AN ANALYSIS OF STRAIN GAGE MEASUREMENTS UNDER TRANSIENT HEATING CONDITIONS.PDF

8/10/2019 AN ANALYSIS OF STRAIN GAGE MEASUREMENTS UNDER TRANSIENT HEATING CONDITIONS.PDF

1/11

STP345 EB/Oct. 1963

A N A N A L Y S I S O F S T R A I N G A G E M E A S U R E M E N T S U N D E R

T R A N S I E N T H E A T I N G C O N D I T I O N S

B Y

C U R T I S E . J O H N S O N

1

S Y N O P S I S

Serious errors are sometimes encountered in strain gage da ta when test

ing is conducted in transien t heating environm ents. Variations in therm al

gradients, temperature compensation, and monitor temperature sensor loca

tions all contribute to the inaccuracies. The temperature of a strain gage wire

is different 150 F with 100 F per sec hea ting rates ) th an t h at of the specimen

surface under or adjacent to the gage. Strain gages respond faster to a step-

function heat input than do thermocouples; resistance thermometers respond

at about the same rate as strain gages. Theoretically, a quartz-compensated

strain gage, when installed with adequate temperature sensors and when

properly calibrated, will result in more accurate d ata because the strain gage

output is independent of the grid wire temperature.

Bonded re s i s t ance s t ra in gages have

been used extensively in the a i rcraf t

indus t ry fo r approximate ly 20 yea rs .

They measure d i rec t lyor as t ransduce r

component sst ra ins , s t re sses , de f l ec

t i ons ,

loads , and o the r pa ramete rs to

ve r i fy the s t ruc tura l in t egr i ty o f com

ponent s o r comple te a ssembl ie s under

l abora tory and f l igh t condi t ions .

Unt i l the advent of missi les , supersonic

a i rc ra ft , and spacec ra f t, env i ronm enta l

t e m p e r a t u r e s w e r e n o r m a l l y w i t h i n a

rang e of 65 F to + 1 5 0 F , and wi th

ra te s o f t empera ture changes se ldom

exceeding 5 F per sec . No w, how ever , the

tempera ture l imi t s a re f rom abso lu te

zero 460 F) to the mel t ing po int of

th e m os t exot ic m ater ia ls to 5000 F)

and wi th heat ing ra tes in the order of

100 F per sec . Sat isfac tory st ra in meas

u r e m e n t s c a n b e m a d e b e t w e e n 65 F

to 350 F only i f heat ing ra tes do not

exceed about 10 F per sec and i f some

1

Research Engineer, Structures Laboratories,

The Boeing Co., Seattle, Wash.

degree of caut ion is taken in the inst ru

m e n t a t i o n , t e s t i n g , a n d d a t a r e d u c t i o n .

The effec ts of these ext reme t ransient

hea t ing condi t ions were revea led in the

evaluat ion of a newly designed tem

p e r a t u r e - c o m p e n sa t e d s t r a i n g a g e .

W h e n t h e i n s t r u m e n t e d sp e c im e n s

were hea ted wi th ra th e r in t ense 50 F

per sec) radiant heat , the s t ra in gage

outpu t s were e r ra t i c . Any mechanica l

s t ra ins p resen t were comple te ly masked

in the s t ra in gage ou tpu t s caused by

t e m p e r a t u r e a l o n e .

S t ra in gage da ta a re even more un

re l i ab le when t e s t ing involves t rans ien t

hea t ing to h ighe r t emp era ture s a t f a s t e r

hea t in g ra t e s . Cryogen ic s t ra in me as

urement s have the i r own pecu l i a r p rob

lems and wi l l not be evaluated in this

paper . )

Because universa l ly accepted def i

ni t ions of terms involved wi th s t ra in

gages are not avai lable , an Appendix

2

See

p. 108.

opyright

963 by ASTMInternational www.astm.org

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2/11

100

MATERIALS FOE AIKCRAPT, MISSILES, AND SPACE VEHICLES

has been prepared with most of the

unusual terms defined.

