Department of Civil Engineering Unsupervised Term Work ...kwon/docs/BASc_Zhang_2019.pdf · Validation and Application of Digital Image Correlation Method for Strain Field Measurement

Validation and Application of Digital Image Correlation Method for Strain Field Measurement

Department of Civil Engineering

Faculty of Applied Science and

Engineering

University of Toronto

Unsupervised Term Work Statement

CIV499H1 F/S Thesis

I hereby certify that I am thoroughly familiar with the contents of this

project/laboratory report/problem set/essay/report. It is substantially my own work, I

have referenced all my sources of information, and I am the sole author.

Name (Please print): Peiying Zhang

Student No.: 1002287795

Supervisor’s Name: Professor Oh-Sung Kwon

Student’s Signature:

Date Submitted: April 11th, 2019


Validation and Application of Digital Image

Correlation Method for Strain Field

Measurement

by

Peiying Zhang

A thesis submitted in conformity with the requirements

for the degree of Bachelor of Applied Science



© Copyright by Peiying Zhang 2019


i

Validation and Application of Digital Image Correlation Method for

Strain Field Measurement

Peiying Zhang

Bachelor of Applied Science



2019

Abstract

Digital Image Correlation (DIC) is a non-contact technique for measuring material

deformation and generating the overall strain field measurement. This thesis presents the

study on developing a robust procedure of running DIC analysis by using an open-source

subset based 2D-DIC algorithms, Ncorr. The procedures will be developed based on the

structural tests of two types of materials: steel and concrete. Full-field strain and

displacement measurement were carried out successfully. The results indicated that the

DIC method could achieve minimum strain errors of 0.71% when comparing DIC to strain

gauge measurement. The proposed procedures of running DIC analysis is expected to

be employed on other structural tests in future research.


ii

Acknowledgements

I would like to express the deepest gratitude to Professor Oh-Sung Kwon, University of

Toronto, for his guidance and advice throughout the preparation, development, and

improvement of this thesis. I am truly thankful for the opportunity to study this project.

I also want to thank all the laboratory and technical staffs at the University of Toronto,

Xiaoming Sun, and Alan McClenaghan for their help in the experimental tests of this

project.

Lastly but the most important, I want to express my heartfelt thanks to my parents. Their

unconditional love, patience, encouragement and support made possible the completion

of this project.


iii

Table of Contents

Abstract ............................................................................................................................ i

Acknowledgements ..........................................................................................................ii

List of Tables ................................................................................................................... v

List of Figures ..................................................................................................................vi

List of Acronyms and Symbols ........................................................................................ix

Chapter 1: Introduction .................................................................................................... 1

Chapter 2: Digital Image Correlation ............................................................................... 3

2.1 Overview ............................................................................................................ 3

2.2 Ncorr DIC Algorithms ......................................................................................... 3

2.2.1 Subset Deformation ................................................................................. 3

2.2.2 Correlation Criteria ................................................................................... 6

2.2.3 Non-linear Optimization Scheme ............................................................. 7

2.2.4 Full Field Displacement ............................................................................ 9

2.2.5 Full Field Strain Measurement ............................................................... 10

2.2.6 Improvements in Ncorr ........................................................................... 11

Chapter 3: DIC Validation Tests ..................................................................................... 13

3.1 Summary of Test Specimen ............................................................................. 13

3.2 Steel Coupons Tensile Test .............................................................................. 16

3.3 Concrete Compression Test ............................................................................. 17

Chapter 4: Steel Coupon Tensile Test ........................................................................... 20

4.1 Steel Coupon Test 1 ......................................................................................... 20

4.1.1 Test 1 Result .......................................................................................... 20

4.1.2 Discussion of Test 1 Result .................................................................... 27


4.2.1 Test 2 Result .......................................................................................... 28



4.3.1 Test 3 Result .......................................................................................... 33


Chapter 5: Concrete Compression Test ........................................................................ 41

5.1 Concrete Cube Test 1....................................................................................... 41

5.1.1 Cube Test 1 Result ................................................................................. 41

5.1.2 Discussion of Cube Test 1 Result........................................................... 48

5.2 Concrete Cube Test 2....................................................................................... 50

5.2.1 Cube Test 2 Result ................................................................................. 50

5.2.2 Discussion of Cube Test 2Result ........................................................... 53

5.3 Concrete Cylinder Test 1 .................................................................................. 55

5.3.1 Cylinder Test 1 Result ............................................................................ 55


iv

5.3.2 Discussion of Cylinder Test 1 Result ...................................................... 58

Chapter 6: Conclusion ................................................................................................... 59

Chapter 7: Recommendations ....................................................................................... 60

7.1 Improvements on Analysis Accuracy ................................................................ 60

7.1.1 Lens Distortion Removal ........................................................................ 60

7.2 Recommendation for Future Application .......................................................... 62

7.2.1 DIC on Observation of Elements Under Thermal Loading ..................... 62

7.2.2 Future Improvements in DIC Algorithms ................................................ 62

References .................................................................................................................... 65

Appendices ................................................................................................................... 68

A. Ncorr Installation ............................................................................................ 68

B. Ncorr DIC Analysis Settings ............................................................................... 70

B-1: Setting of Images .................................................................................... 70

B-2: Setting of DIC Parameters ....................................................................... 72

B-3: DIC Analysis ............................................................................................ 73

B-4: Format Displacement & Strain ................................................................. 76

B-5: Test Data Plotting .................................................................................... 79

C. Further Analysis ................................................................................................. 80


v

List of Tables

Table 4.1 - Strain measurement from DIC and strain gauges for SC-1. ................. 23

Table 4.2 - Strain measurement from DIC and strain gauges for SC-H-1 .............. 25

Table 4.3 - Strain measurement from DIC and strain gauges for SC-H-2. ............. 29

Table 4.4 - Strain measurement from DIC and strain gauges for SC-H-3. ............. 35

Table 4.5 - Strain measurement from DIC and strain gauges for SC-2. ................. 38

Table 5. 1 - Displacement from DIC and MTS load frame for Cube#1. .................. 45

Table 5. 2 - Displacement from DIC and MTS load frame for Cube#2 ................... 47

Table 5. 3 - Displacement from DIC and MTS load frame for Cube#3. .................. 53

Table 5. 4 - Strain from DIC and LVDT for Cylinder#1 ............................................ 57


vi

List of Figures

Figure 2.1 - Linear transformations for subset coordinates (Blaber et al., 2015). ..... 4

Figure 2.2 - Explanation of subset coordinate points (Blaber et al., 2015). .............. 5

Figure 2.3 - Ncorr DIC algorithm process (Blaber et al., 2015). ............................... 7

Figure 2.4 - Process of inverse compositional update (Pan et al., 2013). ................ 8

Figure 2.5 - RG-DIC approach path (Blaber et al., 2015) ......................................... 9

Figure 2.6 - Ncorr implementation of RG-DIC (Blaber et al., 2015). ....................... 12

Figure 2.7 - Updating ROI process (Blaber et al., 2015). ....................................... 12

Figure 3.1 - Schematic of steel specimen. ............................................................. 13

Figure 3.2 - Schematic of steel specimen. ............................................................. 14

Figure 3.3 - Casting process for concrete specimen. ............................................. 15

Figure 3.4 - Curing process for concrete specimen (highlight by red-box). ............ 15

Figure 3.5 - a) priming with first layer of coating b) then coating with a texturized paint.

........................................................................................................................ 16

Figure 3.6 - a) strain gauges at the back. b) marked location of strain gauges at front.

........................................................................................................................ 17

Figure 3.7 - Surface treatment for concrete cubes: paint with primer (left) and stone-

textured paint after priming (right). .................................................................. 18

Figure 3.8 - LVDT set up for Cylinder specimen. .................................................... 19

Figure 4.1 - Camera setup during test. ................................................................... 21

Figure 4.2 - Locations of strain gauges, SC-1 on left and SC-H-1on right. ............ 22

Figure 4.3 - Load vs. Strain Curve for SC-1. .......................................................... 23

Figure 4.4 - Formation of overall strain field (Eyy) for SC-1. .................................. 24

Figure 4.5 - Load vs. Strain Curve for SC-H-1. ...................................................... 25

Figure 4.6 - Formation of strain field under different loading for SC-H-1. ............... 26

Figure 4.7 - a) Reference image b) deformed image. ............................................ 27

Figure 4.8 - Inaccuracy due to the missing painting from deformed image. ........... 28

Figure 4.9 - Locations of strain gauges, SC-H-2 .................................................... 29

Figure 4.10 - Load vs. Strain Curve for SC-2 with ISO 320. ................................... 30

Figure 4.11 - Formation of overall strain field (Eyy) for SC-H-2 with ISO-320. ....... 31

Figure 4.12 - Formation of overall strain field (Eyy) for SC-H-2 with ISO 800 ........ 32

Figure 4.13 - Locations of strain gauges, SC-H-3 left and SC-2 right. ................... 34

Figure 4.14 - Load vs. Strain Curve for SC-H-3. .................................................... 35

Figure 4.15 - Formation of strain field under different loading for SC-H-3. ............. 36

Figure 4.16 - Failure process for SC-H-3. .............................................................. 37

Figure 4.17 - Load vs. Strain Curve for SC-2. ........................................................ 38

Figure 4.18 - Formation of strain field under different loading for SC-2. ................. 39

Figure 5.1 - Experiment setup for compression test on concrete cube. ................. 42

Figure 5.2 - Locations of data collection point. Cube#1 (left) vs Cubbe#2 (right). .. 43


vii

Figure 5.3 - Displacement vs Time for different data point on Cube#1. .................. 43

Figure 5.4 - Displacement vs. Time from MTS measurement and relative

displacement from Ncorr of Cube#1 . ............................................................. 44

Figure 5.5 - Displacement vs Time for different data point on Cube#2. .................. 46


displacement from Ncorr of Cube#2. .............................................................. 46

Figure 5.7 - V displacement field (left) and current image at same stage (right) for

Cube#2. .......................................................................................................... 49

Figure 5.8 - Locations of data collection point in Cube#3. ...................................... 51

Figure 5.9 - Displacement vs. Time curve for Cube#3. .......................................... 52


displacement from Ncorr of Cube#3. .............................................................. 52

Figure 5.11 - Cracking formation for Cube#3. ........................................................ 54

Figure 5.12 - U displacement (left) and current image (right) of Cube#3. .............. 55

Figure 5.13 - Location of data collection points for Cylinder #1. ............................. 56

Figure 5.14 - Displacement vs. Time curve for Cylinder#1. .................................... 57

Figure 5.15 - V displacement (left) and current image (right) of Cylinder#1. .......... 58

Figure 7.1 - Sample of lens distortion (Park et al., 2009). ...................................... 60

Figure 7.2 - Pictures of grid lines............................................................................ 61

Figure 7.3 - Effect of displacement gradients on subset points (Lu and Cary, 2009).

........................................................................................................................ 63

Figure 7.4 - Sample setup for 3-D DIC (Spera et al., 2011).................................... 64

Figure A.1 - Function to run the Ncorr in MATLAB. ................................................ 68

Figure A.2 - GUI for Ncorr. ..................................................................................... 69

Figure B.1 - Setting of reference and current image. ............................................. 70

Figure B.2 - GUI of ROI setting. ............................................................................. 71

Figure B.3 - Sample drawing of ROI. ..................................................................... 71

Figure B.4 - Sample setting of DIC Parameters. .................................................... 72

Figure B.5 - Warning from Ncorr. ........................................................................... 72

Figure B.6 - Setting of DIC analysis. ...................................................................... 73

Figure B.7- Seed placement on DIC analysis. ....................................................... 74

Figure B.8 - Flow chart of RG-DIC algorithm to process (Blaber et al., 2015). ....... 75

Figure B.9 - Warning from Ncorr. ........................................................................... 75

Figure B.10 - DIC analysis is performing. ............................................................... 76

Figure B.11 - Formatting setting. ............................................................................ 77

Figure B.12 - Calibration line for unit conversion.................................................... 77

Figure B.13 - Setting of strain parameter. .............................................................. 78

Figure B.14 - Strain radius: a) strain radius 15 b) strain radius 10 c) strain radius 5.

