Metall. Res. Technol.
Volume 117, Number 3, 2020
|Number of page(s)||7|
|Published online||01 June 2020|
Measurement of the steady state tearing in thin sheets using the contactless system
Faculty of Mining, Ecology, Process Control and Geotechnologies, Technical University of Košice,
Park Komenského 14,
Košice, Slovak Republic
2 Faculty of Mechanical Engineering, Technical University of Liberec, Studentská 2, 461 17 Liberec, Czech Republic
* e-mail: firstname.lastname@example.org
Accepted: 7 May 2020
The purpose of the present paper is the diagnostic method of the steady state tearing tests in thin steel sheets. The camera-based contactless system was used in the experimental research. The MATLAB software was used for the processing of real-time images. The data collected in the experiments were used to establish the R-curves in terms of the CTOD (crack tip opening displacement) based resistance curves. The innovative techniques allow extracting a large amount of geometrical information about the entire tearing process and the crack tip development. The steady state tearing was evaluated using automotive steel sheets and the tearing resistance was determined for three grades of thin sheets. The paper describes a comprehensive method of obtaining the material properties necessary for modelling and simulation. The proposed methodology for the testing and evaluation of the steady state tearing is applicable to thin sheets. The measurement method within the test for the determination of the tearing resistance was based on the image analysis.
Key words: measurement / camera / tearing / automotive steels
© EDP Sciences, 2020
The rapid development of technology has affected the field of material testing. There are several reasons: the automation of testing, evaluation speed, measurement accuracy and a large quantity of the obtained data. There are many ways how to bring the latest technological advances to use; in this case, it was the use of the scanning and computer technology for the contactless measurements of deformation. At present, there are numerous methods available for measuring the deformation and displacement. Unlike, for example, tensometry, the contactless methods facilitate monitoring the entire testing process and measuring even more extensive deformation and provide the information not only on one measured length, but also on the entire area. Moreover, they may also be used in the tests conducted at higher temperatures. The contactless methods of deformation measurements include:
DIC (digital image correlation) ;
ESPI (electronic speckle pattern interferometry);
reflective photoelasticimetry and;
the moiré method.
The identification of the steady state tearing in thin sheets applying the methods generally used for greater thicknesses is quite problematic. The determination of the CTOD parameters for the quantification of the crack propagation is discussed in paper  which specifies the methods of identifying the fracture toughness and R-curves for homogeneous metallic materials subjected to the quasistatic loading while the specimens were notched, precracked by fatigue and tested under the slowly increasing displacement. The steady state tearing is necessary to obtain the reliable and unambiguous fracture toughness data . Tong  proposed a noncontact method – DIC for extracting the plastic deformation field around a growing crack in a ductile thin sheet.
The steady state tearing determination is carried out using various types of test specimens; the one that is most frequently used is the CT (compact tension) specimen . The out-of-plane buckling occurs when the CT specimens of thin sheets are loaded by eccentric tension. The anti-buckling guide plates [6–11] are used to avoid buckling during the testing. The monitoring of the tearing tests is normally carried out using a camera [12,13] which has proven to be very effective. The quantities necessary for creating the R-curve (crack mouth opening displacement CMOD and crack extension Δa) may be obtained through the continuous use of the camera.
The subject of this paper is the proposed methodology for the optimisation and evaluation of the steady state tearing tests in thin sheets using the camera-based contactless measurement.
Due to the rapid development of technology, the contactless methods based on scanning the images with a camera, in various loading conditions, are gradually becoming the preferred ones. Steady state tearing tests are mostly based on the periodical extraction of the crack length information . The automatic detection of cracks from the test images obtained by a digital camera is a difficult task since the quality of the crack images depends on the test conditions. The roughness of the specimen surface, the luminance condition and the camera itself may influence the detection quality . Over the last decades, a lot of image segmentation approaches have been proposed and developed. The reviews of the image segmentation, including the thresholding-based techniques, are presented in [16,17]. The quality of the input images plays a crucial role in the success of any image analysis task. The higher their quality is, the easier and simpler the tasks are .
The program for the automatic measurement of the crack length and the CMOD in every image, developed by MATLAB, is described in this section. The manual measurement without using this program is very time-consuming.
The calculations of the length of the crack and the CMOD are done by finding the positions of certain dots and the position of the crack end. Such positions are used to calculate the desired data.
