using thermoelastic stress analysis to detect damaged and ...€¦ · specific heat coefficient at...

Journal of Mechanics Engineering and Automation 5 (2015) 623-634 doi: 10.17265/2159-5275/2015.11.005

Using Thermoelastic Stress Analysis to Detect Damaged

and Hot Spot Areas in Structural Components

Freire J. L. F.1, Waugh, R. C.2, Fruehmann, R.2 and Dulieu-Barton, J. M.2

1. Mechanical Engineering Department, Pontifical Catholic University of Rio de Janeiro, PUC-Rio, Rio de Janeiro 22453-900 Brazil

2. Faculty of Engineering and Environment, University of Southampton, Southampton SO17 1BJ, UK

Abstract: This paper discusses the suitability of using TSA (thermoelastic stress analysis) as an advanced tool to detect damaged areas and highly stressed (hot spot) areas in structural components. Such components can be, for example, parts of large structural panels built of welded metallic or composite materials. Besides detecting hot spot areas, it is expected that stresses in these areas can be suitably quantified and processed in order to predict crack initiation and propagation due to in-service loads. The paper starts with references to selected review and application articles on the subject. Two simple laboratory experiments are presented which illustrate the quality of the results that can be achieved using TSA. In the first experiment, a stainless steel T-joint designed to model a welded structural component is analysed. The T-joint had a machine-notched crack-like flaw close to the component’s weld toe. The qualitative and quantitative experimental results determined along four specified areas of the T-joint model showed that TSA can indeed be used as a tool to detect loaded cracks and hot spots in large metallic structures, and that stresses can be accurately evaluated. In the second experiment, a prismatic bar made of CFRE (carbon fibre-reinforced-epoxy) was tested to locate three subsurface areas of damage introduced beforehand into the component. Two of these inside damaged areas were detected to be 3.1 mm and 7.1 mm from the observed surface. The positive results achieved with the two lab experiments, along with a review of the selected research publications, indicate that TSA application can be extended to the real-world field of structural components. Topics to be addressed in this research field should have to do with components that work under random or quasi-cyclic service loading, problems where adiabatic conditions do not prevail, and reduction of the cost of infra-red cameras.

Key words: TSA, stress distribution, NDT, stress distribution, stress concentration, crack, T-joint, infra-red.

1. Introduction

TSA (thermoelastic stress analysis) or

Thermoelasticity is an experimental stress analysis

technique based on the thermoelastic effect. The

thermoelastic effect is defined as the change in

temperature at a point on a body due to its elastic

deformation under adiabatic conditions. The

thermoelastic effect was reported by Weber in 1830

and its associated theory was published by Lord

Kelvin in 1853 [1-3].

The thermoelastic effect causes a point on a body

under cyclic loading to undergo a reversible change in

temperature that is proportional to the first stress

invariant. Under adiabatic and plane stress conditions

(surface point on the loaded body) Eq. (1) applies,

where, To is the reference temperature, cσ is the

specific heat coefficient at constant pressure, ρ is the

mass density, α is the linear thermal expansion

coefficient constant, and Δσ is the cyclic change of the

stress invariant [3, 4]. Adiabatic conditions will exist

for the material point under consideration if the heat

conduction rate is negligible in relation to the change

in temperature induced by the thermoelastic effect.

c

TT o .

1... 21 (1)

Eq. (2) is obtained by rewriting Eq. (1) using a

material constant K, defined as K = α/ρ·cσ. The K

values for structural materials are given in Table 1 [2].

This table also gives resolution indications for

determining Δσ values, depending on the ΔT

measurement resolution for the listed materials.

21.. oTKT (2)

D DAVID PUBLISHING

Using T

624

Table 1 Seconstant K va

Material

Carbon steel

Aluminum

Titanium

Epoxy

* for ΔT=10-3

Commerc

infrared em

small tempe

0.001 °C or

tested has

high-emissiv

to provide

load freque

effect runs

resolution ca

is generally

distance of

accomplishe

bonded to u

areas of th

achieved by

composed o

loaded, for

Fig. 1 Sketc

Thermoelastic

ensitivity of alues.