........................................................................................................................ 79

Figure B.15 - Overall displacement field. ............................................................... 80

Figure B.16 - Overall strain field in a) xx direction b) yy direction c) xy direction.... 80


viii

Figure C.1 - GUI for ncorr_post. ............................................................................. 81

Figure C.2 - Sample of scaling the displacement. .................................................. 82

Figure C.3 - Direction of principal strains ............................................................... 82

Figure C.4 - Sample of defining two points for adding extensometer. .................... 83

Figure C.5 - Relative displacement between two selected points. ......................... 83


ix

List of Acronyms and Symbols

𝐸𝑥𝑥 Strain component

𝑓𝑚 Mean grayscale value of the reference subset

𝑔𝑚 Mean grayscale value of the current subset

𝑖, 𝑗 Relative location of the points with respect to the center of the subset

𝑝 Generalized deformation vector

𝑟𝑐 Transformation from reference to current system

𝑆 A set which contains all of the subset points

𝑆𝐶 Steel Coupon

𝑆𝐶 − 𝐻 Steel Coupon with hole

𝑢𝑝𝑙𝑎𝑛𝑒 Plane displacement parameter

𝑢, 𝑣 Displacement parameters

�̃�𝑐𝑢𝑟𝑖 x coordinates of a current subset point

𝑥𝑟𝑒𝑓𝑐 x coordinates of the center of the initial reference subset

𝑥𝑟𝑒𝑓𝑖 x coordinates of an initial reference subsect point

�̃�𝑐𝑢𝑟𝑗 y coordinates of a current subset point

𝑦𝑟𝑒𝑓𝑐 y coordinates of the center of the initial reference subset

𝑦𝑟𝑒𝑓𝑗 y coordinates of an initial reference subsect point

𝜉 Wrap function


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Chapter 1: Introduction

Strain is one of the important parameters for engineering research and even real-world

construction projects. In the past, to measure strain in structures in the laboratory, the use

of strain gauge or fiber optic cable sensor are the main strain measurement methods. In

structural testing, engineers may need to obtain strain data in various locations on

complex structures, and those conventional methods have several limitations. Strain

gauges are limiting by the amount of data they can collect and the cumbersome

installation process. As a point gauge, strain gauge only allows to collect a single point

data and is commonly placed at critical region. Thus, to generate a continuous strain

measurement or strain distribution on critical region, it requires the installation of a large

number of gauges (Hoult et al., 2013). The preparation process of the strain gauge is also

time-consuming which requires the surface of the specimen to be cleaned, smoothed,

and de-greased. When the installation involves large amounts of gauges, it is challenging

to manage and needs large space to restore the strain gauges since they need to be

wired separately. Another strain measurement method is the fiber optic cable sensor

which can provide a spatially continuous strain data along the entire length of the fiber.

Compares to strain gauges, this method is more compact and lightweight which can be

embedded in composites or other material to collect internal strain or other parameters

data such as temperature (Lawrence et al., 1999). In addition, the fiber optic cable sensor

can have a broader field measurement than using the strain gauges. However, it is costly

and cannot generate a full-field strain measurement. These disadvantages that mention

above limit the conventional strain measuring methods to be applied in some real-world

applications. Thus, an alternative approach is needed to improve the strain measurement

by overcoming many of these disadvantages.

In the past two decades, Digital Image Correlation (DIC) had been introduced as a non-


Page | 2

contact technique for measuring material deformation without any further machinery and

permanent setup which can be applied outside the laboratory (Chu et al., 1985). DIC is a

cost-effective method compared to conventional techniques; it requires the use of digital

camera and can be used in analyzing existing structures which conventional methods

have accessibility limitations (Lawrence et al., 1999). DIC measures strain and

displacement through comparing series of digital images of the test sample at different

stages of deformation and calculates the strain and displacement through tracking the

blocks of pixels, therefore generating the overall surface displacement correspondingly

building up the full 2D & 3D strain field based on that (McCormick and Lord, 2010). In

recent years, many open-source tools are developed to perform DIC analysis (Blaber et

al., 2015; Turner et al., 2015). According to recent research by Mbarek and Hoult, DIC

method can be used in various engineering applications such as investigation on the

mechanical behavior of wood-plastic composites, measuring crack movement in

reinforced concrete or even can be used in field monitoring.

The purpose of this thesis is to demonstrate a robust procedure for running DIC analysis

on structural testing of different building materials. The procedure will be developed based

on an open source MATLAB code Ncorr. The detailed test procedure will be developed

based on the result of a series of tensile testing on steel coupons and compression testing

on concrete specimens. During the testing, a digital camera will be set up in front of the

testing machine to capture the pictures of the deformation progress for proceeding the

DIC analysis. Then, after testing, the overall strain and displacement field will be

generated through the DIC analysis and the comparison between the obtained data from

DIC analysis and strain measurement from the conventional method will be made in order

to investigate the accuracy of the Ncorr-DIC analysis. At the end of this thesis, further

improvements and recommendations are included to increase the accuracy of using DIC

for future structural testing.


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Chapter 2: Digital Image Correlation

In order to run the DIC analysis, an open-source MATLAB package, Ncorr, will be used

in this thesis (Blaber et al., 2015). The validation test will be made based on the results

from Ncorr and conventional strain/displacement measurement method. This chapter

outlines the theory behind the Ncorr by explaining its core algorithms, and advantages

compare to other DIC analysis method.

2.1 Overview

The main concept of DIC analysis is to obtain the strain and displacement field within a

region of interest (ROI) for an element undergoing deformation. The basic idea for DIC is

to obtain a one-to-one correspondence between material points in the reference (initial

undeformed picture) and any current (subsequent deformed pictures) configurations

(Blaber et al., 2015). The reference image will be defined as small subsections, which are

named subsets under DIC, and DIC will determine the respective locations of those

subsets in the current configuration (Blaber et al., 2015).

2.2 Ncorr DIC Algorithms

In this section, description of core DIC algorithms used in Ncorr will be explained, and

improvements that had been made compared to conventional DIC algorithms will also be

discussed.

2.2.1 Subset Deformation

In subset-based DIC algorithms, the reference image is partitioned into smaller regions


Page | 4

referred to as subsets. According to Blaber et al. (2015), in Ncorr, the deformation is

assumed to be homogeneous within each subset where can be tracked in the current

image (deformed image). If the subset is small enough, the coordinates of the points

(𝑥𝑟𝑒𝑓𝑖 , 𝑦𝑟𝑒𝑓𝑗) around the subset center (𝑥𝑟𝑒𝑓, 𝑦𝑟𝑒𝑓) in the reference subset can be mapped

to the points (�̃�𝑐𝑢𝑟𝑖, �̃�𝑐𝑢𝑟𝑖) in the deformed subset followed a linear, first-order displacement

mapping function (Blaber et al., 2015):

�̃�𝑐𝑢𝑟𝑖 = 𝑥𝑟𝑒𝑓𝑖 + 𝑢𝑟𝑐 +𝜕𝑢

𝜕𝑥𝑟𝑐(𝑥𝑟𝑒𝑓𝑖 − 𝑥𝑟𝑒𝑓𝑐) +

𝜕𝑢

𝜕𝑦𝑟𝑐(𝑦𝑟𝑒𝑓𝑗 − 𝑦𝑟𝑒𝑓𝑐)

(2.1)

�̃�𝑐𝑢𝑟𝑖 = 𝑦𝑟𝑒𝑓𝑗 + 𝑣𝑟𝑐 +𝜕𝑣

𝜕𝑥𝑟𝑐(𝑥𝑟𝑒𝑓𝑖 − 𝑥𝑟𝑒𝑓𝑐) +

𝜕𝑣

𝜕𝑦𝑟𝑐(𝑦𝑟𝑒𝑓𝑗 − 𝑦𝑟𝑒𝑓𝑐) (𝑖, 𝑗) ∈ 𝑆 (2.2)

𝑝 = { 𝑢 𝑣 𝜕𝑢

𝜕𝑥 𝜕𝑢

𝜕𝑦 𝜕𝑣

𝜕𝑥 𝜕𝑣

𝜕𝑦}𝑇 (2.3)

The mapping functions are illustrated in Equations 2.1 to 2.3 where 𝑝 is defined as a

generalized deformation vector and the deformation parameters are illustrated in Figure

2.1. The indices (𝑖, 𝑗) are used for the relative location of the points with respect to the

center of the subset and 𝑆 is a set which contains all the subset points. The subscript

“𝑟𝑐” used in Equation 2.1 represents the transformation from the reference to the current

coordination system.

Figure 2.1 - Linear transformations for subset coordinates (Blaber et al., 2015).

Ncorr can obtain displacement and strain information through the transformation used to

match the location of the subsets in the current configuration. In Ncorr, subsets are initially

defined as a contiguous circular group of coordinate points that are integer pixel locations

in the reference configuration as illustrated as red crosses in Figure 2.2.


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Figure 2.2 - Explanation of subset coordinate points (Blaber et al., 2015).

Based on this displacement mapping function, later, Ncorr will employ this to the Inverse

Compositional method which is used to obtain the displacement parameters for the

mapping function. The theory of this method will be discussed in the following section. In

order to accommodate the inverse compositional method, the reference subset can

deform within the reference configuration by using Equations 2.4 and 2.5 (Blaber et al.,

2015):

�̃�𝑟𝑒𝑓𝑖 = 𝑥𝑟𝑒𝑓𝑖 + 𝑢𝑟𝑟 +𝜕𝑢

𝜕𝑥𝑟𝑟(𝑥𝑟𝑒𝑓𝑖 − 𝑥𝑟𝑒𝑓𝑐) +

𝜕𝑢

𝜕𝑦𝑟𝑟(𝑦𝑟𝑒𝑓𝑗 − 𝑦𝑟𝑒𝑓𝑐)

(2.4)

�̃�𝑟𝑒𝑓𝑖 = 𝑦𝑟𝑒𝑓𝑗 + 𝑣𝑟𝑐 +𝜕𝑣

𝜕𝑥𝑟𝑟(𝑥𝑟𝑒𝑓𝑖 − 𝑥𝑟𝑒𝑓𝑐) +

𝜕𝑣

𝜕𝑦𝑟𝑟(𝑦𝑟𝑒𝑓𝑗 − 𝑦𝑟𝑒𝑓𝑐) (𝑖, 𝑗) ∈ 𝑆 (2.5)


Page | 6

where (�̃�𝑟𝑒𝑓𝑖 , �̃�𝑟𝑒𝑓𝑖 ) is the coordinates of a deformed reference subset point and “𝑟𝑟 ”

represents the transformation between two different coordinate systems in the reference

image.

2.2.2 Correlation Criteria

To obtain an accurate estimation for the displacement components of the target points,

two correlation (cost) criteria, normalized cross-correlation (NCC) and least square (LS),

had been employed in this algorithm as demonstrated in Equations 2.6 and 2.7 (Blaber

et al., 2015):

𝐶𝐶𝐶 =∑ (𝑓((𝑖,𝑗) ∈𝑆 �̃�𝑟𝑒𝑓𝑖 , �̃�𝑟𝑒𝑓𝑖) − 𝑓𝑚)(𝑔(�̃�𝑟𝑒𝑓𝑖 , �̃�𝑟𝑒𝑓𝑖) − 𝑔𝑚)

√∑ [𝑓((𝑖,𝑗) ∈𝑆 �̃�𝑟𝑒𝑓𝑖 , �̃�𝑟𝑒𝑓𝑖) − 𝑓𝑚]2[𝑔(�̃�𝑟𝑒𝑓𝑖 , �̃�𝑟𝑒𝑓𝑖) − 𝑔𝑚]

2

(2.6)

𝐶𝐿𝑆 = ∑ [𝑓(�̃�𝑟𝑒𝑓𝑖 , �̃�𝑟𝑒𝑓𝑖) − 𝑓𝑚

√∑ [𝑓(�̃�𝑟𝑒𝑓𝑖 , �̃�𝑟𝑒𝑓𝑖) − 𝑓𝑚]2

(𝑖,𝑗)∈𝑆

−𝑔(�̃�𝑟𝑒𝑓𝑖 , �̃�𝑟𝑒𝑓𝑖) − 𝑔𝑚

√∑ [𝑔(�̃�𝑟𝑒𝑓𝑖 , �̃�𝑟𝑒𝑓𝑖) − 𝑔𝑚]2

(𝑖,𝑗)∈𝑆(𝑖,𝑗) ∈𝑆

]2 (2.7)

where 𝑓 and 𝑔 represent the reference and current image grayscale intensity functions

a specified location (𝑥, 𝑦) ; 𝑓𝑚 and 𝑔𝑚 represent the mean grayscale values of the

reference and current subset.

