Experimental analysis of Fiber Reinforced Cementitious Matrix (FRCM) confined masonry columns

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I N T R O D U C T I O N 
OPTICAL METHODS AND FRP 
0.1. Digital Image 
A digital image is a representation of a two-dimensional image using 
ones and zeros, binary code. Depending on whether or not the image 
resolution is fixed, it may be of vector or raster type. Without 
qualifications, the term digital image usually refers to raster images also 
called bitmap images, figure 0.1. 
 
 
Fig. 0.1 – Basic concept of digital image correlation 
 
Raster images have a finite set of digital values, called picture elements or 
pixels. The digital image contains a fixed number of rows and columns of 
pixels. 
Pixels are the smallest individual element in an image, holding quantized 
values that represent the brightness of a given color at any specific point.
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Typically, the pixels are stored in computer memory as a raster image or 
raster map, a two-dimensional array of small integers. These values are 
often transmitted or stored in a compressed form. 
Raster images can be created by a variety of input devices and techniques, 
such as digital cameras, scanners, coordinate-measuring machines, 
seismographic profiling, airborne radar, and more. 
They can also be synthesized from arbitrary non-image data, such as 
mathematical functions or three-dimensional geometric models; the latter 
being a major sub-area of computer graphics. The field of digital image 
processing is the study of algorithms for their transformation. 
Each pixel of a raster image is typically associated to a specific position in 
some 2D region, and has a value consisting of one or more quantities 
related to that position. 
Digital images can be classified according to the number and nature of 
those samples: 
 binary; 
 grayscale; 
 color; 
 false-color; 
 multi-spectral; 
 thematic; 
 picture function. 
The term digital image is also applied to data associated to points scattered 
over a three-dimensional region.
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0.2. Digital Image Correlation 
This dissertation concern the use of optical methods, in particular 
digital image correlation, for displacement measurements during static or 
fatigue tests on specimens. 
The accurate measurement of displacement and strains during deformation 
of advanced materials and devices continues to be a primary challenge to 
designers and experimental mechanicians. The increasing complexity of 
technological devices with stringent space requirements leads to imperfect 
boundary conditions that have to be properly accounted for. The push 
toward miniaturizing devices down to nanometer length scales imparts 
additional difficulties in measuring strains as the application of 
conventional extensometers and resistance foil gages are cumbersome, 
damaging, or even impossible. Compounding this problem is also the fact 
that compliance of small-scale testing machines precludes the use of the 
displacement of external actuators for estimating specimen strain. As a 
consequence, a technique with the following features is extremely 
desirable: 
 no contact with the specimen required; 
 sufficient spatial resolution to measure locally at the region of 
interest; 
 the ability to capture non-uniform full-field deformations; 
 a direct measurement that does not require recourse to a numerical 
or analytical model. 
Optical methods are a logical solution to this litany of challenges.  
One approach is the interferometric strain-displacement gage developed by 
Sharpe. A laser-based technique that affords significant advantages over 
conventional strain measurement methods. 
It utilizes two markers on the surface of the specimen that provide 
interference fringes. This technique offers a very good resolution and local
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strain determination, but is limited to 1D measurements and requires some 
degree of experimental complexity. It also demands the use of markers. 
In the case of thin film mechanical testing where thicknesses are in the 
submicrometre range, hardness indents are out of the question and 
deposited lines can be up to an order of magnitude thicker than the 
specimen itself, which could significantly alter the apparent intrinsic 
properties of the material being tested.  
Digital image correlation techniques have been increasing in popularity, 
especially in micro- and nano-scale mechanical testing applications due to 
its relative ease of implementation and use. 
Advances in digital imaging have been the enabling technology for this 
method and while white-light optics has been the predominate approach, 
DIC has recently been extended to SEM and AFM. Above and beyond the 
ability of image-based methods to provide a “box-seat” to the events that 
are occurring during deformation, these techniques have been applied to 
the testing of many materials systems because it offers a full-field 
description and is relatively robust at tracking a wide range of “markers” 
and varying surface contrast. 
The appeal of these image-based techniques, coupled with the lack of 
flexibility and prohibitive cost of commercial DIC software packages, 
provided the impetus for the development of a custom in-house software 
suite using the mathematical package MATLAB as the engine for 
calculations. 
This resulted in an open-source package that was uploaded to the public 
domain in an effort to provide free tools to users, but also to generate 
feedback for potential improvements and addition to the code.  
DIC for strain measurement constitutes a major field of research and is 
followed by a healthy, vigorous, and dynamic discussion and discourse. 
DIC was first conceived and developed at the University of South Carolina 
in the early 1980s and has been optimized and improved in recent years.
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DIC is predicated on the maximization of a correlation coefficient that is 
determined by examining pixel intensity array subsets on two or more 
corresponding images and extracting the deformation mapping function 
that relates the images, Figure 0.2. 
 