K (Pa-1)

3.5 × 10-1

8.8 × 10-1

3.5 × 10-1

6.2 × 10-1

K

cial systems u

missions are

erature chang

10-3 K. The

to be pain

vity coating t

surface emis

ency used to

in the orde

an be improv

of the order

f about 500

ed satisfactor

uniform strain

he tested bod

y using a sp

of the same

example, un

ch of a simple T

c Stress Ana

the thermoela

Δσ (MProom tem

2 1. 2 0.4 2 1. 1 0.055

used for appl

capable of

ges with a lim

surface of th

nted with a

to behave as a

ssion uniform

o generate th

er of 0.5 to

ved with lens

r of 0.5 mm

mm. Outpu

rily by usin

n fields in w

dy. Calibrati

pecific, cont

material, sa

nder cyclic u

TSA laborator

lysis to Detec

astic method

Pa)—resolution mperature*

lying TSA de

measuring v

mit resolutio

he specimen t

a thin layer

a black body

mity. The cy

he thermoela

20 Hz. Sp

s attachments

m from a dete

ut calibration

ng strain gau

well-known st

ion can also

trolled speci

me coating,

uniform unia

ry experiment.

ct Damaged a

and

at

etect

very

n of

to be

r of

y and

yclic

astic

atial

s but

ector

n is

uges

tress

o be

imen

and

axial

wel

T

sim

The

serv

load

the

load

load

of E

for

high

serv

be

ther

A

who

app

sim

pre

Dis

load

the

high

M

hard

and Hot Spot

ll-known stre

The basic TSA

mple laborator

e structural

vo-hydraulic

d of constant

minute temp

ded structural

ding variation

Eq. (1). More

example, th

hly stressed a

vice, require

read, corre

rmal-strain re

Advantages o

ole field type

plication to a

mple preparati

and post pr

advantages

ding, stress s

infrared dete

h cost of equi

Modern cam

dware and so

t Areas in Str

ss conditions

A principle,

ry experimen

componen

testing mac

amplitude. T

perature varia

l component

ns are correl

e general and

e use of TSA

areas of a stru

that tempera

elated and

elation.

of the TSA m

e of measure

ctual compon

ion for testin

rocessing of

are related

separation tec

ector, experim

ipment and an

meras, lens

oftware make

ructural Comp

s.

as applied no

nt, is illustrat

nt is load

chine under

The infra-red

ations at each

and both tem

lated to allow

advanced app

A to detect

uctural compo

ature and loa

applied to

method are r

ement, the po

nents, the req

ng, and the p

the testing s

to the need

chniques, visu

mental calibra

nalysis softw

systems, an

possible a br

ponents

owadays in a

ted in Fig. 1.

ded into a

a sinusoidal

camera reads

h point of the

mperature and

w application

plications, as

and quantify

onent in field

ading signals

a general

related to the

ossible direct

quirement of

possibility of

ignal output.

d for cyclic

ual access to

ation, and the

ware.

nd computer

road range of

a

.

a

l

s

e

d

n

s,

y

d

s

l

e

t

f

f

.

c

o

e

r

f

Using Thermoelastic Stress Analysis to Detect Damaged and Hot Spot Areas in Structural Components

625

applications. Today’s research and equipment are

intended to increase the advantages of TSA while

simultaneously decreasing its disadvantages as much

as possible. Recent literature published on TSA’s

widespread area points to several applications that

attempt to use the method to conduct non-destructive

evaluation tests; correlate the input (load) and output

(temperature) measurements in situations of

quasi-random loading; detect fatigue cracks; quantify

stresses near crack tips; apply the method to

quasi-adiabatic conditions; detect damage in

composite materials; determine vibration modes in

dynamic problems; and to combine TSA and DIC

(digital image correlation) in the investigation of

stresses near crack-tips [2-9]. Recent research

programs have also aimed at developing and using

lower cost equipment for TSA applications [8].

