determining elastic moduli of high-temperature … 1030 morrell2.pdf · astm c215 concrete,...

DETERMINING ELASTIC MODULI OF

HIGH-TEMPERATURE MATERIALS:

THE IMPACT EXCITATION METHOD

Roger Morrell and Jerry Lord

Parsons Conference, September 2011

Wednesday, 14 September 2011

2

Elastic modulus measurement methods

• For metals, conventionally derived from the

elastic part of a tensile test

– Extensometry

– Strain gauges

– Interferometry

• Accuracy depends crucially on

– Alignment

– Extensometry calibration

– Absence of plasticity

• Quasistatic modulus values

Wednesday, 14 September 2011

3

• For other materials, alternatives are often used:– Quasistatic methods

• Flexure testing

– Dynamic methods

• Resonance

• Natural frequency

• Ultrasonic pulse transmission

• Often these are quicker and simpler, and more adaptable to measurement at higher temperatures

Elastic modulus measurement methods

Wednesday, 14 September 2011

4

Dynamic methods - existing standards

• Non-metallicsASTM C215 Concrete, resonance

ASTM C623 Glass, glass-ceramics, resonance

ASTM C747 Carbon and graphite, resonance

ASTM C848 Ceramic whitewares, resonance

ASTM C885 Refractories, resonance

ASTM C1198 Advanced ceramics, resonance

ASTM C1259 Advanced ceramics, impact excitation

EN843-2, EN820-5 Advanced technical ceramics, ultrasonics, resonance and impact excitation

EN ISO 12680-1 Refractories, impact excitation

EN 14146 Rocks, resonance

EN 15335 Advanced ceramic fibre composites, resonance

ISO 17561 Advanced ceramics, resonance

• MetallicsASTM E1875, Metals,

resonance

ASTM E1876, Metals, impact

excitation

EN 23312, ISO 3312,

Hardmetals, resonance

Wednesday, 14 September 2011

5

This presentation:

• Impact excitation method

• Applications to metal alloys (ASTM E1876)

• Uncertainties

• Use to high temperatures

• Extension to single crystal materials

• Limitations

Wednesday, 14 September 2011

6

Impact excitation method

• Based on ‘free - free’ vibration frequencies of a regular

shaped test-piece (bar, rod, disc)

• Vibrations are excited by striking the test-piece (wheel-

tapper method)

• Vibration sensed by high-frequency microphone or laser

vibrometer

• Eigenfrequencies are determined from detected signal

by fast fourier transform

• Elastic properties are determined from fundamental

vibration modes via well-established equations

• Commercial systems are available for doing this quickly

and efficiently

Wednesday, 14 September 2011

7

Eigenfrequencies

• Flexural modes, Fn/F1

~ 1 : 2.76 : 5.41 : 8.95 : 13.41…

• Torsional modes, Tn/T1

~ 1 : 2.01 : 3.04….

• Longitudinal modes, Ln/L1

~1 : 2 : 3…..

The sequence allows clear

identification of the

frequency peaks observed

Wednesday, 14 September 2011

8

Example FFTs for Nimonic 90 at RT

Nimonic 90

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0 5000 10000 15000 20000 25000 30000 35000 40000

Frequency, Hz

Inte

nsi

ty,

a.u

.

Through-thickness flexure (F)

Flexure and torsion (T)

Sideways flexure (FS)

Longitudinal (L)

F1

FS1

T3T2T1

F6F5F4F3F2

L1

FS3FS2

Test-piece size: 2 x 8 x 70 mm

Wednesday, 14 September 2011

9

Calculations for rectangular-section bars

• Flexure:

• Torsion*:

• Longitudinal:

• Poisson’s ratio

Tt

L

b

mfE

f

3

32

9465.0

22

42422

)/)(536.11408.01(338.61

)/(173.22023.01(340.8868.0)8109.00752.01(585.61

Lt

Lt

L

t

L

tT

A

B

bt

LmfG t

1

4 2

62 )/(21.0)/(52.2)/(4

//

btbtbt

bttbB

2

32

)/(892.9)/(03.12

)/(0078.0)/(3504.0)/(8776.05062.0

tbtb

tbtbtbA

KfLE l24

Lbtm /2

2222

12

)(1/1

L

tbK

t = thickness, b = width, L = length

* Equations for A and B recently modified in ASTM C1876

= (E/2G) - 1

Wednesday, 14 September 2011

10

Uncertainties - main factors

• Input value of Poisson’s ratio for E– Minor effect for ‘slender’ bars (t / L < 0.05)

• Test-piece dimensions– Parallelism of faces better than 0.01 mm

• Effects of single and double taper in test-pieces are unknown

– Minimal roughness of surfaces

• ‘Elastic’ thickness less than micrometer thickness

– Accuracy of thickness measurement

• 0.005 mm on 2 mm thickness gives 0.75% in E

• Equations– Uncertainties not well defined, but probably better than 0.1% for

slender bars

• FFT computer timebase– Better than 1 part in 105

• Overall uncertainty for isotropic material typically:

1% in E and G, 0.003 in

Wednesday, 14 September 2011

11

Example data sets

Assumed

input

Poisson’s

ratio, ν

Through-

thickness

flexure

Through-thickness flexure and torsion In-plane

flexure

Longitudinal

mode

Material

E, GPa E, GPa G, GPa ν E, GPa E, GPa

316 stainless steel 0.300 196.4 ± 0.1 196.3 ± 0.1 76.4 ± 0.1 0.286 ± 0.001 196.8 ± 0.1 197.2 ± <0.1