BASIC OPERATIONAL THEORY

When a surface bearing a properly

mounted strain gage is deformed, the

deformation is transmitted through the

cement and causes similar deformation of

the strain gage. The strain gage reacts

mainly to the strain component parallel

to its direction and is comparatively

insensitive to the strain component in

the transverse direction. The transverse

sensitivity of commercial strain gages

is in the order of 0 to 5 per cent of their

longitudinal sensitivity and is com

monly neglected.

W hen a strain gage of initial resistance

R is subjected to a mechanical strain at

constant temperature, the gage resist

ance changes to a new value, RmThe

change in resistance, AR, is an almost

linear function of the initial gage re

sistance R and the applied strain .

The applied strain, therefore, can be

determined from measurements of gage

resistance before and after straining,

K

R _ \_AR

~ K R

at constant temperature, where K is a

constant of proportionality or gage

factor.

The gage factor is dependent to some

degree on the test temperature and the

strain range. At constant temperature,

the indicated strain, e^, is equal to the

component of the strain parallel to the

direction of the strain gage.

A change in gage resistance can also be

produced by a change in temperature

when the specimen is mechanically re

stricted from dimensional change. Read

out instruments react to any change in

gage resistance by indicating an equiva

lent strain which would be required to

produce the same change in resistance

at the initial temperature. The indicated

strain produced by change in tempera

ture only (without any dimensional

changes) is called the apparent strain,

_ i_ ART

where

AR^

is the change in gage resist

ance caused by change in temperature

and is a function of the gage grid tem

perature only. The apparen t strain varies

between approximately 20 micro-

strains to 0 microstrains per Fahrenheit

degree, depending on gage grid material

(for constantan wire or foil gages).

In general, mechanical strain is pro

duced by mechanical forces which may

include some form of restraint when

temperature changes are involved. When

an unrestrained body, initially at uni

form temperature, is brought to thermal

equilibrium at a different temperature,

the physical dimensions of the body

have usually changed. The strain or

expansion produced by temperature

change only is called thermal strain.

For an isotropic material, the normal

thermal strains are independent of di

rection of measurement and are func

tions of the initial and final tempe rature s

and the material only. The thermal

strain,

e ,

in any direction is given by

6

=

ATfit)

where f{t) is the coefficient of thermal

linear expansion of the material. The

coefficient can be approximated by a

constant for small changes in tempera

ture,

and by a polynomial of the form

fit) = aT + PT^ +

for larger changes, with the number of

terms required dependent on the ac

curacy desired. AT is the change in

temperature of the specimen from a

specified reference, and a, /3, and so on

are experimentally determined coeffi

cients.



3/11

JOHNSON ON STRAIN GAGE MEASUREMENTS

101

When both thermal and mechanical

strain are applied simultaneously, the

indicated strain is the algebraic sum of

th e real strain (e, = e, + to ) and the

apparent strain (neglecting the trans

verse strain sensitivity).

et er ij

TEMPERATURE COMPENSATION

Temperature compensation of strain

gages is an attempt to make Ai? repre

sentative of mechanical strain only.

The best type of compensation for

static temperature conditions is the

du m m y gage. Bo th the active gage

and an identical dummy gage are sub

jected to the same temperature condi

tions,

and are mounted with identical

materials and bonding procedures on

the same type of material with the same

coefhcient of thermal expansion. The

material on which the dummy gage is

mounted is mechanically unstrained and

unrestrained. The specimen material

and dummy plate material may have

been fabricated from the same piece of

stock, but their thermal coefficient of

expansion characteristics may still be

different because of unlike treatment

during fabrication. They may have been

subjected to varying amounts of heat

treatment or cold work or may have had

different thermal histories during the

strain gage installation.

As the test temperatures become

higher, these effects become more seri

ous. For the temperature range of most

present-day strain measurements, these

effects usually result in less than 1

microstrain, n , per deg Fahr error in

the thermal coefficient of expansion.

Under transient heating conditions

it is impossible to keep both active and

dummy gage instantaneously at the

same temperature, so the du m m y

gage technique is inadequate. One ap

proach for transient strain measure

ments, which is also used for static

testing, is to make the strain gage self-

tem pera ture - com pensating; several

schemes are used to achieve this. Strain

gage manufacturers attempt to make

the output of a strain gage independent

of temperature over a specified tempera

ture range on a specific specimen mate

rial by (1) heat treating and cold work

ing the strain gage alloy; (2) selecting

an alloy melt with the proper charac

teristics; (3) combining the proper

2 5 0

- / 5 0 0

-100 0 100 20 0 300 40 0 50 0

Tempera tu re , deg Fahr

FIG.