The basic concept is that Ncorr will tend to find the extremum of the correlation function.

For 𝐶𝐶𝐶, it has a range of [−1, 1] and one represents that the predicted value is perfectly

matched with the actual value. As for 𝐶𝐿𝑆, it has a range of [0,∞] and zero represents a

good match. In Pan’s study in 2012, 𝐶𝐶𝐶 and 𝐶𝐿𝑆 are two commonly used cost function

in DIC algorithms since the 𝐶𝐿𝑆 correlation criterion is insensitive to the scale and offset

of illumination lighting fluctuation and it is also directly related to the 𝐶𝐶𝐶 correlation

criterion by a linear relation as illustrated in Equation 2.8:

𝐶𝐿𝑆 = 2(1 − 𝐶𝐶𝐶) (2.8)


Page | 7

2.2.3 Non-linear Optimization Scheme

As mentioned in the previous section, Ncorr uses the Inverse Compositional Gauss-

Newton (IC-GN) as the nonlinear optimizer to obtain the desired in-plane displacement

components. IC-GN tends to seek an optimal value of 𝑝𝑟𝑐 while minimizing 𝐶𝐿𝑆 when

𝑝𝑟𝑟 = 0. In each iteration, this method will find a small deformation ∆𝑝 (𝑝𝑟𝑟) of the initial

reference subset where it best matches the deformed reference subset described by 𝑝𝑟𝑐

(Blaber et al., 2015). As shown in Figure 2.3, the basic steps in Ncorr is by first to guess

for the displacement 𝑝𝑔 = {𝑢(𝑔) 𝑣(𝑔) 0 0 0}𝑇 , then used this guess as the initial input to

the iterative optimization scheme which in order to find a refined solution 𝑝𝑟 =

{ 𝑢 𝑣 𝜕𝑢

𝜕𝑥 𝜕𝑢

𝜕𝑦 𝜕𝑣

𝜕𝑥 𝜕𝑣

𝜕𝑦}𝑇 (Blaber et al., 2015).

Figure 2.3 - Ncorr DIC algorithm process (Blaber et al., 2015).

The correlation criterion for the IC-GN iterations will be updated from Equation 2.7 to

Equation 2.9 (Blaber et al., 2015):

𝐶𝐿𝑆(∆𝑝) =∑[𝑓 (𝜉𝑟𝑒𝑓𝑐

+ 𝑤(Δ𝜉𝑟𝑒𝑓; ∆𝑝)) − 𝑓𝑚

√∑ [𝑓 (𝜉𝑟𝑒𝑓𝑐 + 𝑤(Δ𝜉𝑟𝑒𝑓; ∆𝑝)) − 𝑓𝑚]2

−𝑔 (𝜉𝑟𝑒𝑓𝑐

+ 𝑤(Δ𝜉𝑟𝑒𝑓; ∆𝑝)) − 𝑔𝑚

√∑ [𝑔 (𝜉𝑟𝑒𝑓𝑐 +𝑤(Δ𝜉𝑟𝑒𝑓; ∆𝑝)) − 𝑔𝑚]2

]2 (2.9)

where 𝜉 is an augmented vector containing the 𝑥 and 𝑦 coordinates of the subset


Page | 8

points and 𝑤 is the warp function. To find the best-matched solution, Ncorr needs to

calculate the minimum value of 𝐶𝐿𝑆 with an iterative procedure. In Ncorr, Taylor series

expansion is employed to search for the minimum 𝐶𝐿𝑆 by the following equation:

𝛻𝛻 𝐶𝐿𝑆(0)∆𝑝 + 𝛻 𝐶𝐿𝑆(0) = 0 (2.10)

where 𝛻 𝐶𝐿𝑆(0) is the gradient of 𝐶𝐿𝑆 at 𝑝 = 0 and 𝛻𝛻 𝐶𝐿𝑆(0) is the hessian matric of

𝐶𝐿𝑆 at 𝑝 = 0. The next approximation of 𝑝𝑟 is calculated by composing the old value

with the inverse of ∆𝑝 and detail of the process is illustrated in Figure 2.4

Figure 2.4 - Process of inverse compositional update (Pan et al., 2013).

The iteration will be updated by setting 𝑝𝑜𝑙𝑑 to 𝑝𝑛𝑒𝑤 at every beginning and the wrap

function is getting updated by the following equations (Blaber et al., 2015):

𝑤(𝛥𝜉𝑟𝑒𝑓; 𝑝𝑛𝑒𝑤) = 𝑤(𝑤(𝛥𝜉𝑟𝑒𝑓; 𝛥𝑝)−1; 𝑝𝑜𝑙𝑑)

(2.11)

[ 1 +

𝑑𝑢

𝑑𝑥𝑛𝑒𝑤

𝑑𝑢

𝑑𝑦𝑛𝑒𝑤𝑢𝑛𝑒𝑤

𝑑𝑣

𝑑𝑥𝑛𝑒𝑤1 +

𝑑𝑣

𝑑𝑦𝑛𝑒𝑤𝑣𝑛𝑒𝑤

0 0 1 ]

=

[ 1 +

𝑑𝑢

𝑑𝑥𝑜𝑙𝑑

𝑑𝑢

𝑑𝑦𝑜𝑙𝑑𝑢𝑜𝑙𝑑

𝑑𝑣

𝑑𝑥𝑜𝑙𝑑1 +

𝑑𝑣

𝑑𝑦𝑜𝑙𝑑𝑣𝑜𝑙𝑑

0 0 1 ]

∗

[ 1 + 𝛥

𝑑𝑢

𝑑𝑥𝛥𝑑𝑢

𝑑𝑦𝛥𝑢

𝛥𝑑𝑣

𝑑𝑥1 + 𝛥

𝑑𝑣

𝑑𝑦𝛥𝑣

0 0 1 ] −1

(2.12)

Finally, when 𝛥𝑝 gets small enough, the iteration will stop.


Page | 9

2.2.4 Full Field Displacement

In the last section, it discussed the core algorithms that Ncorr employed to seek for the

displacement parameters within a subset. To obtain the full-field displacement

measurement, Ncorr uses the Reliability Guided (RG-DIC) method. The difference

between RG-DIC and conventional DIC method is that the RG-DIC can prevent the

propagation of error from the previous iteration. In conventional DIC method, if some

points are wrongly computed due to area discontinuity or deformation discontinuity, the

results of those bad points will be transferred to the next point, leading to the propagation

of error (Pan, 2009). According to Pan’s studies, the RG-DIC needs first to define a seed

point where should be the area of the image that underwent the smallest amount of motion

during test. After selecting the seed point, the algorithms will calculate the corresponding

deformation parameters and 𝐶𝐿𝑆 for the seed point. First, the point with the lowest 𝐶𝐿𝑆

correlation coefficient is removed from the queue, the deformation parameters for the four

surrounding points are being calculated. The next proceed point will be based on the

surrounding points which has the lowest 𝐶𝐿𝑆 coefficient. The complete approach of RG-

DIC is illustrated in Figure 2.5. This approach will continue until the queue is empty.

Figure 2.5 - RG-DIC approach path (Blaber et al., 2015)

The benefits of the RG-DIC is that the robust process will make the bad data point (with


Page | 10

highest 𝐶𝐿𝑆 coefficient) being processed last where it can prevent these data being used

as the initial guess also ensure that the seed point is guided by 𝐶𝐿𝑆 coefficient where the

calculation path is always along the most reliable direction, and error propagation is

avoided.

2.2.5 Full Field Strain Measurement

Strain is more difficult to resolve than the displacement since the calculation of strain

involves differentiation and it is sensitive to noise. In Ncorr, one of the methods to

calculate the strain is by using Green-Lagrangian Strain which is obtained by using four

displacement gradients from IC-GN as illustrated in Equation 2.13 to 2.15:

𝐸𝑥𝑥 =1

2(2𝜕𝑢

𝜕𝑥+ (

𝜕𝑢

𝜕𝑥)2

+ (𝜕𝑣

𝜕𝑥)2

) (2.13)

𝐸𝑥𝑦 =1

2(𝜕𝑢

𝜕𝑦+𝜕𝑢

𝜕𝑥+𝜕𝑢

𝜕𝑥

𝜕𝑢

𝜕𝑦+𝜕𝑣

𝜕𝑥

𝜕𝑣

𝜕𝑦) (2.14)

𝐸𝑥𝑥 =1

2(2𝜕𝑣

𝜕𝑦+ (

𝜕𝑢

𝜕𝑦)2

+ (𝜕𝑣

𝜕𝑦)2

) (2.15)

These displacement gradients are directly obtained from IC-GN scheme. Although strains

can be computed from the numerical differentiation of the estimated displacement filed

by using the Equation 2.13 to 2.15, the numerical differential will amplify the noise that

comes from the displacement calculation (Pan et al., 2009). A pointwise local least square

fitting technique is introduced in Ncorr to smooth the computed displacement field then

the following differentiation would improve the accuracy of strain calculation (Pan et al.,

2009).

In this method, a square window which contains of (2𝑚 + 1)x(2𝑚 + 1) points (i.e., strain

calculation window) is selected. Then, the displacement distributions can be

approximated as a linear plane and the displacement parameters from IC-GN method will


Page | 11

be ignored. It employs a least squares plane fit on a subset of displacement data (𝑢 and

𝑣) to find the plane parameters in Equation 2.16 and 2.17:

𝑢𝑝𝑙𝑎𝑛𝑒(𝑥, 𝑦) = 𝑎𝑢,𝑝𝑙𝑎𝑛𝑒 + (𝜕𝑢

𝜕𝑥𝑝𝑙𝑎𝑛𝑒)𝑥 + (

𝜕𝑢

𝜕𝑦𝑝𝑙𝑎𝑛𝑒)𝑦

(2.16)

𝑣𝑝𝑙𝑎𝑛𝑒(𝑥, 𝑦) = 𝑎𝑣,𝑝𝑙𝑎𝑛𝑒 + (𝜕𝑣

𝜕𝑥𝑝𝑙𝑎𝑛𝑒)𝑥 + (

𝜕𝑣

𝜕𝑦𝑝𝑙𝑎𝑛𝑒)𝑦

(2.17)

where 𝑎𝑢,𝑝𝑙𝑎𝑛𝑒 , 𝑎𝑣,𝑝𝑙𝑎𝑛𝑒 , (𝜕𝑢

𝜕𝑥𝑝𝑙𝑎𝑛𝑒), (

𝜕𝑢

𝜕𝑦𝑝𝑙𝑎𝑛𝑒), (

𝜕𝑣

𝜕𝑥𝑝𝑙𝑎𝑛𝑒) and (

𝜕𝑣

𝜕𝑦𝑝𝑙𝑎𝑛𝑒) are unknown

polynomial coefficients; 𝑥, 𝑦 = −𝑚:𝑚. Now, Equation 2.16 and 2.17 can be rewritten as:

[ 1 −𝑚 −𝑚1⋮1⋮1

−𝑚 + 1⋮0⋮𝑚

−𝑚⋮0⋮𝑚

1 𝑚 𝑚 ]

{

𝑎𝑢,𝑝𝑙𝑎𝑛𝑒𝜕𝑢

𝜕𝑥𝑝𝑙𝑎𝑛𝑒)

𝜕𝑢

𝜕𝑦𝑝𝑙𝑎𝑛𝑒 }

=

{

𝑢𝑟𝑐∗ (−𝑚,−𝑚)

𝑢𝑟𝑐∗ (−𝑚 + 1,−𝑚)

⋮𝑢𝑟𝑐∗ (0,0)⋮

𝑢𝑟𝑐∗ (𝑚 − 1,𝑚)𝑢𝑟𝑐∗ (𝑚,𝑚) }

(2.18)

As illustrated in Equation 2.18, a simple linear least squares method will be used to solve

for those unknown polynomial coefficients. The strains value at the center point of the

local subsets can be computed based on the obtained polynomial coefficients, and the

noises can be largely removed through the local fitting (Pan et al., 2009). Once the

coefficients are determined, they can be substituted back to Equation 2.13 to 2.15 to solve

for 𝐸𝑥𝑥, 𝐸𝑥𝑦 and 𝐸𝑦𝑦. This process will be applied to the entire displacement field, and

the corresponding strain field could be solved.

