Nanoindentation-lecture Notes (1) 441x6o

Instructor: Yury Gogotsi

Introduction to Nano Indentation

Indentation (Hardness) Test Load (P) Indenter

Specimen

Hardness – resistance to penetration of a hard indenter

Acknowledgements: V. Domnich, T. Juliano, M. Barsoum

Hardness

Introduction

Hardness is a measure of a material’s resistance to surface penetration by an indenter with a force applied to it.

• Mechanical measurement in micro scale Microindentations

Hardness Brinell, 10 mm indenter, 3000 kg = Load F/surface area of indentation Vickers: Diamond pyramid indentation. Microhardness Vickers micro-indentation = size of pyramid comparable to microstructural features. You can use to assess relative hardness of various phases or microconstituents. Nanoindentation

This is an optical photo of a Vickers indentation (98N) in silicon nitride. The specimen is tilted to show the three dimensional form of the indentation, including the tip cracking and the side uplift

– To study the mechanical behavior of different orientations we need single crystals – For a bulk sample it’s hard to get a nano-scale response from different grains – Very little information on the elastic-plastic transition

http://moremetallography.com/ceramics/ceramics.htm

Micro- vs. Nano-Indentation

Introduction

Microindentation

– 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.

A prescribed load is applied to an indenter in with a specimen and the load is then removed and the area of the residual impression is measured. The load divided by the area is called the hardness.

d

VH =

P d2

Nanoindentation (depth-sensing indentation) A prescribed load is applied to an indenter in with a specimen. As the load is applied, the depth of penetration is measured. The area of 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 . Shape of the unloading curve provides a measure of elastic modulus.

loading Load (P)

• The depth-sensing nanoindentation method gained popularity with the development of

P = α (h - hf)m unloading

S hc hmax Displacement (h)

Schematic of the various types of indenter tips used in indentation testing: (a) Vickers, (b) Berkovich, (c) Knoop, (d) conical, (e) Rockwell, and (f) spherical

Contours of principal normal stresses in (a) Boussinesq and (b) Hertzian fields, shown in the plane containing axis σ11

0.008 0.0005

0.005

0.0002

-0.008 -0.002

-0.100

σ22

0.008 0.0005

-0.500 -0.025 0.005 0.007

0

0.002

-0.025 0.005

-0.030

-0.002

(a)

(b)

(c)

(d)

(e)

-0.008

-0.128

(f)

σ33

-0.100 -0.750

-0.032

(a)

(b)

-0.250

Tip Geometry - Berkovich

Tip Geometry - Spherical

• Advantages:

•

Advantages: – Extended elastic plastic deformation – Load displacement results can be converted to indentation stress-strain plots – Useful in determination of yield point

– Sharp and welldefined tip geometry – Well-defined plastic deformation into the surface – Good for measuring modulus and hardness values

•

Disadvantages: – Tip geometry is not very sharp and the spherical surface is not always perfect

• Disadvantages: – Elastic-plastic transition is not clear http://www.bbt..ch/kti/success/archiv/nano_micro/f/power.htm

Testing Issues

MTS Tech sheet for spherical tip

Surface Roughness

• Sample Issues – Surface Roughness – Inhomogeneities • • • • • •

Contamination or oxide layers Multi-layered structure Thin films Gradient layers Multi-phase materials Materials that has particles embedded in them

• Machine Issues – Machine compliance – Tip shape function – Drift

• Roughness has significant effect on mechanical properties • A model can be developed to for the roughness • Surface roughness should be significantly smaller in lateral dimension than the indenter tip

http://www.nanoindentation.cornell.edu/

Material Response to Intentation P

surface profile after load removal indenter

Analytical Models • The basic assumptions of this approach are,

hs = ε

initial surface

hr

Pmax S

– Deformation upon unloading is purely elastic – The compliance of the sample and indenter tip can be thought of as a combination of springs in series

