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. iiFULL-FIELD DEFORMATION MEASUREMENT IN WOOD USING DIGITAL IMAGE PROCESSING
bvChandra Prakash Agrawal
August 18, 1989
Blacksburg, Virginia i
FULL-FIELD DEFORMATION MEASUREMENT IN WOOD USING DIGITAL IMAGE PROCESSING
bvChandra Prakash Agrawal
Joseph R. Loferski, Chairman
Wood Science and Forest Products
(ABSTRACT)
A digital image processing system was used to non-destructively measure the full-
field deformation on aluminum and wood specimens Ioaded in compression and
bending. The measurement technique consisted of creating a random speckle pattern
on the specimen surface, recording images before deformation and after deformation,
and computing the relative displacements of small image subsets. Two methods for '
producing speckle patterns on the specimens were studied: spray paint and
adhesive-backed photographic film.
Baseline tests were conducted to evaluate the influence of signal noise on the
measurement system. Uniform translation tests were conducted to evaluate the ca-
pability of the system for measuring finite motion. the technique was used to monitor
the full-field deformation response of aluminum and wood specimens tested in4
bending and static compression. Moderate duration compression creep tests were
conducted on the wood specimens to investigate the suitability of the system for
monitoring the creep response of materials. The results obtalned from the two
speckle techniques were also compared. The results showed that for the magnifica-
tion and speckle patterns tested displacement measurements smaller than 3.29x10·‘I
inch may be unreliable due to signal noise.
The digital image processing technique was shown to be a useful laboratory tool for
measuring full-field displacements on the surface of the materials under stress. Full-
field strains can be derived from the measured displacements. The
displacement/strain measurement technique may be applied to many problems as-
sociated with understanding the mechanical behavior of wood such as stress con-
centrations, verification of analytica! models, and even for non-destructive structural
evaluation of existing buildings.
II
„ ‘ IIIII
Acknowledgements
Acknowledgements ‘ iv
I
Lastly, I wish to express my gratitude to Dr. Geza Ifju for the constant encouragement
I received from him in pursuing the research work. '
IIII
Acknowledgaments v
|
Table of Contents
1.0 INTRODUCTION ............._........................................ 1
1.1 Objectives ......................................................... 2
1.2 Limitations of Conventional Techniques ................................... 3
1.3 White-light Speckle Method ............................................ 5
1.4 Overview ....................................’...................... 6
2.0 LITERATURE REVIEW ................................................. 8
2.1 Initial Studies ...................................................... 11
2.2 Digital Correlation Technique .......................................... 13
3.0 THEORY .......................................................... 16' 3.1 Object Deformations ................................................ 16
3.2 Strain ............................................................ 20
3.3 Reconstruction of Digitally Recorded lntensity patterns ...................... 23
4.0 EXPERIMENTAL MATERIALS .......................................... 26
4.1 General .......................................................... 26
Table of Contents vi
4.2 Hardware .........................................................274.3
Software ......................................................... 29
· 4.4 Speckle Patterns ................................................... 30
4.5 Lighting Arrangement and Camera Mount ................................ 34
4.6 Specimens ........................................................ 36
4.7 Testing Machines ................................................... 36
5.0 EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSION ................. 38
5.1 Baseline Test ...................................................... 39
5.2 Uniform Translation Test ............................................. 42
5.3 Bending Test ...................................................... 45
5.3.1 Aluminum Beams.................................°.............. 48
5.3.2 Wood Beams ................................................... 51
5.4 Compression Tests ................................................. 54
5.4.1 Aluminum Block................................................. 55
5.4.2 Wood Blocks: ParaIleI~to·grain ...................................... 57
5.4.3 Wood Block: Variable grain angle ................................... 62
5.4.4 Wood Block with a Knot ........................................... 63
5.5 Creep Tests ....................................................... 70
6.0 SUMMARY, CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE RESEARCH . . 77
6.1 Summary ......................................................... 77
6.2 Conclusions ....................................................... 80
6.3 Recommendation for future work ....................................... 81
7.0 REFERENCES ...................................................... 82
Appendlx A. DESCRIPTION OF STRAIN TENSOR FORMATION .................... 87
Table of Contents vii
11
A.1 Subscripts ........................................................ 87
A.2 Differential Length .................................................. 88
Appendix B. NUMERICAL PROCEDURE FOR DEFORMATION ANALYSIS USING DIGITAL
IMAGE CORRELATION .................................................. 89
B.1 Background ....................................................... 90
B.2 Iterative Method ................................................... 94
Appendix C. DESCRIPTION OF MATROX6 SOF'I’WARE ........................... 97
Vita ................................................................ 103
111111
Table of Contents vül :1' 11
I
IIIIIIII
I I IList of Illustrations III
Figure 1. White-light speckle pattern and Young’s fringes on a wood block [15]. ....... 4
Figure 2. The Longitudinal, transverse and radial directions in a wood block. ....... 10
Figure 3. Gray—|evel representation of undeformed and deformed digital speckle images[26]. ....................................................... 17
Figure 4. Deformation of a body. ......................................... 19
Figure 5. A typical array of digitized intensity pattern. ......................... 24
Figure 6. Schematic representation of the experimental set-up. .................. 28I
Figure 7. Speckle patterns on wood specimen and their histograms ............... 34
Figure 8. The camera arrangement showing the video camera, Oriel mounting unit andthe circular tubelight. .......................................... 35
Figure 9. Results obtained from translation test at 3 magnitication levels ........... 46
Figure 10. Testing arrangement for bending test ............................... 47
Figure 11. Comparison of displacements of aluminum beam bending, span = 12 inch . . 49
Figure 12. Comparison of displacements of aluminum beam bending, span = 10 inch . . 50
Figure 13. Comparison of displacements for wood beam bending. Yellow-poplar, span =14 inch ..................................................... 52Figure 14. Comparison of displacements for wood beam bending. Southern yellow pine
beam, span = 14 inch ......................................... 53
Figure 15. Loading direction displacements ofthe aluminum block in compression .... 56
Figure 16. Transverse displacements of the aluminum block in compression ......... 58
Figure 17. Loading direction displacements of Southern pine block incompression-parallel-to-grain.............................................. 60 I
Figure 18. Transverse direction displacements of Southern pine block in compression- Iparallel-to-grain ......................................._....... 61 I
I· IList of Illustrations ix I
I
I_ I
II
Figure 19. Displacements of Southern pine block in compression-30°—to-grain ........ 64
Figure 20. Displacements of Southern pine block in compression·45°-to-grain ........ 65
Figure 21. Displacements of Southern pine block in compression-60°-to-grain ........ 66
Figure 22. Displacements of Southern pine block in compression-90°—to-grain ........ 67
Figure 23. Effect of grain angle on compliance of wood in compression in the loading di-rection ..................................................... 68
Figure 24. Effect of grain angle on compliance of wood in compression in the transversedirection .................................................... 69
Figure 25. Compression parallel·to-grain in loading direction in Southern pine block witha knot ...................................................... 71
Figure 26. Creep in a Southern pine block in the loading direction - compression parallel- _to·grain at 50% of the estimated ultimate load . ._..................... 73
Figure 27. Creep in a Southern pine block in the transverse direction · compressionparallel—to-grain at 50% of the estimated ultimate load ................. 74
Figure 28. Creep in a Southern pine block in the loading direction · compression parallel-to-grain at 75% ofthe estimated ultimate load ....................... 75
Figure 29. Creep in a Southern pine block in the transverse direction - compressionparallel-to-grain at 75% of the estimated ultimate load ................. 76
Figure B.1. Local Distortion of a Subset Image [26]. ............................ 91
Figure B.2. Deformation ofa Subimage in a Sampling Grid [26]. .................. 96
Figure B.2. Flow diagram for correlation routine [26]. . ._........................ 92
List of Illustrations x
I
List ef Tables I
Table 1. Baseline test on photographic tilm speckle and spray paint speckle ........ 41
Table 2. Baseline test with image averaging ................................. 43
. I
List of Tables . xl ;
l
1.0 INTRODUCTION
Wood is a natural material and its mechanical properties are highly variable among
species, within species, and even within an individual board. Due to its complex
internal structure wood is characterized as an anisotropic, porous, and inhomogene-
ous material. Experimental stress analysis of wood is complicated by the great vari-
ety of species, the variabillty of the material, the continually changing conditions of
supply, and the many factors affecting test results, such as moisture content and load
duration [56]. Designing safe and economical timber structures requires material
property data and accurate analysis procedures. ln contrast to metals, determining
any wood property to a satisfactory confidence level requires a large sample size and
a statistically valid sampling scheme. Recent advances in structural analysis meth- 4
ods, in concert with advances in computer technology, have produced complex ana-
lytical models for predicting the behavior of structures. The evident question is : How
accurate are these models when applied to a material as complex as wood? Exper-
imental verification is generally used to evaluate the accuracy of analytical pred-
ictions. Such verification requires measuring the material properties of each member
INTRODUCTION 1ll
· . 1l° l
for input to the analysis model, and measuring, the displacements and strains of the lstructural members for comparison to the analytioal predictions.
Many existing methods for displacement measurement can be used to compute the
average strain at a point in the member. Full-field deformation data would be useful
for verification of analytioal models. Practical methods for measuring the full field
deformation and strain in wood members are lacking. The objective of this study is
to investigate the suitability of digital image processing for full field deformation
measurement in wood members. ·
1.1 Objectives
· The objectives of this project are :
• To investigate the suitability of digital image processing for full-field deformation
measurement In wood.• To apply this technique to gain Insight into the mechanical/physical behavior of
wood under compression.
The digital image processing technique involves acquiring and mathematically proc-
essing video images of an object before deformation (called the undeformed image)
and after deformation (called the deformed image). A video camera is linked to a
computer through an image grabbing board. The images captured before deformation
and after deformation are digitized and stored on a disk. A computer program ana- jlyzes the images and computes the relative displacements of small subsets of the z
liN‘rRo¤uc‘rIoN 2 Il
1
1Z
digitized image. The displacements can be used to compute the full-field strain on the ldeformed object surface. i1.2 Limitations of Conventional Techniques :
Dial gages, strain gages, or linear variable differential transducers (LVDT) are the
ccnventional devices for measuring the strain in wood structural elements. Since
these devices measure strain over a limited gage length they may miss the critical
regions of strain that may occur elsewhere in the member. _
The electrical resistance strain gage is commonly used for measuring strain in wood',
but the errors introduced by reinforcement effects, transverse sensitivlty, thermal ef-
fects, etc., [48] reduce its suitability. Moreover, full-field strain measurement requires
placing many strain gages on the specimen surface, reducing its applicability for
full—field strain measurement. l
Holography, moire interferometry, and photoelastic coatings are optical techniques
used extensively for measurement of full-field strain, on metals, on composites, and
to a limited extent on wood [37]-[38]. The photoelastic method has been in use since
1912 [55], but it requires duplication or coating of the specimen with a photoelastic
material. The high cost of the process restrict the methods to relatively small mem-
bers and few replications.
Moiré interferometry works on the principle of interference of an undeformed refer- Eence grating and a deformed specimen grating. lt’s disadvantage is the difficulty of1
INTRODUCTIGN 3
replicating the grating on the specimen surface. Holography offers the maximum
sensitivity in strain measurement but also has limitations. For example, stability re-
quirements and localization of fringes (a type of parallax [53]).
The laser speckle method photographically records the speckle pattern which is re-
flected from the surface of the object when it is illuminated with coherent light. A
speckle pattern is created when reflected coherent light produces a random intensity
pattern. Correlation between the undeformed and deformed surface speckle patterns
gives the strains and displacements.
All the optical techniques described above are based on coherent-light optical sys-
tems. These systems are plagued with artifact noise which severely limits their ap-
plication. Also, the coherent-Iight sources are generally expensive, and the coherent
optical signal processing environment is usually stringent. For example, it requires
a dust-free room and a heavy optical bench [2]. The data processing required to re-
duce the fringe patterns to displacements, is laborious and time consuming.
1.3 White-light Speckle Method Z
ln the white-light speckle method a white-light source is used, (e.g., projector bulb
or flash bulb) instead of laser light. lt is called white-light because it consists of most
of the spectrum of visible light. White-light does not have the "noise" problems of
laser light. An important noise source in an optical signal processor is the random
defects in the input. These defects get suppressed when a broad spectrum light
lNTRoDUcTION 5
l
l
source is used [2]. Digital correlation techniques coupled with white-light speckle is l
a versatile technique and has been applied in many fields of study [13-19,21-32].