The outputs of the experiment include 256 level grayscale images. The recognition of edges, which is necessary in order to determine the positions of the crack end and the dots, requires a threshold operation. The reason is that the edge of an image is picture section where the bright and dark areas meet. This means that the pixel values change from a low value to a high value or vice versa. Therefore, the edge cannot be precisely identified. It is necessary to decide which pixel value belongs to the bright area and which one to the dark area while the threshold must be reached. The pixel values next to the threshold level describe the edge.
The threshold identification and pixels assignment to the dark (black) or bright (white) areas mean converting the grayscale image into a black/white image. In the black/white image, the edges can be easily found by locating the black pixels (or the white pixels, depending on how the search begins). Therefore, the image needs to be thresholded before any other operation is performed.
There are two methods of image thresholding. The first method consists in interpreting the pixel values below the threshold as black and those above the threshold as white. The second method is to interpret the pixel values above the threshold as white and maintain the pixel values under the threshold as they are. This second method basically removes the light gray shades in the image and holds more information (especially around the black dots, the dark gray surrounding is not made black). The images produced applying the first method will be called the black/white images and those produced applying the second method will be called the gray thresholded images.
The program needs at least two dots to measure the CMOD. They are referred to as the reference dots. Another point is needed for determining a special type of the crack length, referred to as the angle dot because it is used for determining the angle displacement of the specimen.
Every image in the specified folder is processed as described above (the threshold operation, finding new positions of the dots and the crack end). In order to locate the new positions of the dots and the crack end, it is assumed that the positions change only a little in individual images. Therefore, the search for the new position is limited to a smaller area around the old position. Furthermore, this provides the advantage of a shorter computation time.
All necessary adjustments can be done with the first image of the experiment. All subsequent images are processed automatically applying the same method as with the first image.
The task of determining the position of the crack end is easy for human eyes but very difficult for a computer. The crack appears in the black/white image as an accumulation of black pixels. It has no specific shape; moreover, the shape obviously changes during the process. Therefore, the pattern recognition is very difficult and not practicable. As a result, it is almost impossible for the program to determine the crack end. In order to solve this problem, it is necessary to determine an area with the crack end in the first image of the experiment (the crack end only, no dots, etc.). The program then searches for the first black pixel, beginning from the left side of the area.
This first found pixel is regarded as the end of the crack (Fig. 1), provided that there are at least 2 more black pixels to the right (this avoids that single black pixels are taken into account). The whole procedure is done in the black/white image because an operation in the grayscale image also requires a threshold for the purpose of determining which pixel value belongs to the crack and which does not. Therefore, the threshold operation should be done before the crack end is searched for.
The task of finding the crack end is very difficult. The computation time is very long when determining the crack end applying more sophisticated methods and they do not necessarily have to be effective since there are big differences between the images and between the experiments. Although the method described above is one of the easiest and simplest techniques of finding the crack end, the main advantages thereof is the short computation time and a simple algorithm. However, it requires perfect preparation of an image and an exact area where the crack end is assumed. The found crack end is drawn into the picture and the picture is saved.
Crack end in the recorded image.
The method of determining the positions of the dots consists of calculating the Euclidean distance and then the position of the centroid of the whole dot. The two positions are then compared. If the differences are too big, the position of the calculation of the Euclidean distance is used (the other black pixels that do not belong to the dot may have caused a bad result of the centroid-calculation).
The process includes the isolation of a small area around the expected position of the dot. Calculating the Euclidean distance between the pattern and the image at every possible position indicates the most probable position of the dot. Calculating the Euclidean distance means searching for the pattern at each possible position in the picture. At each location in the picture, the Euclidean distance D is calculated using the following formula: (1) p is the pixel value of the image; q is the pixel value of the pattern at the positions i and j; and s and t are the dimensions of the pattern in the x- and y-directions. The locations in the picture with the lowest D value determine the positions of the dots (a threshold is necessary to identify the valid points – D must be lower than the threshold). The advantage of this method is that the other black areas do not have any influence. The disadvantage is that the interpolation between the pixels is not possible. The obtained position is a position in the picture and therefore a whole number.