1.Typical Strain Gage Tem peratu re

Compensation.

lengths of two alloys with different

thermal characteristics in one gage; and

(4) placing a temperature-sensitive ele

ment in the strain gage matrix and

placing it electrically in the same cir

cuit as the strain gage. All of these

approaches are inadequate because zero

output cannot be achieved over the

entire temperature range. (See Fig. 1

for typical temperature compensation

curves.) In addition, thermal aging

usually alters the compensation, and

when heating rates are no longer static,



4/11

w

o

g

o

102



5/11

JOHNSON ON STRAIN GAGE MEASUREMENTS

103

^ s

3

o

l)

o>

o

Ci)

o

n

_

500

1000

< 1500

2000

A

^

Gage: AB

Spec imen

S u d d e n

a t 4 5 0

7

0.010 in.

c a r b o n

th ic i

s t ee l

imnners ion in o i l

F

40000 200 300

Specinnen Su r face Tem pe r a tu re , deg Fa t i r

FIG.

3.Apparent Stra in Versus Specimen Surface Temperature During Transient Heating.

^ S -

D

o

a>

n

o

.~

k .

CO

^

-1500

1000

- 5 0 0

0

In d ic a te d

- T e m p e r a

G a g e :

f

S p e c i m

S u d d e n

in o i l

S t r a i n

ture

^B-7

en : 0 . 0 1 0

in . th ick

c a r b o n s i e e i -

i m m e r s k

a t 4 5 0

>n

F

5 0 0

4 0 0

3 0 0

2 0 0

F I G . 4.-

100

0 1 2 3 4 5 6

T i m e , S e c

-Strain Gage and Surface Tliermocouple Responses to a Sudden Temperature Cliange.

the strain gage temperature is not in

stantaneously the same as that of the

structure, and the problems increase.

When a strain measurement under

transient heating conditions is to be

made, the following procedures are

commonly followed: A thermocouple or

other temperature sensor is placed on

the specimen adjacent to the strain

gage. (See Fig. 2 for a typical installa

tion. This photograph also shows the

blistering caused by intense radiant



6/11

104

MATERIALS FOR AIRCRAFT, MISSILES, AND SPACE VEHICLES

heating.) The outputs of both the strain

gage and tem peratu re sensor are recorded

simultaneously. During data reduction

processes, the strain gage output is

corrected for temperature as measured

by the temperature sensor. The output

correction may have been obtained

RESPONSE CHARACTERISTICS

It is frequently assumed tha t the

strain gage and temperature sensor have

the same response characteristics. This

may be nearly true in the case of a

resistance thermometer, but when a

Est {of f

scale)

6 0 0 F

5 0 0 F

4 0 0 F

3 0 0 F

2 0 0 F

l O O F

Rad ian t

Hea t

L a m p

0 . 0 6 i n.

m

Spec imen

Slow heat ra te

3 F per Sec )

Medium heat ra te

33F pe r Sec )

Fast heat rate

O O F p er S e c )

OlD O

FIG. 5.Effect of Heat Rate on Instantaneous Temperatures of a Gage Installation (Specimen

Paral le l to Heat Lamp).

Horizontal scale is symbolic only.

statically from a similar installation,

or it may have actually been determined

from the gage under test with the speci

men unrestrained and unloaded. These

procedures are inadequate when heating

rates exceed approximately 10 F per

sec or when thermal gradients are large.

It is also impossible sometimes because

of thermal effects caused by the speci

men configuration.

thermocouple is used and heating rates

are rapid it is very much in error.

Several tests were conducted to de

termine the relative temperature re

sponse of the strain gages and the

specimen surface as measured with a

thermocouple. To eliminate any possible

effects of gage exposure to high-intensity

radiation, a heated oil bath was used as

a heat source. First, a specimen instru-



7/11

J O H N S O N

O N

S T R A I N G A G E M E A S U R E M E N T S

105

mented with a strain gage and a surface

thermocouple was immersed in the oil

bath at room temperature and the gage

output was recorded against the thermo

couple output as the oil temperature

was slowly increased (at a rate of ap

proximately 10 F per sec to 400 F).