Digital image processing combined with the white—light speckle technique offers a T
unique combination of high sensitivity, excellent contrast, range, and spatial resol-
ution to study the behavior of wood at the micro- and macro-scopic levels. This
technique may also offer an experimental counterpart to the powerful computational
methods of solid mechanics, where displacement fields are the primary output. The
experimental measurements also provide data to evalu_ate the results of computa-l
tional programs. The technique can be used to verify finite element models [39].
The displacement/strain measurement technique may be applied to many problems
associated with the mechanical behavior of wood including stress concentrations,
stress intensity measurements, computation of in-situ strains in a structural member,
and even for non-destructive structural evaluation of existing buildings.
1.4 Overview
Chapter 2 contains review of literature related to digital image processing, a dis-
cussion of wood characteristics, and an introduction to displacement measurement
with the speckle technique.
Chapter 3 discusses the theoretical formulation of displacements, strains and a cor-
relation algorithm developed to compute full-field displacements from video images.
INTRODUCTION 6 }l
. l
Chapter 4 contains details of the experimental techniques, including the hardware
and software systems and coating techniques to produce random speckle patterns
on the specimens. Chapter 5 contains details of the tests conducted to verify the
digital image processing method. The experimental results are also discussed in
chapter 5. Chapter 6 contains a summary and conclusions of this work and rec-
ommendations for future research.
lNTRODUcTl0N 7
l l
2.0 LITERATURE REVIEW
To measure full-field deformation and strain in wood members, it is necessary to
understand its basic cellular structure.
8 Wood is composed principally of carbon, hydrogen, and oxygen. These chemlcal
constituents are comblned into three organic polymers: cellulose, hemicellulose, and
Iignin. Cellulose constitutes almost 50% of the weight of the wood. Cellulose conslsts
of glucose units arranged as a linear polymer. Hemicellulose is a branched polymer
of six -carbon and five-carbon sugars. Lignin is a complex and high molecular weight
polymer built upon phenylpropane units. Lignin is not a carbohydrate but phenolic in
nature.
Wood cells are formed from these three polymers. In the cell wall, long, chainlike
molecules of cellulose form into bundles and are Iaid parallel to each other. These
cellulose bundles are then surrounded with hemicellulose and form larger units
called microfibrils. Cell walls are made of mlcrofibrils Iaid down in layers. Lignin ls
deposited between microfibrils. The cell wall conslsts of inner Iayers called second-
LITERATURE REVIEW 8
ary wall enclosed in the primary wall. The secondary wall is divided into three layers
called ST, S2, and S,. The microfibrils are oriented in different directions in the three
layers.
The wood cell has a hollow center (lumen), is closed at the ends, and ls perforated
with openings called pits. Most of the cells found ln coniferous wood (softwood) are
tracheids, which comprise 90% to 95% ofthe volume ofthe wood. Tracheids are cells
about 100 times longer than their diameter. The functions of conduction and support
of the tree are carried out by the nonllving tracheids. Other type of cells found in
softwood are rays. The rays in softwood are narrow and they provide conduction in
radial direction. Rays also have effect on wood properties, for example, they restrain
dimensional change in the radial direction. The cell structure of hardwood ls very
complex. The fundamental difference between softwood and hardwood is that
hardwoodsl contain a type of cell called a vessel element [65]. .
The seasonal nature of growth of a tree is characterized by growth rings as shown in
Figure 2.
The cell wall composition and orientation in addition to cell bundling makes wood
inhomogeneous and anisotropic. There have been several models proposed to char-
· acterize the load-deformation behavior of wood but none can describe all the loading
conditions. Wood is modeled with Iongitudinal (L), radial (R), and tangential (T) axes
as shown in Figure 2. This modeling leads to 12, elastic constants (3 elastic modulii
EL, ET, and ER , three shear modulii GTR, GRL and GTL and 6 Poisson’s ratlos). Measure-
ment of these elastic parameters is difficult because of inhomogeneity and high vari-
ability in the material and is an important area of research.
LITERATURE REVIEW ‘ 9
~
2aI2.1 Initial
StudiesAlthoughthe phenomenon of speckle is most often associated with the "twinkIing"
appearance of objects illuminated with a laser, the history of speckle, or speckle like
phenomena predates the invention of the laser by well over 100 years [1]. The trou-
blesome effects of laser speckle in holography spurred study of the white-light
speckle methods and eventually brought it to the stage of practical utilization. The
monograph "Speckle Metrology" [1] gives a description of various speckle techniques
and applications.
Because of relative advantages of white light, many scientists experimented with the
white-light speckle technique. The first study in 1972, was on metrology application -
for surface roughness measurement [3]. Subsequently the theory of partially coher-
—ent, polychromatic speckle for surface roughness measurements was developedl
[41-[BL
The major advantages of a white-light system for displacement/strain measurements
are [2]: _
1. It is capable of suppressing the coherent artifact noise;
2. The white-light source is generally inexpensive;
3. The processing environment is not very stringent;
4. The white-light system is easy and economical to maintain; and
5. lt is suitable for color signal or image processing.F
LITERATURE REVIEW 11 Fl° ll
Boone and De Backer [9] applied the white-light speckle technique to strain meas-
urement. The expense of the laser technique was the motivation for investigating
white-light speckling. They performed experiments using surface paint, retro-
reflective paint, surface texture, and light transmission through transparent objects.
The basic phenomena occurring in all the experiments was Young’s fringes. Boone
and De Backer’s [9] work has direct relation to wood research, because it demon-
strated that surface texture can be used to construct Young’s fringes. In one exper-
iment [9] a reinforced concrete cantilever beam coated with speckle pattern was
subjected to a bending moment and a double exposure photograph was made of the
initial and deformed states. The resulting Young’s fringes gave excellent correlation
with theoretical results.
Burch and Forno [10] used a high sensitivity l\/loire grid technique to study deforma-l
tion in large objects. However the method could not convert the data into corre-
sponding x-, y- and z- displacements of the object.
Chiang and Asundi [11] studied the white-light speckle method using a camera lens
that was not "tuned" to a particular frequency. They observed that the uneven dis-
tribution of the beads results in a speckle pattern with a spatial frequency content
much wider than that covered by the range of bead sizes. When recorded by double
exposure, the white-light speckles behaved like laser speckles in that Young’s fringes
representing the displacement vector were generated upon Fourier transform of the
resulting specklegram.
In a later paper Burch and Forno [12] reported new applications of a high resolution
white-light speckle technique. They used this technique to analyze out-of-plane vi-
bration of a car door.
LITERATURE REVIEW 12
l
Chiang and Asundi [13]-[15] developed the theory of white light speckle method. They
also demonstrated its appllcability in different types of measurements including in-
plane displacement, 3-dimensional displacement, interior displacement, and large
deformation measurement. They also investigated ways of improving the sensitivity
of the technique.
2.2 Digital Correlation Technique
All the techniques discussed previously suffer from a basic disadvantage : they em-
ploy coherent light to Fourier transform a double exposure specklegram to obtain
Young’s fringes, and therefore, they are not truly white light speckle methods.
Recently researchers developed a digital image processing tool for measuring dis-
placements and strains from the surface of an object coated with a speckle pattern.
The first experiment was reported by Peters and Ranson [21] in 1982. They correlated
the reference and deformed speckle images (mathematically similar to area corre-
lation [20] in pattern recognition) to obtain full-field displacements of an object’s sur-
face. This method uses a computer system to cross-correlate a reference scene
made by a video camera and stored as digital image, with a digital image photo-
graphed after the specimen was deformed by an applied stress. Extensive math-
ematical techniques have been developed for correlating a reference scene with a
stored image in references [21],[34] and [35]. An important result shown by [21] was
that the measured speckle intensity pattern before and after deformation, can be used
to calculate the object’s full-field displacement vector from the reference and de-
formed configurations of a body. .
LITERATURE REVIEW 13 ElE
I lSubsequently the researchers at the University of South Carolina have improved the
technique [23]-[25],[52] and applied it to problems including rigid body mechanics
[22], displacement measurements in elastic bodies [26], fluid velocity measurements
[27], measurement of crack tip parameters [28], estimation of stress intensity factors
[29], plastic deformation observation [30], and measurement of strains in a paper
tensile specimen [31-32]. Recently they studied the effect of different interpolation
methods and other factors [33] on the accuracy of the technique.
The basic hardware utilized in their technique [26],[52] is similar to that shown in
Figure 6. lt consists of a white-light source, a video camera, a digitizer to convert the .
image into gray levels, a disc storage media to store this information, and a computer
to process the information into displacements and strains.
McNeill [52] has applied the technique to determine stress intensity factors in 2-D
cracked bodies, and used a hybrid numerical-experimental technique by combining
displacement data with a boundary element formulation to compute stresses. The 2-D
correlation technique was also extended to compute 3-D displacement using a non-
converging binocular system.
Sutton et. al. [23] have described an improved algorithm for correlation of reference
and deformed speckle images. This led to reduced computation time and the results
show that the algorithm can compute displacements larger than approximately 0.10
pixels. ln [24] they improved the algorithm by employing optimization theory [41] and
the work reported in reference [25]. The new correlation routine is 20 times fasterl
than the algorithm reported in [23].
I LITERATURE REVIEW 14
Digital correlation has also been investigated in Japan [42]-[44] for measurement of
deformation in inaccessible places such as inside a nuclear reactor. Dudderar et. al.‘ [45]-[46] in U.S. have also investigated this technique using a fiber optics white—light
source. Using a fiber optic bundle, however, requires that the minimum speckle size
must be at least three times the diameter of a single fiber in the bundle [46].
Fiber optics have been used both as a light source in harsh environments and to
transmit the speckle-field image from the remote test specimen back to an electronic
media for digitization and subsequent analysis [46].
To summarlze, surface motion studies using the speckle technique usually fall into
one of the two basic categories: methods that use coherent light to produce fringes
[1] and methods that utilize the digital correlation techniques [21,22]. The former ap-
proach has the advantage of simplicity. The disadvantage is that the few obtainable
fringes are often contamlnated with secondary speckle patterns from the coherentl
light used to process the specklegram. Also, the minimum resolvable deformation
_ is equal to the speckle size. ln contrast, the digital image processing method requires
a complex hardware system and sophisticated computer software. However, these
digital methods obviate the need for photographic work and are not limited to dis-
placements greater than the speckle size [45].
LITERATURE REVIEW 15
. _ ;
Consider an object that is illuminated by a light source. The light—intensity patterns
reflected from the undeformed and deformed object surfaces are shown in Figure 3.
Intensity patterns f(x,y)andf' (x’,y') in Figure 3 correspond to the reflected light
from the undeformed and deformed object configurations. The intensity patterns are
assumed to be in unique, one·to-one correspondence with the respective object
configurations. Therefore, using this basic assumption, one may measure the defor-
mations of small subsets of the image and thereby obtain deformations of small
subsets of the actual object surface [24].
3.1 Object Deformations °
The theory discussed in this section is presented' in detail in [40].
First consider the mathematical description of deformation. Every particle in the body
in an undeformed state has a set of coordinates. When the body deforms, every par-
‘ THEORY 16
I
inteneity Value
Defanned Image f'(x'.y')/‘ I 7/ IUndeformed Image I
" nenn-: H'W'x '
x.Area of Scanning
Figure 3. Gray-level representation of undeformed and deformed digitalspeckle images [26].
‘rHEORv 17
ticle takes a new position described by a new set of coordinates. For example, in
Figure 4, a particle P located originally at (x,y,z) is moved to P' with coordinates
(x’,y’,z') when the body moves and deforms. The displacement vector PP' has
components
x'—x, y’—y, z'—z.
lf the displacement is known for every particle in the body, a deformation can be de-
scribed by the displacement field. Let (x,y,z) refer to any particle in the original
configuration of the body and let (x', y', z') be the coordinates of that particle when
body is deformed. Then the deformation of the body is known if x', y', z' are known
functions of x, y, z ( Description of the subscripts is given in appendix A )
x,' = x,' (x, y, z) (3.1)
This is a transformation (mapping) from x, y,z to x', y', z'. In continuum mechanics .
we assume that deformation is continuous. We also assume that the transformation
is one·to-one; i.e., the functions in Eq. (3.1) are single—valued, continuous and have a
unique inverse for every point in the body. _
x, = x,(x', y’,z’) (3.2)
The displacement vector u is then defined by its components
u, = x/—x, (3.3)
lf a displacement vector is associated with every particle in the original position, we
may write ,
THEORY 18
1
z , z'
x'„y+dy',z+dz')
Q(x · ,y+dy,z+dz) u )xI·yI’zI
ds,P(¤•y•)
. y , yl ~
x , x'
Figure 4. Deformation of a body.
