Nanoindentation Lecture 1 Basic Principle Do Kyung Kim Department of Materials Science and Engineering KAIST Indentation test (Hardness test) Hardness resistance to penetration of a hard indenter Hardness Hardness is a measure of a materials resistance to surf ace penetration by an indenter with a force applied to it.

Hardness Brinell, 10 mm indenter, 3000 kg Load F /surface area of indentation A Vickers, diamond pyramid indentation Microhardness Vickers microindentation : size of pyramid comparabl e to microstructural features. You can use to assess r elative hardness of various phases or microconstituen ts. Nanoindentation Microhardness - Vickers and Knoop Microindentation Mechanical property meas

urement in micro-scale (Micro-indentation) Optical micrograph of a Vickers indentation (9.8 N) in soda-lime glass including impression, radial cracking, and medial cracking fringes. To study the mechanic al behavior of different orientations, we need s ingle crystals. For a bulk sample, it is hard to get a nano-scal e response from differe

nt grains. Very little information on the elastic-plastic tr ansition. Nanoindentation Nanoindentation is called as, The depth sensing indentation The instrumented indentation Nanoindentation method gained popularity with the development of, Machines that can record small load and displace ment with high accuracy and precision Analytical models by which the load-displacement data can be used to determine modulus, hardness

and other mechanical properties. Micro vs Nano Indentation Microindentation A prescribed load appled to an indent er in contact with a specimen and the load is then removed and the area of the residual impression is measured. The load divided by the by the area is called the hardness. Nanoindentation A prescribed load is appled to an inde nter in contact with a specimen. As th e load is applied, the depth of penetr

ation is measured. The area of contac t at full load is determined by the dep th of the impression and the known a ngle or radius of the indenter. The ha rdness is found by dividing the load b y the area of contact. Shape of the un loading curve provides a measure of elastic modulus. Basic Hertzs elastic solution (1890s) Schematics of indenter tips Vickers

Berkovich Knoop Conical Rockwell Spherical 4-sided indenters 3-sided indenters Cone indenters

Indenter geometry Projected area Semi angle () Effective cone angle () Intercep t factor

Geometr y correctio n factor () Sphere A 2RhRhp N/A N/A

0.75 1 Berkovich A = 3hp2Rhtan2Rh 65.3 70.2Rh996 0.75 1.034

Vickers A = 4hp2Rhtan2Rh 68 70.32Rh 0.75 1.012Rh Knoop

A= 2Rhhp2Rhtan1tan2Rh 1=86.2Rh5 2Rh=65 77.64 0.75 1.012Rh Cube Corner A = 3hp2Rhtan2Rh

35.2Rh6 42Rh.2Rh8 0.75 1.034 Cone A = hp2Rhtan2Rh

0.72Rh 1 Indenter type Stress field under indenter - contact field Boussinesq fields (point load) Hertzian fields (spherical indenter)

Brian Lawn, Fracture of Brittle Solids, 1993, Cambridge Press Anthony Fischer-Cripp, Intro Contact Mechanics, 2000, Springer Sharp indenter (Berkovich) Advantage Sharp and well-defined tip geometry Well-defined plastic deformation into the surface Good for measuring modulus and hardness values Disadvantage Elastic-plastic

transition is not clear. Blunt indenter - spherical tip Advantage Extended elastic-plastic deformation Load displacement results can be converted to indentation stressstrain curve. Useful in determination of yield point Disadvantage Tip geometry is not very sharp and the

spherical surface is not always perfect. Data Ananlysis P : applied load h : indenter displacement hr : plastic deformation after load removal he : surface displacement at the contact perimeter Analytical Model Basic Concept Nearly all of the elements of this analysis were first developed by workers at

the Baikov Institute of Metallurgy in Moscow during the 1970's (for a review s ee Bulychev and Alekhin). The basic assumptions of this approach are Deformation upon unloading is purely elastic The compliance of the sample and of the indenter tip can be combined as springs in series The contact can be modeled using an analytical model for contact between a rigid indenter of defined shape with a h omogeneous isotropic elastic half space using where S is the contact stiffness and A the contact area. This relation was pre sented by Sneddon. Later, Pharr, Oliver and Brotzen where able to show that

the equation is a robust equation which applies to tips with a wide range of s hapes. Analytical Model Doerner-Nix Model Doerner, Nix, J Mater Res, 1986 Analytical Model Field and Swain They treated the indentation as a reloading of a pref ormed impression with depth hf into reconformation with the indenter. Field, Swain, J Mater Res, 1993

Analytical Model Oliver and Pharr Oliver & Pharr, J Mater Res, 1992 Continuous Stiffness Measurement (CSM) The nanoindentation syste m applies a load to the inde nter tip to force the tip into the surface while simultane ously superimposing an osc illating force with a force a mplitude generally several orders of magnitude smalle r than the nominal load. It provides accurate measur

ements of contact stiffness at all depth. The stiffness values enable us to calculate the contact r adius at any depth more pr ecisely. Oliver, Pharr, Nix, J Mater Res, 2004 Analysis result Reduced modulus 1 1 2 1 '2 *

E E E' Stiffness dP 2 E * dh Contact area A 3 3h p tan 2 65.3 24.5h p Hardness

P H 2 24.5h p A p Elastic modulus dP 1 1 E dh 2h p

2 * E: modulus of specimen E: modulus of indenter 24.5 2 for Berkovich indenter 1.034for Berkovich indenter

One of the most cited paper in Materials Science Nov 28, 2006 No of citation Nov 2003 - 1520, Nov 2005 - 2436 Material response Nanoindenter tips Berkovich indenter tan 60o

b l a/2 3 a 2 al 3 Aproj a 2 2 4 h cos 65.27 o

b l Projected area a cos 65.3o a h 2 3 sin 65.3o 2 3 tan 65.3o a 2 3h tan 65.3o Aproj 3 3h 2 tan 2 65.3o 24.56h 2 Berkovich vs Vickers indenter Berkovich projected area

