Engineering Series Frederick F. Ling Editor-in-Chief Mechanical Engineering Series A.C. Fischer-Cripps, Introduction to Contact Mechanics, 2nd ed. W. Cheng and I. Finnie, Residual Stress Measurement and the Slitting Method J. Angeles, Fundamentals of Robotic Mechanical Systems: Theory Methods and Algorithms, 3rd ed. J. Angeles, Fundamentals of Robotic Mechanical Systems: Theory, Methods, and Algorithms, 2nd ed. P. Basu, C. Kefa, and L. Jestin, Boilers and Burners: Design and Theory J.M. Berthelot, Composite Materials: Mechanical Behavior and Structural Analysis I.J. Busch-Vishniac, Electromechanical Sensors and Actuators J. Chakrabarty, Applied Plasticity K.K. Choi and N.H. Kim, Structural Sensitivity Analysis and Optimization 1: Linear Systems K.K. Choi and N.H. Kim, Structural Sensitivity Analysis and Optimization 2: Nonlinear Systems and Applications G. Chryssolouris, Laser Machining: Theory and Practice V.N. Constantinescu, Laminar Viscous Flow G.A. Costello, Theory of Wire Rope, 2nd ed. K. Czolczynski, Rotordynamics of Gas-Lubricated Journal Bearing Systems M.S. Darlow, Balancing of High-Speed Machinery W.R. DeVries, Analysis of Material Removal Processes J.F. Doyle, Nonlinear Analysis of Thin-Walled Structures: Statics, Dynamics, and Stability J.F. Doyle, Wave Propagation in Structures: Spectral Analysis Using Fast Discrete Fourier Transforms, 2nd ed. P.A. Engel, Structural Analysis of Printed Circuit Board Systems A.C. Fischer-Cripps, Introduction to Contact Mechanics A.C. Fischer-Cripps, Nanoindentation, 2nd ed. (continued after index) Anthony C. Fischer-Cripps Introduction to Contact Mechanics Second Edition 1 3 Anthony C. Fischer-Cripps Fischer-Cripps Laboratories Pty Ltd. New South Wales, Australia Introduction to Contact Mechanics, Second Edition Library of Congress Control Number: 2006939506 ISBN 0-387-68187-6 e-ISBN 0-387-68188-4 ISBN 978-0-387-68187-0 e-ISBN 978-0-387-68188-7 Printed on acid-free paper. © 2007 Springer Science+Business Media, LLC All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now know or hereafter developed is forbidden. The use in this publication of trade names, trademarks, service marks and similar terms, even if they are not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject to proprietary rights. Printed in the United States of America. 9 8 7 6 5 4 3 2 1 springer.com Mechanical Engineering Series Frederick F. Ling Editor-in-Chief The Mechanical Engineering Series features graduate texts and research monographs to address the need for information in contemporary mechanical engineering, including areas of concentration of applied mechanics, biomechanics, computational mechanics, dynamical systems and control, energetics, mechanics of materials, processing, pro- duction systems, thermal science, and tribology. Advisory Board/Series Editors Applied Mechanics F.A. Leckie University of California, Santa Barbara D. Gross Technical University of Darmstadt Biomechanics V.C. Mow Columbia University Computational Mechanics H.T. Yang University of California, Santa Barbara Dynamic Systems and Control/ D. Bryant Mechatronics University of Texas at Austin Energetics J.R. Welty University of Oregon, Eugene Mechanics of Materials I. Finnie University of California, Berkeley Processing K.K. Wang Cornell University Production Systems G.-A. Klutke Texas A&M University Thermal Science A.E. Bergles Rensselaer Polytechnic Institute Tribology W.O. Winer Georgia Institute of Technology Series Preface Mechanical engineering, and engineering discipline born of the needs of the industrial revolution, is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face profound issues of pro- ductivity and competitiveness that require engineering solutions, among others. The Mechanical Engineering Series is a series featuring graduate texts and research monographs intended to address the need for information in contem- porary areas of mechanical engineering. The series is conceived as a comprehensive one that covers a broad range of concentrations important to mechanical engineering graduate education and research. We are fortunate to have a distinguished roster of series editors, each an expert in one of the areas of concentration. The names of the series editors are listed on page vi of this volume. The areas of concentration are applied mechanics, biomechanics, computational mechanics, dynamic systems and control, energetics, mechanics of materials, processing, thermal science, and tribology. To Dianne, Raymond and Henry Preface This book deals with the mechanics of solid bodies in contact, a subject inti- mately connected with such topics as fracture, hardness, and elasticity. Theoreti- cal work is most commonly supported by the results of indentation experiments under controlled conditions. In recent years, the indentation test has become a popular method of determining mechanical properties of both brittle and ductile materials, and particularly thin film systems. The book begins with an introduction to the mechanical properties of materi- als, general fracture mechanics, and the fracture of brittle solids. This is fol- lowed by a detailed description of indentation stress fields for both elastic and elastic-plastic contact. The discussion then turns to the formation of Hertzian cone cracks in brittle materials, subsurface damage in ductile materials, and the meaning of hardness. The book concludes with an overview of practical meth- ods of indentation. My intention is for this book to make contact mechanics accessible to those materials scientists entering the field for the first time. Experienced researchers may also benefit from the review of the most commonly used formulas and theoretical treatments of the past century. This second edition maintains the introductory character of the first with a focus on materials science as distinct from straight solid mechanics theory. Every chapter has been reviewed to make the book easier to read and more informative. A new chapter on depth sensing indentation has been added, and the contents of the other chapters have been completely overhauled with added figures, formulae and explanations. In writing this book, I have been assisted and encouraged by many col- leagues, friends, and family. I am most indebted to A. Bendeli, R.W. Cheary, R.E. Collins, R. Dukino, J.S. Field, A.K. Jämting, B.R. Lawn, C.A. Rubin, and M.V. Swain. I thank Dr. Thomas von Foerster who managed the 1st edition of this book and Dr. Alexander Greene for taking things through to this second edi- tion, and of course the production team at Springer Science+Business Media LLC for their very professional and helpful approach to the whole publication process. Lindfield, Australia Anthony C. Fischer-Cripps Contents Preface............................................................................................ ix List of Symbols........................................................................... xvii History.......................................................................................... xix Chapter 1. Mechanical Properties of Materials................................1 1.1 Introduction.............................................................................................. 1 1.2 Elasticity .................................................................................................. 1 1.2.1 Forces between atoms ................................................................... 1 1.2.2 Hooke’s law................................................................................... 2 1.2.3 Strain energy ................................................................................. 4 1.2.4 Surface energy............................................................................... 4 1.2.5 Stress.............................................................................................. 5 1.2.6 Strain ........................................................................................... 10 1.2.7 Poisson’s ratio............................................................................. 13 1.2.8 Linear elasticity (generalized Hooke’s law) ............................... 14 1.2.9 2-D Plane stress, plane strain ..................................................... 16 1.2.10 Principal stresses....................................................................... 18 1.2.11 Equations of equilibrium and compatibility.............................. 23 1.2.12 Saint-Venant’s principle............................................................ 24 1.2.13 Hydrostatic stress and stress deviation..................................... 25 1.2.14 Visualizing stresses.................................................................... 26 1.3 Plasticity ................................................................................................ 26 1.3.1 Equations of plastic flow ............................................................. 27 1.4 Stress Failure Criteria ............................................................................ 28 1.4.1 Tresca failure criterion