ES 240 Project: Finite Element Modeling of Nano-Indentation of Thin Film Materials

1. Introduction to Nanoindentation Process2. Model Description3. Model Validation4. Results and Discussion5. Effect of Substrates6. Conclusion and Future Work

Outline

Displacement Sensor

Force Sensor

Film

Substrate

Indenter

Displacement of Indenter h Ap

plie

d L

oa

d o

n I

nd

en

ter

P

LoadingUnloading

dP/dh

1. Introduction to Nanoindentation Process

100 nm

100 nm

1000 nm

900 nm

Indenter: Diamond

Film: Copper

Substrate: 1. Copper 2. Sapphire 3. Silicon 4. Glass 5. Polymer

2. Model Description-Dimensions and Materials of The Model

3.70

Elastic

Materials

E (GPa)

v (-)

Diamond 1147 0.3

Sapphire 440 0.3

Silicon 172 0.3

Glass 73 0.3

Polymer 30 0.3

Elastic/Plastic

Mateirial

E

(GPa)

V(-) Y

(GPa)

Plastic Constitutive

Copper 130 0.3 1.3 nK

0 0.01 0.02 0.03 0.04 0.050

0.5

1

1.5

2

2.5

3

(-)

(G

Pa

) Elastic Plastic

2. Model Description -Materials Properties

Indenter

Film

Substrate

Element Type: 4-Noded Axisymmetric

Element Size (Edge length):~2 nm (Indentation region)~10 nm (Other region)

Mesh Sensitivity:Refined-mesh model gives similar results.

2. Model Description -Mesh and Element

cA

unloadingcr dh

dP

AE

2/12/11

4

Experimental :

Theoretical:

i

i

s

s

r

Ev

Ev

E22 11

1

rE : Reduced Modulus

sE sv : Film’s E and v

sE sv : Indenter’s E and v

: Indenter and film’s contact area

3. Model Validation-Reduced Modulus (copper substrate)

0 5 10 15 20 25 30

0

2

4

6

8

10

12

14x 104

Displacement of Indenter h (nm)

Ap

plie

d Lo

ad o

n I

nden

ter

P (

nN

)

Simulated P vs. hTheoretical P vs. h

Pa)128.6056(GrESimulated:

Theoretical: Pa)128.2340(GrE

3. Model Validation-Theoretical and Simulated Results (copper substrate)

4. Model Results- Mises Stress (copper substrate)

4. Model Results- Effective Plastic Strain (copper substrate)

0 5 10 15 20 25 30 3502468

1012141618

x 104

Displacement of Indenter h (nm)

Fo

rce

on I

nden

ter

P (

nN

)

coppersapphiresiliconglasspolymer

E reducing

Model’s Prediction Experimental Results (W, Nix et al, Acta Materialia, 50, 23, 2002)

5. Effect of Substrates- Load vs. Displacement

0 50 100 150 200 250 300 350 400 450 50060

80

100

120

140

160

180

200

220

Substrate Youngs Modulus Es(GPa)

Re

duce

d Y

oun

gs

Mod

ulus

Er

(GP

a)

coppersappsiliconglasspolymerTheoretical Er

y=-0.00090793*x2

+0.75727*x+46.0508

Model’s Prediction Experimental Results (W, Nix et al, Acta Materialia, 50, 23, 2002)

5. Effect of Substrates- Reduced Modulus

0 100 200 300 400 500 600 700 800 900 1000-12

-10

-8

-6

-4

-2

0

X (nm)

De

flect

ion

of S

ubs

trat

e T

op

Sur

face

(nm

)

coppersappsiliconglasspolymer

5. Effect of Substrates- Deflection of Substrate

1. Nanoindentation process can be simulated using finite element method.

2. The reduced modulus predicted by the finite-element model is very close to analytical results.

3. Stiff substrate tends to overestimate thin film’s modulus, and compliant substrate tends to underestimate thin film’s modulus.

5. Conclusion