1 −υs 1 1 − υi = + Er Ei Es 2

h

hs

surface profile under load

hc

area:

7

hc = hmax − hs

A(hc ) = 24.5hc + ∑ C h 2

1/ 2i i c

i =0

P – applied force h – indenter displacement C - coefficient

hc – depth hr – plastic deformation after load removal hs – surface displacement at the perimeter

2

– The can be modeled as a rigid indenter of defined shape with a homogeneous isotropic elastic half-space where stiffness, S

S=

2 A

Er

π • The main challenge lies in the determination of the actual area, A, at load. Sneddon, I.N., International Journal of Engineering Science, Vol. 3, p. 47, 1965 Pharr, G.M.; Oliver, W.C. and Brotzen, F.R., Journal of Materials Research, Vol. 7, No. 3, p. 613, 1992

Oliver & Pharr, J. Mater. Res. 1992

Analytical Models

Analytical Models • Field and Swain Approach:

They treated the indentation as a reloading of a preformed impression with depth hf into reconformation with the indenter

4 E r R1 / 2 h 3 / 2 3 2/3 ⎛ Pmax ⎞ ⎜ ⎟ − hend h part ⎜P ⎟ part ⎠ ⎝ hf = 2/3 ⎛ Pmax ⎞ ⎜ ⎟ −1 ⎜P ⎟ ⎝ part ⎠ P=

hc hc

• Doerner-Nix Model:

Ac = f (hc )

H=

Pmax Ac

Doerner, M.F. and Nix, W.D., Journal of Materials Research, Vol. 1, No. 4, p. 601, 1986 Fischer-Cripps, A. C., Vacuum 58 (2000), 569-585

⎛ hend + h f a = R(hend + h f ) − ⎜⎜ 2 ⎝ Field, J.S. and Swain, M.V., Journal of Materials Research, Vol. 8, No. 2, p. 297, 1993

⎞ ⎟⎟ ⎠

2

Continuous Stiffness Measurement

Analytical Models • Oliver and Pharr Model:

•

The nanoindenter 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 stiffnesses at all depth.

•

The stiffness values enable us to calculate the radius at any depth more precisely.

P = α (h − h f ) m hc = ht − ε

P S

Ac = f (hc ) Displacement, h

Oliver, W.C. and Pharr, G.M., Journal of Materials Research, Vol. 7, No. 6, p. 1564, 1992

Oliver, W.C. and Pharr, G. M., J. Mater. Res., 19 (1), Jan 2004 Bhusan, B. and Li, X., Materials Characterization 48 (2002), 11-36

How are Stiffness, Hardness and Modulus Calculated?

Load vs. Displacement

Er =

πS 2 β A proj

1 1 −ν 2 1 −ν i = + Er E Ei

2

Elastic hr = 0

Load, P

Load, P

Modulus → Two key equations:

Load, P

Hardness = Maximum Load / Projected Area at Maximum Load = Pmax/Aproj (Pa)

Pmax

Pmax

Pmax

Stiffness = (dP/dh)h=hmax (N/m)

Plastic hr = hmax

β=1 for circular , 1.034 for Berkovich and cube corner ν is estimated/known, Aproj is calibrated, and E is solved for S Displacement, h

0

Er – reduced modulus of elasticity Ei – modulus of elasticity of indenter

hmax

hmax Displacement, h

0

Displacement, h

Energy Considerations

Elastoplastic Material

Elastic energy

Loading P = α1hm

3 Ue = 1 α 2hmax (1- ξr )3 3

Unloading

Unloading P = α2(h-hr)m

Load, P

Load, P

Loading P = α1h2

Hysteresis loop energy

P = α2(h-hr)2

3 Ur = 1 α1hmax ξr 3

Analytical solution

Work of indentation

m = 1 for flat cylinders

WI =

m = 2 for cones m = 1.5 for spheres 0

Displacement, h

Ur 0

Sneddon, Int. J. Engng. Sci. 1965

A Wealth of Different Machines

with ξ r ≡ hr

Ue hf

Displacement, h

hmax

Ur

Vr

hmax

Vr 1 gh 3

= 1-

α1

α2

3 max r

ξ

Sakai, J. Mater. Res. 1999

Nano Indenter XP® (MTS Systems) • Maximum applied load is 500 mN • Indenter load resolution of 50 nN, and displacement resolution of <.02 nm • Obtains reliable characterization data for thin films and individual grains • Testworks 4 software is used for analysis of collected data