Ti-base material 0.300 163.9 ± 0.1 165.9 ± 0.1 64.5± 0.2 0.285 ± 0.003 164.4 ± 0.1 164.8 ± <0.1

Nimonic 90 0.275 220.9 ± 0.1 221.7 ± 0.4 86.6 ± 0.1 0.281 ± 0.002 220.2 ± <0.1 221.4 ± <0.1

Average and standard deviation for five strikes

Wednesday, 14 September 2011

12

Testing at elevated temperature

• Metallic wire/ceramic frame suspension system that keeps test-piece in position during extended testing

• Inert atmosphere

• Automated impactor

• Automated data recording at regular intervals

NPL’s IMCE system

Wednesday, 14 September 2011

13

Getting HT data in a single run

• NPL’s trick is measure F1 and T2 simultaneously

• Then use the RT ratio of F2 to F1, constant with

temperature, to allow fundamental mode

equation to be used.

Strike locationSupport at

flexural nodes

Wednesday, 14 September 2011

14

HT test results - Nimonic 90

Nimonic 90 bar frequencies

0

5000

10000

15000

20000

25000

30000

35000

0 200 400 600 800 1000 1200

Temperature, °C

Fre

qu

en

cy, H

z

F1

T2

F4

F3

F2

F5

Wednesday, 14 September 2011

15

HT test results - Nimonic 90Nimonic 90

0

50

100

150

200

250

0 200 400 600 800 1000 1200

Temperature, °C

Yo

un

g's

mo

du

lus

, G

Pa

Young's modulus

Shear modulus

Nimonic 90 - Poisson's ratio

0.220

0.240

0.260

0.280

0.300

0.320

0.340

0 200 400 600 800 1000 1200

Temperature, °C

Po

iss

on

's r

ati

o

Wednesday, 14 September 2011

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Temperature limitations

• When internal damping becomes excessive– Test-piece no longer rings

well

– Frequency peaks become broadened and less intense

– Frequencies cannot readily be detected against background noise

• Torsional vibrations are often damped out at lower temperatures than flexural modes

• But generally data can be obtained to higher temperatures than with quasistatic methods

WC/11Co

500

520

540

560

580

600

620

640

660

0 100 200 300 400 500 600 700 800 900

Temperature, °C

Yo

un

g's

mo

du

lus, G

Pa

0

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

Dam

pin

g c

oeff

icie

nt

Young's modulus

Damping coefficient

WC/11Co hardmetal: oxidation-limited

Wednesday, 14 September 2011

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Extending to textured materials and single

crystals

• Technique measures axial modulus

• In principle, test-pieces cut in different orientations

can be used to determine the anisotropy of E

• Shear modulus is more difficult, and Poisson’s ratio

cannot be defined

• Strictly, need to resort to tensor analysis

• For cubic single crystal alloys this can be done with

a minimum of three test-pieces to define S11, S12

and S44

Wednesday, 14 September 2011

18

Hermann et al. analysis for round bars

001

010

100

1

11 )2(),( SJSEmeas

2/441211 SSSS

8/)4cos1(sincossin 422 J

1

44 ))1)(4((),( SJSGmeas

Plotting 1/E vs. 2 J has slope -S and intercept S11

Plotting 1/(G(1-)) vs. 4J has slope +S and intercept S44

Can be applied to rectangular bars provided that one of them

is very close to (001) to obtain a good value for S44

Hermann, W., Sockel, H.G., Han, J., Bertram, A., in Superalloys

1996, ed. Kissinger R.D., et al. TMS, 1996, pp 229-238.

Wednesday, 14 September 2011

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Single crystal alloy - example results

y = -0.0067x + 0.0076

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7

2J

1/E

, G

Pa

-1

y = 0.0095x + 0.0074

0.000

0.005

0.010

0.015

0.020

0.025

0 0.2 0.4 0.6 0.8 1 1.2 1.4

4J

1/(

G(1

- ))

, G

Pa

-1

1/E plot 1/(G(1- ) plot

CMSX-486

Poor correlation resulting from no

account being taken in rod theory

of rotational orientation of

rectangular test-piece about long

axis

Wednesday, 14 September 2011

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-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

0.01

0.012

0 200 400 600 800 1000

Temperature, °C

Co

mp

lia

nc

e, G

Pa

-1 S

S11

S44

S12

S

S 11

S 44

S 12

Single crystal alloy - example results

CMSX-486

Wednesday, 14 September 2011

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Conclusions

• Accurate dynamic modulus measurements can

be made simply and economically on isotropic

alloys to high temperature using the impact

excitation method

• Temperature limitations are defined by the onset

of significant damping or oxidation

• Anisotropic materials and single crystals need a

more careful approach, but possible provided

that appropriately orientated test-pieces are

available

Wednesday, 14 September 2011

22

Acknowledgements

• This work was performed in part under Materials Metrology

funding from the National Measurement Office of BIS

(formerly DTI)

• Thanks are due to Ken Harris (Cannon-Muskegon) for

materials and Kath Clay (Hexmat) for single crystal

orientation measurements

© Crown Copyright 2011, reproduced by permission of the Controller of HMSO and

the Queen’s Printer for Scotland