It is also possible to calculate the position of the centroid and use it as the estimated centre of the dot. Either the centroid of the whole dot or the centroid of the boundary of the dot can be calculated. The calculation of the centroid of the boundary needs further calculations to find the boundary points. This requires a longer computation time and can result in more errors. It is therefore not used. The calculation of the centroid of the whole dot can be done either in the black/white or in the gray thresholded images. The pixel value can be seen as the “mass” concentrated at the specific position in the image. Therefore, the centroid position in the x-direction can be calculated using the formula: (2) where xi describes the x-position in the image and pi the pixel value at the given position (black is the highest value, white is the lowest one). The centroid position in the y-direction can be easily calculated by substituting the x-position with the y-position. This method facilitated the best results in terms of stability of the found point position from one image to the next (the found point position always changes a little due to changing lightning conditions and quantization; such changes were less intensive with this method).
The crack length can be determined as the length of abscissa EF (horizontal distance a in Fig. 2). For the horizontal distance a, the line from A to B must be found. The distance a can subsequently be determined by searching in the horizontal direction from E to find the intersection F.
The coordinates of the two opposite points A and B (their x-coordinates must not be the same; in the program, they are the first and second defined reference points) and the position of the crack end are known. Subsequently, the distances a + b and d can be calculated as the differences between the y- and x-coordinates of A and B. The distance c can be calculated as . The desired crack length e (middle length, Fig. 3) can be determined using the x-coordinate of A, the x-coordinate of the crack end and c.
In order to determine the distance b (Fig. 4) parallel to the edge of the widening area, the following steps are necessary:
The points A, B and C with positions (Ax, Ay), (Bx, By) and (Cx, Cy) are known. Assuming that the coordinate originates in point C, the desired length b can be calculated as: (3) and Cx = Cy = 0. The position of D can be found by searching for the intersection of the straight lines g1 and g2. The equation for g1 is: (4)where α and tan(α) can be calculated from the y- and x-positions of 2 measurement dots (in the program, these two dots are the first specified reference dot A and the angle dot E; the angle dot can be any dot on the same side as the first reference dot; it’s assumed that the dots are parallel to the notch). The equation for g2 is: (5)with and d = By − kBx. Prior to the calculation, it is necessary to verify whether Ax and Bx are equal or not. The position of the intersection D can be found as follows:
Ax and Bx are not equal:
Ax and Bx are equal:
The determined positions of the dots and the crack end as well as the calculated lengths are drawn into the original image (bounded to the chosen region of interest, Fig. 2b).
The calculation is completed by entering the scale in pixel/mm. The calculated CMOD, the crack length a and the parallel length b (all in mm) are saved in a text file in the working directory. Every row in the file describes the data for an image.
The image processing task is always difficult. Therefore, poor image quality has a significant negative effect on the result. Especially an improper contrast in the image (black dots on a dark gray background) or a varying contrast may cause bad results and make it very hard or impossible to process the images. Furthermore, the resolution of the images has an effect on the accuracy of the result. The higher the resolution of the image is, the lower the quantization errors are and the results are therefore better. The disadvantage of the higher resolution is that the computation time increases. The task of determining the crack end is challenging too. The threshold level has a big effect on the result. Errors can easily occur when the black pixels other than those of the crack appear in the image. It means that there might be certain potential for the improvement of the crack end determination.
Determination of the crack length.
Measuring the crack length.
Measuring the parallel length.
The experimental research was carried out using 3 kinds of automotive steel sheets: (i) IF – deep drawing interstitial free steel formed with ferrite; (ii) FP – microalloyed ferrite-pearlite steel and; (iii) DP – dual ferrite-martensite phase steel. The tensile properties of the studied steels are shown in Figure 5. The samples of two steels (IF and FP) were taken from the tailored blanks – car body elements fabricated applying the progressive method .
The steady state tearing tests were carried out using the CT specimens (W = 50 mm) with both the electro-spark produced notches (tip radius of 0.1 mm) and the notched specimens (tip radius of 0.4 mm) precracked by fatigue (tip radius of 0.001 mm). The specimens with anti-buckling plates were loaded at 0.0217 mm.s−1 by eccentric tension on a tensile testing machine FP 100/1 while the deformation in the notch area was recorded by a CCD (charge coupled device) camera GANZ FCH-30C (1/3 in mono camera, resolution of 640 × 480 pixels) with the frame rate of 25 fps. The CMOD was obtained by continual recording of the dots applied properly in the notch area (Fig. 6). The application of the dots onto the sample surface was carried out using the ink felt on the coordinate x-y microscope CARL ZEISS JENA Messmikroskop BK 70 × 50 modified for this purpose. The coordinates of the centres of gravity for the dots in the load-line were determined using the program based on the MATLAB software (Sect. 2.1.2). The data from the camera were correlated with the loading curve based on the time dependence.