2.2.6 Improvements in Ncorr

Ncorr allows a Multithreaded RG-DIC and a 4-way connected region will be partitioned in

the ROI. The process of multithreaded RG-DIC is demonstrated in Figure 2.6 which it

starts by growing sub-ROI around each seed point, one point at a time per iteration until

the entire ROI has been segmented.


Page | 12

Figure 2.6 - Ncorr implementation of RG-DIC (Blaber et al., 2015).

Ncorr also allows the conversion from Eulerian to Lagrangian which is used to analyze

discontinuous displacement fields, but it relies on the fact that the discontinuous (cracks)

are visible in deformed image (Blaber et al., 2015). This allows Ncorr to create the ROI

for the deformed image rather than the reference image and perform DIC; then the

displacements can be converted back to Lagrangian perspective through the Eulerian to

the Lagrangian algorithm (Blaber et al., 2015). As shown in Figure 2.6, this illustrates how

the updated ROI technique works which allow the Ncorr to analyze for high strain analysis

or discontinuity analysis (Blaber et al., 2015).

Figure 2.7 - Updating ROI process (Blaber et al., 2015).


Page | 13

Chapter 3: DIC Validation Tests

3.1 Summary of Test Specimen

As described in Chapter 1, the DIC validation tests were conducted on two types of

structural material: steel and concrete. Tensile tests were performed on the steel coupons

which were prepared and modified based on ASTM E8M standard. The material used

was carbon steel with estimated yielding stress around 350 MPa. The detailed dimension

of tested steel coupons was illustrated as shown in Figure 3.1 and Figure 3.2.

Figure 3.1 - Schematic of steel specimen.


Page | 14

Figure 3.2 - Schematic of steel specimen.

As for the compression test, two types of concrete specimens were prepared based on

ASTM C192/C192M.The specimens were cast by a normal-density concrete with a

compressive strength between 35 and 50 MPa, and a maximum aggregate size of 14 mm.

The size of the concrete cube specimen is 150 x 150 x 150 mm and 100 x 200 mm for

the cylinder. The preparation process and curing condition are shown in Figure 3.3 and

Figure 3.4.


Page | 15

Figure 3.3 - Casting process for concrete specimen.

Figure 3.4 - Curing process for concrete specimen (highlight by red-box).


Page | 16

3.2 Steel Coupons Tensile Test

Since the surface of the steel coupon was relatively smooth, the MATLAB script may not

be able to capture enough pixel details to process the DIC analysis. Additional pattern

painting should be used for the specimen surface treatment. The process of the surface

treatment is illustrated as shown in Figure 3.5. First, the steel coupon is painted by a

primer which can create a preparatory coating to increase the adhesion of the pattern

painting, and the durability of the pattern painting. After 24 hours, when the primer painting

gets dried, a stone-textured painting is needed to amplify the pixels.

Figure 3.5 - a) priming with first layer of coating b) then coating with a texturized

paint.

a) b)


Page | 17

After the surface treatment, the next step is to place strain gauges on the untreated

surface of the specimen. In the same time, the locations of the placed strain gauges shall

be marked on the front of the specimen, which is covered by the textured painting. As

shown in Figure 3.6, the marked locations of the strain gauges are highlighted by the red

box.

Figure 3.6 - a) strain gauges at the back. b) marked location of strain gauges at

front.

3.3 Concrete Compression Test

Unlike steel, concrete is a mixture of aggregate and cement where a natural surface

pattern is possible to be formed, and surface treatment could be waived in the preparation

stage. Hence, a comparison test is made between the specimen with surface treatment

a) b)


Page | 18

and the specimen without any painting. Through the comparison test, it tends to analyze

the effect of the surface pattern condition on the accuracy of the results. The preparation

process for the specimen with spray painting is similar to the process that is described in

Section 3.2.

Figure 3.7 - Surface treatment for concrete cubes: paint with primer (left) and

stone-textured paint after priming (right).

A comparison test between DIC measurement and conventional strain gauge

measurement is difficult to make for concrete cube compression tests. Therefore, the

main goal for this validation test is to obtain the displacement field through running DIC

analysis and helps to identify the crack formation on the concrete surface.

Besides the testing on concrete cube sample, a 100 x 200 mm concrete cylinder will also

be tested. In this case, longitudinal strain measurement (LVDT) can be setup; then, the

strain measurement from LVDT can be used to validate the result from DIC analysis. The


Page | 19

experimental setup for LVDT on the concrete cylinder is demonstrated as shown in Figure

3.8.

Figure 3.8 - LVDT set up for Cylinder specimen.


Page | 20

Chapter 4: Steel Coupon Tensile Test

In this chapter, the validation test results for steel coupon test will be presented in the

following sections. During the tensile testing, steel coupons are placed in MTS 1,000 kN

load frame and loaded until they reach necking. Each test has a different experiment

setting. In Test 1, the tensile test is conducted on the specimens which are not prepared

by using a primer. Based on the result from Test 1, in Test 2, the specimens are painted

with primer first and pattern painting later. In addition, a comparison test of different

camera settings is also performed and the discussion of how these settings will affect the

result accuracy. As for the last test, Test 3, improvements are made based on the results

from Test 1 and 2, by improving painting techniques, camera parameters and light

condition.

4.1 Steel Coupon Test 1

4.1.1 Test 1 Result

During the test, a digital camera is required to obtain the deformed images throughout the

experiment. The camera is placed in front of the testing load frame to capture images

throughout the deformation, and the settings of the camera shall be adjusted in

accordance under different lighting condition. Figure 4.1 shows the setup of the sample

test.


Page | 21

Figure 4.1 - Camera setup during test.

In this test, the camera contains the following settings:

Camera model: Olympus OM-D E-M5

Focal length: 50 mm

F-stop: f/6.3

ISO-speed: ISO-800

Exposure time: 1/3 sec

Distance to the specimen: 70 cm

Resolution of captured image: 4608 x 3456 pixels

As discussed in Chapter 3, in the test preparation, strain gauges are placed in the


Page | 22

backside of the steel coupons and their locations have been marked in the front surface

of the steel coupons. After capturing the deformed images, Ncorr can obtain the point

data and compare to the strain gauge value. Locations of the point data are illustrated in

Figure 4.2.

Figure 4.2 - Locations of strain gauges, SC-1 on left and SC-H-1on right.


Page | 23

Table 4.1 - Strain measurement from DIC and strain gauges for SC-1. Applied load (kN)

Strain_SG1 Strain_SG1_DIC Error (%)


10.66 0.0002 0.0006 309.15 0.0002 0.0001 31.65 20.45 0.0003 0.0004 18.00 0.0003 0.0005 42.36

30.70 0.0005 0.0003 29.45 0.0005 0.0000 93.20 40.70 0.0007 0.0008 18.16 0.0007 0.0008 15.15

50.44 0.0008 0.0008 4.28 0.0009 0.0011 25.34 60.48 0.0010 0.0012 14.51 0.0011 0.0013 15.56

70.45 0.0012 0.0011 8.79 0.0013 0.0013 3.66 80.46 0.0014 0.0011 20.61 0.0015 0.0020 31.48

90.51 0.0016 0.0017 5.79 0.0017 0.0020 15.70 100.43 0.0018 0.0020 7.87 0.0019 0.0023 19.77

110.63 0.0020 0.0022 8.17 0.0022 0.0021 4.09 120.17 0.0024 0.0021 12.23 0.0025 0.0026 3.83

123.10 0.0026 0.0029 10.38 0.0027 0.0027 2.30 125.06 0.0031 0.0030 1.18 0.0030 0.0028 7.42

126.05 0.0037 0.0036 2.52 0.0034 0.0034 0.55 127.03 0.0047 0.0049 4.52 0.0044 0.0043 0.74

128.03 0.0061 0.0069 12.49 0.0062 0.0062 0.67 129.03 0.0077 0.0073 4.62 0.0080 0.0078 2.16

130.02 0.0091 0.0098 8.42 0.0095 0.0095 0.52

Figure 4.3 - Load vs. Strain Curve for SC-1.

0.000

0.002

0.004

0.006

0.008

0.010

0.012

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0

Str

ain

(m

m/m

m)

Applied Load(kN)

SC-1 Load -Strain

Strain_SG1

Strain_SG1_DIC

Strain_SG2

Strain_SG2_DIC


Page | 24

Figure 4.4 - Formation of overall strain field (Eyy) for SC-1.


Page | 25

Table 4.2 - Strain measurement from DIC and strain gauges for SC-H-1 Applied load (kN)



10.44 0.0002 0.0003 21.00 0.00011 0.00022 108.21 20.43 0.0005 0.0002 50.32 0.00022 0.00009 55.92

30.53 0.0008 0.0009 21.06 0.00034 0.00384 1045.61 40.39 0.0010 0.0011 8.60 0.00045 0.00018 59.73

50.47 0.0013 0.0015 11.80 0.00057 0.00045 20.59 60.24 0.0016 0.0016 0.00 0.00069 0.00053 22.72

70.29 0.0019 0.0020 1.75 0.00081 0.00092 13.84 80.42 0.0023 0.0021 8.88 0.00094 0.00101 7.49

90.59 0.0028 0.0026 7.64 0.00106 0.00111 4.61 100.49 0.0037 0.0049 31.06 0.00119 0.00102 14.57

105.07 0.0114 0.0108 5.92 0.00129 0.00123 4.53 110.06 0.0274 0.0230 16.18 0.00143 0.00207 44.94

113.05 0.0402 0.0346 14.03 0.00154 0.00149 3.01 115.04 0.0455 0.0431 5.40 0.00163 0.00166 1.57

Figure 4.5 - Load vs. Strain Curve for SC-H-1.

0.000

0.005

0.010

0.015

0.020

0.025

0.030

0.035

0.040

0.045

0.050

0.0 20.0 40.0 60.0 80.0 100.0 120.0 140.0

Str

aain

(m

m/m

m)

Applied Load(kN))

SC-H-1 Load-Strain

Strain_SG3

Strain_SG3_DIC

Strain_SG4

Strain_SG4_DIC


Page | 26

Figure 4.6 - Formation of strain field under different loading for SC-H-1.


Page | 27

4.1.2 Discussion of Test 1 Result

The results from Test 1 showed that most of the strain measurements from DIC analysis

had an error of less than 30% compared to the data from strain gauges. However, there

were some deviant points, and this could come from the spray coating on the specimen

using the DIC method. The surface pattern was created by a stone pebble textured spray

paint which could also create a 3-D texture effect on the surface and light reflection could

occur when the camera is capturing the deformed images.

Another possible cause could be the painting layer may not have enough adhesion to be

bonded on the specimen surface. Since in this test, the steel coupon only had one paint

layer without applying any primer. When the loading force was increasing, the painting

may begin to fall off from the surface which the Ncorr could not obtain enough pixel

information to process the DIC analysis. As shown in Figure 4.7, the right side of the

image is the deformed image, and the painting layer has fallen off due to the increased

loading force. The region with the missing surface pattern would not have enough pixel

details for the MATLAB to process DIC analysis and improve the inaccuracy in strain field

generation as shown in Figure 4.8.

Figure 4.7 - a) Reference image b) deformed image.


Page | 28

Figure 4.8 - Inaccuracy due to the missing painting from deformed image.

After the first test, to ensure the adhesion for the pattern painting on the following tests,

a primer was used for the upcoming tests to create a preparatory coating on the specimen

which can increase the adhesion of the pattern painting and the durability of the pattern

painting.


