3.052 Nanomechanics of Materials and Biomaterials Tuesday 05/08/07 Prof. C. Ortiz, MIT-DMSE I LECTURE 22: THEORETICAL ASPECTS OF NANOINDENTATION

Transcription

1 3.052 Nanomehanis of Materials and Biomaterials Tuesday 05/08/07 Prof. C. Ortiz, MIT-DMSE I LECTURE 22: THEORETICAL ASPECTS OF NANOINDENTATION Outline : REVIEW LECTURE #21 : EXPERIMENTAL SINGLE MACROMOLECULE ELASTICITY... 2 NANOINDENTATION Introdution... 3 Indenter Geometries... 4 Types of Deformation... 5 Oliver-Pharr Analysis : Geometri Set-Up... 6 Oliver-Pharr Analysis :Mathematial Formulation... 7 APPENDIX Detailed Geometry of Indenters Berkovih Contat Area Oliver-Pharr Citations Nanoindentor Instruments Objetives: To understand general theoretial formulations for reduing material properties from nanoindentation experiments Readings: Course Reader Douments 45 (one of the most ited papers in Materials Siene)-46, Additional Historial Ref: Sneddon 1965 Int. J. Engng. 3,

2 3.052 Nanomehanis of Materials and Biomaterials Tuesday 05/08/07 Prof. C. Ortiz, MIT-DMSE SINGLE MOLECULE ELASTICITY OF TITIN (AFM) & DNA (OPTICAL TWEEZERS) - Struture and physiologial role of Titin (Rief, et al. CHEMPHYSCHEM 2002, 3, ) sawtooth fore profiles (Bustamante, et al. Siene 1999, 271, 795) overstrething transition I. low strethed behaves like WLC (p 50 nm under physiologial onditions, muh larger than most polymers ~ 1nm, hene muh smaller fores, need optial tweezers) II. intermediate strethes -some extensibility as apparent by finite slope beyond L ontour (B-form) Fore (pn) III. At 65 pn ~ 0.06 nn, reversible strain-indued onformational transition; hain "yields" and strethes out almost 2 its native B-form ontour length at relatively onstant fore (plateau in fore region) -All of hydrogen bonding and binding between 2 strands is still in tat, tilting of base pairs, tightened helix, redution in diameter "overstrething transition" IV. entropi elastiity of S-form Distane (μm) Biologial Relevane of Overstrething Transition? Ability to swith between different strutures is ritial to the proesses of transription, repliation, ondensaton, e.g. the base pairs are muh more exposed in S-DNA than normal DNA, the transition may be biologially signifiant for aessing information ontained in the DNA ode V. an't see here - if you go to high enough strethes, separation between strains (mehanial "melting") 2

3 3.052 Nanomehanis of Materials and Biomaterials Tuesday 05/08/07 Prof. C. Ortiz, MIT-DMSE INTRODUCTION TO NANOINDENTATION Definition : Controlled ompression and deompression of a probe tip into a sample surfae while measuring fore (load, P) versus indentation displaement or depth, h (nm-sale) ontinuously probe tip is relatively rigid ompared to the sample an measure mehanial properties (e.g. modulus, hardness) on areas nm-μm sale; e.g. thin films and small volume strutures alled "nano" sine the indentation depth is of nanometer sale, however lateral ontat areas and fores an be > nanosale -multiaxial deformation AFM-based Indentation indenter surfae profile at P max initial surfae P max a h max Instrumented or Depth-Sensing Indentation (DSI) P max Fore, F (nn) 0 loading unloading ontat fores 0 jump-to-ontat surfae fores adhesion Tip-Sample Indentation Depth or Separation Distane, D (nm) -e.g. silion or silion nitride indenter probe on a antilever fore transduer -antilever oriented at an angle to the surfae (~11 ) -indenter geometries, e.g. pyramidal (less well defined) -load range ~ nn-mn, smaller ontat radii ~ 10s of nm Load, P loading unloading h max Indentation Depth, h (Hysitron, Miromaterials, Appendix extension of onventional hardness testing to smaller length sale) - diamond indenter - indenter oriented perpendiular to the surfae - variable indenter geometries; Berkovih, ube orner, et. - load range ~ μn-mn, larger ontat radii ~ μm 3

