Strain Measurements with the Digital Image Correlation System Vic-2D

Transcription

1 CU-NEES NEES at CU Boulder The George E Brown, Jr. Network for Earthquake Engineering Simulation Strain Measurements with the Digital Image Correlation System Vic-2D By Rommel Cintrón University of Puerto Rico, Mayagüez Dr. Victor Saouma University of Colorado, Boulder September 2008 Center for Fast Hybrid Testing Department of Civil Environmental and Architectural Engineering University of Colorado UCB 428 Boulder, Colorado

2 Strain Measurements with the Digital Image Correlation System Vic-2D REU Student: Rommel Cintrón REU Mentor: Dr. Victor Saouma Home Institution: University of Puerto Rico, Mayagüez Host Institution: University of Colorado, Boulder Summer 2008 Abstract The Vic-2D is an innovate system that uses the digital image correlation technique to provide strain measurements in a two-dimensional contour map for planar surface specimens. In this research, relations between some of the most important variables involved in the digital image correlation are showed to improve the operation and results with this technique. This paper includes a simple tutorial for the setup and operation of the equipment. Three different tests were performed: (1) preliminary tests, (2) elementary tests and (3) complex tests. The first ones prove the effectiveness of the Vic-2D with a ductile material, based on its known elastic properties. The second ones study the success of the system with brittle materials and the last ones analyze structural components. The results provide the achievements obtained and some limitations with the Vic-2D.

3 Table of Contents 1 Introduction 1.1 Digital Image Correlation Technique 1.2 Relating Image Resolution and Specimen Dimensions 1.3 Relating Focal Length and Distance Between Camera and Specimen 1.4 Distortion Effects 1.5 Speckle Pattern 2 Methods and Materials 2.1 Vic-2D 2.2 Setup and Operation of the System 2.3 Tests and Parameters 3 Discussion of the Results 3.1 Preliminary Tests 3.2 Elementary Tests 3.3 Complex Tests 4 Conclusions and Recommendations 5 Acknowledgement 6 References

4 1 Introduction Strain measurements are very important in mechanical sciences. A strain in any material can be defined as the coefficient of the change in length and the initial length. Strains are involved in many important material properties and parameters (i.e. Stress-Strain Curve, Young s Modulus, Poisson s Ratio, etc.). Recently, new and more complex investigations are requiring strain measurements at any point inside an area of interest to improve the study of the behavior of materials and structural components. For this reason, researchers are interested on a strain map over an entire specimen surface. Some conventional instruments, which measure strains (i.e. strain gage and LVDT), are not accessible to create strain maps, because it would be very expensive and not practical. Owing to the fact that strain maps are needed to perform new investigations, a new technology was develop to obtain these desired results. This technology is the digital image correlation, which provides a contour map of strains of an entire specimen surface subject to mechanical tests. 1.1 Digital Image Correlation Technique The digital image correlation is an optical method that uses a mathematical correlation analysis to examine digital image data taken while samples are in mechanical tests [Correlated Solutions, 2008]. This technique consists on capture consecutive images with a digital camera during the deformation period to evaluate the change in surface characteristics and understand the behavior of the specimen while is subject to incremental loads. To apply this method, the specimen needs to be prepared by the application of a random dot pattern (speckle pattern) to its surface. This technique starts with a picture before loading (reference image) and then a series of pictures are taken during the deformation process (deformed images). All the deformed images show a different random dot pattern relative to the initial non-deformed reference image. With computer software these differences between patterns can be calculated by correlating all the pixels of the reference image and any deformed image, and a strain distribution map can be created (See Figure 1.1).

5 The digital image correlation requires computer software and an appropriate digital camera. To get accurate measurements with this technique it is important to consider some variables. The results are going to depend on the digital image resolution (pixels columns (c) pixels rows (r)), the width (w) and the height (h) of the specimen, the distance between camera and specimen (d), the focal length of the lens (f), and the application of the speckle pattern (See Figure 1.2). 1.2 Relating Image Resolution and Specimen Dimensions The resolution refers to the number of pixels in an image and describes how many details can be appreciated in an image. The image resolution and the specimen surface area can be related to determine the quantity of space that each pixel is going to represent in the specimen image (See Figure 1.3). To determine the quantity of space represented by a pixel in a specimen image, the specimen dimensions (width and height) have to be

