REVIEW LECTURE 22 : THEORETICAL ASPECTS OF NANOINDENTATION Oliver-Pharr analysis- linear Elastic, Isotropic, Continuum Contact Mechanics Theory (Oliver and Pharr, 1992 JMR, 7(6) 1564) : Geometry set-up and definitions of geometric parameters : assumes "sink-in"OLIVER-PHARR ANALYSIS : MATHEMATICAL FORMULATION (Oliver and Pharr, 1992 JMR, 7(6) 1564) HARDNESS, PILEUP, and SINK-INSTRUCTURE OF SEASHELL NACRE (Courtesy of B. Bruet) MECHANICAL PROPERTY AMPLIFICATION NANOINDENTATION OF SEASHELL NACRE (Bruet, et al. JMR 20(9), 2005)ROLE OF MACROMOLECULAR COMPONENT3.052 Nanomechanics of Materials and Biomaterials Thursday 05/10/07 Prof. C. Ortiz, MIT-DMSE I LECTURE 23: NANOINDENTATION 2 :OLIVER-PHARR METHOD AND ONE LITERATURE EXAMPLE : NACRE Outline : REVIEW LECTURE #22 : THEORETICAL ASPECTS OF NANOINDENTATION..................................... 2 OLIVER-PHARR ANALYSIS : MATHEMATICAL FORMULATION ........................................................... 3 HARDNESS, PILE-UP, and SINK-IN ......................................................................................................... 4 SEASHELL NACRE................................................................................................................................5-8 Structure.................................................................................................................................. 5 Mechanical Property Amplification........................................................................................... 6 Nanoindentation ..................................................................................................................... 7 Mechanical Properties and Role of the Macromolecular Component ..................................... 8 Objectives: To understand how nanoindentation experiments can be applied to different biological systems Readings: Course Reader Documents 45 (one of the most cited papers in Materials Science)-46, Bruet, et al. "Nanoscale morphology and indentation of individual nacre tablets from the gastropod mollusc Trochus niloticus," JMR 20(9), 2005. 13.052 Nanomechanics of Materials and Biomaterials Thursday 05/10/07 Prof. C. Ortiz, MIT-DMSE REVIEW LECTURE 22 : THEORETICAL ASPECTS OF NANOINDENTATION -Definition (why called nano?), comparison of AFM based-indentation to instrumented indentation, indenter geometries, -Types of deformation; forms of P-h curves for elastic, plastic, elastoplastic : hr= hf = residual / final depth, Ue = elastic energy, Ur = energy dissipated (elastoplastic / inelastic), Utotal = total work of deformation= Ue+Ur Oliver-Pharr analysis- linear Elastic, Isotropic, Continuum Contact Mechanics Theory (Oliver and Pharr, 1992 JMR, 7(6) 1564) : Geometry set-up and definitions of geometric parameters : assumes "sink-in" P = applied load, Pmax= peak applied load h = indentation depth (at Pmax; h= hmax maximum depth) a = radius of contact circle hc= contact depth, vertical distance along which contact is made between sample and tip hs = displacement of the surface at the perimeter of contact From geometry : h = hc + hs A(hc) = contact (projected) area at hc iisampleindenter1- 1-= reduced modulus22⎛⎞νν⎛⎞=+⎜⎟⎜⎟⎝⎠⎝⎠EE-1rE (i.e. two springs in series) E = modulus ν = Poisson's ratio hf = residual final depth (indicates inelasticity; e.g. viscoelasticity, plasticity) ()= contact initial unloading stiffness =(typically evalulated between 95% and 20% of )⎛⎞⎜⎟⎝⎠maxPmaxdPdhPS hf 23.052 Nanomechanics of Materials and Biomaterials Thursday 05/10/07 Prof. C. Ortiz, MIT-DMSE OLIVER-PHARR ANALYSIS : MATHEMATICAL FORMULATION (Oliver and Pharr, 1992 JMR, 7(6) 1564) Schematic courtesy of B. Bruet is measured directly from the data (typically evalulated between 95% and 20% of )π=→→Sholds for any indent (er geometry takes into account sin nk-i2=−rcmaxmaxcmaxE 1)A(h )S PPhh (2)Sε Tip Geometry ε flat-ended cylindrical punch 1 paraboloid of revolution 0.75 Cone 2(π-2)/π = tip area function; representative of tip geometry, can be calibrated on sampleof known modulus (e.g. fused quartz) by inverting equation ;ccIndenter (Probe Tip) Area Function Calibration :A(h )(1)A(hCarry out indentations at successively higher loads; at each calculate and from (3), these data are fit to a polynomial :⎛⎞π⎜⎟⎝⎠++ + + +2rmax c(max)c2 0.5 0.25 1/8coc1c2c 3c 4c 5S)= (3)4EPhA(h ) A(h )= C h C h C h C h C h CGives (Ideal Berkovich Geometry) 1/16ccc2occhA(h ) for every indentation depth, hC = 24.5; A(h )= 24.5h (4) (see Appendix Lecture 22 for Derivation), coefficients reflect indenter geometry Note : Danielle will be reviewing finite element analysis (numerical/computational approach to reducing material properties from nanoindentation data) in recitation friday 33.052 Nanomechanics of Materials and Biomaterials Thursday 05/10/07 Prof. C. Ortiz, MIT-DMSE HARDNESS, PILEUP, and SINK-IN General Definition : 2P (N)H(Pa)=A (m ) Traditional Definition (microhardness): resistance to plastic or permanent deformation where penetrated by an indenter =2residualresidualP (N)H(Pa)=A (m)A projected area of residual impression after unloadingfor nanoindentation can measure by AFM imaging Berkovich residual indent Nanoindentation Definition : total resistance to penetration (elastic and plastic) max2c(max)P (N)H(Pa)=A (h ) (m ) Pileup : A underestimated → E, H overestimated Sinkin : A overestimated → E, H underestimated 43.052 Nanomechanics of Materials and Biomaterials Thursday 05/10/07 Prof. C. Ortiz, MIT-DMSE STRUCTURE OF SEASHELL NACRE (Courtesy of B. Bruet) outer shell surfaceside view ↑ c-axis 10 μm top view c-axis 10 μmnacre ● multilayered structure, inner nacreous layer has microscale “brick and mortar” structure ~95 wt.% of it is calcium carbonate ~5 wt.% biomacromolecules ● individual nacre tablets are complex organic-inorganic biocomposites in and of themselves (aragonite-based) composed of nanograins (~ 30 nm) with embedded biomacromolecules 53.052 Nanomechanics of Materials and Biomaterials Thursday 05/10/07 Prof. C. Ortiz, MIT-DMSE MECHANICAL PROPERTY AMPLIFICATION (Ashby, 1999) 63.052 Nanomechanics of Materials and Biomaterials