4 3.052 Nanomehanis of Materials and Biomaterials Tuesday 05/08/07 Prof. C. Ortiz, MIT-DMSE NANOINDENTATION : INDENTER GEOMETRIES AFM-Based Indentation a ~18 μm Side and bak view 33º 29º 120º ~18 μm Front view 56º 18º 18º ~9 μm Bottom view 33º ~9 μm 33º 29º ~10 μm Instrumented Indentation Berkovih Residual Berkovih Indent Impression b End radius < 15 nm 71º ontat radius ~ 60 nm Nanomehanially mapped region 2 μm 50 μm Silion tetrahedral probe tip indenter (k~ 56 N/m) 45º Cube Corner See Appendix for full geometri details a=vikers, b= Berkovih, = Knoop, d = onial, e=rokwell, f=spherial 4

5 3.052 Nanomehanis of Materials and Biomaterials Tuesday 05/08/07 Prof. C. Ortiz, MIT-DMSE NANOINDENTATION : TYPES OF DEFORMATION Elastoplasti or Inelasti h r = h f = residual / final depth U e = elasti energy U r = energy dissipated (elastoplasti / inelasti) U total = total work of deformation= U e +U r in.materials.drexel.edu/blogs/280_advaned_materials_lab/attahment/469.ashx Courtesy of Prof. Yury Gogotsi. Used with permission. 5

6 3.052 Nanomehanis of Materials and Biomaterials Tuesday 05/08/07 Prof. C. Ortiz, MIT-DMSE OLIVER-PHARR ANALYSIS: GEOMETRIC SET-UP Linear Elasti, Isotropi, Continuum Contat Mehanis Theory (Oliver and Pharr, 1992 JMR, 7(6) 1564) : Geometry setup and definitions of geometri parameters : assumes "sink-in" h f Courtesy of George M. Pharr and Journal of Materials Researh. Used with permission. P = applied load, P max = peak applied load h = indentation depth (at P max ; h= h max maximum depth) a = radius of ontat irle h = ontat depth, vertial distane along whih ontat is made between sample and tip h s = displaement of the surfae at the perimeter of ontat From geometry : h = h + h s A(h ) = ontat (projeted) area at h -1 E r 1-ν 1-ν = redued modulus = i E sample Ei indenter (i.e. two springs in series) E = modulus ν = Poisson's ratio h f = residual final depth (indiates inelastiity; e.g. visoelastiity, plastiity) S = ontat ( initial unloading) stiffness = (typially evalulated between 95% and 20% of P ) dp dh P max max 6

7 3.052 Nanomehanis of Materials and Biomaterials Tuesday 05/08/07 Prof. C. Ortiz, MIT-DMSE OLIVER-PHARR ANALYSIS : MATHEMATICAL FORMULATION (Oliver and Pharr, 1992 JMR, 7(6) 1564) π E r = S Sneddon Equation holds for any indenter geometry (1) 2 A(h ) S is measured diretly from the data (typially evalulated between 95% and 20% of P ) ε Pmax h = h max (2) S Tip Geometry ε flat-ended ylindrial punh 1 paraboloid of revolution 0.75 Cone 2(π-2)/π max Courtesy of George M. Pharr and Journal of Materials Researh. Used with permission. Indenter (Probe Tip) Area Funtion Calibration : A(h ) = tip area funtion; representative of tip geometry, an be alibrated on sample of known modulus (e.g. fused quartz) by inverting Sneddon equation (1); 2 π S A(h ) = (3) 4 Er Carry out indentations at suessively higher loads; at eah Pmax alulate h from (2) and A(h ) from (3), these data are fit to a polynomial : A(h ) = C h + C h + C h + C h /8 1/16 o Gives A(h ) for every indentation depth, h + Ch + Ch 2 C o = 24.5; A(h ) = 24.5h (Ideal Berkovih Geometry) (4) (see Appendix for Derivation), oeffiients reflet indenter geometry Shemati ourtesy of B. Bruet 7

8 3.052 Nanomehanis of Materials and Biomaterials Tuesday 05/08/07 Prof. C. Ortiz, MIT-DMSE Four appendies removed due to opyright restritions. - Detailed geometry of indenters - Berkovih geometry alulation of ontat area - Web sreenshot: Oliver and Pharr JMR 1992 artile is one of the most ited papers in Materials Siene, has been ited >2975 times - Photos of nanoindentation instruments. 8