The use of TSA in two laboratory experiments is

described herein. The basic principles used in these

experiments are to be further developed in a research

program in order to consistently apply TSA as an

NDT tool to locate damage, crack-like defects, hot

spots, and to quantify stresses in actual structures

under service conditions.

In the first experiment, a stainless steel T-joint

designed to model a welded structural component was

analysed. The T-joint had a machine-notched crack-like

flaw in the model area that simulates the component’s

weld toe. In the second experiment, a prismatic bar

made from CFRE (carbon-fibre-reinforced-epoxy)

was tested to locate subsurface areas of damage

introduced beforehand into the component.

2. TSA Analysis of a Cracked T-joint Specimen

The objectives of the TSA analysis of a T-joint

specimen were to detect and quantify the highly

stressed areas near the tip of a machine-notched

crack-like defect introduced into the toe of one weld,

and to detect the stress concentration site located at

the opposite weld toe. The experiment was meant to

show that a loaded crack and the stress concentration

existing in a hot spot area can indeed be detected.

Furthermore, the experiment had the purpose of

showing that actuating stresses can be satisfactorily

quantified at any visible point belonging to the image

field, the examined point being located in a hot spot

area or in any nominal location of the structure.

A sketch of the T-joint tested model is presented in

Fig. 2. The model was made from stainless steel

classified as ANSI 316L. The model was machined

from a 4.9 mm thick plate and one notch with length a

equal to 10 mm and nominal width of 0.3 mm was

machined with a milling saw. The notch was

introduced to simulate a crack-like flaw. The observed

surface of the T-joint specimen was painted with two

thin layers of Matt Black RS 496-782 to homogenize

and help with the surface temperature measurements.

A sinusoidal tensile load was imposed on the T-joint

web by means of a servo-hydraulic testing machine

INSTRON 8802. Cyclic sinusoidal loading P was

applied to the test specimen from 1 kN to 3 kN, with a

frequency rate of 5 Hz. The constant load amplitude

was equal to 1 kN. Temperature measurements were

taken with an FLIR 5000 infra-red camera, with a

nominal standard temperature resolution of 10-3 K.

During the experiment, the average reference

temperature of the specimen was 20 °C or 293 K.

Temperature (range) variation measurements were in

the order of 0.5 K at the most stressed points. Image

frames were recorded at 383 Hz (acquisition rate) and

integration time was equal to 1,300 µs. Prior

calibration of the 316L stainless steel used in the

experiment furnished a thermoelastic constant K =

4.04 × 10-12 Pa-1 to be used in Eq. (2).

The data acquired with the infra-red camera and

processed using dedicated developed software are

shown in Figs. 3 and 4. The camera reads the reference

temperature at each observed point as well as the

small temperature variations that occur during the test

acquisition time. Full field images of the reference

temperature distributions and of the temperature

(range) variations are shown in Figs. 3a-3d.

Using T

626

(a

(c) Actua

Fig. 2 Test o

The full-fiel

the tempera

present case

give meanin

will give a

of the stres

general, ph

validate the

under adiaba

The full f

TSA can be

stressed area

stress conc

highlighted

in the figure

Thermoelastic

a) Sketch of the

al T-joint mode

of T-joint mod

ld image of

ature ranges

e, phase me

ng to the sig

clue about th

ss invariant

hase measure

assumption t

atic condition

field images

used to dete

as near the n

entration ar

by the grey

es. The same

c Stress Ana

e T-joint tested

l positioned in

del.

phase distrib

is shown in

asurements a

nal of Eq. (2

he positive o

for each po

ements are

that the exper

ns.

(Figs. 3c an

ct high stress

notch root (cr

rea near the

scale or colo

effect was ve

lysis to Detec

specimen

the loading fram

butions relate

n Fig. 3e. In

are importan

2), that is, ph

r negative si

oint analysed

a good way

riment is runn

nd 3d) show

s areas. The m

rack tip) and

e weld toe

our scales sh

erified in Ref

ct Damaged a

me

d to

n the

nt to

hase

ignal

d. In

y to

ning

that

most

d the

are

hown

f. [6].