The resultant curve was approximately

oscilloscope, was recorded photograph

ically. The resultant trace (Fig. 3) was,

unlike the slow-heating trace obtained

from the previous test, highly nonlinear

and irregular. For further study, both

strain gage and thermocouple outputs

were displayed against time as the test

was repeated (Fig. 4). Invariably the

7 0 0

6 0 0

5 0 0

4 0 0

3 0 0

S 2 0 0

CL

E

0)

1 0 0

F IG .

6.ThermalGradients with Heating Rates

of 90 F per sec at

Gage Grid.

a straight line. When the oil was per

mitted to cool, the cooling curve agreed

very closely with the original heating

curve. The specimen was then removed

and cooled to room temperature, and

the oil was heated to 450 F and main

tained at this temperature. The speci

men, now at room temperature, was

suddenly immersed in the 450 F oil

bath, and the gage output, displayed

against the output of the specimen

surface thermocouple on a cathode ray

strain gage showed a much faster initial

response to the sudden change in en

vironmental temperature than did the

thermocouple.

GRADIENTS

Temperature gradients are nearly al

ways present in a test specimen. These

gradients are sometimes in the order of

several hundred degrees per inch. It is

quite obvious that the temperature cor

rections would be in error if a strain



8/11

106

MATERIALS FOR AIRCRAFT, MISSILES, AND SPACE VEHICLES

gage and temperature sensor are not at

the same temperature because of these

gradients. The situation is further com-

pHcated by the presence of the strain

gage and the resulting change in absorp

tivity and emissivity of this area on the

specimen.

A series of tests was conducted to

study temperature distributions around

and through a typical strain gage instal

lation during transient radiant heating.

A 17-7PH stainless steel specimen 0.063

in. thick by 1 in. wide was instrumented

with two bakelite-backed resistance

temperature gages using a bakelite ad

hesive. Except for different sensing ma

terial, these gages are similar to bake

lite-backed strain gages, and they were

selected for their large resistance change

with temperature.

Number 36 chromel-alumel thermo

couples were welded to the specimen in

the area to be under the strain gage but

not directly under the gage wires. The

gages were installed and more thermo

couples were cemented to the surface of

the gages. A thermocouple was installed

on each side of each gage.

Radiant heat lamps were located

parallel to the specimen and the speci

men was heated at several rates. Figure

5 illustrates the resulting temperature

distribution with the various heating

rates.

These results indicate that the

strain gage wire and specimen surface

under the gage are at different tem pera

tures. The magnitude of this difference

is a function of the heating rate. It

should also be noted that the tempera

ture measured on either side of the

gage on the side of the specimen facing

the heat lamps was lower than the

gage wire temperature but higher than

the specimen temperature under the

gage. Figure 6 is reproduced from data

taken during the testing and illustrates

the temperature-time relationships at

several points. When testing was con

ducted with the heat lamps not parallel

to the specimen, the gradients were

more severe and the test data were more

erratic.

Another more common factor which

contributes to the inaccuracies of strain

measurements under transient heating

conditions is the effect of thermocouple

emf's produced at each junction of the

strain gage leads and lead wires. If, as

in the case of heating conditions when

there are gradients present, one of the

junction s is at a different tem pera ture

than the other, there may be a net emf

produced. The magnitude of the result

ing error may be large if the gradient

is significant. Many strain gages have

internal junctions which also may re

sult in net emf's because of thermal

gradients.

INSTRUMENTATION DESIGN

Up to this point, this discussion has

been concerned with problems generally

associated with transient strain meas

urements and some that are not nor

mally considered. If the following pre

cautions are taken, the resulting strain

measurements will be decidedly more

accurate than if they are not considered.

1. W henever a single stra in gage is

used in a heat test of any kind to meas

ure strain, a three-lead connection must

be used. Two lead wires are fastened

to one of the gage leads, the third lead

wire is fastened to the other gage lead.