Vickers projected area Aproj 3 3h 2 tan 2 65.3o 24.56h 2 Aproj 4h 2 tan 2 68o 24.504h 2 Face angle of Berkovich indenter: 65. 3 Same projected area-to-depth ratio as Vickers indenter Equivalent semi-angle for conical indenter: 70.3 2 A h p tan 2

Commercial machines MTS_Nano-Indenter X P CSIRO_UMIS Hysitron_Triboscope CSM_NHT (Ultra-Micro-Indentation System) (Nano-Hardness Tester)

Commercial machine implementation MTS_Nano-Indenter CSIRO_UMIS Inductive force generation system Load via leaf springs by expansion of load actuato Displacement measured by capacitance gage Deflection measured using a force LVDT Hysitron_TriboScope CSM_NHT Two perpendicular transducer systems Force applied by an electromagnetic actuator

Displacement of center plate capacitively measured Displacement measured via a capacitive system Force actuation Electromagnetic actuation Electrostatic actuation most common means Electrostatic force btwn 3-plate transducer applied long displacement range & wide load range Small size (tenths of mm) & good temperature stability Large and heavy due to permanent magnet Limited load(tenths of mN) & displacement(tenths of N

Spring-based force actuation Piezo/spring actuati on Tip attached to end of cantilever & Tip on leaf springs are displaced by piezoelectric actuat Sample attached to piezoelectric actuator Force resolution is very high ( pN range), Displacement of laser determine displacement As resolution goes up, range goes down & Tip rotation Displacement measurement Differential capacitor

C Optical lever method 0 A d Measure the difference btwn C1 and C2Rh due to High precision(resolution < 1 ) & small size Relatively small displacement range Linear Variable Differential Transducer (LVDT)

Photodiode measures lateral displacement Popular method in cantilever based system Detection of deflection < 1 Laser interferometer AC voltage proportional to relative displacement Beam intensity depends on path difference High signal to noise ratio and low output impedance Sensitivity < 1 & used in hostile environment lower resolution compared to capacitor gage Fabry-Perot system used for displacement detectio Factor affecting nanoindentation Thermal Drift Initial penetration depth

Instrument compliance Indenter geometry Piling-up and sinking-in Indentation size effect Surface roughness Tip rounding Residual stress Specimen preparation Thermal drift Drift can be due to vibration or a thermal drift Thermal drift can be due to Different thermal expansion in the machine Heat generation in the electronic devices Drift might have parallel and/or a perpendicular

component to the indenter axis Thermal drift is especially important when studying time varying phenomena like creep. Thermal drift calibration Indenter displacement vs time during a period of constant loa d. The measured drift rate is u sed to correct the load displac ement data. Application of thermal drift correction to the indentation loaddisplacement data

Machine compliance Displacement arising from the compliance of the testi ng machine must be subtracted from the load-displace ment data The machine compliance includes compliances in the s ample and tip mounting and may vary from test to tes t It is feasible to identify the machine compliance by th e direct measurement of contact area of various inden ts in a known material Anther way is to derive the machine compliance as th e intercept of 1/total contact stiffness vs 1/ sqrt(maxi mum load) plot, if the Youngs modulus and hardness are assumed to be depth-independent

Machine compliance calibration Usually done by manufacturer using materials with known properties (aluminum for large penetration depths, fused silica for smaller depth). Using an accurate value of machine stiffness is very important for large contacts, where it can significantly affect the measured loaddisplacement data.

Real tip shape Deviation from perfect shape Sphero-Conical tips Area function calibration Ideal tip geometry yields the following area-to-depth ratio: A = 24.5 hc2 Real tips are not perfect! Calibration

New area function Use material with known elastic properties (typically fused silica) and determine its area as a function of contact A = C1hc2 + C2hc + C3hc1/2 + C4hc1/4 + C5hc1/8 + Surface roughness As sample roughness does have a significant effect on the measur ed mechanical properties, one could either try to incorporate a mo del to account for the roughness or try to use large indentation de

pths at which the influence of the surface roughness is negligible. A model to account for roughness effects on the measured hardne ss is proposed by Bobji and Biswas. Nevertheless it should be noticed that any model will only be able to account for surface roughnesses which are on lateral dimension s significantly smaller compared to the geometry of the indent Pile-up and Sinking-in Phase transition measurement Nanoindentation on silicon and Raman analysis Creep measurement Plastic deformation in all materials is time and

temperature dependent Important parameter to determine is the strain rate sensitivity The average strain rate can be given by ind 1 dhc hc dt It can be done by experiments at different loadin g rate or by studying the holding segment of a n

anoindentation. Fracture toughness measurement Combining of Laugier proposed toughness model and Ouchterlonys radial cracking m odification factors, fracture toughness can be determined. Fracture toughness expression Kc = 1.073 xv (a/l)1/2 (E/H)2/3 P / c3/2 High temperature measurement Nanindentation with or without calibration

Temperature match btw. indenter and sample is important for precision test. Prior depth calibration and post thermal drift correct are necessary. Nanomechanical testing Tests Nanohardness/Elastic modulus Continuous Stiffness Measurements Acoustic Emmisions Properties at Various Temperature Friction Coefficient

Wear Tests Adhesion NanoScratch Resistan ce Fracture Toughness Delamination Common Application s

Fracture Analysis Anti-Wear Films Lubricant Effect Paints and Coatings Nanomachining Bio-materials Metal-Matrix Composit es

Diamond Like Carbon Coatings Semiconductors Polymers Thin Films Testing and Development Property/Processing R elationships