THEORY19
l
¤;(X- v- Z) = X/ (X, v- Z) — X; (3-4)
3.2 Strain
A rigid·body motion induces no stress. Thus, the displacements themselves are not
directly related to the stress. To relate deformation with stress we must consider the
stretching and distortion of the body. For this purpose, let us consider two neigh· ‘
boring points P and Q in the body. See Figure 4. lf they transformed to the points
P', Q' in the deformed configuration, the description of the change in distance be-
tween any two points of the body gives the deformation.
Let us consider an infinitesimal line element connecting the point P(x, y, z) to a
neighboring point Q(x —l- dx, y + dy, z + dz). The square of the length ds, is given by
dsä = dx2 + dy2 + dz2 · (3.5)
when P and Q are deformed to points P’(x’, y', z') and Q'(x’ +dx’, y' + dy', z' +
dz’),
respectively, the square of the length ds of the new element P'Q' is
dsz = dx'2+dy·2 +62*2 (3.6)
By Eq. (3.1) and (3.2) we have
I öx'„, öxm Idx m - öxi dx,, dx,„ - öX,i dx , (3.7)
Hence, on introducing the Kronecker delta, we may write .
‘n-usonv 20
ds = ÖH dx ,dx, = ÖH *5;;* dx, dxm (3.8)
The difference between the squares of the length elements may be written, after se-
veral changes in the symbols for dummy indices, as
öxlöx’ß
We define Lagrangian strain tensor
1 ö><’„„ öX'ß6H — 2 (öaß öxi öxj — ÖH) (3.10)
so that
2 2ds — dso = 26,, dx, dx, (3.11)
The strain tensor 6,, is symmetric; i.e., ·
EU =SjjAs
a consequence of Eq. (3.11) if ds*— dsä = 0 then 6,,= 0 and vice versa. But a de-
formation in which the length of every line element remains unchanged is a rigid-
body motion. Hence, the necessary and sufficient condition that a deformation of a
body be a rigid-body motion is that all components of the strain tensor 6,, be zero
throughout the body.
lf we introduce the displacement vector with components :
THEORY 21
ua =-j x'a—xa (oc=1,2,3) (3.13)
then
öx’a öua— E+Öa; (3.14)
and the strain tensor reduces to the form
_ 1 Öl!] öu, öua öuaEU- 2 öx, + öxj + öx, öxj (3°15)
We make very important assumptions here for digital image processing. First, we
assume that the out-of-plane displacement w does not affect the in-plane deforma-
tion or displacement of the characteristic intensity surfaces. This is typically true
when the object deformation is predominantly in plane; but it is not generaily true.
Secondly, we assume that the derivatives of out-of-plane displacement (i.e., )
are much less than terms like ( ) so that this effect may be excluded from Eq.
(3.15). We get three strains,
au 1 öu 2 öv 2”8""— öx+2|i(öx) +(öx)]’
_ öv 1 öu 2 _Qg_ 2j sw- (3.16)
.. J. E. Q2. £.q..<?y. aßS2"- 2[öy-*-öx+(öx öy+öx öy)i|
11-lEoRY · 22
3.3 Reconstruction of Digitally Recorded Intensity patterns
The first step in the analysis of object deformation is recording the two intensity pat-
terns by a digitizing hardware. The concept of gray-level representation of
undeformed and deformed images is shown in Figure 3. The intensity value at any '
sensor- known as a pixel (short for picture element, appendix B ) - usually ranges
from 0 to 255 (for a 8 bit digitizing board). A typlcal array of digitized intensity pattern
is shown in Figure 5. ‘
The object to be·tested is painted with a random array of black and white regions to
give the ’speckle appearance’. The advantage is each subset of the image is statis-
tically different than any other subset. Discrete values of intensity stored in the com-
puter are not the most advantageous for analysis because interpolation of these
° values is required between pixel locations for accurate subpixel displacement com-putations. Thus a surface fit through the data produces continuous function. One may
use several methods to fit such a surface including, bilinear, cubic, and polynomial
functions.
We should note here that the polynomial interpolation smooths the data much more
than the bilinear interpolation, thereby reducing the frequency content of the data set.
Therefore, the efficiency of the correlation routine is reduced, because the routine
operates better with a wide range of gray-level frequencies.
By using any of the interpolating methods, two intensity patterns (one for the
undeformed object and other for the deformed object) can be reconstructed. The
background information on the correlation and iterative procedure to obtain optimum
THEORY 23
correlation is shown in appendix B. The deformatlons which minlmize the difference
in intensity as given by Eq. (B.6) are defined as the local mapping of the actual object
surface [23].
The procedure for determining the minimum of a function of several variables is an
area of active research and in the future an improved scheme may become available
for minimization of this function.
THECJRY 25”
l
The goals of this research are to investigate the suitability of digital image processing
and computer vision for measuring deformation and strain on wood members, and to
use this method to measure the full-field deformation of two wood species stressed
in compression and bending.
4.1 General
The research work required hardware procurement, development of software, and
the study of fundamental modes of deformation. Data was gathered to evaluate the
digital image correlation method for measurement of deformation and strain in wood.
This work tests the hypothesis that there exists a subset within the body such that the
deformation in the subset may be expressed as a homogeneous deformation. lf sub-
sets are chosen sufficiently small and the various assumptions noted in the theory
section {are valid, then the method described is useful for both large and small def-
EXPERIMENTAL MATERIALS 26
ormations in wood. This hypothesis is supported by strain measurements done by
using this technique for problems in other fields [21-32,42-47].
A data acquisition system as shown in Figure 6 was used for all the experiments in
this project. The system included a video camera, a video monitor, a frame grabber
board, and an IBM PC-XT with a color monitor. The description of each piece of
hardware follows:
~4.2 Hardware ”
The video camera is a Sony CCD (Charge Couple Device) camera model XC-57. This
camera is essentially a transducer consisting of an array of 512x48O photo-sensors
which convert the light lntensity at each sensor into analog voltage that is propor-
tional to the light intensity. Each sensor location is called a pixel.
The video monitor is manufactured by Barco Industries, Belgium, model CD233 and
is used to display the image captured by the video camera. This video monitor oper-
ates at TV signals RS-170.
The frame grabber is manufactured by Matrox Inc., Canada, model PlP1024. lt has
four frame buffer memories and converts the camera signal from analog to digital
form for computer processing. This board can simultaneously accept signals from
three cameras. The frame grabber board can be programmed to continuously ac-
quire images or freeze a single image. A
EXPERIMENTAL MATERIALS 27
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*
om ccu xc-67 numzox PlP1024smzcmm I vmxo cnmm mcmzmz
« IwHnE—L¤cHT s0uRcEum PC
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Figure 6. Schematic representatlon of the experimental set-up.
i EXPERIMENTAL MATERIALS 28
· l
The Vax/VMS 780 computer at the Center for Quantitative Studies, School of Forestry
and Wildlife Resources, Virginia Polytechnic Institute, was used for correiation anal-
ysis and displacement computation.
4.3 Software
The software for image grabbing, Vax emulation, file-transfer from PC to Vax and
digital correiation were written and made available for this project by Prof. McNeiII
[62]. The image grabbing software called MATROX6 [59] synchronizes the camera to
the video terminal for image display. The program also digitizes, stores, and retrieves
images. Several useful functions are available in the MATROX6 software including,
threshold (both on incoming signals and digitized signals), gain, and look-up table.
An important statistical property of any image is its gray-level frequency histogram.
MATROX6 can compute and display this histogram. All the functions available in this
software are described in appendix C.
The Vax emulation software allows an IBM PC to emulate and communicate directly
with a Vax/Vms computer. The file transfer—program called, FASTRAN uses Vax sys-
tem routines to transfer an image from an IBM PC (stored using MATROX6) to the Vax
in binary form.
The other program used in this project was the correiation routine. This routine
reads the gray-levels of the undeformed and deformed images stored in binary format
and correlates image subsets. The coefficients for bilinear interpolation are com-
puted from the gray-values of the deformed image. Next, the cross-correiation coeffi-
EXPERIMENTAL MATERIALS 29
cient for the subset arrays of the undeformed and deformed images are computed.
The location of the undeformed image subset is based on user supplied coordinates.
The location of the deformed image subset is based on the user supplied estimated .
displacements. An area of $10 pixels around the undeformed image is searched for
a local maximum of the cross-correlation coefficient. This search continues lter-
atively and is terminated when the correlation coefficient reaches a predeflned toler-
ance. The details of the algorithm are in appendix B and a flow-chart is given in
Figure B.2 on page 96.
4.4 Speckle Patterns
One problem associated with using digital image processing to measure full-field
deformation is creating a random speckle pattern on the specimen surface. An ideal
speckle pattern will have have the following properties:
1. easy to apply on the specimen surface,
2. the speckle pattern deforms exactly with the specimen surface,
3. minimum speckle size greater than two pixels,
4. a wide gray-scale histogram,
The third attribute ensures that the detail of the speckle is not lost in digitization. The
fourth attribute ensures a large variation in gray-values from one image zone to an-
other. These two attributes strongly influence the correlation between two images.
EXPERIMENTAL MATERIALS 30
lInthis study spray paint and adhesive-backed photographic film were the two meth-
F
ods used to create random speckle patterns on the specimen surfaces. Each method
has advantages and disadvantages for experimental stress analysis. The spray paint
technique has the advantage of creating a very thin coating on the surface which does
not influence the specimen surface deformation. Also different speckle density pat-
terns can be created to suit lighting conditions and magnification levels. The advan-
tage of the adhesive-backed film is its ease of application and its reproducibility. The
disadvantage of the photographic film is that it may not deform exactly with the
specimen surface.
Flat-white and flat-black fast drying spray paint were used to produce a black-dot
foreground on a white background. It was found during initial trials that this combi-
nation produces sharp, high contrast images. The gray-level histogram of a low
contrast image is a relatively narrow cluster of gray-values with other gray·Ievels
unoccupied. The histogram of high contrast images have multiple peaks spanning
most of the gray-level spectrum. The advantage of a high contrast image is that there
is large variation of gray—values from one image zone to another resulting in rapid
correlation convergence [60].
A typical spray paint pattern photographed. from the video terminal is shown in
Figure 7a. The spray paint pattern is created on a smoothly sanded (600 grit), clean
surface. The background is spray painted f|at—white. The black-dot foreground is
produced by using a spray-can with a slightly enlarged nozzle-hole. Researchers at
the University of South Carolina found that natural air currents create an acceptable
random speckle pattern. However, producing a very light coating with this procedure
is more art than science, and can be perfected only by practice.
EXPERIMENTAL MATERIALS r 31
I
The adhesive—backed photographic film (manufactured by Photech Imaging Systems,
Hackensack, New Jersey, type Photech GPF2 adhesive backed strip film) was made
from a photograph of a particularly well formed spray paint speckle pattern. This im-
age was enlarged to produce a pattern in the required scale. This technique has been
pioneered by the Professor McNeill’s research group at the University of South
Carolina. The preliminary experiments showed that the gray-level histogram for a
photographic film speckle pattern was wider gray scale and therefore contained a
better gray-level frequency content than the gray-level histogram obtained from most
spray paint patterns. Furthermore, the photographic film technique can produce en-
larged or compressed speckle patterns to suite the requirements of most exper-
iments. For example, a test with large displacements requires a film with large
patterns. On the other hand, a test with small displacements requires a film with
small patterns.
The film is applied to a smooth (sanded to 600 grit level), clean specimen surface.
Application involves cutting the film to the required size, removing the adhesive pro-
tective strip, and applying the film to the specimen surface with even pressure. Be-
fore an experiment the film surface is cleaned with lens cleaning tissue to remove
any grease or smudge marks.
