Page 1 of 12  

Measuring Hardness and More through Nanoindentation

Author- Rahul Nair, Fischer Technology, Inc.

Co-authors- Matt Taylor, Fischer Technology, Inc., Bernd Binder, Helmut Fischer, GmbH.

Introduction

Indentation Testing is the technique of using a harder material commonly referred to as an indenter to

deform a softer material. The calculated hardness (H) is the applied force (F) divided by the

corresponding area of contact (A); H = F/A. One of the first modern forms of this technique was

implemented by Johan August Brinell in 1900 [1]. A very heavy load, up to 30,000 N, is applied

through a 10mm diameter hard ball onto the test material. The hardness of the material is calculated

by measuring the diameter of the residual imprint.

As materials increased in hardness over the years new techniques had to be developed to measure

this property. Patented in 1914 the Rockwell Test employs smaller indenters; a diamond cone or a

1/16 inch diameter steel ball [1]. A lower fixed load in the range of 600 N to 1,500 N is applied, the

penetration depth measured and the corresponding area of contact calculated.

While the aforementioned techniques are used to measure hardness of metals and ceramics,

Durometers were developed to measure the hardness of soft polymeric materials. Developed in the

1920s, ‘Shore’ hardness of material is characterized through this technique using Durometers with

different spring constants and a conical or spherical shaped indenter per ASTM D 2240 and ISO 868.

Surface treatments of soft steels like case hardening, carburizing and carbonitriding require the

surface mechanical properties to be measured, not the bulk. In order to limit the stress field from an

indent to the treated surface, lower loads have to be applied through smaller indenters. The Vickers

and Knoop hardness were developed in 1921 and 1939 respectively to meet this need. Indenters

used in these techniques are diamond pyramids where the four sides meet at a point. Low loads of up

to 5N are applied through these indenters and the area of the residual imprint is optically measured

per ISO 6507-1, 2, ISO 4545-1, 2 or ASTM E384.

Developments in deposition technology have resulted in an increase in the use of thin films and

coatings for aesthetic, tribological as well as functional purposes. These materials are used for a wide

range of applications like automotive clear coatings, protective metallic coatings, cutting tools,

integrated circuits and biomaterials. While traditional indentation testing can be used to characterize

bulk steel, micro/nano scale layers and components have brought more challenges.

Until recently, measuring the Pencil hardness of thin films according to ISO 15184 has been

commonplace especially in the automotive paint industry. With this method, pencils of different

hardness are moved at a certain angle and with a certain force across the paint surface to be tested.

The ‘pencil hardness’ of the coating is defined by two consecutive levels of pencil hardness, where

Page 2 of 12  

the softer pencil leaves only a writing track, while the harder pencil causes a tangible deformation of

the paint coating.

While Pencil, Vickers and Knoop hardness are still in use, the reliability and reproducibility of these

methods are contentious for reasons mentioned later in this article. Due to stringent quality standards

in the coating industry, it is necessary to be able to test the hardness of coatings with accuracy and

repeatability. The hardness of thin coatings on tool bits, the viscoelasticity of protective coatings on

optical lenses, the low friction coatings in consumer products all require precision application of

millinewtons of force and corresponding measurements of depth in nanometers. This has led to the

development of nanoindentation.

Nanoindentation

Instrumented indentation testing more commonly referred to as nanoindentation or in simpler terms

depth-sensing indentation employs high-resolution instrumentation to continuously control and

monitor the loads and displacements of an indenter as it is driven into and withdrawn from a material.

The analysis of the measured force-displacement curves described in ISO 14577 is based on work by

Doerner and Nix and Oliver and Pharr [2, 3].

Developed in the mid-1970s, nanoindentation is used to characterize a variety of mechanical

properties of any material that can be measured in a uniaxial tension or compression test. While

nanoindenation is most often used to measure hardness, it is also possible to calculate the modulus

and creep using the data collected in this test. Methods using nanoindentation testers have also been

devised for evaluating the yield stress and strain-hardening characteristic of metals, the storage and

loss modulus in polymers, the activation energy and stress exponent for creep. The fracture

toughness of brittle materials can be estimated as well using optical measurement of the lengths of

cracks that have formed at the corners of hardness impressions made with sharp indenters.