4.2.1 Test 2 Result



Focal length: 50 mm


Page | 29

F-stop: f/6.3

Exposure time: 0.62 sec for ISO-800; 1.6 sec for ISO-320



Location of the point data that will be collected from Ncorr and strain gauges is

demonstrated in Figure 4.9.

Figure 4.9 - Locations of strain gauges, SC-H-2

Table 4.3 - Strain measurement from DIC and strain gauges for SC-H-2. ISO 320 ISO 800

Applied Load (kN) Strain_SG5 Strain_SG5_DIC Error(%)

Applied Load (kN) Strain_SG5 Strain_SG5_DIC Error(%)

10.3 0.0024 0.0007 71.4 10.5 0.00022 0.00032 45.34 20.3 0.0025 0.0011 54.5 20.5 0.00044 0.00028 35.38

30.1 0.0026 0.0015 42.5 30.5 0.00067 0.00051 23.21 40.2 0.0027 0.0013 52.8 40.6 0.00091 0.00072 21.17

50.1 0.0028 0.0021 23.5 50.7 0.00119 0.00103 13.78 60.4 0.0029 0.0018 37.8 60.5 0.00153 0.00191 25.04

70.4 0.0030 0.0026 11.7 70.5 0.00200 0.00197 1.73 80.4 0.0031 0.0031 0.7 80.5 0.00276 0.00319 15.41

90.1 0.0032 0.0034 6.0 89.8 0.00421 0.00409 2.72


Page | 30

Figure 4.10 - Load vs. Strain Curve for SC-2 with ISO 320.

Figure 4.11 - Load vs. Strain Curve for SC-2 with ISO 800.

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

0.0040

0.0045

0.0 20.0 40.0 60.0 80.0 100.0 120.0

Str

ain

(m

m/m

m)

Applied Load (kN)

SC-H-2 Load- Strain (ISO 320)

Strain_SG5

Strain_SG5_DIC

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.0030

0.0035

0.0040

0.0045

0.0 20.0 40.0 60.0 80.0 100.0

Str

ain

(m

m/m

m)

Applied Load (kN))

SC-H-2 Load- Strain (ISO 800)

Strain_SG5

Strain_SG5_DIC


Page | 31

Figure 4.11 - Formation of overall strain field (Eyy) for SC-H-2 with ISO-320.


Page | 32

Figure 4.12 - Formation of overall strain field (Eyy) for SC-H-2 with ISO 800


Page | 33


In Test 2, the comparison test was made by using different camera parameters on the

same testing specimen for running DIC analysis. The first one had a setting with ISO-800

and an exposure time of 1/3 second. The second one had a setting with ISO-320 and an

exposure time of 1.6 seconds. ISO measures the sensitivity of the image sensor; a higher

ISO number means the camera can be more sensitive to light and can be used in a dark

environment (Mikota and Pavlovic, 2009). But high ISO may also create a noisy or grainy

image which may cause a greater inaccuracy while using the DIC method (Mikota and

Pavlovic, 2009). Comparing the load vs. strain curve from Figure 4.10 and Figure 4.11,

the curve with a high ISO setting is closer to the strain measured from the strain gauge

which indicates it has a less error than the low ISO setting. The reason that the high ISO

setting has a higher actuary in this experiment is that the low ISO setting has a longer

exposure time than the higher one. One possible explanation here could be the minor

shaking by manually taking images when pushing the shutter during the long exposure

time. This minor shaking could induce the high correlation coefficient when setting the

seed placement.

Based on the discussion above, one suggestion to increase the accuracy of DIC is to set

the camera parameters with low ISO value, and short exposure time. In addition, a good

lighting condition should be taken into consideration which can be used to reduce the ISO

value in the future test.


4.3.1 Test 3 Result

Test 3 is conducted upon on previous two tests; the camera settings are modified based


Page | 34

on the results from Test 2 which has a low ISO value and shorter exposure compare to

the earlier tests. In Test 1 and 2, steel coupons were only loaded until the material reached

the necking stage. In Test 3, the steel coupon had been continued loaded until it failed to

validate whether DIC method can analyze the discontinuity region (i.e., cracks).



Focal length: 50 mm

F-stop: f/6.3

ISO-speed: ISO-250




Location of the point data that will be collected from Ncorr and strain gauges is

demonstrated in Figure 4.9.

Figure 4.13 - Locations of strain gauges, SC-H-3 left and SC-2 right.


Page | 35

Table 4.4 - Strain measurement from DIC and strain gauges for SC-H-3. Applied Load (kN) Strain_SG_6 Strain_SG_6_DIC error(%)

10.2 0.00021 0.00019 5.40 20.7 0.00042 0.00033 21.83 30.5 0.00064 0.00074 16.54 40.4 0.00087 0.00071 18.55 50.7 0.00115 0.00104 9.46 60.5 0.00148 0.00147 0.71 70.5 0.00195 0.00181 7.28 80.4 0.00269 0.00262 2.41 90.6 0.00434 0.00382 11.95

100.1 0.01096 0.00993 9.35 104.1 0.01791 0.01651 7.80 105.1 0.02006 0.01857 7.41

Figure 4.14 - Load vs. Strain Curve for SC-H-3.

0.000

0.005

0.010

0.015

0.020

0.025

0.0 20.0 40.0 60.0 80.0 100.0 120.0

Str

ain

(m

m/m

m)

Applied Load (kN)

SC-H-3 Load-Strain

Strain_SG_6

Strain_SG_6_DIC


Page | 36

Figure 4.15 - Formation of strain field under different loading for SC-H-3.


Page | 37

Figure 4.16 - Failure process for SC-H-3.


Page | 38

Table 4.5 - Strain measurement from DIC and strain gauges for SC-2. Applied

load (kN) Strain_SG3 Strain_SG3_DIC Error

(%) Strain_SG4 Strain_SG4_DIC Error

(%)

10.56 0.00015 0.00035 140.85 0.00016 0.00039 153.33 20.59 0.00030 0.00051 73.25 0.00032 0.00044 39.52

30.72 0.00045 0.00049 9.47 0.00048 0.00066 39.90 40.23 0.00060 0.00067 12.83 0.00064 0.00078 22.10

50.37 0.00076 0.00086 13.45 0.00081 0.00105 30.46 60.38 0.00094 0.00104 11.35 0.00100 0.00114 14.53

70.57 0.00112 0.00107 4.91 0.00120 0.00137 14.10 80.52 0.00133 0.00136 2.56 0.00142 0.00147 3.47

85.54 0.00145 0.00147 1.12 0.00155 0.00167 7.72 90.52 0.00158 0.00168 6.36 0.00170 0.00195 14.70

95.59 0.00173 0.00181 4.64 0.00187 0.00202 8.20 99.53 0.00186 0.00217 16.45 0.00202 0.00229 13.60

Figure 4.17 - Load vs. Strain Curve for SC-2.

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0.00 20.00 40.00 60.00 80.00 100.00 120.00

Str

ain

(m

m/m

m)

Applied Load (KN)

SC-2 Load -Strain

Strain_SG_7

Strain_SG_7_DIC

Strain_SG_8

Strain_SG_8_DIC


Page | 39

Figure 4.18 - Formation of strain field under different loading for SC-2.


Page | 40


The setting of Test 3 is based on the results from the earlier test results. First, the camera

has an ISO of 250 and exposure time of 1/13 sec. Looking back to the strain value from

SC-H-3, it has the highest error percentage of 21.8%, and the lowest value is 0.71%. In

SC-H-2, the strain value for using ISO-320 and ISO 800 has unstable performance which

most of the data has an error greater than 30%, and the highest point can have an error

up to 71.4%.

By comparing the error with previous tests, Test 3 has shown an improved accuracy on

obtaining the strain than the previous tests. However, from the data, when the strain value

is small, the error is greater than the data has a high strain value. For example, in SC-2,

the strain value has an error of 153% when the applied load is around 10.5 kN. The

possible explanation could be traced back to the setting of using Ncorr. As explained in

Chapter 2, Ncorr is subset-based DIC algorithms, and it analyzes the images by

partitioned the reference image into multiple subsets with adjustable size. The size of the

subset can be modified through the beginning of the analysis. If the pixel movement is

relatively small, the inaccuracy could be induced due to the incorrect selection of the

subset size.

To further explore the application of DIC, the steel coupon SC-H-3 was loaded until

fractures. However, this exceeds the maximum value of strain gauges. Hence, no

comparison results could be made to discover the accuracy of DIC analysis for the

material under yielding or fracture conditions. By the results, it shows that the DIC can

identify the fracture pattern which can be used to identify any fracture patterns that occur

in the material surface.


Page | 41

Chapter 5: Concrete Compression Test

In this chapter, the validation test results for concrete compression test will be presented

in the following sections. During the compression testing, concrete specimens are placed

in MTS 4,500 kN load frame and loaded until they fail. Each test has a different experiment

setting. In Test 1, a comparison test of pained surface and the unpainted surface has

been made. After Test 1, a steel block is placed on top of the concrete cube which aims

to create a concentrated load for large crack formation in the concrete failure mechanism.

As for the last test, Test 3, a compression test is performed on the cylinder specimen.

LVDT strain gauge can be placed on the concrete cylinder, and the strain measurement

can be used to validate the accuracy of the strain from DIC analysis.

5.1 Concrete Cube Test 1

5.1.1 Cube Test 1 Result

The experiment setup for concrete compression test is similar to the setup of steel tensile

test. A digital camera is placed in front of the testing load frame to capture images

throughout the deformation. The deformed images are captured by a time interval of 8

second. Figure 5.1 shows the setup of the sample test.


Page | 42

Figure 5.1 - Experiment setup for compression test on concrete cube.

In this test, the camera contained the following settings:


Focal length: 50 mm (Cube#1) 46 mm (Cube#2)

F-stop: f/6.3 (Cube#1) f/8 (Cube#2)

ISO-speed: ISO-320

Exposure time: 1/8 sec (Cube#1) 1/10 sec (Cube#2

Distance to the specimen: 60 mm


Images interval: 8 sec


Page | 43

For the compression test on the concrete cube, strain gauges are difficult to place, and

no data can be used to validate the accuracy of DIC analysis. The proposed validate test

is through comparing the displacement value from Ncorr along the centerline of the

concrete cube as illustrated in Figure 5.2 and to the displacement value which is

measured from the load frame by the hydraulic jack movement.

Figure 5.2 - Locations of data collection point. Cube#1 (left) vs Cubbe#2 (right).

Figure 5.3 - Displacement vs Time for different data point on Cube#1.

-2.500

-2.000

-1.500

-1.000

-0.500

0.0000 50 100 150 200 250 300 350 400

Dis

pla

cem

ent in

y d

ire

ction

(m

m)

Time (sec)

Cube#1 Displacement vs Time

1

2

3

4

5

6

7

8


Page | 44

The relative displacement for the concrete cube is obtained by calculating the difference

between the point which is the closest to the loading region and the farthest from the

loading region. The loading mechanism for the MTS 4,500 kN is that the top of the

concrete cube is being held under the loading and the compression load comes from the

hydraulic jack which locates in the bottom of the specimen. Hence, the closest point to

the loading region is point 8, and the farthest is point 1. The following equation obtains

the relative displacement:

∆RD = ∆8 − ∆1

(5.1)


displacement from Ncorr of Cube#1 .

-2.000

-1.800

-1.600

-1.400

-1.200

-1.000

-0.800

-0.600

-0.400

-0.200

0.0000 50 100 150 200 250 300 350 400

Dis

pace

me

nt in

y d

ire

ction

(m

m)

Time (sec)

Cuve#1 Displacement vs Time

MTS

Relativedisplacement


Page | 45

Table 5. 1 - Displacement from DIC and MTS load frame for Cube#1.