For comparison, a theoretical random speckle pattern was produced using a uniform
pseudo-random generator subroutine in International Mathematical and Statistical
Library (IMSL) [61].
The patterns and the histograms obtained from spray paint, photographic film and
from the theoretical random pattern are shown in Figure 7 a,b, and c respectively.
EXPERIMENTAL MATERIALS 32
l §l
4.5 Lighting Arrangement and Camera Mount
Lighting of the specimen surface plays an important role in producing sharp, high
contrast images, and also in producing images with a wide gray-level spectrum [63].
Uniform luminescence on the speckle pattern ensures that the gray-level character-
istics of the deformed and undeformed images are similar. This is important because
the light source does not translate with the specimen during deformation. Non-
uniform light may result in poor correlation between the undeformed and the de-
formed images because the change in light intensity is interpreted as a change in
gray-level. ln this study two types of light sources were used. First two incandescent
Photo-Ect Sylvania 500 Watts, 120V photographic bulbs were used; one was mounted
on each side of the camera (Figure 6). Second, a Sylvania 22 Watt fluorescent cir-
cular tube was arranged so that the camera pointed through the center _of the tube
as shown in Figure 8. The configuration produced more uniform light with less glare
than the incandescent bulbs.
ln most of the tests a standard photographic tripod was used for a camera mount. ·
The remaining tests used a Oriel Newport 36 series slide camera mount. This unit has
» a built-in micrometer for fine adjustment in two planes. Figure 8 shows the camera
and fluorescent light attached to this mount.1
The tests were conducted to establish accuracy (closeness to the true value),
preci-sion(closeness of a series of measurements to each other), and resolution of the
digital correlation method. The experimental procedure, results and discussion are
presented in the next chapter.
EXPERIMENTAL MATERIALS 34
l
4.6 Specimens
Aluminum was used as the isotropic material in the study. The aluminum beams were
0.6 inch x 0.75 inch x 14 inch long. The aluminum compression block was of dimen-
sions 1 inch x 1 inch x 4 inch. The bending test used two wood species: Southern
yellow pine (Plnus spp.) and Yellow-poplar (Liriodendron tulipifera). The moisture
content of the YeIIow—poplar beam was 11.9% and specific specific gravity was 0.545.
Moisture content in Southern pine beam was 10.01% and its specific gravity was
0.543. The wood beams were 1 inch x 1 inch x 16 inch long. All the compression
wood samples were machined from southern pine boards. The parallel-to-the—grain
samples for static compression and creep compression tests were machined from a
4 feet long x 2 inch nominal thickness board. The measured moisture content of the
board was 10.07% and specific gravity was 0.544. The angle-to-the graln samples
were machined from a 6 feet long x 2 inch nominal thickness board. The compression
.sample with the knot was also machined from the second board. The moisture con- Ä Ä
tent and specific gravity of this board were 10.01% and 0.593 respectively. T
4.7 Testing Machines
All the experiments involving load application used a 22,000 pound capacity Material
Test System (MTS) servo-hydraulic testing machine. This machine has many advan-
tages for experimental testing of materials. For example, the machine can operate
with either load or displacement as the controlling variable. Load control causes the
hydraulic loading ram to move at a user defined load rate. Displacement control
ExPERiMEN‘rAL MATERIALS . 36
l
causes the loading ram to move at user defined stroke rate. With either control vari-
able the hydraulic ram can be held at a desired load or displacement. This capability
can be used for creep tests (load control) or relaxation tests (displacement control).
i ExPERlMEN1'AL MATERIALS — 37
l
5.0 EXPERIMENTAL PROCEDURES, RESULTS AND —
DISCUSSION
To determine the utility of the digital image processing method for displacement
measurement on wood, 5 series of tests were conducted: baseline tests, uniform
translation tests (rigid body motion), beam bending tests, static compression tests,
and creep compression tests. The baseline and uniform translation tests were con-
ducted to verify the hardware and software systems and to establish the minimum
sensitivity of the technique. The bending and compression tests were conducted on
both aluminum and wood specimens. Aluminum was included in this study because
the image processing method has been verified by other researchers on isotropic
materials and the material properties of aluminum are accurately known. Thus, the
displacement measurements can be compared to theoretical predictions for verifica-
tion of the hardware and software systems. After establishing the accuracy, sensitiv-
ity, and resolution of the system with the baseline tests and the translation tests,
experiments were conducted on wood specimens to measure displacements. As de-
scribed in chapter 4 several methods of applying the speckle pattern to_ wood sur-
EXPERIMENTAL PROCEDURES, RESULTS AND ¤lscUssl0N 38l
I
Ifaces were studied to determine ifthe methods developed for lsotropic materials [24]
_
are satisfactory for wood specimens.
5.1 Baseline Test y
Because digital image processing consists of a complex system of hardware, soft-
ware, and experimental skills the first series of tests were conducted to determine
the basic accuracy and precision of the method. The baseline test consisted of
producing two images of a speckle pattern on a stationary, unstressed specimen and
measuring the apparent displacements from the two images. ldeally, there will be no
measured displacements. In practice, however, random electrical noise in the image ·
signal can cause the gray-value at any pixel to vary from image to image. The details
of how an image is acquired by the image grabbing board can be found in reference
[57]. The random variation in the gray-values with respect to the mean gray-value is
called the signal to noise ratio. Baseline tests were conducted with both the speckle
techniques.
Table 1 contains the results of the baseline tests for both speckle techniques. Thetable shows the computedapparent displacements (in pixels) in the horizontaI(v) and
vertlcal(u) directions, and the cross-correlation coefficients at nine image zones de-fined by the x and y pixel coordinates. The results show that inherent system noise
for the spray paint speckle coating method is a maximum of 0.074 pixels for the ver-
tical direction and 0.276 pixels for the horizontal direction. For this image magnifica-
tion these displacements correspond to 2.84x10·° inch and 1.27x10·‘ inch in thevertical and horizontal direction respectively. The maximum cross-correlation coeffi-
EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSION 39
_ i
cient (computed from 1 — r) is 0.0001, indicating an excellent match between the two
images.
The inherent system noise for the photographic film technique is a maximum of 0.06
pixels in the vertical direction and 0.71 pixels in the horizontal direction. For this
magnlfication these displacements correspond to 2.30x10·‘ inch and 3.29x10·‘ inch
respectively. The maximum cross-correlation is 0.00015 indicating an excellent
agreement between the two images.
These results indicate the level of noise to be expected in the image analysis system,
and the minimum displacement measurable at this magnlfication level with these
speckle patterns. At higher magnlfication the system resolution may be improved. For
wood testing these minimum resolvable displacements are adequate.
Image averaging is a useful technique to reduce the effect of random noise [58]. A
composite image is produced from the numerical average of the grey level at each
. pixel obtained from a sequence of images. ln general, gray—Ievel frequency content
of the composite or averaged image is more reproducible and is more stable than
that of an unaveraged single image. To examine the usefulness of image averaging
for displacement measurement a second baseline test was conducted on another
spray painted speckle pattern surface. In this experiment, two composite images
were produced and compared. The composite images were made by adding gray
values at corresponding pixels from two images acquired in sequence and dividing
the sum at each pixel by number of images. The baseline test was repeated by av-
eraging over three and four images.
EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSION 40
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EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSION 41
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Table 2 contains the results of the image averaging experiment. The table contains
the computed apparent horizontal and vertical displacements for an unaveraged im-
age, and composite images obtained from the average of two, three, and four images.
The results show that the maximum horizontal and vertical apparent displacements
for the unaveraged image are less than that of any averaged composite image. For
example, the maximum apparent displacements are 0.012 pixels, 0.034 pixels, 0.048
pixels, and 0.094 pixels for the unaveraged image, and composite images averaged
over two, three and four images, respectively. A similar trend is observed for the
apparent horizontal displacements. This finding shows that the image noise is not
additive [58] and cannot be reduced by image averaging. Furthermore, the numerical
treatment of composite images may produce truncation errors.°Therefore, unaver-
aged images were used for all subsequent tests in this study.
5.2 Uniform Translation Test
After completing the baseline tests, the noise effects, operating oharacteristics, and
fundamental precision of the measuring system were ascertained. The baseline test
represents measurement of infinitesimal motion caused by vibrations and noise in
the signal. The translation test was used to determine the accuracy obtainable from
digital image processing for finite motion.
The goal was to determine the resolution and accuracy obtainable from digital image
processing. This test was conducted by moving the specimen a known distance and
correlating the images taken before and after the translation.EXPERIMENTAL PRDCEDURES, RESULTS AND DIscUssl0N 42
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EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSION ‘ 43
l
The undeformed image was displayed on the video terminal and the coordinates and
the gray-level value of an individual point on the image were determined by the
l\/IATRÖXG software (see appendix C for details). Then the deformed image was dis-
played on the terminal and the new coordinates and gray-level value of the same in-
dividual point was recorded. The change in coordinates of the point between the two
images provides an estimate of the displacements (in pixels) and is used as a starting
point in the correlation routine. The displacements obtained from the correlation
method were then compared to the known translation to determine the accuracy.
A specimen coated with a speckle pattern was attached to a micrometer with a re-
solution of 0.001 cm. The translation test was conducted at various levels of magni-
_ fication so that the accuracy obtainable at each magnification could be determined.
The tests were conducted on wood specimens. Speckle patterns produced by bothi
the spray paint and the photographic film techniques were used on the specimens.
To obtain displacements in the horizontal and vertical directions the camera was
mounted first in the direction to measure horizontal displacements and then rotated
through 90° to measure vertical displacements. This arrangement simplified the tests
because it allowed the micrometer to remain stationary and thus minimized problems
with mounting the specimen to the micrometer. 1
Figure 9 shows the relationship between the known translation and the computeddisplacement for horizontal and vertical motion at three different magnification levels.
The figure shows excellent agreement between the actual and computed motion at
each magnification level. The maximum error is less than 3% and corresponds to thesmallest translation. Such a small displacement challenges the accuracy of themicrometer. Therefore, based on the results of the baseline test and translation test
EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSION 44
1
the digital image correlation method seems capable of computing finite displace-
ments with excellent accuracy and low noise effects.
5.3 Bending Test
Bending tests were conducted to determine the measuring capability of the digital
imaging system because bending produces large displacements and displacement is —
the primary variable measured by the system.
All the experiments were conducted on simply supported beams with a single, center
point load. Cantilever beam bending tests were not used in this study because ofthe
difficulty of producing a truly fixed support condition due to the crushing of the wood
near the support.
A test frame with adjustable roller supports was used to produce a simply supported
boundary condition. By moving the supports it was possible to change the span for
various tests. Two sets of bending tests were conducted. First two aluminum beams
with cross-sections of 0.6 inch x 0.75 inch (width x depth) were tested. Then two wood
beams with 1 inch x 1 inch cross-section were tested. Two dial gages (accurate to
0.001 inch) were mounted under the beams, one at the center of the span, and the
other at a point away from the center. Figure 10 shows the testing arrangement.
EXPERIMENTAL PRDCEDURES, RESULTS AND DISCUSSION 45
0.140 = Vertical diaplacement
Magnification — 14-2.2 pixels/cm._ 0.12 -
E A = Vertical displacemcnt0I Magnification — 671.9 pixels/cm.
_g 0.10g e = Horizontal displacementg Magnification — 503.9 pixels/cm.8 0.08E
.9‘¤c.9 0.06EÜ AEU 0.04
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Micrometer movement — cm.
Figure 9. Results obtained from translation test at 3 magnification levels
1 EXPERIMENTAL PRDCEDURES, RESULTS AND DISCUSSION 46
5.3.1 Aluminum Beams
The speckle pattern on the aluminum beams was the adhesive backed photographic
film. The first beam was tested over a span of 12 inch. One thousand pound of load
was applied in steps of approximately 200 pound each. The camera was located par-
allel to the centerline of the span and focused on the center (neutral axis) of the
beam. The beam was destructively tested (beyond the yield point) and was not used
in subsequent tests. Images were acquired at each load step and compared to the
initial undeformed image to measure displacements.
Figure 11 shows the deflections measured with a dial gage and the deflections com-
puted from digital correlation at each load level. The maximum error between the
measurements is less than 2%.
The second aluminum beam was tested over 10 inch span to a load of approximately
550 pound in steps of approximately 100 pound each. The test was repeated three
times. The camera was mounted so that images were acquired at the span centerline
in the first test, 2.5 inch away from the centerline in the second test, and 1.25 inch
away from the centerline in the final test.
