nano indentation lecture1

47
Nanoindentation Lecture 1 Basic Principle Do Kyung Kim Department of Materials Science and Engineering KAIST

Upload: muhammad-yousuf-soomro

Post on 21-Nov-2014

163 views

Category:

Documents


6 download

TRANSCRIPT

Page 1: Nano Indentation Lecture1

NanoindentationLecture 1

Basic Principle

Do Kyung Kim

Department of Materials Science and Engineering

KAIST

Page 2: Nano Indentation Lecture1

Indentation test (Hardness test)

• Hardness – resistance to penetration of a hard indenter

Page 3: Nano Indentation Lecture1

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

Page 4: Nano Indentation Lecture1
Page 5: Nano Indentation Lecture1

Microhardness - Vickers and Knoop

Page 6: Nano Indentation Lecture1

Microindentation

Optical micrograph of a Vickersindentation (9.8 N) in soda-lime glassincluding impression, radial cracking,and medial cracking fringes.

• 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 response from different grains.

– Very little information on the elastic-plastic transition.

Page 7: Nano Indentation Lecture1

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.

Page 8: Nano Indentation Lecture1

Micro vs Nano Indentation

• MicroindentationA prescribed load appled 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.

• NanoindentationA 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

Page 9: Nano Indentation Lecture1

Basic Hertz’s elastic solution (1890s)

Page 10: Nano Indentation Lecture1

Schematics of indenter tips

Vickers Berkovich Knoop Conical Rockwell Spherical

Page 11: Nano Indentation Lecture1

4-sided indenters

Page 12: Nano Indentation Lecture1

3-sided indenters

Page 13: Nano Indentation Lecture1

Cone indenters

Page 14: Nano Indentation Lecture1

Indenter geometry

Indenter type

Projected areaSemi angle

()

Effective cone angle

()

Intercept factor

Geometry

correction factor

()

Sphere A 2Rhp N/A N/A 0.75 1

Berkovich A = 3hp2tan2 65.3 70.2996 0.75 1.034

Vickers A = 4hp2tan2 68 70.32 0.75 1.012

KnoopA =

2hp2tan1tan2

1=86.25 2=65 77.64 0.75 1.012

Cube Corner A = 3hp2tan2 35.26 42.28 0.75 1.034

Cone A = hp2tan2 0.72 1

Anthony C. Fischer-Cripps, Nanoindentation, 2002, Springer

Page 15: Nano Indentation Lecture1

Stress field under indenter - contact field

Boussinesq fields (point load) Hertzian fields (spherical indenter)

Brian Lawn, Fracture of Brittle Solids, 1993, Cambridge PressAnthony Fischer-Cripp, Intro Contact Mechanics, 2000, Springer

Page 16: Nano Indentation Lecture1

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.

Page 17: Nano Indentation Lecture1

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.

Page 18: Nano Indentation Lecture1

Data Ananlysis

• P : applied load• h : indenter displacement

• hr : plastic deformation after load removal

• he : surface displacement at the contact perimeter

Page 19: Nano Indentation Lecture1

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.

Page 20: Nano Indentation Lecture1

Analytical Model – Doerner-Nix Model

Anthony C. Fischer-Cripps, Nanoindentation, 2002, Springer

Page 21: Nano Indentation Lecture1

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

Page 22: Nano Indentation Lecture1

Analytical Model – Oliver and Pharr

Oliver & Pharr, J Mater Res, 1992

Page 23: Nano Indentation Lecture1

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

Page 24: Nano Indentation Lecture1

Analysis result

• Hardness

'

'111 22

* EEE

p

AE

dh

dP *2

222 5.243.65tan33 pp hhA

5.24

1

2

1* phdh

dPE

25.24 ph

PH

• Elastic modulus

• Contact area

• Stiffness

• Reduced modulus

034.1 for Berkovich indenter

E: modulus of specimenE’: modulus of indenter

for Berkovich indenter

Page 25: Nano Indentation Lecture1

Nov 28, 2006No of citationNov 2003 - 1520, Nov 2005 - 2436

One of the most cited paper in Materials Science

Page 26: Nano Indentation Lecture1

Material response

Anthony C. Fischer-Cripps, Nanoindentation, 2002, Springer

Page 27: Nano Indentation Lecture1

Nanoindenter tips

Page 28: Nano Indentation Lecture1

Berkovich indenter

Projected area

222

2

56.243.65tan33

3.65tan32

3.65tan323.65sin32

3.65cos

27.65cos

4

3

2

2

3

2/60tan

hhA

ha

aah

b

h

aal

A

al

a

l

oproj

o

oo

o

o

proj

o

b

Page 29: Nano Indentation Lecture1

Berkovich vs Vickers indenter

• Face angle of Berkovich indenter: 65. 3

• Same projected area-to-depth ratio as Vickers indenter

• Equivalent semi-angle for conical indenter: 70.3 22 tanphA

222 56.243.65tan33 hhA oproj 222 504.2468tan4 hhA o

proj

• Berkovich projected area • Vickers projected area

Page 30: Nano Indentation Lecture1

Commercial machines

• MTS_Nano-Indenter XP

• CSM_NHT•(Nano-Hardness Tester)