The

the

sho

B

plau

TSA

com

L

def

info

Hor

pas

(cra

use

web

and Hot Spot

(b) Sinusoid

(d) TFLIR

e hot spot de

TSA method

uld be pursue

Besides show

usible detecti

A can be use

mplex stress f

Lines 1 to 4,

fine the se

ormation wa

rizontal line

ses at a dist

ack tip). Line

d in analysin

b of the T-joi

0

0.5

1

1.5

2

2.5

3

3.5

Tes

t lo

ad P

(k

N)

t Areas in Str

dal constant amapplied to the s

Test set up arranR SC 5000infra

etection areas

d, and its app

ed.

wing that T

ion tool, this

ed to quantify

fields.

as depicted i

ets of poin

as acquired

1 is orthogo

ance of 1.5

e 2 defines th

ng the uniaxia

int specimen

ructural Comp

mplitude loadingspecimen

ngement with a-red camera

s are a real a

lication to fie

TSA can be

s section also

y stresses in

in Fig. 3f, we

nts where

in the prese

nal to the no

mm from th

he cross sect

al stress distri

caused by te

Ciclic testfrequency

ponents

g (P)

advantage of

eld structures

used as a

o shows that

nominal and

ere chosen to

quantitative

ent analysis.

otch line and

he notch root

tion that was

ibution in the

ensile load P.

t load -y = 5Hz

f

s

a

t

d

o

e

.

d

t

s

e

.


627

(a) Test temperature To (b) Test temperature To, colour processed

(c) Full field ΔT map, gray scale (d) Full field ΔT map, colour processed

(e) Full field ΔT Phase map and detail near the crack tip (f) Lines along which data on ΔT and To were requested from the

experiment file. Processed data of ΔT/To from lines 1-4 will furnish (σ1 + σ2) along these lines

Fig. 3 Images and raw data from the T-joint test.


628

Line 3 defines a cross section in the horizontal

element of the T-joint. The cross-section defined by

line 3 was chosen for measuring the bending stresses

caused by the reaction support load ΔP/2. Vertical line

4 coincides with the continuation of the crack-like

notched surface plane and its first acquisition point

was located 1.0 mm in front of the notch root.

Figs. 4a and 4b give the temperature range and the

reference temperature for points on lines 1 to 4, i.e.,

the acquired data in terms of ΔT and To. This

information, processed using Eq. (2), gives the

results for stress invariants (σ1 + σ2) along the

specified lines. Results for (σ1 + σ2) invariants along

lines 1 to 4 are presented in Figs. 5-8.

Line 2 defines a nominal region of the specimen,

where the maximum tensile stress ranges Δσ1 = ΔσN

caused by the normal force is expected to be:

APN / (3)

or 13.6 MP and the minimum stress range Δσ2 is

expected to be zero. In Eq. (3), ΔP is the range of

applied force equal to 2 kN, and A is the cross section

area of the loaded specimen. A plot of the measured

stress invariant of line 2 is given in Fig. 5. It can be

seen that the TSA measurements indicate a strong

presence of bending stresses in this section, superposed

on the stresses N caused by the normal load. The

maximum and minimum bending stresses were equal

to plus and minus 9.5 MPa, respectively. The average

uniaxial stress measured using TSA is equal to 15.6

MPa and this value agrees satisfactorily (13% difference)

with the nominal calculated value of 13.6 MPa.

The measured TSA stresses along line 3 and the

expected bending stresses calculated for this line are

plotted in Fig. 6. The normal stresses were calculated

by using the simple bending equation

3.

..212

Ht

yLP

M

(4)

where, L is the distance from the right support to the

cross section defined by line 3, and H and t are,

respectively, the height and thickness of the cross

section. Coordinate y is the height of a point being

considered with respect to the neutral fibre. It can be

seen in Fig. 6 that the agreement among TSA

experimental and simple bending equation results can

be considered excellent, since both tendency lines (not

plotted) are almost identical.

