Two laser speckle methods are described to measure strain in high temperature environment and thermal strain caused by high temperature. Both are non-contact, non-destructive and remote sensing techniques that can be automated. The methods have different but overlapping ranges of application with one being more suitable for large plastic deformation

Chiang, Fu-Pen

English

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N93-13673
Elastic and Plastic Strain Measurement
in High Temperature Environment Using Laser Speckle*
F.P.Chiang
Laboratory for Experimental Mechanics Research
State University of New York at Stony Brook
Stony Brook, New York 11794-2300
SUMMARY
Two laser speckle methods are described to measure strain in high temperature environment and
thermal strain caused by high temperature. Both are non-contact, non-destructive and remote
sensing techniques that can be automated. The methods have different but overlapping ranges of
application with one being more suitable for large plastic deformation.
INTRODUCTION
In order to measure thermal strain accurately it is paramount that the output of the measuring
device not be influenced by temperature. Both mechanical and electrical strain gages require
compensation schemes to overcome thermal effect. But compensation becomes difficult if not
impossible when temperature extremes or large temperature gradients are involved. The situation
becomes worse when the loading is a thermal shock. Optical techniques such as moire or moire
interferometry require that a grating or grid be attached to the specimen surface over an area.
Although it has been shown [1] that by appropriately mixing a certain ingredient into the
photoresist, it can sustain temperatures up to about 560°C, at higher temperatures the grating or
grid tends to disintegrate. Holographic interferometry has also been used for measuring thermal
strain. However, since it is not easy to apply it to measuring in-plane strain, its application is
limited.
In this paper we describe two non-contact, non-destructive and remote sensing methods of thermal
strain measurement using laser speckles. In principle thermal strain up to the melting point can be
measured without the aid of an auxiliary device. Other than the impingement of photons from a laser
beam nothing touches the specimen. Recording can be done remotely using a telephoto lens and
data analysis can be computerized.
LASER SPECKLE TECHNIQUES OF STRAIN ANALYSIS
Two laser speckle techniques are described in this article. Each has its own range of applicability
and the two ranges overlap and complement each other. The first technique is the so-caLled speckle
photography or one beam laser speckle interferometry [2,3]. When an expanded coherent laser beam
illuminates a specimen surface which is optically rough (i.e.) its RMS roughness is much larger than
*Work supported by Army Research Office, Engineering Science Division Grant No. DAAL0388K0033
223
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the wavelength of the light from the laser), multiple reflection (scattering) occurs. Th.e reflected
wavelets, being still coherent, mutually interfere to form a random interference pattern called
speckles. An example of such a speckle pattern after magnification is shown in Fig.'1. These are the
equivalent optical displacement "gages" that are used for thermal strain measurement. Under the
condition of small strain and small displacement these speckles move as if they were physically
attached to the specimen surface. When they are recorded on a photographic film via a camera
before and after the specimen's deformation, the superimposed speckle pattern is called a double
exposure specklegram. The specklegram may be processed either in a pointwise or a full field
manner. For pointwise processing, a thin laser beam impinges upon the specklegram as shown in
Fig.2. Its far field diffraction pattern is a circular halo modulated by a series of uniformly
distributed fringes. It can be shown [3] that the in-plane displacement vector at the probed point
can be expressed as follows:
AL_
d= (1)
where ; is a unit vector perpendicular to the fringes, L the distance of the screen from the
specklegram where the halo is received, A the wavelength of the laser light that is used to probe the
specklegram and S is the fringe spacing.
The full field processing technique uses an optical bench as shown in Fig.3. It can be shown [3] that
the intensity of the diffraction spectrum displayed at the transformed plane of the first field lens is
given by the following equation:
I(r,,r_)= Kcos2k--ff-I.(r,,r2) (2)
where I,(rx,,-2) is the diffraction pattern of a single exposure specklegram with (rl, r2) being the
coordinates of the spectrum plane, k(= 2_r/,_) is the wave number; d is the displacement vector at a
point; _ is a position Vector at the spectrum piane; K is a proportional constant and L is the
distance between the specklegram and the spectrum plane. Alternating bright and dark fringes are
observed when the following condition is met:
d._=nAL, rt = 0, +l, +2, .... (3)
By placing an aperture at e and reconstructing the specimen image through the second field lens,
isothetic (contours of equal displacement component) fringes similar to moire fringes are observed
covering the specimen surface and they are governed by the following equation:
u = a==  AL/I -.I = np=, = 0, +1, 4-2,.... (4)
v = = = LII - I = "G, = 0,+1,+2; .... (5)
where r-z and r-_ are the position vectors of the apertures sequentially located along rl and r2 axes,
respectively, tt and v are the displacement components along z and V directions, respectively; and
P=(= ,_L/[r-,[) and Py(= ,_L/I_vi) are the equivalent "pitches" of moire gratings if they were used
for the determination of strain. This technique is suitable only for the determination of small
strains unless single exposure specklegram and mechanical superposition are adopted. The process
has been automated as a result of our recent development of CASI (Computer Aided Speckle
Interferometry) [4].
