Image Processing Applications For The Study Of Displacements and Cracking In Composite Materials
B. Mobasher, S. D. Rajan Department of Civil and Environmental Eng. Arizona State Univ., Tempe, AZ, USA,
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Outline of Presentation Introduction Image processing using Matlab Image processing applications for cracks and displacement fields Case Studies Fabric composites for crack spacing Ring Specimen for crack width Calibration using tensile tests on rubber and fabrics Displacement measurement in Fan blade out test.
Conclusions
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Scope of Work Crack characteristicslength, width and spacing
2-D Full-field displacement measurement based on Cross correlation Approach White light illumination Not real-time results, Post-Processing needed Tension test Samples and Ring static tests. Sub-pixel accuracy
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Image Processing Software Image Acquisition using a variety of frame grabbers and digital cameras. Image Processing Toolbox in MATLAB. Full flexibility for customization. Economical, versatile, and use-friendly interface. A comprehensive library of canned routines for image processing.
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Fabric Reinforcing Methodology
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Lamina stacking optimization for strength and toughness 60 50
Unidirectional
Stress, MPa
40
[0/-45/45/90]s
30 20 10 [45/-45]s 0 0.000
0.005
0.010 0.015 0.020 Strain, mm/mm
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0.025
Various stages of cracking
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Image Definition The most convenient method for expressing locations in an image is to use pixel coordinates. In this coordinate system, the image is treated as a grid of discrete elements The intensity ranges from 0-1 for binary images, 0-255 for grey images, and three distinct levels of 0-255 for color images. Image is represented as a matrix of scalar, or logical variables, i.e, 256x256, 512x512, 1028x1028, or 640x480
c 1,1 1,2 1,3 1,4 2,1 2,2 2,3
r
3,1 3,2 4,1
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Binary Level processing Filters Dilation and Erosion
Morphological Reconstruction Pixel Connectivity Flood-Fill Operations
Objects, Regions, & Feature Measurement Properties of objects of Binary Images
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Processing Steps Image Capture/Acquisition Grey Image processing Adjust the Image Contrast Histogram equalization Filters
clear all I2=imread('4.bmp'); figure(1), imshow(I2)
Thresholding Object Segmentation
Binary Level processing Feature Extraction Measurements
Reporting
bw3 = im2bw(I2,level);
L = bwlabel(bw3); stats = imfeature(L,'all');
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Crack Spacing
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Crack Spacing
allength = [stats.MajorAxisLength]’; average_width=mean(allength'); [m,s]=stat(allength'); You created this PDF from an application that is not licensed to print to novaPDF printer (http://www.novapdf.com)
Crack Spacing measurement Damage evolution measurement using image analysis. Crack spacing and the stress-strain response of AR Glass fiber composites
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Stiffness degradation & Crack Spacing Relationship 1000
Tangent Stiffness, MPa
Glass Fabrics 100
10
1 80
Polyethylene Fabric
60 40 20 Crack Spacing, mm
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0
Crack Width Measurements Concrete
Steel Tube
Strain gages
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Shrinkage Crack tracking through Image Mosaics
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0.8 TRM_30FA Crack Width
Crack Width, mm
0.6
0.4
0.2
0
0
10
20 Age, Days
30
40
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Cross Correlation Techniquesliding neighborhood operation Select a single pixel and determine its neighborhood. Apply a function to the values of the pixels in the neighborhood. This function must return a scalar. Find the pixel in the output image whose position corresponds to that of the center pixel in the input image. Set this output pixel to the value returned by the function. Repeat steps 1 through 4 for each pixel in the input image.
c(u, v) f ( x, y ) * t ( x u, y v) x, y
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Cross-Correlation The value of an output pixel is computed as a weighted sum of neighboring pixels. The matrix of weights is called the correlation kernel. Example: compute the (2,4) output pixel of the correlation of A, assuming h is correlation kernel: Slide the center element of the correlation kernel so that lies on top of the (2,4) element of A. Multiply each weight in the correlation kernel by the pixel of A underneath. Sum up the individual products from step 3. The (2,4) output pixel from the correlation is: 1-8 + 8-1+ 15- 6 + 7-3 + 14- 5 + 16- 7 + 13- 4 + 20- 9 + 22-2 = 585
h=
8
1
6
3
5
7
4
9
2
A=
17 23 4 10 11
24 5 6 12 18
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1 7 13 19 29
8 14 20 21 2
15 16 22 3 9
Image 1Original Template
n pixels
subimage a subimage b
v n pixels
Image 2Matching Template
u
d 2f,t (u,v) f ( x, y ) t ( x u, y v)
2
x, y
A 3x2 template matching to calculate the cross correlation function:
d(i,j)= corr2(double(b),double(a)); pp=(d = = max(d(:))); [x,y]=find(pp= = 1); You created this PDF from an application that is not licensed to print to novaPDF printer (http://www.novapdf.com)
Crack Propagation and opening
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Calibration
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Comparison of the load displacement measured using the LVDT and the cross correlation technique. 2500 Cross Correlation LVDT
Force, lbs
2000 1500 1000 500 0
0
0.02
0.04
0.06
Elongation, in
The uniaxial tension test of dry Kevlar fabric
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0.08
Displacement Field between stages 4 and 5
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Displacement Field between stage 5 and 6
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Penetration resistance Engine wraps subjected to Fan blade out Static Experiments
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Initial Condition
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Stage 0-1
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Stage 1-2
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Stage 2-3
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Stage 3-4
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Stage 13-14
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Kevlar: 1,2,4,8 and 24 layer tests 35000 30000
Load, lbs
25000
1 Layer 2 Layers 4 Layers 8 Layers 24 Layers
P
20000 15000
d 10000
P 5000 0 0.00
1.00 2.00 3.00 Actuator Stroke, in
4.00
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Conclusions Imaging techniques using Matlab based applications are shown to significantly improve our ability to extract more information from experimental data. The method is easy to use and versatile in various applications. Measurement of full displacement field using cross correlation approach is a powerful technique in understanding the localization processes.
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