 
Fig. 0.2 – Basic concept of digital image correlation 
 
The cross correlation coefficient 
ij
r is defined as: 
   
   
2
* *
2
* *
) , ( ) , (
) , ( ) , (
1 ) , , , , , (
G y x G F y x F
G y x G F y x F
y
v
x
v
y
u
x
u
v u r
j
j
j i
i
j
j
j i
i
ij
i
x
i
x
 
 
 








 
 
 
Here ) , (
j i
y x F is the pixel intensity or the gray scale value at a point 
) , (
j i
y x in the undeformed image. ) , (
* *
j
y x G
i
x
 is the gray scale value at a 
point ) , (
* *
j
y x
i
x
 in the deformed image. F and G are mean values of the 
intensity matrices F and G, respectively. The coordinates or grid points 
) , (
j i
y x and ) , (
* *
j
y x
i
x
 are related by the deformation that occurs between 
the two images. If the motion is perpendicular to the optical axis of the 
camera, then the relation between ) , (
j i
y x and ) , (
* *
j
y x
i
x
 can be 
approximated by a 2D affine transformation such as:
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y
y
u
x
x
u
u x x 


 


  
*
; 
y
y
v
x
x
v
v y y 


 


  
*
. 
Here u and v are translations of the center of the sub-image in the x and y 
directions, respectively. The distances from the center of the sub-image to 
the point ) , ( y x are denoted by x  and y  . Thus, the correlation 
coefficient 
ij
r is a function of displacement components ) , ( v u and 
displacement gradients: 
y
v
x
v
y
u
x
u








; ; ; . 
DIC has proven to be very effective at mapping deformation in 
macroscopic mechanical testing, where the application of specular markers 
or surface finishes from machining and polishing provide the needed 
contrast to correlate images well. 
However, these methods for applying surface contrast do not extend to the 
application of freestanding thin films for several reasons. First, vapor 
deposition at normal temperatures on semiconductor grade substrates 
results in mirror-finish quality films with roughnesses that are typically on 
the order of several nanometers. 
No subsequent polishing or finishing steps are required, and unless electron 
imaging techniques are employed that can resolve microstructural features, 
the films do not possess enough useful surface contrast to adequately 
correlate images. 
Typically this challenge can be circumvented by applying paint that results 
in a random speckle pattern on the surface, although the large and turbulent 
forces resulting from either spraying or applying paint to the surface of a 
freestanding thin film are too high and would break the specimens. In 
addition, the sizes of individual paint particles are on the order of μms,
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while the film thickness is only several hundred nms, which would be 
analogous to supporting a large boulder on a thin sheet of paper. 
Very recently, advances in pattern application and deposition at reduced 
length scales have exploited small-scale synthesis methods including nano-
scale chemical surface restructuring and photolithography of computer-
generated random specular patterns to produce suitable surface contrast for 
DIC. 
The application of very fine powder particles that electrostatically adhere 
to the surface of the specimen and can be digitally tracked is one approach. 
For thin films, fine alumina abrasive polishing powder was initially used 
since the particle sizes are relatively well controlled, although the adhesion 
to films was not very good and the particles tended to agglomerate 
excessively. 
A light blanket of powder would coat the gage section of the tensile sample 
and the larger particles could be blown away gently. The remaining 
particles would be those with the best adhesion to the surface, and under 
low-angle grazing illumination conditions, the specimen gage section 
would appear as shown in Figure 0.3.
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Fig. 0.3 – Basic concept of digital image correlation 
 
While the surface contrast present is not ideal for DIC, the high intensity 
ratio between the particles and the background provide a unique 
opportunity to track the particles between consecutive digital images taken 
during deformation. This can be achieved quite straight forwardly using 
digital image processing techniques, although the resolution is always 
limited to a single pixel. To attain tracking with subpixel resolution, a 
novel image-based tracking algorithm using MATLAB was developed, 
dubbed Digital Differential Image Tracking.
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0.3. Differential Digital Image Tracking 
The differential digital image tracking method exploits the shape of 
these powder particles when digitally imaged in the intensity domain as 
shown in Figure 0.2. The resemblance of the particles to mathematical 
functions that are adept at describing peak shapes with precise center 
locations and broadening allow them to be fit to a given function and thus 
tracked. 
It is perhaps coincidental that the symmetric normal distribution function 
proficiently fits the intensity profiles of the particles. This function can also 
be described in two dimensions. 
The quality of the Gaussian fit to a peak profile is shown in Figure 0.4. 
 