(a) ΔT data from the experiment file. Data requested from lines 1-4

(b) To data from the experiment file. Data requested from lines 1-4

Fig. 4 Temperature data collected along the chosen lines (1-4) to be analysed.


629

Fig. 5 Plot of TSA measured and calculated stress invariants at points located along line 1. Note the strong influence of bending stresses superposed on stresses caused by normal force.

Fig. 6 Bending stress plot across the section defined by line 3. Plot of TSA measured and calculated stress invariants at points located along line 3.

Stresses calculated in an area near the tip of the

machine-notched simulated crack-like flaw were

experimentally and analytically determined for

comparison purposes. Two sets of data were acquired

from the TSA experiment and are represented by lines

1 and 4. Horizontal line 1 was passed at a distance of

1.5 mm from the crack tip so that the geometry of the

notch root would not influence the theoretical and

experimental stress analysis carried out for comparing

stresses determined by both methods. Vertical line 4

was passed in continuation of the flaw surface.

The stress analysis of the TSA measured data

acquired along lines 1 and 4 passing near the notch

root (or crack tip) can be analysed in two different

ways. The first approach uses measured stress values

for each spatial point location. These stresses and

point locations are then used to determine the stress

intensity values for the machine-notched crack-like

flaw. The second approach, employed in this article,

uses literature equations of stress intensity factors [10]

to determine the stress invariants along lines 1 and 3.

For comparison purposes, these analytically

determined data were plotted in Figs. 7 and 8 together

with the TSA measured invariant stress data.

The analytical equation used to determine the first

stress invariant range as a function of known Mode I

0

5

10

15

20

25

0 10 20 30

Ten

sile

str

ess

(MP

a)

Position along section represented by line 2 -2 (mm)

TSA uniaxial stress measurements

Tensile stress calculations

线性 (TSA uniaxial stress measurements)

-80

-60

-40

-20

0

20

40

60

80

-20 -10 0 10 20Ben

din

g st

ress

(M

Pa)

Position along the height of section 3-3 (mm)

TSA bending stress measurements

Bending stress calculations


630

and Mode II ranges of stress intensity factors ΔKI and

ΔKII, respectively, is [10]:

1 2 I II

2.cos .sin

2 22 .K K

r

(5)

where, r and θ are the coordinates (relative to the

notch root or crack-tip) at each spatial point on lines 1

and 4. From this expression, it can be seen that the

influence of KII is expected to be small for points

along line 1 when they are close to the notch root, due

to the small value of their θ coordinate and,

consequently, of the sine value of θ/2. Values for KI

and KII for similar geometry and loading conditions

were determined (using Photoelasticity) in an earlier

report [11]. In that investigation, the values for KI

were seen to approach standard solutions of cracked

bars under three or four point bending, and the values

for KII were small as 20% of the KI values. For the

present report, the linear elastic analytical equation

used to determine ΔKI represented the standard case of

a bar of isotropic material under four point bending, as

given in Ref. [10]:

4I 3/ 2

.6. . 2 tan( ).2 2. . 0.923 0.199(1 sin( ))

.. 2cos( )2

n

P aLaHK

at H HH

(6)

where, a = 10 mm is the length of the

machine-notched crack-like flaw and Ln = 45 mm is

the distance between the left support of the specimen

and the section containing the notch.

Fig. 7 shows the TSA-measured and the calculated

stress invariant ranges at points located along line 1.

This line passes 1.5 mm below the notch root. The

calculated values employed Eqs. (5) and (6) for the

stress invariant and ΔKI determinations, respectively.

A plot of calculated stresses considering the influence

of ΔKII =0.20ΔKI is also shown, and it can be seen

that the influence of ΔKII is negligible for points along

the line. A satisfactory comparison of the measured

TSA and the analytically calculated results can also be

seen.