The three lead wires are routed so that

they are subjected to the same tempera

tures.Th ese lead wires change resistance

as a function of temperature, but they

are wired into the bridge circuit in such

a way that the like resistance changes

of the three wires have no net effect on

the total bridge resistance change except

for a change in circuit sensitivity if

lead lengths are long.

2. The strain gage and temperature

sensors should be as small as possible



9/11

J O H N S O N

ON S TR A I N G A G E M E A S U R E M E N T S

107

so that their presence does not signifi

cantly altertheabsorptivity oremissivity

characteristics of the specimen, or so

tha t the structural strength of the

specimen

is not

changed

by

relatively

large transducers.

3. If the thermal gradients are not

severe but high heating rates are ex

pected, a resistance thermometer should

be used as a temperature sensor rather

than a thermocouple because the re

sponse characteristics of the resistance

thermometer more nearly match thatof

a strain gage.

4.

If the

heating gradients

are

large

bu t the heating rates are tolerable, as

many thermocouples

as

practical should

be positioned around the strain gage.

Smaller thermocouples have faster re

sponse characteristics than do larger

ones.

If both large gradients and high

heating rates are predominant, a com

promise is required if the more conven

tional transducers are used. A theo

retically superior installation isproposed

laterinthis paper.

5. The strain gage installation must

be cured to ahigher 50 to 100 F) tem

perature than the test temperature so

that maximum stability is obtained.

6 . The strain gage adhesive shouldbe

as thinaspossible tom inimize the ther

mal gradients throughtheinstallation.

7. A split thermocouple one inwhich

the

two

wires

are

attached

to the

speci

men at different points) may be used

effectively to measure the average tem

perature

of a

specimen

on

opposite

sidesof an installed strain gage.If large

gradients arepresent, one or more split

thermocouplesmay be used to measure

the average specimen temperature with

a minimumofmeasurements.

QXJARTZ-COMPENSATION THEORY

Strain gage data will be improved if

the above precautions are taken, but

it

is

believed th at even greater accura

cies

in

transient strain measurements

are obtainab le.

Mechanical strain, e^, is normally

desired from strain gage measurements.

Some method isrequired toeliminateor

predict the strain gage output causedby

other factors. From a practical stand

point,the strain gage shouldbeinstalled

onanyspecimen m aterialandaccurately

measure the mechanical strain and be

independent of any effects of thermal

expansion, , or apparent strain,ey.

I t is sometimes possible to install a

strain gage

on an

unrestrained unloaded

specimen and statically measure +

ey. The nthespecimenmay berestrained

or loaded and the output corrected for

a +

ij

This condition is sometimes

impossible because

of the

specimen

or

test configuration inducing strains.

An

other

way to

accomplish essentially

the

same resultsbut with some degradation

in accuracy is tomeasure + tj stati

cally

on a

specimen

of the

same mate

rial and then assume that the gage

installedon theactual test specimenhas

identical characteristics.

Another techniquemay at first seem

to be no improvement, but if carefully

analyzed it can be seen that improved

accuracies will result.

If a strain gage were fabricated so

tha t its output contained no component

representing

ey,

then,

no

matter what

the instantaneous temperature of the

specimen is relative to the gage, the

output of the gage represents only the

strainin thespecimen + tm

Such

a

strain gage

is

normally identi

fied as being quartz-co mp ensated.

The commercially available gages

of

this type have nonlinear compensation

curves similar in shape to those shown

in Fig. 1. Th ey

are

still superior, thou gh,

to gages compensated for a particular

specimen material because the gage



10/11

108

M A T E R I A L S F O R A I R C R A F T , M I S S I L E S , A N D S P A C E V E H I C L E S

t e m p e r a t u r e a n d sp e c i m e n t e m p e r a t u r e

do not have to be ident ica l .

I f the nonl inear character is t ics of a

quar t z -compensa ted s t ra in gage can be

neg lecte d (ey = 0) , an d if th e th er m al

coefficient of expansion of the specimen

i s accu ra te ly known, then sa t i s fac tory

s t r a i n m e a su r e m e n t s m a y b e m a d e w i t h

only the spec imen t empera ture be ing

measured so the ou tpu t may be cor

rec ted for

ta

Addi t iona l accuracy may be ob ta ined

i f a min ia ture the rmocouple o r re s i s t ance

the rm om ete r i s p l aced in the gage m a t r ix

and i t s ou tpu t i s used to cor rec t the

s t ra in gage ou tpu t fo r ey .