6 divided by the resolution of the camera (pixel columns and pixel rows). Two different equations can be used to determine the pixel space represented on an image. The equation 1 allows to calculate the pixel width represented on the specimen image, where ς w is the pixel width, w is the specimen width and c is the number of pixel columns in the image. The equation 2 allows to calculate the pixel height represented on the specimen image, where ς h is the pixel height, h is the specimen height and r is the number of pixel rows in the image. As the resolution increase, the ς value is going to decrease, and as the specimen dimensions increase, the ς value is going to increase. Independently of the specimen dimensions, the values of ς w and ς h for an individual specimen always are equal. All the digital camera resolutions have a 4:3 or a 3:2 aspect ratio. The majority and most common digital cameras have a 4:3 aspect ratio image resolution (i.e , , , etc.). To explain the relation between image resolution and specimen dimensions, 4:3 aspect ratio resolutions are going to be used. It is important to point out that the samples must occupy the majority of the space as possible in an image

7 to maximize the quantity of pixels used. With a 4:3 aspect ratio resolution the ideal surface area in a specimen to use all the pixels in an image is a rectangle with a 4:3 aspect ratio too (i.e. 4 3, 8 6, 12 9, etc.). In this case, equations 1 and 2 can be used (See Figure 1.4). If the specimen surface area is a square or a rectangle, which its wide is less than 1.33 times the height, the only equation that can be used is the equation 2. The equation 1 cannot be considered, because all the pixel columns are not going to be used to represent the specimen in the image. It is obvious that in the square specimen the quantity of pixel columns that are going to show the specimen image are going to be the same quantity of pixel rows, but in the rectangular specimen that is not very simple to identify. In the rectangular specimen the quantity of pixel columns that are going to show the specimen image can be determined by geometry, but that is not necessary, because the results of equations 1 and 2 always are going to be the same. If the pixel rows and specimen height are known, that is enough (See Figure 1.5).

8 If the specimen has a rectangular shape, which its wide is more than 1.33 times the height, the only equation that can be used is the equation 1. The equation 2 cannot be considered, because all the pixel rows are not going to be used to represent the specimen in the image. The quantity of pixel rows that are going to show the specimen image can be determined by geometry, but that is not necessary. If the pixel columns and specimen width are known, that is enough (See Figure 1.6). 1.3 Relating Focal Length and Distance between Camera and Specimen The focal length is the distance in millimeters between the optical center of the lens and the focal point in the surface of the sensor of the camera when the subject is in focus (See Figure 1.7). There are three categories for the focal length. The three categories are wideangle lens (focal length < 35 mm), normal lens (35 mm < focal length < 55 mm) and

9 telephoto lens (focal length > 55 mm). The higher the focal length, the closer the image is going to be registered in the digital camera. It is not necessary to know an exact distance or focal length for each different specimen dimensions, because they can be adjusted in different ways to get the specimen focused with the camera. If the camera needs to be very far from the specimen, the image can be focused by using a long focal length and vice versa. The distance between camera and specimen also depends on the specimen dimensions. The higher the specimen dimensions, the higher the distance between camera and specimen will be needed. 1.4 Distortion Effects The distortion effects are a problem that still affects all the digital cameras. The distortion can be defined as the lens defect that produces an imperfect image. Distortion effects can appear when the lens is zoomed. Zoom lenses at their maximum wide-angle (28 mm) or telephoto (> 80 mm) setting can be affected by barrel or pincushion distortions, respectively (See Figure 1.8). Also, to avoid distortion effects, the images need to be centralized.

10 1.5 Speckle Pattern The specimen surface to be studied must have a random dot pattern [Limess, 2008]. The speckle pattern is essential, because it permits the software to be able to identify and calculate the displacements with accuracy. To obtain accurate results with the digital image correlation it is important to get an adequate speckle pattern. An adequate speckle pattern must have a considerable quantity of black speckles with different shapes and sizes (See Figure 1.9). The effectiveness of the speckle pattern can be determined by the quantity of pixels per black speckle. A good speckle pattern must have small black speckles (10 pixels), medium black speckles (20 pixels) and large black speckles (30 pixels). The quantity of pixels per black speckle size is approximated (See Figure 1.10). To identify the ideal size of any black speckle in a specimen, a relation between the black speckle size desired (small, medium or large) and the quantity of space represented by a pixel in a specimen image (ς w or ς h ) can be made. Knowing the quantity of pixels that any black speckle size must have and the pixel size represented in a specimen image, their product are going to give us the proper dimensions of the black speckles in the specimen.