The TSA-measured and the calculated stress

invariant ranges at points located along line 4 are

shown in Fig. 8. This line starts 1.0 mm below the

notch root. The calculated values employed Eq. (6) for

calculating stress intensity ΔKI. Points along this line

have coordinate θ = 0 and therefore, the calculations

using Eq. (5) are not influenced by ΔKII. One can also

Fig. 7 Plot of TSA-measured and calculated stress invariant rangesat points located along line 1 passing 1.5 mm below the notch root.

0

50

100

150

200

250

300

350

400

450

500

-20 -10 0 10 20

Str

ess

Inva

rian

t al

ong

lin

e 1-

1 (M

Pa)

Position along line 1-1 (mm)

TSA stress measurements

Near field KI LEFM stress calculations

Near field KI and KII stress calculations


631

Fig. 8 Plots of TSA-measured and calculated stress invariants at points located below the notch root and along line 4.

see a satisfactory comparison of the TSA-measured

and the analytically calculated results for points as

close as 1.0 mm to the notch root and as far as 4 mm

from the notch root.

For the cases of points located along lines 1 and 4,

the validity of analytical equations has to be

considered in terms of the point coordinate locations

having to do with the notch root or crack tip. Eq. (5) is

valid only in the so-called crack tip near field, which

in the present case is bounded by two spatial limits.

One is a very-near-field limit that must consider the

geometric shape of the notch root and its radius of

influence on the stress distribution [12]. The other is

the far field limit. The size of the far field limit

considers the influence of the far field stresses, which

depend on, for example, the size of the remaining

ligament area, the nominal loading, and the proximity

of the crack tip to the horizontal free-boundary of the

bar. To take into account the very-near and far field

influences, stress Eq. (5) would need the insertion of

terms as shown in Refs. [13-15].

The qualitative and quantitative experimental

results presented in this section illustrate how the TSA

method can be thought of as a tool to detect loaded

cracks and hot spots in large structures, and how those

stresses can be quantitatively evaluated. Advanced

research on extending the application of TSA to real

world field structural components, where quasi-cyclic

service loading actuates and adiabatic conditions do

not prevail, is on-going, as discussed in Refs. [6, 8, 9]

for example.

3. Inspection of a Composite Thick Slab with Delamination Defects

The inspection of composite structures is in great

demand due to an exponential increase in the use of

materials in structures that carry high static and

dynamic loads, such as components used in the

aeronautical and automotive fields. Nowadays,

advanced experimental stress analysis and NDT

(non-destructive testing) techniques, which are

appropriate for these materials, are needed in every

phase of their fabrication and in-service life.

Techniques such as Shearography [16] and TSA [4]

were developed as reliable tools some time ago for

this purpose, but today they are being revisited to

extend and enhance their applicability as feasible tools

for inspecting damaged composite panels [5, 17].

The thermoelastic response of composite materials

is not simply proportional to the change of the stress

invariant, but TSA can be an important tool to indicate

damage areas in composite specimens even if these

areas are located beneath the observed surface [2].

The potential for applying the TSA method as an

-200

-150

-100

-50

0

50

100

150

200

250

300

350

-10 0 10 20

Str

ess

Inva

rian

t al

ong

lin

e 4-

4 (M

Pa)

Position along line 4-4 , starting near the crack tip (mm)

TSA stress measurements

Near field LEFM stress calculations

Far field non valid LEFM stress calculations

Using T

632

inspection to

laboratory

(carbon fibr

with lamina

in three dif

depicted in

areas to the

7.1 mm and

= 30, 50 a

surface.