224
The second laser speckle technique is the so-called LSS (Laser Speckle Sensor). A schematic of this
method is shown in Fig.4. A narrow laser beam impinges upon a point on the specimen surface
where the strain is to be determined. The specimen surface has to be sufficiently sniooth such that
its scattering speckle field is f_irly restricted. Upon deformation the surface roughens resulting in a
more spread out speckle pattern whose autocorrelation function can be used as a means of assessing
the underlying surface strain. The quantity that is most sensitive to strain is the coefficient of
autocorrelation function of the speckle pattern g(i,j) defined as
v,M %--N
co[g(i, j), sj] = ,..,=1 g(i, j) × g[(i - s,), (j - 6;)1
M
E,=l EN=I g2(i,J)
(6)
where 6i and 6j are shifting distances along i and j directions, respectively.
One can use light scattering theory to compute the autocorrelation coefficient for various amounts
of plastic strain [5]. An example is given in Fig.5 where a three dimensional view of the laser
speckle field at three different levels of plastic strain in a copper alloy specimen is depicted. The
corresponding experimental result is shown in Fig.6 and the agreement is quite good. The
calculated autocorrelation functions for different levels of plastic strain and for different lag lengths
are depicted in Figs. 7 and 8, respectively. It should be noted that the lag length is the shifting
"distance" between the speckle field and its image that is used in the calculation of autocorrelation.
Since the speckle field denotes the spatial frequency (see Figs. 5 and 6) of the light disturbance from
the specimen surface, its dimension is in terms of lines/mm. If the area under the curve of the
autocorrelation function is integrated and expressed as a function of strain, the relation can be
approximated by a straight line as shown in Fig.9. Thus fo r plastic shear strain 7 <--3.5%, the linear
relationship between the integrated autocorrelation coefficient and 7 is
C1 = 29.23' - 0.04 (7)
with an error band of 10%. For higher strains the relation is no longer linear. The broadening of the
scattering speckle field becomes saturated at higher strains. In aluminum specimens we have shown
that LSS can be effectively used for strains up tO 20%.
APPLICATION TO THERMAL STRAIN PROBLEMS
Fig.10 shows the u and v fields' isothetics representing the thermal strain distributions of an
aluminum plate at elevated temperatures. The specimen was a quarter inch thick aluminum plate
of about 2' x 2' in size. It was heated at the left lower corner with a propane torch. This place
manifests itself as a dark spot in the pictures, especially at higher temperatures. When the torched
place became red-hot at the back side, the flame was extinguished and the plate was allowed to cool
naturally by thermal convection. A series of double exposure specldegrams were taken. At near the
top of the plate a thermal couple was mounted to monitor the temperature change. (The wiring of
the thermal couple is vaguely visible as a vertical line near the top of the picture.) The temperature
reading at the time of each exposure was recorded and is indicated in the figure. A 1-joule ruby
laser (A "_ 0.69 × 10-sin) was used to record the specklegrams. It was a pulsed laser with a pulse
width of about 60 nsec. The laser only gave a single pulse and needed to be repumped after each
firing. The time separation between the two pulses and the resulting temperature difference as
225
indicatedon the picture represent the amount of cooling between the exposures. Since the thermal
couple was located far away from the heat source, it is reasonable to expect that the temperature near
the heat source was much higher than those indicated on the picture.
The double exposure specklegram was Fourier processed using the full-field processing scheme
shown in Fig.3. Filtering aperture_ were placed at two orthogonal directions to yield the u- and
v-field fringe patterns, respectively. A qualitative way to read the fringe pattern is as follows.
Uniform strain is depicted by uniformly spaced fringes whoSe spacing is inversely proportional to
the local average strain. Thus one can see from the pictures that at the earlier stages of thermal
relaxation, the strain distribution is quite nonuniform and the strain is higher. As the convection
cooling progresses the fringe becomes less dense (indicating smMIer Strain) and more uniform
(indicating lower strain). A quantitative calculation of strain near the point where the thermal
couple was located was carried out and the result is depicted in Fig.11. in the course of about 120
seconds the thermal strain has relaxed from about 0.2% to about (I.02%. The difference between
horizontal and vertical normal strains also decreases with time as indicated by the gap between the
two data points. A comparison of thermal strain at various temperatures for this material using data
from an Alcoa Aluminum Handbook was also plotted. Within the range where comparison can be
made the agreement is quite good.