11 The equation 3 allows to calculate the dimensions of a black speckle in a specimen, where ζ is the black speckle length in a specimen, p is the quantity of pixels that the desired black speckle size must have and ς is the pixel size represented in a specimen image (ς w or ς h ) (See Figure 1.11). It is important to notice that the results of ζ are an approximation to have an idea of how the black speckles length must be in any specimen. Also, to get accurate results is very important to avoid black speckles bigger than the large black speckles. 2 Methods and Materials 2.1 Vic-2D The Vic-2D uses the digital image correlation technique to make strain measurements [Limess, 2008]. This system is able to provide two-dimensional strain maps of an entire planar specimen surface. The equipment consists of computer software and a digital camera with appropriate lens and resolution (See Figure 2.1). The digital camera records the pictures during the mechanical testing process and the software analyzes the images and calculates axial and transversal displacements, as well as axial, transversal and shear strains.

12 2.2 Setup and Operation of the System For the success of strain measurements with the Vic-2D, it is indispensable to get a good speckle pattern. The speckle pattern can be naturally occurring or can be applied. It can be applied with white and black paint. First painting the surface with a thin layer of white paint (it could be brush or spray paint) and then applying a black mist of paint (spray paint) to create the black speckles. To apply the black mist of paint it is essential to keep approximate two feet of distance between specimen and spray can (See Figure 2.2). The speckle pattern needs to be applied considering the relation between the pixel size represented in a specimen image and the amount of pixels per black speckle (equation 3) (See Figure 2.3). To take the pictures during the deformation period, the specimen needs to be prepared to be subject to the mechanical test. After the sample and the universal testing machine are settled, select an accessible position for the digital camera and adjust the focal length to fix and acquire a clear image (See Figures 2.4 and 2.5). Set the aperture range of the

13 camera lens with the lowest f-number as possible to let the entrance of the maximum amount of light. The illumination has to be appropriate. The sample must be illuminate by a standard white light source. If ambient illumination is not sufficient, additional lighting may be needed. Before starting the test, a picture is taken for reference (nondeformed image). While the specimen is subject to external loads, consecutive pictures are taken (deformed images). To operate the software, the pictures taken during the deformation process need to be open in the Vic-2D. Let the subset and step sizes as default (i.e. subset: 29 and step: 5). To determine where the specimen strain map is going to be seen, select an area of interest in the reference image. Then, choose a point inside the area of interest (seed point) and make the initial guesses in all the deformed images. The seed point needs to be in a place where black speckles are easy to identify. After all the initial guesses are finished, run the correlation. It is important to notice that during the correlation the number of average iterations is shown for every image. This number of average iterations needs to be less than five to make sure that the correlation for the strain map is adequate. When the correlation is finished, calibrate the reference image with its true length. Finally, make the program calculates the strains. After this process, the Vic-2D is going to be able to show displacement and strain maps in any deformed image. Also, an animation with all the deformed image maps in sequence can be seen. 2.3 Tests and Parameters First preliminary tests were performed with and inches aluminum samples. Based on aluminum properties known by theory (i.e. Young s Modulus and Poisson s Ratio) the results of these tests can determine the effectiveness of the Vic-2D. Then, elementary tests with inches mortar and clay brick samples were performed. Two different sample dimensions were used for the bricks: and inches. These elementary tests are useful to determine how the Vic-2D works with brittle materials. The inches bricks were tested with extensometers added to compare the strain measurements in the Vic-2D. Finally,

14 complex tests with inches brick-mortar prisms (brick wall) were performed. These complex tests are useful to determine how the Vic-2D works with structural components. It is essential to see if the Vic-2D can generate the difference in strains between both materials. The mortar-brick prisms were composed of three stack bricks joined by two mortar bed joints (See Figure 2.6). All the samples were subjected to compression tests with a MTS universal testing machine. The deformation rate in the universal testing machine was inches per second in all the tests. The pictures for the prism tests were taken every 6 seconds for a period of 4 minutes. The pictures for all the other tests were taken every 5 seconds for a period of 5 minutes. A digital image resolution was used for all the pictures. The bricks and brick-mortar prisms were capped on both sides with a plaster of Paris to ensure evenness and continuous contact between the samples and the plates of the universal testing machine [Tusini, 2008]. 3 Discussion of the Results 3.1 Preliminary Tests The axial and transversal displacement maps, and the axial, transversal and shear strain maps were obtained in the preliminary tests. The maps in all the aluminum samples are very logical and useful to see the behavior of the material when is subject to compression loads (See Figure 3.1). All the strain measurements have more uniformity and almost the same values in the strain maps corresponding to the sample images taken during the elastic period of aluminum. In the strain maps corresponding to the sample images taken during the plastic period there is more variation of the strain values (See Figure 3.2). The maps consist of a range of colors, where the violet and red are the left and right boundaries, respectively. In the displacement maps the violet color represents the highest