Sec ∆1 y disp (mm) ∆8 y disp(mm) ∆𝑅𝐷(mm) ∆𝑀𝑇𝑆 (mm)

8 -0.450 -0.485 -0.035 -0.034 16 -0.484 -0.529 -0.045 -0.071 24 -0.507 -0.561 -0.054 -0.106 32 -0.573 -0.630 -0.058 -0.140 40 -0.601 -0.663 -0.062 -0.176 48 -0.632 -0.702 -0.070 -0.211 56 -0.659 -0.737 -0.078 -0.246 64 -0.698 -0.781 -0.084 -0.281 72 -0.734 -0.824 -0.090 -0.316 80 -0.767 -0.867 -0.100 -0.352 88 -0.800 -0.905 -0.106 -0.386 96 -0.819 -0.933 -0.114 -0.422

104 -0.862 -0.989 -0.127 -0.457 112 -0.878 -1.017 -0.139 -0.493 120 -0.900 -1.050 -0.150 -0.528 128 -0.914 -1.081 -0.167 -0.563 136 -0.941 -1.125 -0.184 -0.598 144 -0.945 -1.146 -0.201 -0.633 152 -0.957 -1.172 -0.215 -0.669 160 -0.982 -1.206 -0.223 -0.704 168 -1.006 -1.247 -0.241 -0.739 176 -1.020 -1.286 -0.266 -0.774 184 -1.036 -1.310 -0.274 -0.809 192 -1.049 -1.342 -0.294 -0.845 200 -1.060 -1.372 -0.312 -0.880 208 -1.082 -1.411 -0.329 -0.915 216 -1.090 -1.436 -0.346 -0.950 224 -1.106 -1.468 -0.362 -0.985 232 -1.124 -1.507 -0.383 -1.021 240 -1.132 -1.532 -0.400 -1.056 248 -1.154 -1.567 -0.412 -1.091 256 -1.165 -1.593 -0.428 -1.125 264 -1.184 -1.631 -0.447 -1.161 272 -1.197 -1.663 -0.466 -1.197 280 -1.220 -1.700 -0.480 -1.232 288 -1.226 -1.732 -0.506 -1.267 296 -1.242 -1.760 -0.518 -1.302 304 -1.249 -1.785 -0.536 -1.338 312 -1.260 -1.817 -0.557 -1.373 320 -1.276 -1.846 -0.570 -1.408 328 -1.290 -1.881 -0.591 -1.442 336 -1.291 -1.914 -0.624 -1.479 344 -1.291 -1.935 -0.644 -1.513 352 -1.303 -1.971 -0.668 -1.549 360 -1.313 -2.006 -0.694 -1.583 368 -1.323 -2.043 -0.720 -1.619 376 -1.334 -2.079 -0.745 -1.654 384 -1.335 -2.106 -0.771 -1.689 392 -1.351 -2.154 -0.804 -1.724 400 -1.352 -2.182 -0.831 -1.759


Page | 46

Figure 5.5 - Displacement vs Time for different data point on Cube#2.


displacement from Ncorr of Cube#2.

-2.000

-1.500

-1.000

-0.500

0.000

0.500

1.000

1.500

2.000

0 50 100 150 200 250 300 350 400

Dis

pla

cem

ent in

y d

ire

ction

(m

m)

Time (sec)


1

2

3

4

5

6

7

8

-2.000

-1.500

-1.000

-0.500

0.000

0.500

0 50 100 150 200 250 300 350 400

Dis

pla

cem

ent in

y d

ire

ction

(m

m)

Time (sec)


MTS



Page | 47

Table 5. 2 - Displacement from DIC and MTS load frame for Cube#2


8 0.754 0.923 0.169 -0.035 16 0.738 0.896 0.158 -0.070 24 0.717 0.865 0.148 -0.105 32 1.534 1.656 0.122 -0.141 40 0.463 0.447 -0.016 -0.176 48 0.423 0.399 -0.024 -0.211 56 0.413 0.378 -0.035 -0.246 64 0.375 0.328 -0.047 -0.282 72 0.351 0.293 -0.059 -0.317 80 0.326 0.258 -0.068 -0.353 88 0.280 0.212 -0.068 -0.388 96 0.269 0.193 -0.076 -0.424

104 0.247 0.160 -0.087 -0.459 112 0.232 0.131 -0.101 -0.494 120 0.195 0.082 -0.113 -0.530 128 0.165 0.037 -0.128 -0.565 136 0.157 0.017 -0.140 -0.600 144 0.122 -0.029 -0.150 -0.638 152 0.111 -0.053 -0.164 -0.673 160 0.094 -0.083 -0.177 -0.707 168 0.075 -0.119 -0.194 -0.741 176 0.070 -0.139 -0.210 -0.776 184 0.044 -0.182 -0.226 -0.810 192 0.036 -0.205 -0.241 -0.845 200 0.021 -0.239 -0.260 -0.880 208 0.015 -0.261 -0.276 -0.915 216 -0.009 -0.306 -0.298 -0.951 224 -0.036 -0.359 -0.323 -0.986 232 -0.032 -0.380 -0.348 -1.021 240 -0.029 -0.403 -0.374 -1.056 248 -0.053 -0.453 -0.400 -1.091 256 -0.067 -0.489 -0.422 -1.126 264 -0.073 -0.528 -0.455 -1.161 272 -0.073 -0.563 -0.490 -1.197 280 -0.071 -0.594 -0.523 -1.232 288 -0.081 -0.648 -0.566 -1.267 296 -0.090 -0.694 -0.605 -1.302 304 -0.081 -0.729 -0.648 -1.337 312 -0.072 -0.766 -0.695 -1.373 320 -0.065 -0.819 -0.754 -1.408 328 -0.066 -0.876 -0.810 -1.443 336 -0.064 -0.934 -0.870 -1.478 344 -0.073 -1.006 -0.933 -1.513 352 -0.048 -1.044 -0.996 -1.548 360 -0.056 -1.116 -1.061 -1.582 368 -0.014 -1.140 -1.126 -1.618 376 -0.242 -1.416 -1.174 -1.652 384 -0.031 -1.261 -1.230 -1.686 392 -0.027 -1.304 -1.277 -1.721


Page | 48

5.1.2 Discussion of Cube Test 1 Result

In Test 1, concrete cubes with different surface conditions had been tested by MTS Stiff

Frame 4,500 kN. During the test, the hydraulic grip gripped the top of the concrete cube

and the compression load was applied by the hydraulic jack to the bottom of the cube. In

Figure 5.3 and 5.5, the displacement verse time curves are obtained by eight different

points along the centerline of each concrete cube. Number 8 locates at the bottom of the

specimen where it has the greatest displacement in the y-direction and number 1 has the

smallest displacement since it is the farthest point from the load region. The behaviors

from the curves match with the experiment setup since the point near to the load region

which will undergo the greater deformation.

However, the relative displacement does not match with the displacement data from the

MTS Frame. From the displacement curves in Figure 5.4 and 5.6, at the beginning of the

loading, the displacement from Ncorr matches the initial displacement from the MTS

Frame. When the load increases, the difference between the MTS displacement and the

relative displacement from the concrete cube becomes larger. The loading from the

hydraulic jack could also carry the displacement from the load frame which induced the

difference between MTS measurement and the DIC analysis.

Besides comparing the displacement, another way to validate the test is to examine the

displacement rate from the DIC analysis. The test machine has an applied load at a rate

of 0.0044 mm/sec. From the strain curves in Figure 5.4 and 5.6, they show that at the

beginning, all locations have a linear behavior with a slope equal to the machine rate.

However, when the time increases, the data locations which are further than the applied

load location show that the slope is decreased, and the displacement became smaller on

top. The curve indicated that the point that closes to the applied load has the largest

displacement and the point which is the farthest to the applied load has the smallest


Page | 49

displacement.

The strain curves from Cube#1 and #2 have shown that they present the same behavior.

But, at the beginning of the curve in Cube#2 has a positive y displacement which indicates

that the concrete cube has been loaded in tension and does not match to the experiment

setup. This unreasonable result could be due to the unpainted concrete surface could not

have enough pixel content for the script at the initial stage of the loading. When the load

increases, the concrete surface may occur more cracks due to the increased compression

load which helps the script to obtain enough pixel information to process the DIC analysis.

Figure 5.7 - V displacement field (left) and current image at same stage (right) for

Cube#2.

Another issue from this comparison is that the Ncorr can only identify the major cracks

and fail to detect the small cracks. In Figure 5.7, Ncorr could only identify major cracks in

Cube#2. The contour shape from the displacement field matches with the major large

cracks compare to the current images (under deformed). By the counter color, it shows

that the concrete cube has been divided into two parts due to the cracking. The bottom

section in blue counter has greater displacement than the top portion. Some points from

the top portion have a displacement close to zero which indicates rigid body movement


Page | 50

could occur. However, as shown in the red box in the right side image, the displacement

field is lack of the information of those relatively smaller cracks.

In general, Test 1 shows that the Ncorr can run usefully on concrete material which has a

clear surface pattern. However, the accuracy of the DIC analysis should be verified in

further tests since the displacement which is measured by the machine could have large

effects from the overall stiffness of the test frame.

5.2 Concrete Cube Test 2

5.2.1 Cube Test 2 Result

In Test 2, the failure mechanism is different from the Test 1. A 2-inch steel block had been

placed on top of the concrete cube to create a concentrated load which large cracks can

occur during the compression test.

In this test, the camera contained the following settings:


Focal length: 40 mm

F-stop: f/6.3

ISO-speed: ISO-320





In Test 2, the way to obtain the displacement from Ncorr is the same as Test 1. The

displacement is obtained from the points that along the centerline of the concrete cube


Page | 51

as illustrated in Figure 5.8.

Figure 5.8 - Locations of data collection point in Cube#3.


Page | 52

Figure 5.9 - Displacement vs. Time curve for Cube#3.


displacement from Ncorr of Cube#3.

-3.000

-2.500

-2.000

-1.500

-1.000

-0.500

0.0000 50 100 150 200 250 300 350 400

Dis

pla

cem

ent in

y d

ire

ction

(m

m)

Time (sec)


1

2

3

4

5

6

7

8

-1.800

-1.600

-1.400

-1.200

-1.000

-0.800

-0.600

-0.400

-0.200

0.000

0.200

0 100 200 300 400

Dis

pla

cem

ent in

y d

ire

ction

(m

m)

Time (sec)


MTS



Page | 53

Table 5. 3 - Displacement from DIC and MTS load frame for Cube#3.


8 -0.895 -0.836 0.059 -0.035

16 -0.987 -0.942 0.045 -0.070 24 -1.031 -0.998 0.034 -0.105

32 -1.080 -1.057 0.023 -0.140 40 -1.129 -1.116 0.014 -0.176

48 -1.141 -1.143 -0.002 -0.211 56 -1.184 -1.199 -0.015 -0.246

64 -1.213 -1.240 -0.027 -0.282 72 -1.244 -1.285 -0.041 -0.317

80 -1.276 -1.330 -0.054 -0.351 88 -1.296 -1.364 -0.069 -0.387

96 -1.312 -1.393 -0.081 -0.422 104 -1.345 -1.438 -0.093 -0.457

112 -1.370 -1.471 -0.102 -0.492 120 -1.389 -1.502 -0.113 -0.528

128 -1.421 -1.543 -0.122 -0.563 136 -1.453 -1.586 -0.134 -0.598

144 -1.474 -1.618 -0.145 -0.633 152 -1.496 -1.651 -0.155 -0.668

160 -1.505 -1.670 -0.165 -0.703 168 -1.535 -1.710 -0.175 -0.739

176 -1.561 -1.746 -0.185 -0.774 184 -1.591 -1.781 -0.190 -0.809

192 -1.618 -1.811 -0.193 -0.844 200 -1.638 -1.836 -0.199 -0.880

208 -1.663 -1.868 -0.205 -0.915 216 -1.692 -1.905 -0.214 -0.949

224 -1.707 -1.928 -0.221 -0.985 232 -1.770 -1.998 -0.228 -1.020

240 -1.801 -2.022 -0.220 -1.056 248 -1.815 -2.042 -0.228 -1.091

256 -1.877 -2.110 -0.234 -1.126 264 -1.915 -2.158 -0.242 -1.162

272 -1.945 -2.198 -0.254 -1.197 280 -1.952 -2.241 -0.290 -1.232

288 -1.996 -2.347 -0.351 -1.267 296 -1.984 -2.363 -0.379 -1.302

304 -1.993 -2.408 -0.415 -1.338 312 -2.019 -2.453 -0.434 -1.374

320 -2.046 -2.506 -0.460 -1.408 328 -2.089 -2.575 -0.486 -1.444

336 -2.088 -2.607 -0.519 -1.478 344 -2.128 -2.671 -0.543 -1.514

352 -2.120 -2.709 -0.589 -1.549 360 -2.151 -2.765 -0.613 -1.584

368 -2.188 -2.821 -0.633 -1.619

5.2.2 Discussion of Cube Test 2Result

As shown in Figure 5.9, the strain curves for Cube#3 has similar performance as Cube#1,

and Cube#2 which the data point near to the applied load has the greatest displacement


Page | 54

and the slope is approximately equaled to the machine rate. As shown in Figure 5.11,

through the overall displacement field from Ncorr, it is clearly shown the formation of the

main cracks that occur along the centerline of the concrete cube.