Another exampie is the application of the laser Speckle method to the determination of stress-strain
relation at high temperature and high heating rate. _'ig.i2 is the schematic of a medium strain rate
test-ing machine with a resi-stance heating attachment. TWo types of testing wereperformed [6]. One
was a soaking test at elevated temperature and the other a high heating rate test. In both tests the
strain rate was kept at 10 -_ sec -I. Strain gages were mounted on the tensile specimen as a
comparison with the laser speckle result. The ruby laser was fired once before the beginning of the
test and a second time at an appropriate delay time. A camera was used to record the laser
illuminated specimen. The double exposure specklegram was pointwisely processed by probing
different points along the axial direction within the gage length of the specimen. The resulting
Young's fringes represent the absolute displacement at the probed points between the exposures.
Since the strain field is homogeneous within the gage length, the difference in displacement between
two probed points divided by the separating distance is nothing but the strain. The results of the
soaking test and high heating rate test are depicted in Figs.13 and 14, respectively. As can be seen
from the data presented, the difference between the strain gage reading and laser speckle result is
only a few percent. We have thus demonstrated the reliability of the speckle method at high
temperature tests. At extreme temperatures the strain gage may fail but the laser speckle method will
not. It can even be applied to specimens giving off a wide spectrum of radiation which may include
the radiation of the laser. However, thermal radiation, being incoherent, does not produce speckles.
To prevent thermal radiation from fogging the film, a narrow band (10.&) interference filter can be
mounted on the lens of the recording camera to allow only the laser light to enter the camera.
For:tests that are not repeatable, single exposure: Specklegram at different times Can be recorded
using a continuously pulsing laser (such as a copper vapor laser) and a high speed framing camera.
Two single exposure specklegrams at different instances can be mechanically superimposed to yield
the difference between the two stages of loading. However, the strain difference between the two
cannot be too large, for otherwise decorreiation of the speckle pattern will result.
When either the strain variation or the absolute strain is large, decorrelation of laser speckle tends
to occur. In sucha situation the LSS(LaserSpeckleSensor)technique should be used. The
advantages of LSS technique are that only single exposure is required and speckle decorrelation will
not affect the result. Currently we are in the process of applying LSS to high temperature testing
and the results will be reported in the near future.
References
1. Burch, J.M. and Forno, C., "High resolution moire photography," Optical Eng vol. 21(4),
1982, pp.602-614.
2. Khetan, R.P. and Chiang, F.P., "Strain analysis by one-beam laser speckle interferometry h
Single aperture method," Applied Optics, vol. 15(9), 1976, pp. 2205-2215.
3. Chiang, F.P., "A family of 2D and 3D experimental stress analysis techniques using laser
speckles," Solid Mechanics Archives, vol. 3(1), 1978, pp.1-32.
4. Chen, D.J. and Chiang, F.P., "Computer speckle interferometry," Proc. Society for
Experimental Mechani_ 1990 Fall Meeting, 1990., pp.49-58.
5. Dai, Y.Z. and Chiang, F.P., "Scattering from plastically roughnened surfaces and its application
to mechanics," Optical Engineering, vol. 30(9), 1991, pp.1269-1276.
6. Emslie, J., Green, J., Chou, S.C. and Chiang, F.P., "The application of laser speckle
interferometry to measuring strain and strain rate under dynamic conditions," Proc. Society
of Experimental Mechanics, 1990 Fall Meeting, 1990, pp.59-66.
227
Fig.1
I
d ×2
Typical Laser Speckle Pattern
(Original figures unavailable.)
Loser
beam
speckle
poll"tern
L Young's fringes
diffraction halo
in
Pig.2 Pointwise Processing of Specklegram
228
[I I
I FILTERING
_.i_i !i::i_" > [/!/APERTURE
\
_ '_; :._.',
I 1F('_"_'-_,I ITnANSFORM _"_ 1
TRANSFORM AND
FILTERING PLANE
RECORDING
LENS IMAGE
PLAN E
Fig.3 Full-field Processing of Specklegram
He-Ne Laser
• / I
G ",?.., • I "_
Fig.4 Schematic of LSS (Laser Speckle Sensor)
229
tOO"
0.75
_ o.5o "_ = 000%
o.25_
0.oo
It 0
_) ¢1'i"1 _eOr.. ' (_ .,0 . ,_iO(_U '11c'
'quency t_ o Spatil! r,
tOO] /1
o_s' _ _........