15 displacement to the left in the transversal map and the highest displacement down in the axial map, and the red color represents the highest displacement to the right in the transversal map and the highest displacement up in the axial map. In the strain maps the violet color represents the lowest positive strain values or the highest negative strain values and the red color the highest positive strain values or the lowest negative strain values. The strain values obtained in the preliminary tests are not the expected. Using the Young s Modulus of aluminum known by theory (E=70GPa) and the universal testing machine reading (loads), the expected strains were calculated. The data (strains values) in the strain maps was export from the Vic-2D to an Excel document file. An average of all the axial strains of each strain map corresponding to the sample images taken during the elastic period was calculated to compare the Vic-2D results with the expected strains. In the inches aluminum samples the strains obtained from the Vic-2D are very high (See Table 3.1 and Figure 3.3). However, in the inches aluminum samples the strains obtained are better, but still a little bit higher (See Table 3.2 and Figure 3.3). A Strain vs. Stress graph (not Stress vs. Strain) was made to compare the strains. In this case, with the Strain vs. Stress graph is easier to see and understand the differences between strains. The Strain vs. Stress graph of the aluminum samples shows that the

16 strains obtained with the Vic-2D present a faster increase than the strains obtained by theory (See Figure 3.3).

17 To compare the proportion between the axial and transversal strains in the Vic-2D, the Poisson s Ratio known by theory of aluminum (ν=0.35) was used. The average of the axial and transversal strains of each strain map corresponding to the sample images taken during the elastic period was calculated to compare the Poisson s Ratios obtained in the Vic-2D with the Poisson s Ratio known by theory. The Poisson s Ratios obtained in the Vic-2D are between 0.20 and These results show that the proportion between the axial and transversal strains obtained with the Vic-2D is not always exact. 3.2 Elementary Tests In the elementary tests the axial and transversal displacement maps, and the axial, transversal and shear strain maps were obtained. In this case, the displacement and strain maps show the behavior of the materials during the deformation in a logical way too. Owing to the fact that mortars and bricks are brittle materials, big cracks appear during the tests. Running the correlation in the Vic-2D to get the strain maps, some unexpected uncolored spots appear in the contour maps. These uncolored spots in the strain maps coincide with the images that show cracks in the specimen. Also, the pictures that show the uncolored spots in the strain maps had average iterations above five during the correlation, so that means that the correlation was not adequate in those pictures. The uncolored spots are not desired, because there is no way to identify the strain values inside the uncolored areas. A good fact is that before the specimen shows cracks, the axial strain map is able to show the areas where the cracks are going to appear in the specimen (See Figures 3.4 and 3.5).

18 Some strain values obtained in the elementary tests are good, but others are not. Using the Young s Modulus of mortar (E 7GPa) determined with extensometers in other research with the same mix of mortar [Tusini, 2008] and the universal testing machine reading (loads), the expected strains for mortars were calculated. The axial strains from the Vic-2D in the elementary tests were calculated in the same way that the axial strains were calculated in the preliminary tests. Comparing the expected strains with the Vic-2D results, the strains obtained in the Vic-2D of the inches mortar samples are a little bit higher than the expected strains (See Table 3.3 and Figure 3.6). In this case, the strains obtained with the Vic-2D present a faster increase than the strains obtained by theory too (See Figure 3.6).

19 Using the Young s Modulus of brick known by theory (E 15Gpa) and the universal testing machine reading (loads), the expected strains for bricks were calculated. Comparing the expected strains with the Vic-2D results, the strains obtained in the Vic- 2D are close to the expected strains. In the inches brick samples the strains obtained with the Vic-2D are a little bit below from the expected strains (See Table 3.4 and Figure 3.7). In the inches brick samples the strains obtained with the Vic-2D are a little bit above from the expected strains (See Table 3.5 and Figure 3.7). It is important to point out that the Young s Modulus of brick is very approximated, so the results of the Vic-2D cannot be considered as good or bad. Also, the inches brick samples were performed with extensometers added and the results of the Vic-2D and the extensometers are very similar, so in this case the Vic-2D results can be considered as acceptable (See Table 3.5 and Figure 3.7). Besides, in the brick tests the expected strains and the strains obtained with the Vic-2D present a similar rate of increase (See Figure 3.7).

