Introduction and literature review
1.1 Introduction to repair technology
1.1.5 Experimental techniques for strain measurements
Traditionally, researchers have used reflection polariscope [19] and strain gauges [20], for strain measurements in repair study. Reflection photoelasticity involves bonding of a reflective coating layer on to the specimen. It is not a straight forward process and one has to be adept in bonding the coating layer on to the specimen. In case of strain gauges measurement is highly localized and one cannot get the whole field strain distribution. Of late, digital image correlation (DIC) is used in the field of experimental mechanics due to its accuracy and relatively simple optics capable of whole field estimation of displacement and strain. The DIC refers to the class of non-interferometric, non-contact optical methods of experimental stress analysis that acquire images of an object, store these images in digital form and perform image analysis to extract full-field shape and deformation measurement [21-23]. It directly provides information about the displacements and strains by comparing the digital images of the specimen surface in the un-deformed (or reference) and deformed states respectively. In principle, DIC is based on pattern matching and numerical computing [22]. In DIC, one of the most commonly used approaches employs random patterns and compares sub-regions (subsets) from ‘un-deformed’ and ‘deformed’ images to obtain a full- field sensor-plane measurements [21]. The basic principle of DIC is the matching of the small subsets between the digitized images of the specimen surface recorded in un-deformed (reference) and deformed state as schematically illustrated in Fig. 1.8. The matching process is performed to locate the corresponding position of each reference subset within each
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deformed image. In order to evaluate the degree of similarity between the subsets from reference image and the deformed image, a zero-normalized cross-correlation (C) coefficient is used which is defined in Eq. 1.2:
1 1
2 2
1 1 1 1
( , ) ( ' , ' )
( , )
( , ) ( ' , ' )
m m
i j i j
i j
m m m m
i j i j
i j i j
f x y f g x y g
C u v
f x y f g x y g
(1.2)
0
0
where,
= mean intensity value of reference subset = mean intensity value of deformed subset '
' f g
u u
x x u dx dy
x y
v v
y y v dx dy
x y
where, f(x, y) and g(xʹ, yʹ) represent the gray levels of reference and deformed images, respectively; and (x, y) and (xʹ, yʹ) are the co-ordinates of a point in the subset before and after deformation respectively. Once the maximum value of this correlation coefficient is detected, the position of the deformed subset is determined. Then, in-plane displacement vector at any point can be calculated using the difference in the positions of the reference subset center and the deformed subset center [21].
f (x,y)
Sub Window y
x
f (x,y) y
x
g (x´, y´) y´
x´
Figure 1.8: Schematic of subset matching in DIC technique (a) un-deformed state (b) deformed state
(a) (b)
In many fields, experimental estimation of material properties and prediction of whole field strain distributions is more important and desirable. But, less work has been focused on the reliable estimation of strain fields from the displacement field given by DIC [21]. Probably, this can be attributed to the fact that the displacement gradients or strains can be directly calculated using the Newton-Raphson method. Typically, the relationship between the strain and displacement can be described as a numerical differentiation process. The numerical differentiation process is considered as an unstable and risky, because it can amplify the noise contained in the computed displacement. Therefore, the resultant strains are unreliable if they are calculated by directly differentiating the estimated noisy displacements [21].
There are different algorithms which are developed for smoothing the displacement field followed by a numerical differentiation of the smoothed data to get the in-plane strain components [24-26]. More recently, Pan et al. [27] used the point wise local least-squares fitting technique for strain estimation. They proposed that this technique is a simpler and most effective one for the calculation of strains for the points located at the image boundary, hole, cracks and the other discontinuity areas.
There are two configurations being used in DIC, namely 2D and 3D setup and its schematic is shown in Fig. 1.9. In 2D DIC [23], the plane surface of the specimen is observed by a single camera and is preferred for measurement of in-plane displacements (see Fig. 1.9 (a)).
Investigators have extended DIC concepts to stereovision systems. A typical stereovision system employs two or more cameras to record digital images of a common object region from two or more viewpoints. In 3D DIC, the surface of the specimen is observed by two cameras as shown in Fig. 1.9 (b). It involves detailed calibration procedure to get distance in terms of camera coordinate system. Once the cameras are calibrated, the sensor plane locations in the two views for the same object point can be used to determine an accurate estimate for the three-dimensional position of the common object location. After the calibration, the image acquisition process is synchronized so that both the camera acquires images simultaneously after triggering. In case of 3D DIC, one can get out of plane displacement in addition to in plane displacement and strain. The method has seen remarkable growth in recent years, with applications in various fields. The 3D-DIC system is theoretically capable of extracting accurate, in-plane surface deformations, even when the object is undergoing large, three-dimensional rigid body rotation and translation.
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The method of DIC has many advantages over other optical methods. Firstly, any class of material could be studied and the specimen surface preparation is simpler. Secondly, optics involved is quite simpler. Thirdly, the displacement information is retrieved by direct comparison of the speckle patterns before and after deformation, therefore no fringe analysis and phase-unwrapping is needed in this method. Fourthly, there is no fringe density
Computer
Load
Specimen CCD camera
Light source
Testing Machine Image Acquisition
Computer
Load Specimen
CCD camera
Light source
Testing Machine Image Acquisition
(a)
Figure 1.9: Schematic of data acquisition system (a) 2D DIC set up (b) 3D DIC setup (b)
limitation in DIC, so the measurement range is much larger than other techniques.
Additionally, it is truly a non-contact by nature and provides full field data.
Nevertheless, DIC still suffers some disadvantages. It requires specimen with random speckle pattern and needs optical access to the specimen. It is sensitive to light fluctuations and rigid body motion. It requires moderately large amount of computation time and poses difficulty of correlation at the edge. It does not provide full-field strain resolution better than 0.1%. The DIC technique provides displacement resolution of sub-pixel accuracy typically 1/50th of a pixel and the maximum strain accuracy is of the order of 0.02 %. The least strain that can be measured using DIC is 50 micro strain [28].