Thermomechanical analysis of material behaviour - strong coupling effects to quantify stresses

Janice Dulieu-Barton Richard Fruehmann, Duncan Crump, Rachael Waugh, Gary Battams

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Summary

• Background to IRT/TSA

• Application to actual structure

• Damage studies

• Field work – strain based NDE

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Imaging techniques

• Infra-red thermography (pulse phase, TSA)

• White light -Digital image correlation (DIC), Microscopy

• Coherent light -Electronic speckle pattern shearing interferometry (ESPSI)

• X-ray computed tomography

Thermography overview

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• Infrared Thermography (IRT)

• Pulsed and Pulsed Phase Thermography (PPT)

• Thermoelastic Stress Analysis (TSA)

Stress vs Time

-1

1

0 1

time

Str

ess

Temperature vs Time

-1

0

1

0 1

Time

Tem

per

atu

re

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Thermomechanical coupling

• William Thomson – Lord Kelvin 26 June 1824 – 17 December 1907

• Mathematician, Physicist and Engineer

• Thermodynamics – ca 1850

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Thermoelastic effect

0 ij

ij

T QT

C T C

for i, j = 1, 2, 3

where:

T is the temperature

T0 is the absolute (reference) temperature

Cε is the specific heat at constant strain

Q is the rate of heat production per unit volume

ρ is the mass density

σij is the stress tensor

ij is the rate of change of the strain tensor

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Thermoelastic stress analysis

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pC

TT

2211

pC

TT

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Stress-strain temperature equations

2 ( )ij ij kk ijT 1 for

0 forij

i j

i j

)23( 2(1 )

E

(1 )(1 2 )

E

2ij

ij kk ijTT T T T

ij

ijT

Neglecting temperature derivatives of the material elastic properties

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Thermoelastic equation

0kk

TT

C

0

2

1 2

3kk

TT

C E

kk is the rate of change of the sum of the first stress

invariant (σ11+ σ22+ σ33)

2

03

(1 2 )p

E TC C

0kk

p

TT

C

)(C

TT

p

210

pCK

10

11 1990

2000

Detector specification

• Model:

– Cedip Silver 480 M

(now the FLIR SC5000)

• Array:

– 320 x 256 elements

– 30 μm pitch

– ½” chip (12.3 mm diagonal)

– Indium Antimonide (InSb)

– 3-5 μm wavelength band

• Standard operational range:

– 278 to 583 K

– maximum frame rate: 383 Hz (at full frame)

– sensitivity 4.12 mK / DL (at 298 to 299 K)

(electronic noise ~17 mK)

• Example of a typical noisy measurement signal in TSA.

– Noise and signal are of similar amplitude.

• A reference signal is used that contains only the frequency of interest.

– The reference signal is split into a sine and cosine part.

Lock-in processing

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Radiometric calibration

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Derivation of the thermoelastic constant

•Calibration against known stress

)(KTT 21

Why TSA?

• Hetrogeneous materials

• Monitor damage evolution

• Stress metric

• Small parasitic effects - not kinematic

• High resolution

• High speed

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Stresses in secondary aircraft structure

• Increased use of composite materials in aircraft structure

– weight saving

– improved life time

• Development of new manufacturing techniques and new materials

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Crump, D.A., Dulieu-Barton, J.M. and Savage, J., “The manufacturing procedure for aerospace secondary sandwich structure panels” Journal of Sandwich Structures and Materials, 2010, DOI :10.1177/1099636209104531

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Generic panel

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Face sheet material characterisation UD prepreg/autoclaved NCF RFI Oven cure

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Thermoelastic constants

M1, KL M1, KT M2, KL M2, KT

Thermoelastic

constant

MPa-1

(x 10-6

)

1.592 ± 0.83

3.112 ± 1.19

1.58 ± 0.81

2.837 ± 1.55

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Full-scale tests

Panels cyclically loaded at 1 Hz on custom design rig to

allow a pressure load – imparting 10 ± 5 kPa

Generic Panel

Supported Plate Loading Section

Unloaded

Water filled cushion

Loaded

Crump, D.A., Dulieu-Barton, J.M. and Savage, J.,

“Design and commission of an experimental

test rig to apply a full-scale pressure load on

composite sandwich panels representative of

aircraft secondary structure”, Measurement

Science and Technology, 2010, 21, (16pp).

DOI: 1088/0957-0233/21/1/015108

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Results

• Standard autoclaved prepreg offered a panel with a maximum deflection of 6.3 mm whilst RFI, NCF panel deformed by 4.6 mm.

• The measured stress response indicated a reduction in stress peak when using RFI and NCF.

Autoclaved RFI, NCF

Crump, D.A. and Dulieu-Barton, J.M., “Performance assessment of aerospace sandwich secondary structure panels using thermoelastic stress analysis”, Plastics, Rubber and Composites, 2010, 39, pp 137-147. DOI: 10.1179/174328910X12647080902691

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Woven material

• Damage in textile composites can occur at very low stress levels, < 20 % of σf.