 
Fig. 0.4 – Peak profile of marker with corresponding Gaussian fit 
 
First, images are captured during the course of a mechanical test. Second, a 
list of image filenames is generated and the image capture times are
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extracted from the original images in order to synchronize the DDIT data 
to that of the data acquisition system. 
The markers are then automatically detected in the first image by an image 
processing algorithm that labels connected components in a binary image 
and subsequently, information regarding the size and shape of these 
components are extracted. 
Particles with properties that do not conform to specifications for ideal 
shapes are thrown out, and the remaining markers in the first image are fit 
to a Gaussian function using a nonlinear least-squares algorithm in both the 
longitudinal and transverse directions. 
The normalized residuals of the fit of the peak to the function are 
calculated for every peak and again, fits deemed poor as given by the value 
of the residual are removed from the analysis. 
This process now continues for every image in the sequence, and the result 
includes the position of the peak center, which is then post-processed using 
a visualization and data analysis script that allows visualization and output 
of the quantities of interest. [1] 
A digital image correlation process in shown in figure 0.5.
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Fig. 0.5 – Digital image correlation process [2]
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0.4. Application of Digital Image Correlation 
Digital Image Correlation offers characterization of material 
parameters far into the range of plastic deformation. 
Its powerful data analysis tools allow the determination of the location and 
amplitude of maximum strain, which are important functions in material 
testing. 
DIC is also ideal for fracture mechanics investigation. The full-field 
measurement delivers exact information about local and global strain 
distribution, crack growth, and can be used for the determination of 
important fracture mechanics parameters. 
The next figure shown typical application for DIC: 
 
 
Fig. 0.6 – Material properties 
 
 
Fig. 0.7 – Fracture mechanics 
 
 
Fig. 0.8 – Component test
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0.5. Resolution of Digital Image Correlation 
The resolution that one can achieve in practice using these image-
based techniques depends on a number of factors, including but not limited 
to camera resolution, lens optical quality, and marker size and quality. 
For a digital image the resolution can be described in many different ways: 
 pixel resolution: the term resolution is often used as a pixel count in 
digital imaging, even though international standards specify that it 
should not be so used, at least in the digital camera field. An image 
of N pixels high by M pixels wide can have any resolution less than 
N lines per picture height, or N TV lines. But when the pixel counts 
are referred to as resolution, the convention is to describe the pixel 
resolution with the set of two positive integer numbers, where the 
first number is the number of pixel columns and the second is the 
number of pixel rows. Another popular convention is to cite 
resolution as the total number of pixels in the image, typically 
given as number of megapixels, which can be calculated by 
multiplying pixel columns by pixel rows and dividing by one 
million. Other conventions include describing pixels per unit length 
or pixels per unit area, such as pixels per inch or per square inch. 
None of these pixel resolutions are true resolutions, but they are 
widely referred to as such; they serve as upper bounds on image 
resolution, figure 0.9. 
 
 
Fig. 0.9 – different pixel resolution 
 
 spatial resolution: the measure of how closely lines can be resolved 
in an image is called spatial resolution, and it depends on properties
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of the system creating the image, not just the pixel resolution in 
pixels per inch. For practical purposes the clarity of the image is 
decided by its spatial resolution, not the number of pixels in an 
image. In effect, spatial resolution refers to the number of 
independent pixel values per unit length. 
 
 
Fig. 0.10 – resolution test target 
 
 Spectral resolution: color images distinguish light of different 
spectra. Multi-spectral images resolve even finer differences of 
spectrum or wavelength than is needed to reproduce color. That is, 
they can have higher spectral resolution. that is the strength of each 
band that is created. 
 Temporal resolution: movie cameras and high-speed cameras can 
resolve events at different points in time. The time resolution used 
for movies is usually 15 to 30 frames per second, while high-speed 
cameras may resolve 100 to 1000 frame per second. Many cameras