FINITE ELEMENT ANALYSIS OF INSTRUMENTED INDENTATION OF
TRANSVERSELY ISOTROPIC MATERIALS
Talapady S Bhat And
T. A. Venkatesh Department of Materials Science & Engineering
Stony Brook University
2
Power Law Hardening and Transversely Isotropic Materials
Finite Element Modeling and Computations
PART-3
PART- 4 Results and Discussion
OUTLINE
PART- 5 Conclusions
PART- 1
PART- 2 Instrumented Indentation
nE
+= εσ
σσ0
0 1
σ Yield stress at plastic strain ε σ0 Yield stress at zero plastic strain
E Young’s modulus n Strain hardening exponent
POWER LAW HARDENING
0σσ >for
0.0E+00
2.0E+08
4.0E+08
6.0E+08
8.0E+08
1.0E+09
1.2E+09
0.00E+00 5.00E-03 1.00E-02 1.50E-02 2.00E-02
Stre
ss in
Pa
Strain
E×= εσ for 0σσ ≤
X2 (L)
X1 (T)
X3 (T) Plane of isotropy
Normal to Transverse plane
TRANSVERSELY ISOTROPIC MATERIALS
MICROSTRUCTURE
REASON FOR TRANSVERSE ISOTROPY
REASON FOR TRANSVERSE ISOTROPY
References: Jiantao Liu " Texture and Grain Boundary Evolutions ;2002; Univ of Kentucky
REASON FOR TRANSVERSE ISOTROPY
References: Jiantao Liu " Texture and Grain Boundary Evolutions ;2002; Univ of Kentucky
EXAMPLES
MATERIAL USE
COLD ROLLED ALUMINUM ALLOYS
CARBON FIBER ALUMINUM COMPOSITES
SURFACE COATINGS
ACCUMULATIVE ROLL-BONDING FORMED MATERIALS
UFG MATERIALS OF HIGH INTEREST DUE TO EXCEPTIONAL MECHANICAL
PROPERTIES
Independent elastic properties: EL, ET, νLT, νT and GL.
ELASTIC PROPERTIES
Applying Hill’s criterion to transverse isotropy
Assuming power law hardening
Independent plastic properties: σL, σT, τL, τT and n
PLASTIC PROPERTIES
Total number of independent material parameters: 10
Using approximations the number of parameters can be reduced to 5 namely: EL, ET, σL, σT, and n*
* References: Nakamura et al. 2007, Mechanics of materials; 39, 340
APPROXIMATIONS
INSTRUMENTED INDENTATION
INSTRUMENTED INDENTATION
Transverse Indentation Longitudinal Indentation
•Relatively simple and versatile.
•Can be used to test materials at the micro/nano scale.
•Virtually non-destructive.
•Multiple experiments can be carried out on a single sample.
•Well suited for the determination of localized properties.
ADVANTAGES:
INSTRUMENTED INDENTATION
P=Ch2
Wp
We
mhdhdP |
Wt = Wp + We
C = P/h2
Sm = Rw = Wp/Wt
mhdhdP |
INSTRUMENTED INDENTATION
MATERIALS
INDENTATION OF ->
ISOTROPIC TRANSVERSELY ISOTROPIC ANISOTROPIC
ELASTIC
•Yan et al., 2010. •Kim et al., 2006 •Scholz et al., 2003 •Rosenberg et al., 2007
•Sakamoto et al., 1991 •Vlassak et al., 1993 •Shi et al. 2003 •Klindukhov et al., 2009
?
ELASTIC-PLASTIC
•Giannakopoulos et al., 1999 •Dao et al., 2001 •Chollacoop et al., 2003 •Cheng et al., 2004
? THIS STUDY
To develop a framework of relations between material properties and indentation response parameters for
transversely isotropic materials.
GOAL OF THE STUDY
DIMENSIONAL ANALYSIS
= θ
σσσ ,,,,,, 00 n
EEEhPP
T
L
T
L
Π= θ
σσ
σσ θ ,,,,
0
01
20 n
EEEhP
T
L
T
L
DIMENSIONAL ANALYSIS
Π== n
EEE
hPC
T
L
T
L ,,,0
0102 σ
σσ
σ
Π= n
EEEhS
T
L
T
Lmm ,,,
0
020 σ
σσ
σ
Π== n
EEE
WWR
T
L
T
L
T
PW ,,,
0
03 σ
σσ
COMPUTATIONAL MODEL
COMPUTATIONAL MODEL
0 5E+10 1E+11 1.5E+11 2E+11
E 0 in
Pa
0.E+00 5.E+08 1.E+09 2.E+09 2.E+09
σ 0 in
Pa
1 1.5 2
E L\E
T
1 1.5 2
σ L\σ
T
0 0.2 0.4
n
DATABASE OF 120 COMPUTATIONAL MODELS
DATABASE OF 120 COMPUTATIONAL MODELS
0.E+00
2.E+08
4.E+08
6.E+08
8.E+08
1.E+09
1.E+09
1.E+09
2.E+09
2.E+09
2.E+09
0.00E+00 5.00E-03 1.00E-02 1.50E-02 2.00E-02
Stre
ss (P
a)
Strain
Lowest stiffness
Highest stiffness
DATABASE DIVISION
• Two cases considered: Transverse and Longitudinal indentation. • Variation of each response parameter with individual material properties was observed. • Curve fits giving the exact form of the dimensionless equations were obtained. • A constant equation form was maintained throughout the six parts.
COMPUTATIONS AND DATA ANALYSIS
RESULTS AND DISCUSSION
Direction of indentation C SM RW
Longitudinal Indentation Error % 0.255 0.209 0.06
Transverse Indentation Error % 0.736 0.327 0.148
Curve fit results:
Direction of indentation C SM RW
Longitudinal Indentation Error % 1.652 0.343 0.376
Transverse Indentation Error % 2.2 1.225 0.481
Relations tested on ten sample materials:
Direction of indentation % Variation in Material
Properties % Variation in Indentation
Response
Longitudinal Indentation ±5 ±7.5
Transverse Indentation ±5 ±10
Sensitivity analysis:
CONCLUSIONS
•Instrumented indentation of Transversely Isotropic materials is
simulated using Abaqus.
•Indentation is performed both in Longitudinal and Transverse
directions.
•Relations between material properties and indentation
response are formulated.
•The accuracy and sensitivity of the relations is verified.
The present study was supported in part by a
National Science Foundation grant DMR-0836763.
ACKNOWLEDGEMENT
The present study was supported in part by a National Science Foundation grant DMR-0836763.
Thank You
Questions?
