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


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


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


5

This presentation:

• Impact excitation method

• Applications to metal alloys (ASTM E1876)

• Uncertainties

• Use to high temperatures

• Extension to single crystal materials

• Limitations


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


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


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


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


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


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


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


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


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


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


16

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


17

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


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.


19

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


20

-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


21

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


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

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