0.00 .0
"'°_2,
1.0
_uellCy le 0
,.oo]
°'1 Nttl
o.,oI .................
o.oo ,o 0'0 0"0 e_Cy
SD=tillPreqLtenc_o .1.0 Freq"
_eo 5p8tisl
23O
Fi8.5 Theoretical Laser Speckle Field at Different Leve|s of Pl=tic Siren of a Copper
Alloy Specimen
,oo 
o o
00t It
0 . _1.0
_._.6
Copp er
Fig.7
o
.roll
cD
I..
O
¢.)
o
1.0
08
0.8
0.4
0.2
0.0
_ i t I I I
<,,\ Strain y (_)
l',_\',.,_\ ooo,........l\\ , 08 ......tI:',l_.,,,\ \ ,_ ....
II;_l\\ \ '.. ,, _s ....
',1" \'. " 2o .-- --n:._i\.,, \ ,, ,, .....
I1:;_\ :\ . \ _, --.-
I1',_',\ \.". \ \ 32 ....
nli,,\, \.,..\, ___
tli",',\'.,\./Q-,
I I'- '._,,.,.._ _----__ "',----'_- ":_.-"-- --..,,_ --
0 20 40 dO O0 t00
Lag Length (xl.2 Lines/ram)
120
Theoretical Autocorrelation Function of Speckle Pattern at Different Levels of
Plastic Strain
l.O [_ , i l , I
I_,_.. Strain 7 (_)
Ilia,_\",,\", o_ ....I[_\\ ,',\ o, .......IF',%v" _. \ I, ------
II:',_ , \ \\.-. 1.7 .....
_, II:,_% \ _ _. "x x 21 --'--
I1:' ,,_ \ \ \\ \ 28 ....
Ili!,,_' \'.\ \,. ,,
•\\ .i_% _
If"..',, '_... '_"....:'-_.:-.._>-_
0.0 L.t " _I -.. _l .... _i'_._-----_'----""-------
0 20 ,_0 80 O0 too 20
Lag Length (xI.2 Lines/ram)
Fig.8 Experimental Autocorrelation Function of Speckle Pattern at Different Levels of
Plastic Strain
232
tO
0B
06
04
O.2
O0
0.0
• ..... [rror E4u;d , _ "
:J S co,,.r  oy]
0.7 L.4 2., z8 _.s
Plastic Strain y (%)
Fig.0 Integrated Autocorrelation Coefficient aa a Function of Plastic Strain
a68 _-aZ _] }_8 °-32"Z 29_°-266°C 243"-227°C 2_2°- 99°C .87°-_6'S
'-J 2-u 3-u' 4-- 5-u 6-0
u-FIELD
3-v 4-v 5-v 6-v
v -F;ELD
Fig.10 Distribution of ThermM Strain Relaxation of an Aluminum Plate Heated at
Lower Left Corner.
233
2 0
1.8
16
I 4
P_
i 12
o
xlO
4 8
6
4
.2
0
- \
&
_ \
I
20
\
• _ x EXPERIMENTAL
• _'y EXPERIMENTAL
--ALCOA AL HANDBOOK 1962
---- PROJECTED
\
.',,\
I j_ 1. J_ l I
40 60 (_) I00 120 140
TIME (SECONDS)
234
Fig.ll Thermal Strain Relaxation as a Function of Time at a Point near the Thermal
Couple
AC
POWER
INPUT MEDIUMS]RAIN
VARIAC i! _
_ 10 II II_ l A_ql II
COMPUTER i --_-
SIGNAL TO TRANSFORMER
RELAYS _
Fig.12 Medium Strain Rate Testing Using Laser Speckle Resistance Heating
._.=.
..to
o
Io-
5O
4O
3O
y = - 4 3375 * 2 64Gge 2x 11"2 = 0 9 -03_---
• D •
: "•
J *Speckle [ = slope = 25.85 ,z lO*psl
% dlffewence = 2.34
2o T
2000 30001000
Strain (mlcrostralns)
Fig.13 Results of a Soaking rrest at 250"F and _ --- 10-' sec- '
at
o
w
o_
/o
raO.
54)
40
30-
20-
y = I 3942 , 2 4{;940 2= I|*_' = O 980
li •
• O
D * psi
/ * Spe(kle [ = slope = 25.5'i It Ill L IJ$1
7. diileren(e = ].t
%000 2000 3o00
Slrain (miclostlains)
Fig.14 Results of a lligh lleating Rate Test at 250"F/see. and _ = 10- [sec.
235



Elastic and plastic strain measurement in high temperature environment using laser speckle

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