Figure 5.11 - Cracking formation for Cube#3.


Page | 55

As shown in the figure below, the displacement contour shows that the concrete cube has

been separated into two parts due to the applied concentrated load. Compare to the

deformed image, the location of the separation line in the displacement field matches with

the cracks in the deformed image.

Figure 5.12 - U displacement (left) and current image (right) of Cube#3.

In conclusion, the result from running the Ncorr indicates that it can identify the cracking

location.

5.3 Concrete Cylinder Test 1

5.3.1 Cylinder Test 1 Result

In this test, LVDT is placed to obtain the strain and compared to the strain value from

Ncorr to validate the accuracy of DIC analysis on concrete specimen. In this test, the

camera contained the following settings:



Page | 56

Focal length: 50 mm

F-stop: f/6.3

ISO-speed: ISO -320


Distance to the specimen: 60 mm



LVDT measures the displacement value from the top and bottom of the cylinder sample,

and the average displacement value between these two points. The strain from the LVDT

can be determine by the following equation:

𝐸𝑦𝑦 = ∆𝑎𝑣𝑔

𝐿𝐿𝐷𝑉𝑇 (5.2)

Figure 5.13 - Location of data collection points for Cylinder #1.


Page | 57

Figure 5.14 - Displacement vs. Time curve for Cylinder#1.

Table 5. 4 - Strain from DIC and LVDT for Cylinder#1

sec Eyy,1(mm/mm) Eyy,2(mm/mm) Average Eyy SG_Avg Error (%)

8 0.0016 0.0016 0.0016 0.0018 22464.41

16 0.0019 0.0015 0.0017 0.0016 27667.11 24 0.0020 0.0013 0.0017 -0.0032 12998.33

32 0.0003 0.0000 0.0002 -0.0119 420.98 40 -0.0001 0.0001 0.0000 -0.0202 100.00

48 -0.0003 -0.0002 -0.0003 -0.0323 96.77 56 -0.0002 -0.0005 -0.0004 -0.0452 96.67

64 -0.0002 -0.0005 -0.0004 -0.0591 50.52 72 -0.0003 -0.0006 -0.0005 -0.0733 55.91

80 -0.0006 -0.0007 -0.0007 -0.0876 88.47 88 -0.0006 -0.0009 -0.0008 -0.1023 86.19

96 -0.0009 -0.0011 -0.0010 -0.1175 116.19 104 -0.0010 -0.0010 -0.0010 -0.1327 91.45

112 -0.0009 -0.0012 -0.0011 -0.1482 79.93 120 -0.0011 -0.0012 -0.0012 -0.1638 78.36

128 -0.0013 -0.0015 -0.0014 -0.1800 97.55 136 -0.0013 -0.0016 -0.0015 -0.1970 86.94

144 -0.0015 -0.0017 -0.0016 -0.2144 89.51 152 -0.0015 -0.0017 -0.0016 -0.2326 74.71

160 -0.0015 -0.0018 -0.0017 -0.2517 66.51 168 -0.0019 -0.0021 -0.0020 -0.2734 85.79

176 -0.0021 -0.0022 -0.0022 -0.2978 83.37 184 -0.0020 -0.0022 -0.0021 -0.3234 64.91

-0.0030

-0.0025

-0.0020

-0.0015

-0.0010

-0.0005

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

0 50 100 150 200

Str

ain

in

yy d

ire

ction

(m

m/m

m)

Time (sec)

Cylinder #1 Strain vs Time

1

2

average

LVDT


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5.3.2 Discussion of Cylinder Test 1 Result

In Test 3, a 100 x 200 mm cylinder has been tested under compressive strength test.

LVDT has been placed to measure the relative displacement from the top and bottom of

the cylinder. By comparing the data from Ncorr to the LVDT, as shown in Figure 5.14 and

Table 5.4, Ncorr has a large deviation from the strain curve from LVDT. From the curve, it

presents that the cylinder has a positive strain value in the y-direction and the concrete

specimen is under tension rather than in compression. This result does not match the

strain curve from the LVDT. When the load increases, the value of strain gets more stable

where it matches the curve shape from the obtained strain curve. However, the overall

error percentage from the DIC analysis is above 50%. This could be caused by the DIC

algorithms in Ncorr only valid for the 2-D deformation. Since concrete cylinder has a

curved surface and the deformation mechanism for the cylinder is under expansion which

the movement for the pixel along surface could be out of the plane. Hence, a 3-D

deformation could exist in this test. Besides the possible 3-D deformation, the curved

surface may also create additional lenses distortion where the pixel information gets

distorted which also increase the inaccuracy of the result.

Figure 5.15 - V displacement (left) and current image (right) of Cylinder#1.


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Chapter 6: Conclusion

In general, the validation tests for both steel and concrete material prove that the Ncorr

can be successfully applied to structural testing for obtaining any point data or generating

full-field displacement & strain measurement. From the test results that present in Chapter

4 and Chapter 5, they all show that the measurement from Ncorr can match the actual

material behavior. However, the accuracy of the measurements from Ncorr still need

further improvement. The Ncorr shows unstable analysis when the strain or displacement

value is relatively small. One action could be taken to improve the accuracy is by

redefining the DIC parameters when using the Ncorr. A smaller subset size is needed for

measuring the small strain value.

Based on the results from the validation tests, a robust procedure of running DIC analysis

by using Ncorr has been developed. Additional study is needed to further improve the

accuracy of running DIC analysis. At the end of this thesis, a manual on how to use Ncorr

has been included in Appendix A and B. Recommendations have been made based on

previous test results and will be discussed in detail in the following chapter.


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Chapter 7: Recommendations

In this chapter, two types of recommendations were made. First part will include the

suggested improvements that could be made in the future experiment where it can use

to improve the accuracy of the results. The second part will include recommendations

about how the algorithms can be adjusted to meet the future research application.

7.1 Improvements on Analysis Accuracy

7.1.1 Lens Distortion Removal

One possible cause for the inaccuracy on DIC analysis could come from the lens

distortion of the camera. Pictures captured by the digital camera usually contain

deformation, though typically slight. As shown in Figure 7.1, this kind of distortion is

referred as the aberration, with which the straight lines are bent physically, therefore

affecting the geometry of the image (Park et al., 2009). This phenomenon could reduce

the accuracy of the DIC method. Thus, it is better to factor in the lens distortion on the

images and to remove it before analyzing.

Figure 7.1 - Sample of lens distortion (Park et al., 2009).


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To check if the lens distortion exists, a simple gird picture was used to be taken by the

camera as shown in Figure 7.2.

Figure 7.2 - Pictures of grid lines.

In Figure 7.2, the lines on the edges are slightly bent, which indicates barrel distortion

exists in this camera. Lens distortion removal is needed for using this camera.

In the future study, the lens distortion can be removed before running the DIC analysis.

One proposed approach to solve this issue is by applying Camera Calibrator from

MATLAB to remove lens distortion. Additionally, a better camera lens with zero lens

distortion shall be used for capturing the deformed images and improving the overall

accuracy.


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7.2 Recommendation for Future Application

7.2.1 DIC on Observation of Elements Under Thermal Loading

DIC can be applied to the tests that strain gauges or other conventional method are not

available. For example, the study of the structural behavior under fire or thermal loading

requires to test the structural system at an element-level which the elements will be placed

in the furnace and loaded follow a standard fire curve. In this case, it is challenging to

obtain the strain or displacement data since those instruments cannot function properly

under a high-temperature condition. The application of DIC is possible to help to collect

the displacement data of the structural elements and achieve a better understanding of

the non-linear behavior, and complex characteristics for the structural elements. It is also

possible to use DIC as the tool to obtain the input of the displacement from the tested

structural element then running of numerical analysis of the full-scale structural system at

each time step under the same fire scenario.

7.2.2 Future Improvements in DIC Algorithms

As discussed in Chapter 2, the background of the DIC, most of the current DIC algorithms

use the first order transformation for the displacement mapping function. For the material

under non-linear behavior or complex characters on deformation, the accuracy of using

the first-order transformation is unknown. When the actual deformation consists of higher

order displacement gradient and tends to distort the infinitesimal strain measurement (Lu

and Cary, 2009). To improve accuracy, the DIC Algorithms could employ a second-order

transformation as an alternative analysis tool. The mapping function around point (𝑥0, 𝑦0)

can be approximated based on the following second-order transformation:

�̃� = 𝑥0 + 𝑈0 + 𝑈𝑥∆𝑥 + 𝑈𝑦∆𝑦 +1

2𝑈𝑥𝑥∆𝑥

2 +1

2𝑈𝑦𝑦∆𝑦

2 + 𝑈𝑥𝑦∆𝑥∆𝑦 (7.1)


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�̃� = 𝑦0 + 𝑉0 + 𝑉𝑥∆𝑥 + 𝑉𝑦∆𝑦 +1

2𝑉𝑥𝑥∆𝑥

2 +1

2𝑉𝑦𝑦∆𝑦

2 + 𝑉𝑥𝑦∆𝑥∆𝑦 (7.2)

In second-order transformation, twelve mapping parameters had been introduced as

mentioned in Equation 7.1 and 7.2 : 𝑈0 and 𝑉0 , the displacement components; 𝑈𝑥 ,

𝑉𝑥 , 𝑈𝑦 and 𝑉𝑦 , the first-order displacement gradients; 𝑈𝑥𝑥 , 𝑉𝑥𝑥 , 𝑈𝑦𝑦 , 𝑉𝑦𝑦 , 𝑈𝑥𝑦 and 𝑉𝑥𝑦

are the second-order displacement gradients as illustrated in Figure 7.3 (Lu and Cary,

2009).

Figure 7.3 - Effect of displacement gradients on subset points (Lu and Cary,

2009).

As discussed in section 7.1.1, one potential application of apply DIC analysis is to use on

the structural testing under fire loading. Under this condition, structures may have

deformation higher than first-order. The improvement of the core algorithms could be

made to accommodate various testing situations.


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In this thesis, the DIC analysis tool: Ncorr is only valid in 2-D deformation. For future

research, it is necessary to apply DIC for 3-D deformation. Based on the existing DIC tool,

one proposed approach to achieve this goal is by placing cameras in different position to

obtain a three-dimensional deformation field. In Sepra’s study, the research group can

obtain the full-field measurement over more than 180 ° an intervertebral disc by

sequentially moving a single camera through seven fixed position in order to cover the

required angle of vision (see Figure 7.4). This approach allows correlating structural

response with the entire 3-D strain & displacement filed.

Figure 7.4 - Sample setup for 3-D DIC (Spera et al., 2011).

In the future study, DIC analysis could be modified based on the recommendations listed

to accommodate for other complex tests with a higher degree of accuracy.


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References

Blaber, J., Adair, B., & Antoniou, A. (2015). Ncorr: Open-source 2D digital image

correlation matlab software.Experimental Mechanics, 55(6), 1105-1122.

doi:10.1007/s11340-015-0009-1

Chu, T., Ranson, W., & Sutton, M. (1985). Applications of digital-image-correlation

techniques to experimental mechanics. Experimental Mechanics, 25(3), 232-244.

doi:10.1007/BF02325092.