Figure 12 shows the deflections measured with a dial gage and the deflection com-
puted from the digital correlation method at each load level and at the three locations.
The figure shows excellent agreement between the measurements. The maximum
error is less than 3%.
EXPERIMENTAL PRDCEDURES, RESULTS AND DISCUSSION 48
1 L1° 11
0.20w
¤ = At the centerline
.éI
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0.000.00 0.05 0.10 0.15 0.20
Di¤l goge deflections — in.
Figure 11. Comparison of displacements of aluminum beam bending, span =12 inch: Photographic film speckle method used. Deflectionsmeasured at the centerline.
EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSION 49
1 l
0. 06_
I0 = At thecenterline.5
1 0- 05 A = 2.5 inch from centerlinem$5 w = 1.25 inch from centerline (°
E 0.04 A9Q Qi
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Diol goge deflections — in.
Figure 12. Comparison of displacements of aluminum beam bending, span =10 inch: Photographic film speckle method. Deflections measuredat three locations.
EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSION 50
i
5.3.2 Wood Beams
One yellow-poplar and one Southern pine beam of 1 inch x 1 inch cross section were
tested over a 14 inch span. The speckle pattern on the yellow-poplar beam was
produced with spray paint and photographic film was used on the Southern pine
beam. Load was applied in 100 pound increments to the center of the beam and im-
ages were recorded at each load level. Each test was stopped when a load of 500
pound was reached. Each beam was tested twice and images were recorded at the
center of the span and 3.5 inch from the span centerline.
The results for the yellow- poplar beam are in Figure 13. The figure compares the
deflections measured with a dial gage to the deflections computed from the digital
correlation method at each load level and at two locations on the beam. The maxi-
mum error between measurements is less than 6% and for most load levels the error
is approximately 5% for both locations on the beam.
Figure 14 shows the results of the Southern pine beam coated with the photographic
film speckle instead of spray paint as in the yellow-poplar beam in Figure 13. The
figure shows a larger error (8% maximum, 6.2% average) between the measured and
computed deflections at the span centerline than was observed with the yellow-
poplar beam. However, at the off-centerline location the error between computed and
measured deflections was less than that of the yellow-poplar beam. For the off-center
location the average error for the Southern pine beam was 3% and maximum error
was 6.5%.
ExPERnviENTAL PRocE¤uREs, RESULTS AND mscusslou 51
1
0.150©_ Q = At the centerline
.9I 0.125
L: A = 3.5 inch from centerline ©äE8 0.100
. g ©¤. A.9 .E 0.075 1.9E ¤·’935 0.050o A
Tg, inE5 0.025 ‘
0.0000.000 0.025 0.050 0.075 ” 0.100 0.125 0.150
Diol goge deflections — in.
Figure 13. Comparison of displacements for wood beam bending. Yellow-poplar, span = 14 inch: Spray paint speckle method. Deflectionsmeasured at two locations.
EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSION 52
0.20
¤ = At the centerline
A = 3.5 inch from centerlineI_gg 0.15 ©5g A0:8E- ©E A·¤C 0.10.945 ©ELEQ A.
E co*5, 0.06A.
Q3
0.000.00 0.05 0.10 0.15 0.20
Diol goge deflections -1n.
Figure 14. Comparison of dispiacements for wood beam bending. Southern _yellow pine beam, span = 14 inch: Photographic film specklemethod used. Deflections measured at two locations.
EXPERIMENTAL PRocE¤uREs, RESULTS AND DISCUSSION 53
The results show that for wood specimens the spray paint and photographic film
speckle techniques give similar error magnitudes for displacements measured near
the point of load application. Although the error is consistently lower for the spray
paint pattern than for the film pattern at the centerline location a reverse trend is ob-
served for the off-centerline location. The aluminum beams showed no significant
difference in error magnitude between measurement locations. One reason for the
difference between the excellent performance of the film on the aluminum and in-
consistency of the film on the wood may be due to bonding characteristics of the
film’s adhesive. Apparently, the adhesive makes a better bond on the aluminum than
on the wood surface. Consequently, the film deformation lags behind the wood de-
formation. Also, the bond quality may not have been consistent at both locations
leading to different displacement error magnitudes at the two locations on the
Southern plne beam.
5.4 Compression Tests
After investigating the suitability of the digital correlation technique for measuring
deformation in beams, the method was applied to study its suitability for computing
compression deformations. A sub-objective was to compare the response of the two
types of speckle patterns on aluminum and wood specimens.
EXPERIMENTAL PROCEDURES, REsuLTs AND DISCUSSION 54
I
’ . · I
5.4.1 Aluminum Block
The aluminum compression specimen was 1 inch x 1 inch x 4 inch long. First, the
experiment was conducted with the photographic film speckle pattern. Then, the film
was removed and the specimen was coated with a spray painted pattern. Images
were recorded at t.he same location on the specimen for both tests. ln each test the
center of the image was 1 inch below the top of the specimen. Load was applied
in 2000 pound increments and images and strain were recorded at each load level.
Each test was stopped at 8000 pound.
Figure 15 compares the displacements in the load direction on the aluminum block
measured with both speckle techniques. —The displacements measured with the
spray paint method are consistently greater than those measured with the film pat-
tern. This result indicates thatideformation of the film pattern lags behind the defor- ~
mation of the aluminum block, since we assume apriori that the spray paint pattern
deforms perfectly with the block. However, the magnitude of the difference between
the two speckle methods is small and either method can be used to compute dis-
placements in the load direction.
Figure 16 compares the displacements in the transverse direction (due to Poisson’s
effect) measured with both speckle techniques. For comparison, at 8000 pound of
load the theoretical transverse displacement is 2.47x10“4 inch. The displacements
measured with the spray paint pattern was 5.62x10“4 inch and the displacement
measured with the film pattern was 19.72x10’4 inch. This indicates that for these
speckle patterns and this magnification the digital correlation method does not accu-
rately measure transverse deformations. One reason for the error may be due to
EXPERIMENTAL PROcEDUREs, RESULTS AND DiscUssl0N 55
9000
8000 A with photographic film A O
7000 0 with spray paint
6000 AouiEI 5000 ·
1:¤ .3 4000 A Q
3000
2000 Ao
· 1000
00 5 10 15 20 25 30 35 40
deflection — 1e—O4 inch
Figure 15. Loading direction displacements of the aluminum block in com-pression: Images were recorded at 1{E- inch from the top edgeof the specimen using both the speckle techniques.
EXPERIMENTAL PRocEDuREs, RESULTS AND DISCUSSION 56
lnoise effects because the magnitude of the transverse deflections is on the orderofone
pixel. The baseline tests showed that for this the system noise effect may be on .
the order of i 0.5 pixels. Therefore, when measuring very small displacements errors
are expected in the results. Another reason for the large error may be due to misa-
Iignment of the specimen plane with the image sensing plane in the camera. A slight
nonparallel arrangement would produce a parallax effect, and consequently, with very
small transverse displacements a large apparent displacement. The effect is not sig-
nificant in the load direction because of the relatively large magnitude of defor-
mations (3 to 4 pixels). Another reason for large difference between the theoretical
displacements and the digital correlation displacements is the edge effect (Saint
Venant’s effect) has not been accounted for when computing the theoretical dis-
placements. U
5.4.2 Wood Blocks: Parallel-to-grain
To compare the response of the two types of speckle patterns two straight grain
Southern yellow pine (Pinus Spp.) compression samples (1 inch x 1 inch x 4 inch
long ) were machined from one board. The first series of tests used the photographic
film speckle pattern and the second series used spray paint speckle pattern. For the
first test series specimen A was tested non-destructively, paralIel—to-grain with the
film speckle pattern located at 1.5 inch from the top and the bottom edges of the
sample. Specimen B was tested non-destructively, parallel—to-grain with the film
speckle pattern located at 1.5 inch from the top and bottom edges of the sample. After
completing the first test series the speckle film was removed from each specimen,
the sample surfaces were sanded, cleaned, and coated with a spray painted speckle
EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSION 57
‘ I9000
8000 A 0
7000
6000 A 0uiEI 5000
‘¤03 4000 A O Awith photogrophic film
$000 O with sproy point
2000 A 0
1000
0 5 10 15 20 25
deflection — 1e—O4 inch
Figure 16. Transverse displacements of the aluminum block incompression: Images were recorded at 1% inch from the topedge of the specimen using both the speckle techniques.
EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSION 58
l
pattern. The compression tests were repeated on the same samples and images
were recorded at the same locations on each specimen as in the first test series.
For both test series images were recorded at the following load levels: 300, 600, 1000,
1500, 2000, and 2500 pound. All the tests were stopped below the proportional limit
to avold damaglng the specimens. This test series produced 48 images: 2 images,
6 load levels, 2 speckle techniques, 2 locations, per specimen.
Figure 17 compares the deformations measured in the load direction with both
speckle methods at two locations on the specimen. The two speckle methods
produced similar deformation measurements at the top measurement location. How-
ever, at the bottom measurement location the dlsplacement of the film speckle pat-
terns consistently lagged behind those of the spray paint pattern. This indicates that
the photographic film adhesive may not have bonded properly to the wood surface.
Figure 18 shows the transverse deformations measured with both the speckle meth-
ods, at the top location on the specimen. Both methods produced similar dlsplace-
ments. For comparison, the theoretical transverse dlsplacement at 2200 pound is
6.32x10"'4 inch. The measured deformations by both speckle methods are an order
of magnitude greater than the theoretical value. Since the measurement location is
near the load point the theoretically computed dlsplacement may be erroneous due
to Iocalized stresses and Saint Venant’s effect. Therefore, no conclusion can be
drawn regarding the accuracy of the transverse deformation measurements. —
EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSION 59
I
2500
1.5 inch from topAwith photographic film ¢* Oo with spray paint20001.5 inch from bottom Aa with photographic film0 with spray paint 4 O
ß 1500I A
E er ¤O.1 1000A .
Q O
500A‘ Ü
00 10 20 50 40 50
deflection —- 1e—O4 inch
Figure 17. Loading direction displacements of Southern pine block incompression-parallel-to-grain: Images recorded at 1.5 inch fromthe top and bottom edges of the specimen using both the speckletechniques.
EXPERIMENTAL PRDCEDURES, RESULTS AND DISCUSSION 60
. I
2500
4- 0 O
2000A
4- <> OU; 1.5 inch from topQ 1 500 Awith photographic film
I A o with spray paint
* O O 1.5 inch from bottom.1 owith spray paint
1 000A
4 with photographic film
4- O
500A
*0
0 10 20 30 40 50
deflection — 1e—O4 inch
Figure 18. Transverse direction displacements of Southern pine block incompression-paraIlel-to-grain: Images recorded at 1.5 inch from ~the top and bottom edges of the specimen using both the speckletechniques.
EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSION 61
5.4.3 Wood Block: Variable grain angle
This test series was conducted to study the behavior of Southern pine (Pinus Spp.)
loaded in compression at various angles to grain, and the suitability of the digital
correlation method to measure displacements using both speckle techniques. Twotangentially edge-matched specimens for each of the following targeted grain angles
were machined from one board: 30°, 45°, 60°, 90° The exact grain angle of each sam-
ple was measured and recorded after machining. One sample of each grain angle
was coated with the film speckle pattern and its matched sample was coated with the
spray painted speckle pattern. images were recorded on the radial surface 1.5 inch
from the top of each sample at the load levels shown in Figure 19 to Figure 22.
Figure 19 to Figure 22 show the load—displacement relationship measured by both
speckle methods for the 30°,45°, 60°, and 90° to—the-grain specimens respectively.
‘Each figure shows the response in both the loading direction and the transverse di-
rection. The figures show that the compliance in the loading direction increases with
increasing grain angle. The figures also show that the compliance in the transverse
direction decreases with increasing grain angle.
For the 30° to the grain specimens (Figure 19) the displacements from the speckle
method were larger than those from the spray paint method for both the loading di-
rection and the transverse direction. The difference in the response between the two
speckle methods may not be solely due to the methods themselves but may be due
to the variation in the wood material since matched specimens were used for these
tests. A better experimental approach would utilize two cameras to simultaneously
record images from both speckle methods on a specimen.
EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSION 62
Sl
For the 45° to the grain specimens (Figure 20) the displacements from the speckle
method were larger than those from the spray paint method for both the loading di-
rection and the transverse direction. A similar trend was observed for the 60°(Figure 21 ) and 90° (Figure 22) specimens.
Figure 23 shows the effect of grain angle on the load-displacement relationship in the
loading direction and Figure 24 shows the effect in the transverse direction meas-
ured by the spray paint speckle method.”
5.4.4 Wood Block with a Knot
Knots are natural growth characteristics that form when branches grow from the trunk
of a tree. A Southern pine specimen (1 inch x 1 inch x 4_ inch) with a tight knot (7%-
inch diameter) on the tangential plane was tested to determine if the digital corre-
lation method was suitable for measuring deformations at discontinuities in the ma-
terial. The specimen was coated with a spray painted speckle pattern and tested in
compression paraIlel—to-the—grain. Images were recorded at load steps of 200, 500,
1000, 1500 and 2000 pound.
Figure 25 shows the displacements in loading direction computed at four locations
around the knot at each load level. The figure illustrates that the stiffness ofthe clear
[
EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSION 63
1
10003 750 O A
A1; 600 °¤ O AO 259 A n 6 .61—* ¤ A 6 $,,3,5 ,„L1'1‘l
00 25 50 75 100125
defl. x1e—O4 inch
3
1000‘ 750 O Ao A1; 600
¤ O A¤ A 16 6 .6*1-1 ”° 6 A 6 §„?„$,„L1'„?60
- 0 25 50 75defl. x1 e—O4 inch
b
Figure 19. Displacements of Southern pine block incompression—30°-to-grain: Images recorded at 1.5 inch from thetop edge of the specimen using both the speckle techniques -a)Loading direction b)Transverse direction
sxpznimaum. pnocsoumzs, Rssuus Ann mscussuou 64
I
750ui Q9
I 500 Q;ig OA-! 250 (A Aphoto. film
Osproy point
00 50 100 150 200
defi. x1e—O4 inch
a
750ui O A9I 500 o A"S o A
-3 250 A hoto filO A P „ FTIOsproy paint
00 25 50 75 100
defl. x1e—O4 inch
b
Figure 20. Displacements of Southern pine block incompression-45°-to-grain: Images recorded at 1.5 inch from thetop edge of the specimen using both the speckie techniques -a)Loading direction b)Transverse direction
EXPERIMENTAL PRocEDUREs, RESULTS AND DISCUSSION 65
625. 500 O A— 575TL 0 A
8 250 Aphoto.fiIm.11 25 O A O spray paint
00 50 100 150 200 .
def!. x1e—O4 inch
8
500 , AuiL f
575 A6 ”° 1 ht 1p o 0. ifm3 125 6 A
O spray paint0
0 25 50 75def!. x1e—O4 inch
b
Figure 21. Displacements of Southern pine block incompression—60°-to-grain: Images recorded at 1.5 Inch from thetop edge of the specimen using both the speckle techniques -a)LoadIng direction b)Transverse direction
ExPER11v1EnTA1. PROCEDURES, REsu1.‘rs AND DISCUSSION 66
1. 1
300U; Aphoto. film '
E AI ZÜÜ osproy point
OB A I3 100 AI <>
00 50 100 150 200
def!. x1e—O4 inch
a
300U; A photo. film£ A
I 200 o aproypoint
E ° A100 O.1 O A
00 5 10 15
defl. x1e—O4 inch‘
Figure 22. Displacements of Southern pine block incompression-90°-to-grain: Images recorded at 1.5 inch from the‘ top edge of the specimen using both the speckle techniques -a)Loading direction b)Transverse direction
EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSION 67
I
1000
A6ta1'
600 66444** Ao¤xs5° 0
600 «¤tsa¤° AI
E <> <>3 400 A ·0 0
200 A O0 ” *
**
00 25 50 75 100 125 150 175 200
deflection — 1e—O4 inch
Figure 23. Effect of grain angle on compliance of wood in compression in theloading direction: Results shown for images recorded at 1.5 inchfrom the top edge of the specimen using spray paint speckle tech-nique.
axpsmmsnrm Pnocsounss, Rssuurs Ann oiscussnon 68
1000
A ¤t31·
600 6 ¤t44• Ao ¤ts6° O
(ig 600 6 (1t9Ü• A1
E <> <>3 400 A
o
200 OA2 A-
_ *0051015 20 25 30 35 40 45 50
deflection - 16-04 inch
Figure 24. Effect of grain angle on compiiance of wood in compression in thetransverse direction: Results shown for images recorded at 1.5inch from the top edge of the specimen using spray paint speckletechnique.
Ann mscussuou 69
l
wood is higher than that of the knot wood. Similar results are presented in reference
[64]. These results also illustrate the versatility ofthe technique in measuring full-field
deformation at the discontinuities.
5.5 Creep Tests
Creep is a phenomena of deformation with time under a constant load. Wood is a
rheological material and exhibits creep behavior particularly when exposed to cycllc
humidity conditions. At room temperatures aluminum does not exhibit marked creep
behavior. The objective of this test series was to determine if the two speckle tech- ·
niques are suitable for measuring the deformation over time on wood compression
samples.
Creep tests were conducted in compression parallel-to-grain on two pairs of matched
Southern pine specimens. Each pair of end·matched specimens were machined from
one 1 inch x 1 inch x 8 inch long board. One speclmen of each matched pair was
tested with the film speckle pattern and the other matched speclmen was tested with
the spray paint speckle pattern.
A constant load of 4000 pound ( approximately 50% of the ultimate load) was applied
to the first pair of matched specimens and images were recorded 1.5 inch from the
top ofthe specimens at the following times: O min., 0.5 min., 1 min., 2.5 min., 5 min.,
10 min., 15 min., 20 min., 30 min. and 40 min. A constant load of 6000 pound (ap-
proximately 75% of the ultimate strength) was applied to the second pair of matched
ExPERlMEn1‘Al. PRocEDuREs, REsuL.Ts AND DISCUSSION 70
· l
2000A center of knot0 inner boundary 0* *40 outer boundary
1 ÖÜÜ w clear wood
_ 6* Qß 1200 _I .
‘¤¤O.1 800 O D
400Q
00 5 10 15 20 25 30
deflection — 1e—O4 inch
Figure 25. Compression parallel-to-grain in loading direction in Southern pineblock with a knot: 5/16 inch diameter tight-knot located on thetangential surface at 2 inch from the top edge.
EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSION 71
I I
specimens and images were recorded 1.5 inch from the top of the specimen at the
same time steps as the other load case.
Figure 26 to Figure 28 show the relative creep deformation versus time, measured
by both speckle methods for the specimens tested at 50% and 75% of the estimated
ultimate load respectively.
The response in the loading direction and the transverse direction are shown in Fig-
ure 26 and Figure 27 respectively for 50% load condition. The relative deflection for
both the loading direction and the transverse direction are remarkably similar. The
relative deflection measured by both speckle methods are also in close agreement
to each other. The film method measured consistently greater deflections in the
loading direction than did the spray paint speckle method, but the difference may be
due to the natural variation of wood material rather than the methods themselves.
For the specimens tested at 75% of the ultimate load Figure 28 and Figure 29 show
the response for the loading direction and transverse direction respectively. The
relative deflection for the loading direction and the transverse direction are of similar
order. The creep observed in the specimen coated with the spray paint speckle pat-
tern was twice that in the specimen coated with the photographic film pattern. The
relative deflections computed from digital correlation also show the similar trend for
the two speckle methods.
EXPERIMENTAL PROCEDURES, REsULTs AND Discussiou 72
1
109
AA
g 8nvi 6 OE 6 A O
4. A
O A with photographie filmO 0 with sproy point
G).2 O§ 2 Azu*— O1
° .0
0 5 10 15 20 25 30 35 40 45 50
Time — min.
Figure 26. Creep in a Southern pine block in the loading direction - com-pression parallel-to-grain at 50% of the estimated ultimate load:images recorded at 1.5 inch from the top edge ofthe specimen usingboth the speckle techniques.
EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSION 73
_ 2
8A with photographic film
7 A_: o with spray paintE 6 og 6 A o
· é9 6 6[ A
E 4 6 ¤-4-JU2 o0)
G.) O.2§ 2gg Ao
1 O
0° 0 5 10 15 20 25 30 35 40 45 50
Time — min.
Figure 27. Creep in a Southern pine block in the transverse direction - com-pression parallel-to-grain at 50% of the estimated ultimate load:Images recorded at 1.5 inch from the top edge ofthe specimen usingboth the speckle techniques.
Expsmmaum. mocsounss, Rssums Am: mscussicm 74
· I
50O
L 25 °0EE O(L 20T" O
| A15 o
02 A“<$ A'Ugp io O A photographie film~ .2 A“6 .Q A o spray paintS.
5 O A . ’q\A
00 5 10 15 20 25 30 55 40 45 50
Time — min.
Figure 28. Creep in a Southern pine block in the loading direction - com- 'pression parallel-to-grain at 75% of the estimated ultimate load:Images recorded at 1.5 inch from the top edge of the specimen usingboth the speckle techniques.
EXPERIMENTAL PROCEDURES, RESULTS AND DISCUSSION 75
l5 0
0.CE 4 O<r?Q) O
n 3 _E ¤*6 A A„ij A.g 2 0 A A0).2*6 A A photogrcphic filmEA. O
1 A o aprcy point
gl
A
00 5 10 15 20 25 30 35 40 45 50
Time — min.
Figure 29. Creep in a Southern pine block in the transverse direction - com-pression parallel-to-grain at 75% of the estimated ultimate load:Images recorded at 1.5 inch from the top edge ofthe specimen usingboth the speckle techniques.
[
Exi>ERi~iEmAi. Pnocsoumss, Rssums Ann oiscussiou 76
l
6.0 SUMMARY, CONCLUSIONS AND
6.1 Summary
A digital image processing system was used to measure the full—fieId deformation on
aluminum and wood specimens loaded in compression and bending. The measure-
ment technique consists of creating a random speckle pattern on the specimen sur-
face, recording images before deformation and after deformation, and computing the
relative displacements of small image subsets. Two methods for producing speckle
patterns on the specimens were studied: spray paint and adhesive—backed photo-
graphic film.
To evaluate the influence of signal noise on the measurement system baseline tests
were conducted by computing the apparent displacements of two images recorded
from the same location on an unstressed Specimen. The results showed that for the
SUMMARY, coNcLUs¤oNS AND REcoMMEN¤ATloNS FOR FUTURE RESEARCH 77
}magnification and speckle patterns tested displacement measurements smaller than
3.29x10'4 inch (8.35x10'3 cm.) may be unreliable due to signal noise.
Uniform translation tests were conducted to evaluate the capability of the system for
measuring finite motion. The system was verlfied with a minimum translation of
5.9x10"3 inch ( 0.015 cm.). Finer resolution may be achieved with higher magnifica-
tion and micrometers with higher accuracy.
Bending tests were conducted on aluminum and wood specimens. Displacements
obtained from the digital method were compared with deflections measured with a
dial gage. Excellent results were obtained for the aluminum beams coated with pho-
tographic film speckle patterns (less than 3% error). However, the results for the
wood specimens had a higher magnitude of error. The deflections measured by the
spray paint method were approximately 6% higher than the dial gage deflections. The
deflections measured by photographic film speckle method were 8% greater than the
deflections measured with the dial gages.
To determine if the speckle method influences the results aluminum and wood com-
pression were tested with both speckle methods. On aluminum, the displacements
measured by the photographic film method were consistently less than those meas-
ured by the spray paint method for both load the direction (12% maximum difference)
and the transverse direction (70% maximum difference).
On wood, the displacements measured in the loading direction by the photographic
speckle method were approximately 15% greater than those measured by the spray
paint speckle method. ln the transverse direction the displacements measure by theSUMMARV, CoNCl.USloNS AND RECDMMENDATIDNS FOR FUTURE RESEARCH 78
i
photographic film speckle method were approximately 70% lower than those meas-
ured with the spray paint speckle method.
Compression samples loaded at four grain angles were also tested with both speckle
methods. The results show good agreement between displacement measurement by
both speckle methods for the displacements in the loading direction. For the trans-
verse to-load direction large differences _existed between the displacements meas-
ured by the two speckle methods. However, since the compression tests were
conducted on matched specimens, the material property variation from specimen to
specimen may contribute to the error. The edge effects will also contribute to the er-
ror.