Micro Photonics CSM Nano Hardness Tester

CSIRO Ultra-Micro Indentation System

Hysitron Triboindenter

• Scratches can be made with this machine

Indenter Tips: Pyramidal Nanoindentation Systems

Berkovich load frame loading actuator load sensor load train indenter

displ. sensor

specimen sample holder

Controlled loading. Depth resolution <1nm

SEM image of a typical nanoindentation in GaAs [Berkovich tip; 50 mN loading; (111) surface]. GaAs

1 µm

The total included angle on this tip is 142.3°, with a half angle of 65.35°. This makes it a very flat tip. This tip geometry has been used as the standard form nanoindentation. This tip is used primarily for bulk materials and thin films greater than 100nm thick. The average radius of curvature for a Berkovich tip is typically between 100nm and 200nm.

Cube Corner (90 degree) The total included angle of this tip is 90° and has the same shape as the corner of a cube. Because it has sharper angles and a higher aspect ratio, the radius of curvature can be much smaller than that for a Berkovich tip. These tips specialty is ultra thin films, where plastic deformation should be kept to a more confined volume.

Indenter Tips: Sphero-Conical Radius 1 – 3 µm These tips can be used for indentation & scratch testing. Samples that would need these for indentation may include polymers that are too soft to image with Berkovich tips. Because of the nondirectional geometry at the end of these tips, they are good scratching tips for harder materials, where plastic deformation is desired. For ultra thin films, it may be best to have a cube corner tip for scratching. Radius 3 – 200 µm These tips are used for indenting in very soft materials. Samples may include very soft polymers and biological samples. They are also good for scratching on harder materials when no plastic deformation is desired (e.g. to find coefficient of friction).

Pile-up and Sink-in

Point-Force Indentation Loading geometry

Load-displacement curve

c

c

Conversion to Stress-Strain ‡

Spherical Indentation Loading geometry

P=

Load-displacement curve

4 E r Rhe3 3

hc = ht − 0.75

a= hs c c

hs

MTS Nanoindenter with Continuous Stiffness Measurement

σ=

P S

2Rhc − hc P πa 2

Strain = a/R

2

Choosing an Appropriate Indenter Sharp indenters: Characteristic strain is constant regardless of the load or displacement. Thus, the sharper the cone or pyramid, the larger the characteristic strain. To obtain the stress-strain relationship of a material, multiple tests using indenters with different included angles is required.

Spherical indenters: Characteristic strain changes continuously as the indenter penetrates into material. In principle, one can determine the elastic modulus, yield stress, and strain-hardening behavior of a material all in one test.

ε = 0.2 cot (ψ) ψ – included angle of the indenter

0.2 a ε= R a – radius of R – radius of the indenter

Machine Stiffness Calibration Usually done by manufacturer using materials with known properties (aluminum for large penetration depths, fused silica for smaller depth).

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 area of various indents in a known material

•

Another way is to derive the machine compliance as the intercept of 1/total stiffness vs. 1/sqrt(maximum load) plot, if the Young’s modulus and hardness are assumed to be depth-independent.

Oliver, W.C. and Pharr, G.M., Journal of Materials Research, Vol. 7, No. 6, p. 1564, 1992

Thermal Drift • Drift can be due to vibration or a thermal drift. • Thermal drift can be due to – Differential thermal expansion in the machine – Heat generation in the electronic devices

Using an accurate value of machine stiffness is very important for large s, where it can significantly affect the measured loaddisplacement data.

