talapady s bhat and t. a. venkatesh€¦ · t. a. venkatesh . department of materials science &...

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?