A southern pine sample with a knot was tested with the spray paint speckle tech-
nique. The results show that the clear wood is stiffer than the knot wood. These re-
sults agree with the results in the literature [64].
l\/latched wood samples were tested for creep in compression parallel-to—grain to
evaluate the system’s suitability for long-term measurements. The results indicate
that both speckle methods produced similar results for both the load direction and the
transverse direction.
Since the spray paint speckle method was assumed apriori to produce reliable dis-
placements, the computed displacements from the compression tests were not veri-
fied against displacements from an independent test. This is a limitation of this work.
SUMMARY, CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE RESEARCH 79
l
6.2 Conclusions
This work supports following conclusions:
1. The digital correlation method is capable of accurately measuring rigid body dis-
placements as shown by the translation and bending tests.
2. The digital correlation method did not accurately measure the transverse dis-
placements of compression samples; probably due to several reasons including
misalignment effects, edge effects, and the small magnitudes of the displace-
ments.
3. The digital correlation method is capable of measuring displacements in the
loading direction from static and creep compression tests.
4. On wood, the adhesive film speckle method produces inconsistent results in
bending, static compression and creep compression. The fiIm’s response gener- Lally lags behind the specimen surface response; probably due to an incompat-
ibility between the wood surface and the adhesive. But, on the aluminum
compression samples the displacements measured with the film lagged behind ·
those measured by the spray paint speckle method. Therefore, the adhesive
backed film system may not perform adequately in compression even on alumi-
num specimens.
5. The film and the spray paint speckle pattern on same the specimens produced
different results. Therefore the film system needs to be modified to improve its
performance.·
l
I
SUMMARY, coNci.UsloNs AND RECOMMENDATIONS FOR FUTURE RESEARCH 80
I· I
6.3 Recommendation for future work
FulI—field strains were not computed in this study. A program to compute full-field
strain would help in understanding the behavior of wood. The full-field strain meas-
urement can be used to study the discontinuities arising because of natural variation
in wood material, for example, the discontinuity between the early—wood and late-
wood zones. Computation of full-field displacements on wood specimens in tension
and shear will verify the image processing system for different loading conditions and
help in understanding the response of the two speckle methods.
A method of superimposing the wood image on the full—field displacements computed
from the digital correlation method would be useful for studying the effect of anatomy
on mechanical behavior of wood.
A study of different speckling techniques to produce random patterns on the speci-
men surface is also recommended. For example, photocopy powder when hot
pressed can create a semi·permanent speckle pattern. Other combinations of film
material and adhesive may also produce speckle patterns with better response on
wood.
Another area of study recommended here is the development of a full-field displace-
ment computation system which does not rely on a random pattern. This system will
widen the scope of digital image processing and allow the method to be used on
structures where speckle patterns cannot be applied. Research is already being car-
ried out to compute displacements and strains for television images [51] and this
principle can be used to develop the recommended system.
SUMMARY, CDNCLUSIDNS AND RECDMMENDATIDNS FOR FUTURE RESEARCH 81
i•
[1] Erf, Robert K. (ed.) "Speckle MetroIogy" Academic Press, New York, 1978,pp.331
[2] Yu, Francis T. S. (ed.) "White Light Optical Signal Processing " John Wiley &Sons, Inc., New York, 1985, pp.116
[3] Sprague, R. A. "Surface roughness measurement using white light speckle,"Applied Optics vol.11, no.12, Dec. 1972, pp. 2811-2814
[4] Parry, G. "Some Effects of Surface Roughness on the Appearance of Speckle ·° in Polychromatic Light," Optical Communications, vol.12, no.1, sept.1974, pp.75-77
[5] Parry, G. "The Scattering of Polychromatic Light from Rough Surfaces : FirstOrder Statistics," Optical Quantum Electron., vol.7, no. 4, 1975, pp. 311-319
[6] Hariharan, P. "Speck|e Patterns: A Historical Retrospect," Optica Acta, vol.19,no. 8, 1972, pp. 791-799
[7] McKechnie, T. S., "lmage-Plane Speckle in Partially Coherent Il|umination,"Optical Quantum Electron., vol.8, no.7, 1976, pp. 61-
[8] Fujii, H., and Asakura, T., "StatisticaI Properties of Image Speckle Patterns inPartially Coherent Light," Nouv. Rev. Opt., vo|.6, no.3, 1975, pp. 5-19
[9] Boone, P. NI., and De Backer, L. C., "Speckle Methods using Photography andReconstruction in lncoherent Light," Optik, vol.44, no.3, 1976, pp. 343-355
[10] Burch, J. NI., and Forno, C., "A High Sensitivity Moiré Grid Technique forStudying Deformation in Large Objects," Opt. Engg., vo|.14, no.2, 1975, pp.178-185
[11] Chiang F. P., and Asundi A., "White Light Speckle Method of Experimental StrainAnalysis," App/. Opt., vol.18, no.4, 1979, pp. 409-411
[12] Burch, J. NI., and Forno, C., "High Resolution Moire Photography," Opt. Engg.,vol.21, no.4, Jul-Aug 1982, pp. 602-614
REFERENCES 82
III
[13] Chiang, F. P., and Asundi, A., "Theory and Applications of White Light SpeckleMethod for Strain Analysis," Opt. Engg., vol.21, no.4, Jul-Aug 1982, pp. 670-680
[14] Asundi, A., and Chiang, F.P. "Separation of 3-D Displacement Components inthe White Light Speckle Method," Optics and Laser Tech., vol 14, 1982 pp. 11-45
[15] Asundi A., "White Light Speckle Method for Strain AnaIysis," Ph.D. Dissertationin Mech. Eng. State University of New York, Stonybrook, Dec., 1981, 145 pp.
[16] Krishna Mohan, N., Joenathan, C., Sharma, D. K., and Sirohi, R. S. "Applicationsof Multi-Aperture White Light Speckle Photography," Optik, vol.79, no.1, Apr.1987, PD. 7-11
[17] Burch, J. M., and Forno, C. "Optical Methods for Measuring Strain," Stressesand Strains in Textile Structures, Shirley Inst., S10c, 1973, pp.6
[18] Benckert, L., Jonsson, M., and Molin, N-E “Measuring True In-Plane Displace-ment of a Surface by Stereoscopic White Light Speckle Photography," Opt.Engg., vol.26, no.2, Feb. 1987, pp. 167-169
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[24] Sutton, M. A., Cheng, Mingqi, Peters, W. H., Chao, Y. J., and McNeilI, S. R."Application of an Optimized Digital Correlation Method to Planar deformationAnaIysis," Image & Vision Computing, vol.4, no.3, Aug. 1986, pp. 143-150
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[28] Peters, W. H., Ranson, W. F., Kalthoff, J. F., and Winkler, S. R. "A Study of Dy-namic Near-Crack-Tip Parameters by Digital Image Analysis," Journal DePhysique, Colloque C5, suppl, au n.8, Tome 46, aut 1985, pp. 631-638
[29] McNeiII, S. R., Peters, W. H., and Sutton, M. A. "Estimation of Stress IntensityFactor by Digital Image Correlation," Engineering Fracture Mechanics, vol.28,no.1, 1987, pp. 101-112
[30] Lee, C., Peters, W. H., Chao, Y. J., and Sutton, M. A. "lmproved Digital ImageProcessing Technique to lnvestigate Plastic Zone Formation in Steel," Imageand Vision Computing, vol.4, no.4, Nov. 1986, pp. 203~207
[31] Sutton, M. A., and Chao, Yuh J. "Measurement of Strains in a Paper TensileSpecimen using Computer Vision and Digital Image Correlation, Part 1: Dataacquisition and Image Analysis System," Tappi Journal, vol.71, no.3, Mar. 1988,pp. 173-175
[32] Chao, Yuh J., and Sutton, NI. A. "Measurement of Strains in a Paper TensileSpecimen using Computer Vision and Digital Image Correlation, Part 2: Tensilespecimen test," Tappi Journal, vol.71, no.4, Apr. 1988, pp. 153-156
[33] Sutton, M.A., McNeill, S.R., Peters, W.H., Jang, J., Balai, M., and Chao, Y.J."Error Estimate for Sub-Pixel Measurement of Object Deformations fromQuantized Image Intensity Data," Society for Photo Instrumentation Engineers,voI.814, Photomechanics and Speckle Metrology, 1987 pp. 774-784
[34] Bailey, H.H., Blackwell, F.W., Lowery, C.L. and Ratkovic J.A. "lmage Corre-lation: Part l Simulation and Analysis," Rand report R—2057l1-PR, Nov. 1976
[35] Wesley, H.W. "lmage Correlation: Part ll Theoretical Basis," Rand reportR-2057/2-PR, Nov. 1976
[36] Hoadley, R.B., "Strain Analysis in Wood by Means of Moiré Patterns," ForestProduct Journal, vol.16, no.5, May 1968, pp. 48-50
[37] Wilkinson, T.L., and Rowlands, R.E. · "Analysis of Mechanical Joints in Wood,"Experimental Mechanics, vol.21, no.11, Nov. 1981, pp. 408-414
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[40] Fung, Y.C. "A First Course in Continuum Mechanics" Prentice—Hall, lnc.,Englewood Cliffs, N.J., 1977, 340 pp.
[41] Everitt, B.S. "lntroduction to Optimization Methods and their Applications inStatistics" Chapman and Hall, London, New York, 1987, 88 pp.
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ß REFERENCES 86
_ 2i
Appendix A. DESCRIPTION OF STRAIN TENSOR
FORMATION
A.1 Subscripts
Ali the subscripts used in section 3 (i,j, /, m, oc etc.) vary from 1 to 3. The sub-
scripts in 1,2,3 directions stand for x,y,z or x', y', z' directions respectively. That
TTIQHUS,
ua (oc = 1, 2, 3) stands for u, v, w respectively
Appandax A. osscmpnou or STRAIN ranson •=oRiviA7¤o~ 87
iI
‘ ·
IA.2 Differential Length
Hence Eq. (3.7) using Eq. (3.4) can be expanded in two dimension as:
, _ öx’ 0x'dx - ——öX dx-)-Ty dy, dx’=
lj—dx—I-dx—I-ädyöx 0ydy’=dx
öy, - Q Qdy —
öxdx—I—dy—I—
öy dy
Appendix A. DESCRIPTION OF STRAIN TENSOR FORMATION 88
l
Appendix B. NUMERICAL PROCEDURE FOR
DEFORMATION ANALYSIS USING DIGITAL
IMAGE CORRELATION
The digitization of a video image gives an array of numbers, each number re-
presenting the average light intensity over small areas of the image sensing
plane. The numbers representing the average light intensity are referred to as
gray levels and the areas their average value are taken over referred to as pixel.
Pixels are typically arranged in a grid like pattern [52].
Description given in this appendix is presented in detail in [21,26].
Appendix B. NUMERICAL PROCEDURE FOR DEFORMATION ANALYSIS USING DIGITAL IMAGEGORRELATION 89
II
B.1 Background
Consider a small subset of the undeformed object centered at P before defor-
mation, as shown in Figure B.1. After deformation, the subset center moves to
a new point P' and the subset deforms. lf we use the deformation assumption
made earlier, we can write the intensity values at positions P and P' as:
I f(P) = f(><„y) (B 1)F (P') = Fix + u(P), y + v(P)] ‘ °
Similarly, for a point Q at position (x + dx, y aj dy) on the undeformed object,
and O' being corresponding point on the deformed object, we can write the in-
tensity values at positions Q and Q' by:
f(O) = f(x + d><„ y + dy) (B 2)_ f’(Q’) = f'[x + dx —I— u(Q), y -I— dy + v(Q)] '
Finally, if we assume that the intensity pattern deforms but does not alter its Io-
cal value due to deformation we have:
f(P) = f’[x + u(P), y + v(P)] B 3f(Q) = f'[x + dx —+- u(Q), y + dy -I— v(Q)] ( ' )
Appendix B. NUMERICAL PRDGEDURE FDR DEFORMATION ANALvsIs USING DIGITAL IMAGEcoRRELATIoN so
I
II
fix.!)f'(¤'.y')
Deformed Subimage
t'<P'>Undeformed Image.4 (Alf
1—lI ’ "”
x , x' Area of Scanning
Figure B.1. Local Distortion of a Subset Image [26].