A similar

(a) Sketch olaminate fobserved su

su

C(c) Acquired

Fig. 9 Carbwrinkle-like f

Thermoelastic

ool is shown

test. A pris

re reinforced

-wrinkle and

fferent positi

Fig. 9a. Dis

observed su

9.1 mm. The

and 75 mm

r testing arr

of the CFRE priflaws δ (distancurface. Longitu

urface of the flaw

DL (digital levindicate inter

bon fibre reinflaws.

c Stress Ana

in this sectio

smatic spec

epoxy) resin

d delamination

ions across

stances δ fro

urface (Fig. 9

ese flaws wer

from the sp

rangement d

ismatic specimee) = 3.1; 7.1 an

udinal positionsws: p = 30, 50 a

vel) temperaturernal damage ponforced epoxy

lysis to Detec

on by means

imen of CF

n was fabric

n defects loc

its thickness

om the dama

a) were 3.7 m

re, respectivel

pecimen’s up

described in

en with wrinklend 9.7 mm froms from the top (gand 75 mm

e range image. Aositions

composite sp

ct Damaged a

of a

FRE

cated

cated

s, as

aged

mm,

ly, p

pper

the

prev

insp

with

sinu

by

880

rate

max

T

sho

ima

e-like m the

grip)

Arrows (d) A

pecimen used

and Hot Spot

vious sectio

pection test.

h two thin l

usoidal tensil

the servo-hy

02. Cyclic sin

e of 5 Hz to

ximum tensil

The full field

wn in Figs.

age is presen

(b) Acqui

Acquired phase in

in the non-d

t Areas in Str

n was repe

The compo

ayers of Ma

le load was i

ydraulic test

nusoidal load

the test spec

e loads of 0 a

d temperatur

9b and 9c. T

nted in Fig. 9

ired reference te

temperature ranternal damage

destructive test

ructural Comp

eated for th

site surface

att Black RS

imposed on t

ting machine

ding P was

cimen with m

and 20 kN, re

re processed

The reference

9b, while the

emperature ima

ange image. Arrpositions

t to detect in

ponents

e composite

was painted

496-782. A

the specimen

e INSTRON

applied at a

minimum and

espectively.

d images are

e temperature

e temperature

age

rows indicate

nternal lamina

e

d

A

n

N

a

d

e

e

e

a


633

range image is shown in Fig. 9c. The scale in Fig. 9c

indicates the temperature ranges using DL (digital

level) temperatures, which still have to be processed

and converted to Kelvin degrees. A temperature phase

distribution image is given in Fig. 9d.

Avisual inspection of the images shown in Figs. 9c

and 9d show that the experimental results obtained

with the TSA method can indicate with satisfactory

resolution the positions of the two closest damaged

surface areas of the composite specimen. All three

damaged areas are highlighted by arrows in Figs. 9c

and 9d. The first and second damaged areas are

located at depths of 3.7 mm and 7.1 mm from the

observed surface and can be visually detected,

although noise is present in the images. The third

damaged area, located 9.1 mm from the observed

surface, could not be detected in this experiment.

The overall conclusion from this experiment is that,

although noisier signals are to be expected, careful

examination of CFRE composites will indicate

internal damaged areas, and that these damaged areas

can be as much as 6 mm (a safer distance) from the

observed surface.

4. Conclusions

This paper has shown that TSA can be used as an

advanced tool to detect damaged areas and highly

stressed (hot spot) areas in structural components, and

that stresses in these areas can be suitably quantified.

Two laboratory experiments were presented to

illustrate the quality of the results that can be achieved

using TSA. In the first experiment, a stainless steel

T-joint designed to model a welded structural

component was analysed. The T-joint had a

machine-notched crack-like flaw close to the

component’s weld toe. In the second experiment, a

prismatic bar made of CFRE was tested to locate three

subsurface areas of damage previously introduced into

the component. Two of these inside damaged areas

were detected to be 3.1 mm and 7.1 mm from the

observed surface. The positive results achieved with

the two lab experiments, along with the review of

selected research publications, indicate that TSA

application can be extended to the real-world field of

structural components. Topics to be addressed in this

research field should have to do with components that

work under random or quasi-cyclic service loading,

problems where adiabatic conditions do not prevail,

and reduction of the cost of infra-red cameras.

References

[1] Thomson, W. 1853. “On the Dynamical Theory of Heat.” Trans. R. Soc (Edin) 20: 161-283.