Construction of Testing Equipment

Equipment used to perform nanoindentation consists of three basic components as shown in Figure

1.

(a) An indenter mounted onto a rigid column

(b) An actuator for applying the force

(c) And a sensor for measuring the indenter displacements

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Figure 1: Schematic of typical nanoindentation tester with a force actuator and displacement sensor

Small forces are generated either electromagnetically with a coil and magnet assembly or

electrostatically using a capacitor with fixed and moving plates or with piezoelectric actuators.

Displacements may be measured by eddy current sensors, capacitive sensors, linear variable

differential transducers or laser interferometers.

A diamond is typically used to make indenters because it has high hardness and elastic modulus.

This minimizes the contribution to the measured displacement as compared to those that are made of

other less-stiff materials like sapphire or tungsten carbide in which case the elastic displacements of

the indenter must be accounted for. Vickers geometry indenter, a four-sided pyramid, is most

commonly used in higher load nanoindentation tests for its durability. The Berkovich geometry

indenter is used for measurements of a few nanometers for two reasons; they are very sharp thus

they cause plastic deformation even at very small loads and they are easier to manufacture precisely

as they have only three sides. Cube corner indenters are even sharper than the Berkovich causing

higher stresses and strains. They can be used to estimate fracture toughness at relatively small

scales. While using spherical indenters as the contact stresses small and produce only elastic

deformation at low loads, they could be used to examine yielding and work hardening, and to

generate the entire uniaxial stress-strain curve [4].

Hardness, Modulus and Creep

During a nanoindentation measurement the indenter is driven into the material as shown in Figure 2,

both elastic and plastic deformation processes occur. This produces an impression with a projected

area Ap and surface area As of contact that depends on the shape of the indenter to a contact depth,

hc.

Force Actuator

Displacement Sensor

Indenter

Test Specimen

F

 

The na

indentat

where th

maximu

The slop

depth a

ASTM E

Figu

noindentatio

tion load (F)

he data was

m depth (hm

pe of the upp

nd stiffness

E2546. The h

Figure

ure 2: Schem

on measurem

plotted aga

s obtained fo

max) of penet

per portion of

are determi

hardness and

e 3: Load-dis

matic of inden

ment includ

inst the disp

or one comp

ration, the p

f the unloadi

ned using th

d elastic mod

splacement c

nter (blue) de

es a loadin

placement (h

plete indenta

peak load (F

ng curve, S

he Oliver-Ph

dulus are der

curve measu

eforming tes

ng and unl

h) relative to

ation cycle. T

Fmax), and the

is known as

harr method

rived from th

red on a nan

t material (gr

oading cycl

o the surface

The importa

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the contact s

as describe

ese quantitie

noindentation

Pa

reen)

le. Figure 3

e before defo

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after unload

stiffness. The

ed in ISO 14

es.

n tester

age 4 of 12 

3 shows

ormation,

s are the

ding (hr).

e contact

4577 and

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In nanoindentation the Martens Hardness is determined from the loading portion of the load-

displacement curve and includes the materials resistance to both plastic and elastic deformation. The

Martens Hardness can be plotted as a function the indentation depth. Martens Hardness is given by,

Instrumented Indentation Hardness correlates to traditional forms of hardness as it is a measure of

the resistance to plastic deformation. Instrumented Indentation Hardness is given by

Reduced elastic modulus, Er that is indicative of the stiffness of the sample is given by

pr

A

SE

2

β is a constant that depends on the geometry of the indenter.

The reduced elastic modulus accounts for the elastic displacement that occurs in both the indenter

and the sample. For a test material with elastic modulus EIT it can be calculated by

1 1 1

Here ν is the Poisson’s ratio for the test material, and Ei and νi are the elastic modulus and Poisson’s

ratio of the indenter, respectively.

Creep can be used to characterize material behavior at a constant load. Indentation Creep is defined

as an increase in penetration depth under constant load. As shown in Figure 4 the selected final load

is kept constant for defined time duration and the indentation depth is measured.