20 3.3 Complex Tests The axial and transversal displacement maps, and the axial, transversal and shear strain maps were obtained in the complex tests too. The displacement and strain maps in all the mortar-brick prism samples look very logical, like in the tests before mentioned. The axial strain maps are able to show the difference in strains between the mortars and bricks, where the mortar presents the highest strain values (See Figure 3.8). During these tests, the unexpected uncolored spots also appear when the images show cracks in the specimen.

21 The strain values of the complex tests obtained with the Vic-2D are acceptable. The results with the inches mortar-brick prism samples are very similar to the results obtained with the inches brick samples in the elementary tests (See Table 3.6). In fact, in all the prism tests the brick fails first than the mortar. 4 Conclusions and Recommendations The Vic-2D is able to provide logical and useful displacement and strain maps to show the behavior of the materials during the deformation process. The system is capable to detect the areas with higher strains inside the area of interest. The Vic-2D cannot provide displacement and strain maps after the specimens show cracks. The maps obtained from the specimen images that show cracks are not adequate to determine the strain values in some points inside the area of interest. Some strain measurements obtained with the Vic-2D are acceptable, but others are not the expected. The strain values obtained with the aluminum and mortar samples are higher than the strains expected. In these tests the strains obtained with the Vic-2D present a faster increase than the strains obtained by theory. Also, the majority of the

22 Poisson s Ratios obtained with the Vic-2D in the aluminum samples do not coincide with the Poisson s Ratio known by theory. On the other hand, the strain values obtained with the brick samples are close to the expected strains. In these tests the expected strains and the strains obtained with the Vic-2D present a similar rate of increase. Also, in the brick samples tested with the extensometers the results obtained with the Vic-2D are very similar to the results obtained with the extensometers. The results obtained with the brick and mortar-brick prism samples can be considered as acceptable, but cannot be considered as accurate. The good results on strain measurements coincide with the samples with dimensions higher than inches and the unexpected strains obtained coincide with the samples with inches dimensions or lower. That means that maybe the Vi-2D is not able to provide accurate strain measurements in specimens with inches dimensions or lower. Preliminary tests with bigger specimens must be considered for future work to verify the accuracy on strain measurements with the Vic-2D. It is essential to put more emphasis in the application of the first thin layer of white paint to create the speckle pattern on the specimens. The layer of white paint has different properties compared to the materials tested. These differences could affect the accuracy on strain measurements with the Vic- 2D. There was a margin of error in time between the pictures taken during the tests and the load lectures in the universal testing machine. The digital camera and the universal testing machine should be synchronized to start at the same time to get more accurate expected strains. 5 Acknowledgement This research was supported by the George E. Brown, Jr. Network for Earthquake Engineering Simulation (NEES) and the National Science Foundation (NSF). The author would like to thank the University of Colorado at Boulder (CU) and the NEES Research Experience for Undergraduates (REU) for brings the opportunity to undergraduate students to gain experience on research work. The author is very grateful with his mentor Victor Saouma for guides him in the way to complete this research, Kaspar Willam for the assistance with the results, Ben Blackard for facilitates the resources to perform the tests and Kent Polkinghorne for the help on the understanding of the research objectives. Finally, the author needs to mention Ryan Doheny, Evan Tusini and all the CU structures and materials laboratory staff.

23 6 References Correlated Solutions, Inc., Digital Image Correlation, 16 Jun < content&task=view&id=23&itemid=36>. Hild, F. and Roux, S. [2006] Digital Image Correlation: from Displacement Measurement to Identification of Elastic Properties, The Authors, Journal compilation, Blackwell Publishing Ltd, Strain 42, Limess Messtechnik & Software GmbH, Vic-2D, 16 Jun < 24&Itemid=58>. Tusini, E. [2008] Performance Evaluation of Reinforced Concrete Masonry Infill Walls, Concentration on Evaluation of Masonry Infill Properties, Research paper, Civil Engineering Dept., University of Colorado, Boulder, Colorado.