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The Handbook off Nanoindentation by A.C. Fischer-Cripps P.O. Box 9, Forestville NSW 2087 Australia. www.ibisonline.com.au The IBIS Handbook of Nanoindentation Anthony C. Fischer-Cripps ISBN 0 9585525 4 1 Copyright © Fischer-Cripps Laboratories Pty Ltd 2009 You may download, print and reproduce this handbook in unaltered form only for your personal, non-commercial use. Apart from any use as permitted under the Copyright Act 1968, all other rights are reserved. Information provided in this book is believed to be accurate and reliable, however, no responsibility is assumed by Fischer-Cripps Laboratories Pty Ltd for its use; nor for any infringements of pattentts or otthher riighhtts off tthhiirdd parttiies whhiichh may resulltt ffrom iitts use. IBISis a registered trademark of Fischer-Cripps Laboratories Pty Ltd. Published by: Fischer-Cripps Laboratories Pty Ltd P.O. Box 9, Forestville NSW 2087 Australia Email: [email protected] Web: www.ibisonline.com.au The IBIS Handbook of Nanoindentation 3 Contents Part 1. Theory of Nanoindentation 1.1 Mechanical Properties of Materials 6 Stress and strain,, combined stresses,, elasticityy,, Poisson's ratio,, plastic deformation, fracture mechanics, visco-elasticity. 1.2 Contact Mechanics 14 Hertzian contact, spherical indenter, conical indenter, other indenters, contact stiffness, Hertzian fracture, plastic zone, constraint factor, hardness testing,. 1.3 Theoretical Analysis 23 Load-displacement curve, theoretical analysis, Oliver and Pharr mmeetthhoodd, FFiieelldd aanndd SSwwaaiinn mmeetthhoodd, iinnddeenntteerr oorr aarrbbiittrraarryy sshhaappee, energy method, theoretical modelling, finite element analysis, creep, dynamic nanoindentation, multiple-frequency nanoindentation, residual stress. Part 2. Practical Nanoindentation 2.1 Nanoindentation Testing 38 Sppecimen pprepparation,, indenters,, nanoindentation testingg,, 10% rule, step-height, scratch testing, fracture mechanics, . 2.2 Applying Corrections 47 Thermal drift, contact determination, instrument compliance, indenter shape correction, piling-up. 2.3 Analysing the Data 53 Fitting the unloading curve, image analysis, nanoindentation results, do's and don’t's. Part 3. More Information 3.1 Books 58 3.2 Literature 59 3.3 Manufacturers 60 Fischer-Cripps Laboratories Pty Ltd 4 The IBIS Handbook of Nanoindentation Fischer-Cripps Laboratories Pty Ltd The IBIS Handbook of Nanoindentation 5 Part 1 Theory of Nanoindentation 1.1 Mechanical Properties of Materials 11.22 CCoonnttaacctt MMeecchhaanniiccss 1.3 Theoretical Analysis Fischer-Cripps Laboratories Pty Ltd 6 The IBIS Handbook of Nanoindentation 1.1 Mechanical Properties 55 mm Precise positioning capability of a nanoindenter can allow one to measure the properties of the individual constituent phases of complex microstructures. Copyright © Fischer-Cripps Laboratories Pty Ltd 2009 The IBIS Handbook of Nanoindentation 7 11..11..11 SSttrreessss aanndd SSttrraaiinn PP Normal stress: Force F  A A Area (normal to ddiirreeccttiioonn ooff ffoorrccee)) FF P Shear stress: Force P P P  A A Area (parallel to direction of force) P P Normal Change in length ssttrraaiinn: ll  l l Original length l P x Shear Change in length strain: x (opposite) P tan h Height (adjacent) h  x  h Copyright © Fischer-Cripps Laboratories Pty Ltd 2009 8 The IBIS Handbook of Nanoindentation 11..11..22 CCoommbbiinneedd SSttrreesssseess Stresses at an angle  xcos2ysin22xysincos y 1  1   2 x y 2 x y cos2xysin2      ssiinnccooss ssiinn2ccooss2   x y xy x 1  z     sin2 cos2  2 x y xy Principal stresses Cartesian Axis-symmetric   x y  x y 2 2   r z  r z2 2 1,2 2  2  xy 1,3 2  2  rz   2 2        x y   2 max   xy 1  2       max 1 3 2 1     22 1 2 Hydrostatic stress   x y z d1 1m m 3    d2 2 m  123 d3 3m 3   1  2  2  212 oct 3 2 3 3 1 1 2 Copyright © Fischer-Cripps Laboratories Pty Ltd 2009 The IBIS Handbook of Nanoindentation 9 11..11..33 EEllaassttiicciittyy Hooke’s law (1676) Pkx kk ddeeppeennddss oonn tthhee type of material and the dimensions of the specimen. x 2x P Young’s modulus (1807) 2P PPkkx Start with Hooke’s law P kx Divide both sides by A, the cross-sectional area  A A of the specimen kl x  Multiply and divide by l, the length of the A l specimen kl Let E A P x E The elastic modulus (or Young's modulus) Eis a A l material property which describes the elasticity, or stiffness of a material. It is not the same thing as "hardness". Stress Strain In shhear, we hhave: 1 Shear modulus    xy xy G E G 1 21    yz yz G 1 Bulk modulus    xz G xz E KK  312 Copyright © Fischer-Cripps Laboratories Pty Ltd 2009 10 The IBIS Handbook of Nanoindentation 11..11..44 PPooiissssoonn’ss RRaattiioo P Poisson’s ratio is the ratio of the fractional change in one w l dimension to the fractional w  change of the other dimension. l l Poisson’s ratio is a measure l of how much a material tries tto maiinttaiin a consttantt volume under compression w or tension. w When the material contracts inwards (plane stress) under an applied tensile stress  , there is no sideways stress T induced in the material. If the sides of the material are held in position by external forces or restraints (plane strain), then there is a stress induced, the value of which is ggiven byy:  TT In terms of stresses and strains, in plane strain conditions (sides held in position), there is an effective increase in the stiffness of the specimen due to the induced sideways stresses. Hooke’s law becomes: E   12 Cartesian Axis-symmetric   1       1     x E x y z r E r  z   11       11     y E y x z  E  z r   1       1     z E z x y z E z r   Plane Plane y stress strain  x  0;  0;  0 z xz yz  0;  0;  0 1   z xz yz       z E x y z x y Copyright © Fischer-Cripps Laboratories Pty Ltd 2009