• Drift might have a parallel and/or a perpendicular component to the indenter axis • Thermal drift is especially important when studying time varying phenomena like creep.

Oliver, W.C. and Pharr, G.M., Journal of Materials Research, Vol. 7, No. 6, p. 1564, 1992

Thermal Drift Calibration Indenter displacement vs. time during a period of constant load. The measured drift rate, 0.31 nm/s, is used to correct the load-displacement data

Application of thermal drift correction to the indentation loaddisplacement data

Real Indenter Tips: Deviation from Perfect Shape

Radius 100 µm

Radius 1 µm Sphero-Conical

Area Function Calibration Ideal tip geometry yields the following area-to-depth ratio: A = 24.5 hc2 Real tips are not perfect !

Calibration:

hc2

(hc)

Use material with known elastic properties (typically, fused silica) and determine its area as a function of depth. Then fit the experimental data to the expression

A = C1hc2 + C2hc + C3hc1/2 + C4hc1/4 + C5hc1/8 + … Now, use the new area tip function for all measurements.

Thin Films: NiP on Copper

Typical Load-Displacement Curves in Nanoindentation Experiments 40

Load, mN

0

elbow & pop-out

0

100 200 300 400 500

Displacement, nm

Raman Analysis of Nanoindentations in Silicon

15

elbow

Average Pressure (GPa)

Applied load (mN)

0

5

0

elbow & pop-out

20

6 GPa

0 15 10

20

40

0

10

20

40

20

0

Effect of Phase Transformations the Shape of Indentation Curves pop-out

elbow

20

(b)

h

40

40

40

silicon (a)

pop-out

20

most elastoplastic materials P

areas (dashed lines) and stresses at the interface of the regular tetrahedral pyramid penetrating into the half-space. The maximum stresses are observed in the center of indentation zone and decrease according to the stress isobars (solid lines). (a) Stress singularities in the purely elastic loading and (b) their reduced form when the non-linearity of the half-space is taken into .

5

4 GPa

200 400 Displacement (nm)

Nanoindentation

Si-I (cd) Si-III (bc8) Si-XII (r8)

350 433 394 521

500 nm

10

0

0

Pristine Si

382

0 15

5

0

Analysed spot

5 GPa 200 400 Depth (nm)

- (111) polished Si wafer - 50 mN max load - 3 mN/sec loading rate

166

520

200

400

600

200

Wavenumber, cm-1

400

600

Application of Quasi-static Nanoindentation

Creep Measurement •

Si II

• •

Si I

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 hc dt It can be done by experiments at different loading rates or by studying the holding segment of a nanoindentation .

ε ind =

Si III and Si XII

Juliano, T., Domnich, V. and Gogotsi, Y., J. Mater. Res. 19[10], 2004

Example of Creep Measurement Poly Tetra-Fluoro Ethylene

Bhusan, B. and Li, X., Materials Characterization 48 (2002), 11-36

•

Mayo, M.J. and Nix, W.D., Strength of Metals and Alloys, Proceedings of the 8th International Conference on the Strength of Materials, p. 1415, 1988

Fatigue Measurement •

Nanoscale fatigue has not been studied extensively because of lack of instruments.

•

CSM can provide sinusoidal force cycles at high frequencies.

•

Change in stiffness can give us fatigue behavior as stiffness is sensitive to damage formation.