[2] Greene, R. J., Patterson, E. A., and Rowlands, R. E. 2008. “Thermoelastic Stress Analysis.” In Springer Handbook of Experimental Mechanics, Chapter 26, edited by Sharpe, W. N. New York: Jr., Springer & Society for Experimental Mechanics (SEM), Springer Science + Business Media, L. L. C.

[3] Stanley, P. 2008. “Beginnings and Early Development of Thermoelastic Stress Analysis.” Strain 44: 284-97.

[4] Bakis, C. E., and Reifsnider, K. L. 1989. “Adiabatic Thermoelastic Measurements.” In Springer Handbook of Experimental Mechanics of Composite Materials, Section VIIB, edited by Pendleton, R. L., and Tuttle, M. E. Society for Experimental Mechanics (SEM), 139-46.

[5] Waugh, R. C., Dulieu-Barton, J. M., and Quinn, S. 2013. “Thermographic Identification of Defects in Adhesively Bonded Joints.” In Proceedings of the 2013 SEM Annual Conference on Experimental and Applied Mechanics, 347-51.

[6] Robinson, A., Dulieu-Barton, J. M., Quinn, S., and Howarth, D. 2013. “Crack Detection in Large Welded Components under Fatigue Using TSA.” In Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics, 47-50.

[7] Zhang, S., Dulieu-Barton, J. M., and Thomsen, O. T. 2013. “Experimental Characterization of Thermomechanically Induced Instability in Polymer Foam Cored Sandwich Structures.” In Proceedings of the 2013 Annual Conference on Experimental and Applied Mechanics, 103-8.

[8] Wong, A. K. 2012. “Making the Invisible Visible: Joining the Dots from Lord Kelvin to Fighter Jet Fatigue.” Presented at the 28th International Congress of the Aeronautical Sciences, Australia.

[9] Tomlinson, R. A., Du, Y., and Patterson, E. 2011. “Understanding Crack Tip Plasticity.” Applied Mechanics and Materials 70: 153-8.

[10] Anderson, T. L. 1995. Fracture Mechanics: Fundamentals


634

and Applications. 2nd edition. New York: CRC Press, Inc. [11] Freire, J. L. F., and Arai, H. 1983. “Use of Photoelasticity

in Fracture Mechanics.” Presented at the International Congress on Fracture Prevention in Energy and Transport Systems, Brazil.

[12] Schroedl, M. A., and Smith, C. W. 1975. “A Study of Near and Far Field Effects in Photoelastic Stress Intensity Determination.” Eng. Fract. Mech. 7: 341-55.

[13] Freire, J. L. F., Carvalho, E. A., and Cavaco, M. A. M. 1993. “Determination of Stress Concentration Factors for Shallow and Sharp V-Notches Using a Hybrid Method.” Applied Mechanics Reviews 46 (11): 129-35.

[14] Sanford, R. J. 2003. Principles of Fracture Mechanics. New York: Prentice Hall.

[15] Freire, J. L. F., and Rebello, J. R. 1989. “Photoelastic Determination of Stress Intensity Factors for Cracks near

Plane and Tubular T-joint Specimens Subjected to Tension.” In Proceedings of the 1986 SEM Spring Conference on Experimental Mechanics, 273-9.

[16] Hung, Y. Y. 1989. “Shearography: A New

Strain-Measurement Technique and a Practical Approach

to Nondestructive Testing.” In Handbook of Experimental

Mechanics of Composite Materials, Section IVB, edited

by Pendleton, R. L., and Tuttle, M. E. Society for

Experimental Mechanics, (SEM), 81-96.

[17] Andonian, A. A. T. 2008. “Shearography and Digital

Shearography.” In Springer Handbook of Experimental

Mechanics, Chapter 29-3, edited by Sharpe, W. N. New

York: Jr., Springer & Society for Experimental

Mechanics (SEM), Springer Science + Business Media, L.

L. C.

using thermoelastic stress analysis to detect damaged and ...€¦ · specific heat coefficient at...

Documents