AN ANALYSIS OF STRAIN GAGE MEASUREMENTS UNDER TRANSIENT HEATING CONDITIONS.PDF
Transcript of 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
Copyright by ASTM Int'l (all rights reserved); Tue Mar 9 06:08:12 EST 2010Downloaded/printed byLupatech+ SA (Lupatech+SA) pursuant to License Agreement. No further reproductions authorized.
-
8/10/2019 AN ANALYSIS OF STRAIN GAGE MEASUREMENTS UNDER TRANSIENT HEATING CONDITIONS.PDF
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.
Copyright by ASTM Int'l (all rights reserved); Tue Mar 9 06:08:12 EST 2010Downloaded/printed byLupatech+ SA (Lupatech+SA) pursuant to License Agreement. No further reproductions authorized.
-
8/10/2019 AN ANALYSIS OF STRAIN GAGE MEASUREMENTS UNDER TRANSIENT HEATING CONDITIONS.PDF
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,
Copyright by ASTM Int'l (all rights reserved); Tue Mar 9 06:08:12 EST 2010Downloaded/printed byLupatech+ SA (Lupatech+SA) pursuant to License Agreement. No further reproductions authorized.
-
8/10/2019 AN ANALYSIS OF STRAIN GAGE MEASUREMENTS UNDER TRANSIENT HEATING CONDITIONS.PDF
4/11
w
o
g
o
102
Copyright by ASTM Int'l (all rights reserved); Tue Mar 9 06:08:12 EST 2010Downloaded/printed byLupatech+ SA (Lupatech+SA) pursuant to License Agreement. No further reproductions authorized.
-
8/10/2019 AN ANALYSIS OF STRAIN GAGE MEASUREMENTS UNDER TRANSIENT HEATING CONDITIONS.PDF
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
Copyright by ASTM Int'l (all rights reserved); Tue Mar 9 06:08:12 EST 2010Downloaded/printed byLupatech+ SA (Lupatech+SA) pursuant to License Agreement. No further reproductions authorized.
-
8/10/2019 AN ANALYSIS OF STRAIN GAGE MEASUREMENTS UNDER TRANSIENT HEATING CONDITIONS.PDF
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-
Copyright by ASTM Int'l (all rights reserved); Tue Mar 9 06:08:12 EST 2010Downloaded/printed byLupatech+ SA (Lupatech+SA) pursuant to License Agreement. No further reproductions authorized.
-
8/10/2019 AN ANALYSIS OF STRAIN GAGE MEASUREMENTS UNDER TRANSIENT HEATING CONDITIONS.PDF
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
Copyright by ASTM Int'l (all rights reserved); Tue Mar 9 06:08:12 EST 2010Downloaded/printed byLupatech+ SA (Lupatech+SA) pursuant to License Agreement. No further reproductions authorized.
-
8/10/2019 AN ANALYSIS OF STRAIN GAGE MEASUREMENTS UNDER TRANSIENT HEATING CONDITIONS.PDF
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
Copyright by ASTM Int'l (all rights reserved); Tue Mar 9 06:08:12 EST 2010Downloaded/printed byLupatech+ SA (Lupatech+SA) pursuant to License Agreement. No further reproductions authorized.
-
8/10/2019 AN ANALYSIS OF STRAIN GAGE MEASUREMENTS UNDER TRANSIENT HEATING CONDITIONS.PDF
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
Copyright by ASTM Int'l (all rights reserved); Tue Mar 9 06:08:12 EST 2010Downloaded/printed byLupatech+ SA (Lupatech+SA) pursuant to License Agreement. No further reproductions authorized.
-
8/10/2019 AN ANALYSIS OF STRAIN GAGE MEASUREMENTS UNDER TRANSIENT HEATING CONDITIONS.PDF
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
Copyright by ASTM Int'l (all rights reserved); Tue Mar 9 06:08:12 EST 2010Downloaded/printed byLupatech+ SA (Lupatech+SA) pursuant to License Agreement. No further reproductions authorized.
-
8/10/2019 AN ANALYSIS OF STRAIN GAGE MEASUREMENTS UNDER TRANSIENT HEATING CONDITIONS.PDF
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