Bhusan, B. and Li, X., Materials Characterization 48 (2002), 11-36

Example of Nano-fatigue Measurement (Silicon)

Bhushan, B. and Li, X., Surface and Coatings Tech., 163-164(2003), 521-526

Biocomposite •

Human bone: – 45 - 60 % mineral: Hydroxyapatite – 20 - 30 % matrix: collagen – 10 - 20 % water

•

New Bone replacement material:

Case Stusy: in vitro interfacial mechanics of a bioactive composite A bioactive composite of hydroxyapatite (HA) and polymethylmethacrylate (PMMA), with an addition of a co-polymer coupling agent was examined for a mandible replacement. The influence of the coupling agent on the local mechanical properties of the system before and after in vitro immersion conditions was determined via the application of nano-indentation onto the interface between HA and PMMA of the cross-section of the composite. The fracture mechanism and position of each indent mark was analyzed at up to 5000x magnification under field emission environmental scanning electron microscopy. Coupling the microscopic analysis with the loaddisplacement curve provided a more comprehensive local analysis than has previously been accomplished. The in vitro mechanical properties of the HA particulates showed a reduction of bulk bending properties, local elastic modulus and local hardness with increase of immersion time. While the coupling agent improved the interfacial mechanical properties up to 72 hours immersion, it did not affect the surface bioactivity of the system as shown in the measurement of calcium and phosphate concentration uptake. Emily Ho &. Michele Marcolongo, Drexel U

Nano indentations on Bioactive Composites To determine the local mechanical properties of a bioactive composites a function of immersion period in simulated body fluid (SBF).

(a)

salt

(b)

– Ceramic (reinforcement) + polymer (matrix) Polymer matrix: Polymethylmethacrylate

indentation Ceramic filler: Synthetic Hydroxyapatite

indentation

FE-SEM photos of the 72 hours SBF immersed composites with indentations at: (a) the center of the bioactive ceramics particle (3500x) and (b) the ceramics/polymer interface (5000x).

The “in vitro” Local Mechanical Properties of the Bioactive Composites as a Function of Surface Bioactivity

Summary •

Controls

•

12

Un-immersed

72 hours

10

immersed

Load [mN]

8 6

• •

4

•

2 0 0

100

200

300

400

500

600

700

Displacement [nm]

Nanomechanical Testing

•

Nanoindentation is an important technique to determine various mechanical properties of a material in nanoscale The continuous stiffness measurement or dynamic indentation method is useful in measuring stiffness, elastic modulus, hardness, creep resistance and fatigue properties of the materials CSM probes the mechanical property changes in situ during indentation CSM indentation creep tests can detect creep displacement and stress relaxation at small volumes Nanoscale fatigue tests are important for applications like MEMs and magnetic storage devices Future versions of dynamic nanoindenters should have the capability of measuring at a wide frequency range and also some models has to be developed to for viscoelasticity

Nanoindentation Testing Suggested reading:

Tests • NanoHardness/ Elastic Modulus • Continuous Stiffness Measurements • Acoustic Emissions • Properties at Various Temperatures • Friction Coefficient • Wear Tests • Adhesion • NanoScratch Resistance • Fracture Toughness • Delamination

Common Applications • Fracture Analysis • Anti-Wear Films • Lubricant Effects • Paints & Coatings • Nanomachining • Bio-materials • Metal-Matrix Composites • Diamond Like Carbon Coatings • Semiconductors • Polymers • Thin Film Testing & Development • Property/ Processing Relationships

Fischer-Cripps, A.C., "A review of analysis methods for sub-micron indentation testing," Vacuum, 58, 569-585 (2000). Hay, J.L. and Pharr, G.M., "Instrumented indentation testing," Mechanical Testing and Evaluation, eds. Kuhn, H. and Medlin, D., ASM International (2000). Baker, S.P., "Between nanoindentation and scanning force microscopy: measuring mechanical properties in the nanometer regime", Thin Solid Films, 308-309, 289-296 (1997).

Nanopatterning of Si Wafers

10 µm

40 µm

Optical images of Berkovich nanoindentations on Si, 50 mN load.

Through control of loading conditions, amorphous silicon, Si-III (bc8), and Si-XII (r8) phases with different electronic and optical properties can be produced. Patterns of spots with varying shape or lines can be readily repeated indefinitely.