S U M M A R Y

The accuracy of t rans ien t s t ra in

m e a su r e m e n t s d e p e n d s g r e a t l y o n t h e

care taken in the design of a test and in

the procedures used in t e s t ing and da ta

reduc t ion .

Some of the improvements can be

obta ined a t l i t t le or no ext ra cost to the

te s t p rogram; o the rs a re ve ry expens ive

and complex and should only be used i f

the des i red accurac ies war ran t such

ext reme measures .

R E F E R E N C E S

(1) Peter K. Stein, Measurement Engineering

(preliminary rough draft from the forth

coming book), Stein Engineering Services,

Inc.

(1962).

(2) Mintauts F. Andreika, StressDetermination

-with Bakelite Backed Strain Gages, 23-TC-

(5?-J, Ins trum ent Soc. of America, Summer

Instrum ent - Automation Conference,

Toronto, Canada, June 5-8, 1961.

(3) W. M. Murray and P. K. Stein,StrainGage

Techniques, Massachusetts Institute of

Technology, Cambridge, Mass. (1958).

APPENDIX

D E F I N I T I O N S O F T E R M S IN V O L V E D I N S T RA I N GA G E M E A S U R E M E N T S

Gage Factor, K (dimensionless).The gage

factor is the ratio of the unit change in

resistance of a strain gage installation

to the unit elongation of the surface

upon which it is mounted caused by a

uniaxial stress in the direction of the

gage axis, all other variables remaining

constant . Mathematically,

K =

AR/R

AL/L

where:

L = initial length of the specimen un

der the gage,

R = resistance of the strain gage in

stallation at length L,

AL = change in initial leng th L of the

test surface, and

AR = change in resistance, R, caused by

AL.

Matrix.The matrix is the material used by

the gage manufacturer to hold in posi

tion the various gage elements, such as

sensing element and leads, and which are

an integral part of the gage structure.

Thermal Output.The thermal output is the

algebraic sum of the thermal and apparent

strains.

Transverse Sensitivity.The transverse sen

sitivity of a strain gage is the ratio of the

indicated strain which would result if the

gage were mounted 90 deg from the axis

of a uniaxial strain to the indicated strain

which would result if the same gage had

been mounted parallel to the axis of the

same uniaxial strain.

Apparent Strain, ey, in micro inches per

inch.Apparent strain is that portion of

indicated strain which is the algebraic

difference between indicated strain and

real strain:

Indicated Strain, u , in microinches per

inch.Indicated strain is that quantity

available directly from the analog signal,

after indicator and accessory equipment



11/11

J O H N S O N O N S T R A I N G A G E M E A S U R E M E N T S

109

errors have been accounted for and prop

erly adjusted from the indicated reading,

without further adjustment or correction.

This quantity is a gross indication of

strain:

et = e; + r

ii = e,- + e + e

Mechanical Strain,

, in m icroinches per

inch.Mechanical strain is that unit

deformation of a specimen which occurs

when mech anical loads are applied ;

within the elastic limits of the specimen

material, mechanical strain is propor

tional to unit mechanical stress, a or T:

E

or -

G

Thermal Strain, ta , in microinches per inch.

Thermal strain is that unit deforma

tion of a specimen which would occur if

the specimen were unrestrained and sub

jected to a uniform change in tempera

ture of AT:

6a = aAT = a{Ti To)

where:

a = th e the rm al coefficient of linear

expansion of the test specimen,

Ti = temp erature of the test specimen,

and

Ta =

reference or initial tem per atur e of

the test specimen.

Real Strain, tr

, in microinches per inch.

Real strain is that unit deformation

present in a specimen as a result of ther

mal changes and mechanical loads ap

plied. It is possible for two components

of real strain to exist simultaneously.

These components are thermal strain and

mechanical strain.

Copyright by ASTM Int'l (all rights reserved); Tue Mar 9 06:08:12 EST 2010

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