• Hysitron_Triboscope

• CSIRO_UMIS•(Ultra-Micro-Indentation System)

Page 31: Nano Indentation Lecture1

Commercial machine implementation

• MTS_Nano-Indenter • CSIRO_UMIS

• Hysitron_TriboScope • CSM_NHT

• Inductive force generation system• Displacement measured by capacitance gage

• Two perpendicular transducer systems• Displacement of center plate capacitively measured

• Load via leaf springs by expansion of load actuator• Deflection measured using a force LVDT

• Force applied by an electromagnetic actuator• Displacement measured via a capacitive system

Page 32: Nano Indentation Lecture1

Force actuation• Electromagnetic actuation

• Electrostatic actuation

• Spring-based force actuation

• Piezo/spring actuation

• most common means• long displacement range & wide load range• Large and heavy due to permanent magnet

• Electrostatic force btwn 3-plate transducer applied• Small size (tenths of mm) & good temperature stability• Limited load(tenths of mN) & displacement(tenths of N)

• Tip attached to end of cantilever & • Sample attached to piezoelectric actuator• Displacement of laser determine displacement

• Tip on leaf springs are displaced by piezoelectric actuator• Force resolution is very high ( pN range), • As resolution goes up, range goes down & Tip rotation

Page 33: Nano Indentation Lecture1

Displacement measurement• Differential capacitor • Optical lever method

• Linear Variable Differential Transducer (LVDT)

• Laser interferometer

• Measure the difference btwn C1 and C2 due to • High precision(resolution < 1 Å) & small size• Relatively small displacement range

d

AC

0

• Photodiode measures lateral displacement• Popular method in cantilever based system• Detection of deflection < 1 Å

• AC voltage proportional to relative displacement• High signal to noise ratio and low output impedance• lower resolution compared to capacitor gage

• Beam intensity depends on path difference• Sensitivity < 1 Å & used in hostile environment• Fabry-Perot system used for displacement detection

Page 34: Nano Indentation Lecture1

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

Page 35: Nano Indentation Lecture1

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.

Page 36: Nano Indentation Lecture1

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

Page 37: Nano Indentation Lecture1

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

Page 38: Nano Indentation Lecture1

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.

Page 39: Nano Indentation Lecture1

Real tip shape

• Deviation from perfect shape

Sphero-Conical tips

Anthony C. Fischer-Cripps, Nanoindentation, 2002, Springer

Page 40: Nano Indentation Lecture1

Area function calibration

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

A = 24.5 hc2

• Real tips are not perfect!

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

• New area function

A = C1hc2 + C2hc + C3hc

1/2 + C4hc1/4 + C5hc

1/8 + …

Page 41: Nano Indentation Lecture1

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

Page 42: Nano Indentation Lecture1

Pile-up and Sinking-in

Page 43: Nano Indentation Lecture1

Phase transition measurement

• Nanoindentation on silicon and Raman analysis

Page 44: Nano Indentation Lecture1

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

• It can be done by experiments at different loading rate or by studying the holding segment of a nanoindentation.

dt

dh

hc

cind

1

Page 45: Nano Indentation Lecture1

Fracture toughness measurement

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

Fracture toughness expression

Kc = 1.073 xv (a/l)1/2 (E/H)2/3 P / c3/2

Page 46: Nano Indentation Lecture1

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.

Page 47: Nano Indentation Lecture1

Nanomechanical testing

• Tests– Nanohardness/Elastic

modulus– Continuous Stiffness

Measurements– Acoustic Emmisions– Properties at Various

Temperature– Friction Coefficient– Wear Tests– Adhesion– NanoScratch

Resistance– Fracture Toughness– Delamination

• Common Applications– Fracture Analysis– Anti-Wear Films– Lubricant Effect– Paints and Coatings– Nanomachining– Bio-materials– Metal-Matrix

Composites– Diamond Like Carbon

Coatings– Semiconductors– Polymers– Thin Films Testing and

Development– Property/Processing

Relationships