Hoult, N. A., Andy Take, W., Lee, C., & Dutton, M. (2013). Experimental accuracy of two

dimensional strain measurements using digital image correlation. Engineering

Structures, 46, 718-726. doi:10.1016/j.engstruct.2012.08.018

Hoult, N. A., Dutton, M., Hoag, A., & Take, W. A. (2016). Measuring crack movement in

reinforced concrete using digital image correlation: Overview and application to

shear slip measurements. Proceedings of the IEEE, 104(8), 1561-1574.

doi:10.1109/JPROC.2016.2535157

Lawrence, C.M., Nelson, D.V., Udd, E. et al. (1999). fiber optic sensor for transverse

strain measure . Experimental Mechanics, 39, 202-209.

doi:10.1007/BF02323553.

Lu, H. & Cary, P.D. (2000). Deformation measurements by digital image correlation:

Implementation of a second-order displacement gradient. Experimental

Mechanics, 40 (4), 393-400. doi: 10.1007/BF02326485

https://doi.org/10.1007/BF02323553


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Mbarek, T., Robert, L., Hugot, F., & Orteu, J. (2011). Mechanical behavior of wood–plastic

composites investigated by 3D digital image correlation. Journal of Composite

Materials, 45(26), 2751-2764. doi:10.1177/0021998311410466

McCormick, N., Dr, & Lord, J., Dr. (2010). Digital image correlation. Materials

Today, 13(12), 52-54. doi:10.1016/S1369-7021(10)70235-2

Mikota, M. & Pavlovic, I. (2010). ISO speed as the technical and creative element of the

digital portrait photographs. DAAAM International Scientific Book, Annual, p9+.

doi:10.2507/daaam.scibook.2010.02

Nezerka, V. (2014). Ncorr_Post: DIC Post-Processing Tool, Prague: Czech Technical

University in Prague.

Pan, B. (2009). Reliability-guided digital image correlation for image deformation

measurement. Applied Optics, 48(8), 1535-1542. doi: 10.1364/AO.48.001535

Pan, B., Asundi, A., Xie, H., & Gao, J. (2009). Digital image correlation using iterative

least squares and pointwise least squares for displacement field and strain field

measurements. Optics and Lasers in Engineering, 47(7-8), 865-874.

doi:10.1016/j.optlaseng.2008.10.014

Pan, B., Dafang, W., & Yong, X. (2012). Incremental calculation for large deformation

measurement using reliability-guided digital image correlation. Optics and Lasers

in Engineering, 50(4), 586-592. doi:10.1016/j.optlaseng.2011.05.005

Pan, B., Li, K., & Tong, W. (2013). Fast, robust and accurate digital image correlation

calculation without redundant computations. Experimental Mechanics, 53(7),

https://doi.org/10.1364/AO.48.001535


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1277-1289. doi:10.1007/s11340-013-9717-6

Park, J., Byun, S., & Lee, B. (2009). Lens distortion correction using ideal image

coordinates. IEEE Transactions on Consumer Electronics, 55(3), 987-991.

doi:10.1109/TCE.2009.5278053

Sprea, D., Genovese, K., & Voloshin, A. (2011). Application of Stereo-Digital image

correlation to Full-Field 3-D deformation measurement of intervertebral disc. Strain,

47, 572-587. doi:10.1111/j/1475-1305.2009.00658.x

Turner, D., Lehoucq, R., and Reu, P. (2015). DICE-Digital Image Correlation Engine,

Livermore: National Technology and Engineering Solutions of Sandia.


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Appendices

A. Ncorr Installation

In this thesis, an open source MATLAB software was used which can be obtained from

http://www.ncorr.com/. The Ncorr requires the computer to install a supported C++

compiler to successfully run the analysis, and it also needs to first navigate the current

folder of MATLAB to the directory where the Ncorr has been saved. Then, as shown in

Figure A.1, type ‘‘handles_ncorr=ncorr’’ in the command window to run the script.

Figure A.1 - Function to run the Ncorr in MATLAB.

Once the script compiles properly, a graphic user interface (GUI) for Ncorr will appear as

shown in Figure A.2.

http://www.ncorr.com/


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Figure A.2 - GUI for Ncorr.


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B. Ncorr DIC Analysis Settings

In this section, a detailed description will be included for illustrating how to setup the DIC

parameters to accommodate various testing requirements.

B-1: Setting of Images

To run the script, a reference image and the images of the deformed specimen are

required. If the camera saved the images in the raw file, it needs to first convert the images

into tiff. file or other formats since Ncorr can only accept images file in jpg., tif., png., and

bmp. format. As shown in Figure B.1, the GUI will displace the reference image and the

last image of current images when the uploading process finishes.

Figure B.1 - Setting of reference and current image.

Moreover, the region of interest (ROI) should be defined for running the analysis. As

shown in Figure B.2 the ROI can be loaded or drawn in Ncorr according to the shape of

the specimen.


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Figure B.2 - GUI of ROI setting.

Ncorr allows to draw the ROI to accommodate on analyzing various shapes of the testing

specimen. As shown in Figure B.3, Ncorr has different drawing tools and on those drawing

tools “+” means adding a portion to ROI and “-” means subtracting portion from ROI. After

completing the drawing of ROI, this ROI will be automatically applied to every selected

image.

Figure B.3 - Sample drawing of ROI.


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B-2: Setting of DIC Parameters

Next step is to set the DIC parameters; this setting can be found under the Analysis by

selecting Set DIC Parameters. Usually, the script will automatically fill out the key

components. These key components can be adjusted according to different analysis

requirements. A sample set of DIC parameters has been included in Figure B.4.

Figure B.4 - Sample setting of DIC Parameters.

If the drawing of ROI from the last section is too close to the edges of the image, a warning

message will be displaced from the Ncorr as shown in Figure B.5 which indicates this

may cause the problem in further analysis.

Figure B.5 - Warning from Ncorr.


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B-3: DIC Analysis

In this step, DIC analysis is performed under Analysis by selecting DIC Analysis. First, it

requires to select a contiguous region to process the DIC. As shown in Figure B.6, it only

allows to select one region in the sample analysis since the computer for running this

analysis only has one CPU. If the computer has more than one CPU, Ncorr allows to

select multiple regions to perform the analysis.

Figure B.6 - Setting of DIC analysis.

Then, the seed placement is required to set up for running the analysis as shown in Figure

B.7.


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Figure B.7- Seed placement on DIC analysis.

The seed point is used to calculate the corresponding deformation parameters for the

center point of a subset as a loaded queue point, and then the script can use this

information to calculate the deformation parameters for the four surrounding points

(Blaber et al., 2015). Once the script finished calculating the first loaded queue point, the

queue point will shift to next and repeated the calculation process until the calculation of

full-field displacement had been completed (Blaber et al., 2015). The location of the seed

point usually should be the centroid of the region of interest (Blaber et al., 2015). Details

of the process are shown in Figure B.8.


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Figure B.8 - Flow chart of RG-DIC algorithm to process (Blaber et al., 2015).

If one of the seed propagations is under high deformation which may be caused by rigid

movement when taking the pictures, the script will have a waning which indicates high

correlation coefficient exists and may affect the accuracy of the analysis as shown in

Figure B.9.

Figure B.9 - Warning from Ncorr.


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After setting all the required parameters, the script will automatically run the analysis as

shown in Figure B.10 For more detailed explanation of setting the DIC parameters,

instruction could be found in http://www.ncorr.com/download/ncorrmanual_v1_2_2.pdf.

The running time of the analysis depends on the computer hardware. To run the sample

test, the computer has the following features:

Intel® Core™ I7-6700HQ at 2.60 GHz processor

32.0 GB RAM (installed memory)

1 TB solid state drive

This computer was used to analyze the images with resolution of 1536 x 3456 pixels and

a region of interest of 50 mm x 180 mm. It will take Ncorr around 40-60 minutes to analyze

for per image.

Figure B.10 - DIC analysis is performing.

B-4: Format Displacement & Strain

Once the Ncorr completes the analysis, it can now start to format the displacement which

is under Analysis by selecting Format Displacements. The GUI of formatting

displacements as shown in Figure B.11.

http://www.ncorr.com/download/ncorrmanual_v1_2_2.pdf


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Figure B.11 - Formatting setting.

In Figure B.12, Ncorr allows to covert the unit of images from pixel to mm by setting a

calibration line in the reference image.

Figure B.12 - Calibration line for unit conversion.

Another formatting parameter can be set is strain. This can be found under Analysis by


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selecting Calculate Strain.

Figure B.13 - Setting of strain parameter.

In Figure B.13, strain radius can be varied according to the different requirement on the

strain analysis. Strain radius is the radius of a circle and the points in that circle are used

to fit into a plane as shown in the highlighted red box in Figure B.13. Strain radius is a

key component to the strain calculation result and the larger the radius will contain more

data points for the calculation of local fitting, weakened the noises influence which comes

from local fluctuations of the displacement calculation and eventually improves the

smoothen the overall strain field (Blaber et al., 2015). If the tested specimen has a

homogenous deformation, the larger the strain radius will result in increasing the accuracy

of the strain calculation (Blaber et al., 2015). However, in inhomogeneous deformation,

the strain radius needs to be carefully adjusted for balancing between accuracy and

smoothness (Blaber et al., 2015). Besides, the selected circle is also draggable in preview

image and the author of Ncorr suggested to drag the circle to the area of high deformation

region to see if those points still have a reasonable fitting to the plane.


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The default setting of the script has a strain radius of 15, and a smaller radius will result

in a less nosey strain data. In the right side of the setting which is highlighted by a red

box can be used to view the deformation curve of the selected point in the preview image.

In the red box, the two horizontal axes represent the size of pixels in x and y-direction,

these circular marks are the points data from the selected circle in the preview image,

and the color code represents the size of displacement.

Figure B.14 - Strain radius: a) strain radius 15 b) strain radius 10 c) strain radius

5.

In Figure B.14, a strain radius of 15 may be too large for this analysis and a radius of 5 is

too small. Reducing the radius to 10 could generate a better strain filed curve to fit the

plane. In this sample test, a strain radius of 10 had been choosing to perform the plotting

of strain field

B-5: Test Data Plotting

After the setting of format, Ncorr now is ready to export displacement and strain field

images in different coordinates (xx, yy, and xy) as shown in Figure B.15 and B.16 Test

data plotting can be achieved under Plot by selecting View Displacement Plots or View

Strain Plots. The plotting of the data can be saved as images or gif.


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Figure B.15 - Overall displacement field.

Figure B.16 - Overall strain field in a) xx direction b) yy direction c) xy direction.

C. Further Analysis

Another open source application was developed based on Ncorr and could be used to

export images or videos on the strain or displacement development from Ncorr. The script

is Ncorr_post and can be downloaded from

http://mech.fsv.cvut.cz/~nezerka/DIC/index.htm. Since the author developed this script

http://mech.fsv.cvut.cz/~nezerka/DIC/index.htm


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based on the MATLAB 2011, it is better to use MATLAB version earlier than 2012.

Otherwise, some major functions such as adding extensometer may be missing while

using a higher version of MATLAB.

To add the Ncorr_post script to the MATLAB, it needs to first select Ncorr_post folder then

adds it into a path then the script can be opened in MATLAB by running the file named

“ncorr_post.m”. Once the MATLAB successfully run the script, the GUI of Ncorr_post will

appear as shown in Figure C.1.

Figure C.1 - GUI for ncorr_post.

The Ncorr_post can load data directly from Ncorr or any saved project on the computer.

It requires to first scale the displacement by defining the distance of two certain points

from the images as shown in Figure C.2.


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Figure C.2 - Sample of scaling the displacement.

In Figure C.3, Ncorr_post can analyze the direction and magnitude of principal strains by

selecting the Arrow mode. The size of arrow and the grid density can be adjusted based

on different requirements of the analysis.

Figure C.3 - Direction of principal strains


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Ncorr_post also allows to add six extensometers which are used to measured

displacement in x and y-direction along two certain points. To add the extensometers, it

must scale the displacement first then by selecting the add virtual extensometers. Then

the script will need first to define the locations of two points, and the extensometer will be

added into the image as show in Figure C.4. Later, select extensometer data, the

displacement diagram along these two points in x and y directions will be exported as

shown in Figure C.5.

Figure C.4 - Sample of defining two points for adding extensometer.

Figure C.5 - Relative displacement between two selected points.

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