Indentation Creep, CIT is calculated as

. 100%

h1: indentation depth at the start of the creep test

h2: indentation depth at the end of the creep test

 

Figu

Compar

As hard

correlati

Vickers

Surface

tradition

most bu

microha

layer. A

collected

indent. I

still a re

geometr

nanoind

between

ure 4: Load-d

ring Traditio

dness is alre

on between

s Hardness v

hardness o

al microhard

ulk materials

rdness teste

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d are affecte

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elationship b

ry indenter is

entation sim

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eady being

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etween Instr

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measured f

onal forms o

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epth is used

dentation Ha

en the Berkov

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p period at m

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and Instrume

sured with V

still reliable

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re affected b

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r’s definition

to calculate

ardness and

vich geomet

kers geomet

s Hardness is

T [5]

maximum loa

rdness

is importan

nted Indenta

Vickers or K

e to characte

ms. The loa

by the proper

cibility and a

of the diago

the area of

d Vickers Ha

ry indenters

ry indenter. T

s defined as

Pa

ad measured

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ation Hardne

Knoop inden

erize the har

ds used in tr

rties of the un

accuracy of

onals of the

contact. But

ardness as a

that are also

Thus the rela

age 6 of 12 

d on a

stand the

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ters with

rdness of

raditional

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the data

residual

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a Vickers

o used in

ationship

 

Shore H

A study

nanoind

data in g

of 60 se

for soft

effects.

F

Figure

HM2000

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In the fo

hardnes

the resu

Hardness vs

measuring M

entation test

graph in Figu

econds and a

coatings an

Figure 5: FIS

6: Martens

0 S

Hardness vs

ollowing stud

ss testing. Th

ults of multi

s. Nanoinden

Martens hard

ter shown in

ure 6 are fro

a creep time

d thin films

SCHERSCOP

Hardness (

s. Nanoinde

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ow indentatio

00 S for the d

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pencils of va

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on depths a

determination

dards perfor

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arious hardn

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a FISCHERS

pencils used

00 S. Figure

The large

age 7 of 12 

2000 S, a

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substrate

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Figure 8

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these coating

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9780198507

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7765

or interpreting

Nix, Journal o

nt of hardne

ng and refin

esearch, Vol

e depth-depe

al properties

ents in coa

acceptance.

of off-the-sh

ny industries

al hardness t

derstanding o

ation about th

f a material.

from soft po

user-influenc

or coating.

, D. Tabor, O

g the data fro

of Materials R

ess and ela

nements to

. 19, No. 1, J

endent profile

s of materials

ating and

. Combinat

helf options f

s.

testing techn

of the intera

he mechanic

Additionally,

olymers to ha

ce and sub

Oxford Unive

om depth-se

Research, Vo

stic modulus

methodolog

Jan 2004

e of the Marte

s boosts perf

surface tre

tion of ISO

rom different

niques, nano

ctions betwe

cal properties

, a single too

ard ceramics

bjectivity from

ersity Press,

ensing indent

ol. 1, No. 4, J

s by instrum

y, W.C. Oliv

ens Hardnes

formance an

eatment tec

O and AS

t vendors ha

indentation t

een surfaces

s derived fro

ol can be us

s. Most impor

m the test

Aug 3, 2000

tation instrum

Jul/Aug 1986

mented inden

ver and G.M

Pag

ss of the DLC

d increases

chnology ha

STM standa

as also contr

testers are v

s or against

om a nanoind

sed to chara

rtantly, this te

and allows

0, ISBN 0198

ments, M.F.

6

ntation: Adv

M. Pharr, Jo

ge 11 of 12 

C coating

life cycle

as seen

ards for

ributed to

iewed as

abrasive

dentation

acterize a

echnique

s one to

8507763,

Doerner,

ances in

ournal of

Page 12 of 12  

4. A simple predictive model for spherical indentation, J.S. Field and M.V. Swain, Journal of

Materials Research, Vol. 8, No. 2, 1993

5. The IBIS Handbook of Nanoindentation, Anthony C. Fischer-Cripps, ISBN 0 9585525 4 1