Figure B.2 shows a small subset on the undeformed object surface centered at
P, together with its deformed shape centered at P'. lf we assume that the sub-
set is sufficiently small that straight lines remain straight after deformation, then
we can use Eqs. (A.1) to describe the position of point Q' as:
Appendax B. NUMERICAL PRocE¤uRE FOR DEFORMATION AI~IALYsIs USING DIGITAL IMAGECORRELATION 91
I
I
Uudeformed aubimage Area of Iaeanuing +V0 YP fe Tr
I II !•!'I Ar , „ AY"
· I I II
-III--Il--III--.-IIIIIIIIIIIIIIIIIIII--IIIIIIIIIIIIlllllllllllllllll_ ___ IIIIIIIIIIIIIIIII’Ax III-EQIIIIIIIIIIIzi ‘— IEIIISIIIIIIIIIIIIIIIIlEF===§IIIx'; ··—· =l=l=l=Il=CIIlIII ¤¤bi¤¤¤z¤jf __ IIIIIIIIIIIIIIII Pixel‘° IIIIIIII!§ll-!IIII ¤¤¤¤¤¤¤lllllllllllnulll g¤;äpu¤¤
III.----------- "-I--III-III---.
+ x,x'
Figure B.2. Deformation of a Subimage in a Sampling Grid [26].
Appendax B. NUMERIGAL PROCEDURE FDR DEFDRMATIDN ANALYSIS USING DIGITAL IMAGECORRELATION 92
. E
(XII, yII) (XI + dxl, yl+=[x -4- u(P) -4- dx’, y + v(P) -4- dy']
· öu öu- [x + u(P) + ÖX dx -4- öy dy + dx, (B.4)
öv övy+v(P)+ öx dx-l- ay dy+dy]
Using Eq. (B.4), Eq. (B.3) can be re-written as:
, öu öuf'(Q) = f[x -4- u(P) -4- E- (P)dx -4-E
(P)dy + dx,
+ v(P) d (P) + d ](BIS)
y öx öy y y
Thus, if we know the displacement of the center point P of a subset and if we
. . . öu öu . .obtain the derivative terms 797(P), —5(P), then the position of any nearby
_ point Q' is determined. Conversely, if we assume values for
öu öu öv öv .u(P), v(P), öx (P), öy (P), öx (P), and öy (P), then we can compute esti-
mates for the positions of the the point P' and all points Q' that are within the
small subset surrounding P' This last statement is the foundation for the nu-
merloal computation of local deformation.
Appendix B. NUMERIGAL PROGEDURE FOR DEFORMATION ANALYsIs USING DIGITAL IMAGEGORRELATION 93
l
B.2 Iterative Method
To obtain accurate values for the six variables of interest in any subset, we must
compare subsets of intensity pattern. The method for comparing two subsets is
given by cross-correlation coefficient, C, [23-26,34-35]
öu öu öv öv[ - C(U’V’öx’öy’öx’öy)
= fAMf(><„y)¢”(><+ é,v+v)<//I (B-6)f r 2dA f r 26 2
where AM is subset in undeformed image .
AM' is subset in deformed image '
‘öu öuand §—u—l—ÖX Ax+ öy Ay
öv öv‘
ry—v+ ax Ax-l- öy Ay
The values of u, v, Qi, E-, -@2-, and gg- which maximize C are theöx öy öx 0y
local deformation values for a subset. As a first approximation only (u, v) are
assumed to vary; while rest of the variables are set to zero. This gives
(u1, v1), which are first approximation of translation of point P. Next, (u, v) are
held at (u1, v1) and %,—g—;§ are chosen to vary while jä-,%(‘L are zero.
[
Appendix B. NUMERICAL PROCEDURE FOR DEFORMATION ANALYSIS USING DIGITAL IMAGEcoRmsi.AT¤ou 94
EThis gives a first approximation on image dilation terms (%9-) and (%) .X 1 V 1Finally, liU1,V1,()1,()1] are held constant and are made to
vary to give first estimates (-9:9-) (jl) .0y 1 öx 1
The entire procedure is repeated with smaller ranges of values for (u, v) around
(L11, v1) with other values held constant as obtained from the previous iteration.
This two parameter model procedure is repeated until all the values lie within
tolerance limit.
Appendix B. Null/lERlcAL PROCEDURE Fon ¤6i=oRMATioN ANALYSIS usmc oicrrm. uviAcECORRELATION ss
START
Input :Undeformed surface dataDeformed surface dataVariable limitsTerminating limits
l Starting valueprocedure Initialize variables
Find estimates for u and v
Find estimates for QL-L and Äöx öy
Find estimates for andäy öx
IReiniatialize variable ranges
lteration .procedure Find u, V, %-, gé,
andAllowranges to converge simultaneously
Terminate the lteration when thecorrelation coefficientis acceptably small
Output :Values for u, V, Ä, Ä/-,-Qi
öx öy öyand ßl
öxvalue for the correlation coefficient
RETURN
Figure B.2. Flow diagram for correlation routine [26].
Appendix B. NUMERICAL PROCEDURE FOR DEFORMATION ANALYSIS USING DIGITAL IMAGECORRELATION 96
,Appendix C. DESCRIPTION OF MATROX6
lNote imageseg refers to 0,1,2, or 3; the 4 available image spaces on the matrox
board.
INP F12 allows to choose one of the three video inputs. lt is used by entering
|NP(imageseg). On the Matrox board input one is the top plug, two is the
center, and three is the bottom. This feature is useful to alternate
among 2 or 3 cameras coupled to the matrox board. .
CAM F2 sets the matrox board to display a live image. lt is used by entering
CAM imageseg.Th€ old image in that space is replaced by a live image
by this operation.
DIG F1 saves an image in the memory on the Matrox board. It is used by en-
IQVITIQ DIG imageseg.
I
Appendix C. DESCRIPTION OF MATROX6 SOFTWARE 97
IWIH F24 writes an image from a disk (floppy, RAM, or hard) to the Matrox board.
It is used by entering WIH imageseg (file_name). fiIe_name is the name
of the image on the disk. If the image is stored on a disk other than the
default then the disk name has to be include (i.e. ac, bz etc.),
NOTE the file name (and disk name) must be in parenthesis. This dif-
fers from WIM in that it reads images stored as HEX (using RIH) values
and the image is in two files which are AfiIe_name and BfiIe_name.
WIM F3 writes an image from a disk (floppy, RAM, or hard) to the Matrox board.
It is used by entering WIM imageseg (fiIe_name) file_name is the name
of the image on the disk. lf the image is stored on a disk other than the
default then the disk name has to be include (i.e. az, bz etc.),
NOTE the file name (and disk name) must be in parenthesis. The im-
age in the image space is replaced by the image of file_name.
RIH F23 reads an image from the Matrox board to a disk (floppy, RAM, or hard).
lt is used by entering RIH imageseg (fiIe_name) fiIe_name is the name
of where the image is to be stored on the disk. If the image is to be
stored on a disk other than the default then the disk name has to be
include (i.e. az, b: etc.), _
NOTE the file name (and disk name) must be in parenthesis. This dif-
fers from RIM in that the file is stored in HEX format and in two files
named Afile_name and BfiIe_name. This requires twice as much data
storage as the RIM.
Appendix c. ¤EscRlP1‘loN OF MATROX6 SOFTWARE 98
lRIM F23 reads an image from the Matrox board to a disk (floppy, RAM, or hard).
‘lt is used by entering RIM imageseg (file_name). file_name is the name
where the image is to be stored on the disk. lfthe image is to be stored
on a disk other than the default then the disk name has to be included
(i.e. az, bz etc.).
I
NOTE The file name (and disk name) must be in parenthesis.
IDIS F4 changes the image space being displayed by the matrox board. lt is
used by entering DIS imageseg
NOTE If a live image is being displayed changing the display will de-
stroy the old image in that space.
CUR F5 puts a cursor on the screen and can be moved to different spots using
the arrow keys. lt will work on both live and digitized images. No in-
formation is destroyed by using it on digitized images. CUR will display
the location and the gray level at the cursor center. The cursor position
can be saved to a file named "cursor.dat" by pressing the space bar.
NOTE Any old cursor.dat files will be lost. On live images the gray
level is only updated when a key is pressed. NOTE if the gray level on
a live image is needed, then without moving the cursor, press any key
other than an arrow key.U
RES F15 resets the matrox board to its original configuration.I
SYN F14 _ changes the sync source for the output from internal to external or vice
versa. lf a camera is not connected (and on) to the Matrox board and
Appendax c. DESCRIPTION OF MATROX6 SOFTWARE 99
_ I
we wish to view a digitized image we MUST enter SYN. lf later a cam-
era is connected, to view the live image SYN must be entered again.
How do we know when to enter SYN? lf the image is unstable (i.e.
rolling) then entering SYN should clear the image.
BAR F13 places a bar pattern in the memory of the Matrox board and is used to
insure your monitor is set up correctly. lt is used by entering BAR
imageseg.
NOTE Any prior image in the memory space used will be replaced by
bar pattern.
HIS F8 performs and displays a histogram of the gray levels of an image. It is
used by entering HIS imageseg.
NOTE The image will be destroyed by this process and should be
saved (using RIM or RIH ) if it is needed later. At increments of gray
levels of 50 the lines are black in the histogram.
GAN F16 sets the gain used on the input video signal. It is used by entering GAN
(x) where x is a number from 0 to 255. 0 is maximum gain and 255 is
minimum gain.
OFS F17 sets the offset used on the input video signal. lt is used by entering
OFS (x) where x is a number from 0 to 255. 255 is maximum and 0 is
minimum.
FLI F18 is to flick images. That is, two images are displayed one at a time one
Second apart and will continue to change until the < Esc> is pressed.
Appendix c. ¤EscRIPTION OF MATROX6 SOFTWARE 100
Slt is used by entering FLI (x,y) where x and y are numbers O, 1, 2, or 3
representing one of the four image spaces. x is the first to be displayed
y is the second.
AVG F11 will average incoming video images. It is used by entering AVG (x)
where x is the number of images to be averaged. x is a number be-
tween 1 and 255. lt is a very useful feature for noise reduction in the
I in-coming video signals (58).
NOTE Image space 0, 1, and 2 is destroyed by this operation. The av-
eraged image is stored in image space 0.
END F10 exits from this program back to DOS.
THI F6 is for thresholding the input video signal. lt is used by entering‘ Tl;lI(t,u,v,w), where t is the lower threshold limit and u is the gray value
U
which will be displayed. (i.e. gray levels g t will be set equal to u).
Similarly v is the upper limit and w is the gray value. ( i.e. gray levels
2 v will be set equal to w).
NOTE The image is stored in the matrox memory and original gray
levels are not available. This function works only on live images.
THO F7 is for thresholding the output video signal. lt is used by entering
THO(t,u,v,w), wheret is the lower threshold limit and u is the gray value
which will be displayed. (i.e. gray levels g t will be set equal to u).
Similarly v ls the upper limit and w is the gray value. ( i.e. gray levels
Appendax c. ¤EscRlP1'loN OF MATRox6 SOFTWARE 101
2 v will be set equal to w) lf a live image is digitized when thresholded
all gray levels are saved.
REC F22 puts a rectangle on the screen and can be moved to different spots
using the arrow keys. lt works on both live and digitized images. No
information is destroyed by using it on digitized images. REC will dis-
play the location and the gray level at the cursor center. The center
position can be saved to a file named "cursor.dat" by pressing the
space bar.
NOTE Any old cursor.dat files will be lost. On live images the gray
level is only updated when a key is pressed. NOTE if the gray level on
a live image ls needed then, without moving the cursor, pressing any”
key other than an arrow key will give the gray value.
SET F21 changes the mode ofthe PIP640 boards from 1024 to 640 mode. ln the
640 mode images are 780x512 pixels. Only 2 image spaces are avail-
able in the 640 mode.
LUT F25 changes between the 8 available look up tables. To use enter LUT x,
where x is between 0 and 7.
SYS F26 allows to enter DOS commands. To use enter SYS dos_command. Ex-
ample SYS DIR will display the contents of the current directory.
Appendix c. ¤EscRlPTloN OF MATR¤X6 SOFTWARE 102
1III