• Damage can be identified using TSA despite the heterogeneous thermoelastic material response.

• Phase data provides a means for damage identification without a priori knowledge of the thermoelastic field.

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Complete set of high resolution TSA data from the

WRE581T specimen loaded at 10 % of the failure stress

Frühmann, R.K., Dulieu-Barton, J.M. and Quinn, S., “Assessment of fatigue damage evolution in woven composite materials using infra-red techniques” Composites Science and Technology, 2010. DOI: /10.1016/j.compscitech.2010.02.009

Is a test machine required?

Frühmann, R.K., Dulieu-Barton, J.M. and Quinn, S., “Thermoelastic stress and damage analysis using transient loading” Experimental Mechanics, 2010. DOI: 10.1007/s11340-009-9295-9

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Advanced MUlti-scale Strain-basED non-destructive evaluation (AMUSED)

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Full-scale inspection-Demonstrator

• TSA measurement of full-scale secondary aircraft panel with incremental damage.

Data from forced loading

Data from natural frequency loading

Full-scale inspection

Forced loading data Natural frequency loading data

GFRP Damage Propagation

FRP material Stacking Sequence

Quasi-static properties

Young’s Modulus UTS

Glass-Epoxy ACG MTM 28-1

[90,0,90,0]S 21.22 ± 0.72 GPa 513 ± 40 MPa

Damage created at three points across specimen width using a punch and hammer

Specimens coated in matt black paint, followed by a light coat of white speckles to enable DIC processing

Cyclically loaded at 10 Hz, 4.5 kN ±3 kN

σmean = 141 MPa

Δσ = 188 MPa

R ratio = 0.2

Specimen found to fail at around 4400 cycles

Damage propagation can be clearly seen in the normalised TSA data

Initial regions of damage coalesce forming a central region which shows little thermoelastic output. Central region therefore has very little load bearing properties

GFRP Damage Propagation

1 1 2 20

TK K

T

1 2

1 2, where , p p

K KC C

Normalised data proportional to stress sum

200 cycles 800 1600 2400 3200 4000 4200

ΔT/T

5 x 10-3

0

GFRP Damage Propagation

Cell size = 31 x 31 pixels, stepsize of 15

0.32 mm/strain data point

Longitudinal strain εyy

Image correlations performed between an unloaded reference image and images captured at the point of maximum load

εyy (%)

0

5

Central area experiences high strain but a low stress sum

Final DIC plot before failure Final TSA plot before failure

εyy (%)

5

0

2

1

3

4

ΔT/T

5 x 10-3

0

1 x 10-3

2 x 10-3

3 x 10-3

4 x 10-3

GFRP Damage Propagation

Challenges :

1.Triggering the saving of image sets automatically at various points in fatigue cycle without interrupting cyclic load.

2.High resolution white light cameras preferred for enhanced DIC accuracy. Accurate camera triggering and intense light therefore required.

Time

∆σ

Methodology development: Combining TSA and DIC

IR Camera (Cedip Silver 480M)

90°

2 x white light cameras (Manta G504-B/C, 5Mpixel)

Calibrated 3D DIC setup to be used to account for out of plane movement and camera perspective

IR images taken

σm

Load

White light images taken

Lock-in Application to DIC

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Under sampling?

• Example:

– Signal frequency: 7.1 Hz

– Recording frequency: 2.0 Hz

– Reconstructed signal: 0.9 Hz

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Brazilian disc

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• Visual comparison between static and dynamic results.

Static 0.75 Hz

7.1 Hz 21.1 Hz

Fruehmann, R.K., Dulieu-Barton, J.M., Quinn, S., and Tyler, J.P., “Digital image correlation applied to cyclically loaded components,” Optics and Lasers in Engineering. Submitted.

Lock-in DIC and TSA

TSA

Cedip 480M infrared photon detector

20 mK threshold, reduced to ~4 mK

using lock in

Altair and Altair LI software

DIC

3D DIC

2 x LaVision E-lite 5 MP

NILA LED lighting

DaVis software

Loading LDS V201 permanent magnet shaker from Brüel & Kjær Rigid stinger used to impart load attached via beeswax.

Aluminium plate – mode 2

TSA

DIC

ΔT/T

z-displacement

Phase

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Conclusions

• Introduced TSA and described the basic physics

• Shown how full-field experimental mechanics techniques can be used to validate FEA

• Presented convincing case studies that demonstrate the applicability and ease of using TSA in damage studies

• Shown potential as a strain based NDE technique

• Shown how TSA can be combined with DIC during the same test

Learn more about thermography/TSA

• BSSM Experimental Mechanics Workshop, University of Southampton, 23rd -27th 2015.

• See flyer in pack

• Covers also DIC, GM, ESPI, high speed imaging.

• Hands on

• Data processing

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