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 material’s resistance to surface 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 comparable to microstructural features. You can use to assess relative hardness of various phases or microconstituents.

• Nanoindentation

Microhardness - Vickers and Knoop Microindentation

• Mechanical property measurement in micro-scale (Micro-indentation)

– To study the mechanical behavior of different orientations, we need single crystals. – For a bulk sample, it is hard to get a nano-scale Optical micrograph of a Vickers response from different indentation (9.8 N) in soda-lime glass grains. including impression, radial cracking, and medial cracking fringes. – Very little information on the elastic-plastic transition. 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 displacement 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 applied to an indenter 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 indenter in contact with a specimen. As the load is applied, the depth of penetration is measured. The area of contact at full load is determined by the depth of the impression and the known angle or radius of the indenter. The hardness is found by dividing the load by the area of contact. Shape of the unloading curve provides a measure of elastic modulus.

Anthony C. Fischer-Cripps, Principles of nanoindentation, training lecture Basic Hertz’s elastic solution (1890s) Schematics of indenter tips

Vickers Berkovich Knoop Conical Rockwell Spherical 4-sided indenters 3-sided indenters Cone indenters 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 stress-strain 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 see 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 homogeneous isotropic elastic half space using

• where S is the contact stiffness and A the contact area. This relation was presented 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 shapes. Analytical Model – Doerner-Nix Model

Anthony C. Fischer-Cripps, Nanoindentation, 2002, Springer Analytical Model – Field and Swain

• They treated the indentation as a reloading of a preformed

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 system applies a load to the indenter tip to force the tip into the surface while simultaneously superimposing an oscillating force with a force amplitude generally several orders of magnitude smaller than the nominal load. • It provides accurate measurements of contact stiffness at all depth. • The stiffness values enable us to calculate the contact radius at any depth more precisely.

Oliver, Pharr, Nix, J Mater Res, 2004 Analysis result υ 1 1− 2 1−υ'2 • Reduced modulus = + E: modulus of specimen E* E E' E’: modulus of indenter

dP A •Stiffness = 2E* dh p

2 2 2 •Contact area A = 3 3hp tan 65.3 = 24.5hp for Berkovich indenter

P •Hardness H = 2 24.5hp

* dP 1 1 π • Elastic modulus E = β β =1.034 for Berkovich indenter dh 2hp 24.5 Indenter geometry

Effective Geometry Semi angle Intercept Indenter type Projected area cone angle correction factor (θ) (α) factor (β)

Sphere A ≈π2Rhp N/A N/A 0.75 1

2 2 Berkovich A = 3hp tan θ 65.3 ° 70.2996 ° 0.75 1.034

2 2 Vickers A = 4hp tan θ 68 ° 70.32 ° 0.75 1.012

2 θ1=86.25 ° Knoop A = 2hp tanθ1tanθ2 77.64 ° 0.75 1.012 θ2=65 °

2 2 Cube Corner A = 3hp tan θ 35.26 ° 42.28 ° 0.75 1.034

2 2 Cone A = πhp tan αα α 0.72 1

Anthony C. Fischer-Cripps, Nanoindentation, 2002, Springer One of the most cited paper in Materials Science

No of citation Nov 28, 2006 Nov 2003 - 1520, Nov 2005 - 2436 Material response

Anthony C. Fischer-Cripps, Nanoindentation, 2002, Springer Nanoindenter tips Berkovich indenter

l tan 60o = a / 2 3 l = a b 2 al 3 A = = a2 proj 2 4 h cos65.27o = b Projected area a cos65.3o a h = = 2 3 sin 65.3o 2 3 tan 65.3o

a = 2 3h tan 65.3o

2 2 o 2 Aproj = 3 3h tan 65.3 = 24.56h Berkovich vs Vickers indenter

• Berkovich projected area • Vickers projected area

2 2 o 2 2 2 o 2 Aproj = 3 3h tan 65.3 = 24.56h Aproj = 4h tan 68 = 24.504h

• Face angle of Berkovich indenter: 65. 3 ° • Same projected area-to-depth ratio as Vickers indenter π • Equivalent semi-angle for conical indenter: 70.3 ° 2 2 A = hp tan α Commercial machines

• MTS_Nano-Indenter XP •CSIRO_UMIS •(Ultra-Micro-Indentation System)

• Hysitron_Triboscope •CSM_NHT •(Nano-Hardness Tester) Commercial machine implementation

• MTS_Nano-Indenter • CSIRO_UMIS

• Inductive force generation system • Load via leaf springs by expansion of load actuator • 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 µN) • Spring-based force actuation • Piezo/spring actuation

• Tip attached to end of cantilever & • Tip on leaf springs are displaced by piezoelectric actuator • 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 • Optical lever method

ε ⋅ε ⋅ A C = 0 d

• Photodiode measures lateral displacement • Measure the difference btwn C1 and C2 due to ∆ • High precision(resolution < 1 Å) & small size • Popular method in cantilever based system • Relatively small displacement range • Detection of deflection < 1 Å

• Linear Variable Differential • Laser interferometer Transducer (LVDT)

• AC voltage proportional to relative displacement • Beam intensity depends on path difference • High signal to noise ratio and low output impedance • Sensitivity < 1 Å & used in hostile environment • lower resolution compared to capacitor gage • Fabry-Perot system used for displacement detection 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 load. The measured drift rate is used to correct the load displacement data.

Application of thermal drift correction to the indentation load- displacement data Machine compliance

• Displacement arising from the compliance of the testing machine must be subtracted from the load-displacement data

• The machine compliance includes compliances in the sample and tip mounting and may vary from test to test

• It is feasible to identify the machine compliance by the direct measurement of contact area of various indents in a known material

• Anther way is to derive the machine compliance as the intercept of 1/total contact stiffness vs 1/ sqrt(maximum load) plot, if the Young’s 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 load- displacement data. Real tip shape

• Deviation from perfect shape

Sphero-Conical tips

Anthony C. Fischer-Cripps, Nanoindentation, 2002, Springer Area function calibration

• Ideal tip geometry yields the following area-to- depth ratio:

2 A = 24.5 hc

• Real tips are not perfect!

• Calibration Use material with known elastic properties (typically fused silica) and determine its area as a function of contact • New area function

2 1/2 1/4 1/8 A = C1hc + C2hc + C3hc + C4hc + C5hc + … Surface roughness

• As sample roughness does have a significant effect on the measured mechanical properties, one could either try to incorporate a model to account for the roughness or try to use large indentation depths at which the influence of the surface roughness is negligible. • A model to account for roughness effects on the measured hardness 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 dimensions 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

1 dhc ε ind = hc dt • It can be done by experiments at different loading rate or by studying the holding segment of a nanoindentation. Fracture toughness measurement

Combining of Laugier proposed toughness model and Ouchterlony’s radial cracking modification factors, fracture toughness can be determined.

Fracture toughness expression

1/2 2/3 3/2 Kc = 1.073 xv (a/l) (E/H) P / c 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 • Common Applications – Nanohardness/Elastic – Fracture Analysis modulus – Anti-Wear Films – Continuous Stiffness – Lubricant Effect Measurements – Paints and Coatings – Acoustic Emmisions – Nanomachining – Properties at Various – Bio-materials Temperature – Metal-Matrix Composites – Friction Coefficient – Diamond Like Carbon – Wear Tests Coatings – Adhesion – Semiconductors – NanoScratch Resistance – Polymers – Fracture Toughness – Thin Films Testing and – Delamination Development – Property/Processing Relationships