The crack extension Δa was evaluated using the above mentioned program in MATLAB on the basis of the recorded images (Sect. 2.1.3). The CMOD values were transformed into the CTOD values using the plastic hinge model .
Stress-strain diagrams of the examined steels.
Dots applied in the notch area.
The measurement of material deformation belongs to the basic methods of identification of the material’s response to loading. Contactless methods are advantageous because they facilitate the measurements of deformation at any place of the tested specimen, using even several cameras, while the measurements themselves have no effects thereon. The development of these measurement methods is determined by the development of the image analysis or the development of the software-assisted method of the evaluation of scanned images, but mainly by the application requirements from real operations. They are based on scanning the surface of a test specimen and recording the changes thereof over time. Every contactless system comprises several variations for scanning images (various fields of view, different resolutions) and various connection combinations.
The identification of the steady state tearing in thin steel sheets applying the commonly used methods for thick steel sheets is problematic. As a crack opens under eccentric tension, thin steel sheets deflect from the load plane (buckling). In order to eliminate the deformation caused by such deflection, guide plates must be used. The steady state tearing was identified applying the R-curve method and the contactless system which facilitates simultaneous recording of the Δa and CMOD.
Under eccentric tension in the elastic-plastic area, a sharp tip of the initiation crack (generally a fatigue crack) begins to become blunt. The crack initiation in the plastic zone is preceded by the shear deformation of the crack tip, manifested by the crack tip elongation, which is not yet regarded as the crack extension, but represents the stretch zone . The initiation is followed by the steady state tearing. The R-curve with all stages in terms of CTOD, referred to as the δR-curve, is shown in Figure 7.
According to the literature, there are no differences in the steady state tearing characteristics for both the precracked by fatigue and the sharp notched CT specimens. Figure 10 shows the CT specimens at the end of the tests where the steady state tearing occurred.
The effect of the stress concentrator on the tearing resistance was determined on the δR-curves since this type of R-curve has a wider validity range, i.e. they are less sensitive to the specimen geometry. The established δR-curves were assessed using the basic mathematical and statistical methods for the steady state tearing. The estimates of coefficients of the searched regression models were made using the regression analysis. The values listed in Table 1 were used to produce several relations with a better predicative ability. The monitored relations were described by a linear regression model.
The tearing resistance characterizes the resistance of the material to the crack propagation [22,23]. The sequence of the resistance of the investigated steels, determined on the CT specimens with the electro-spark notches, is the same as for the fatigue precracked specimens. The IF steel exhibited the highest tearing resistance and the FP steel  exhibited the lowest. The δR-curves of the electro-spark notched specimens for the investigated steels lie higher than the δR-curves of the fatigue precracked specimens. The fatigue crack has a sharper root than the electro-spark notch. The stress concentration at the sharper root is high, but it covers a smaller area. As a result, the fatigue crack blunting is less intensive than that of the electro-spark notch, and thus the CTOD for the fatigue precracked CT specimens is lower.
The δR-curve slope dCTOD/da represents the tearing resistance. The tearing resistances (slope dCTOD/da; Tab. 2) of the investigated steels did not exhibit any significant differences with different stress concentrators (both the fatigue crack and the electro-spark notch).
Schematic of the δR-curve.
Detail of the notched CT specimen with a fatigue crack.
Detail of the notched CT specimen – an electro-spark notch.
Steady state tearing on the CT specimens with different stress concentrators (the red arrow represents the end of the concentrator; the yellow arrow represents the end of the notch).
Regression models for the δR-curve of the studied steels.
Slope dCTOD/da for different stress concentrators.
The camera-based contactless measurement offers a wide range of applications [4,25]. The proposed approach is definitely suitable for the determination of steady state tearing in thin steel sheets. The main advantage is a large amount of the geometrical information about the crack tip development that may be obtained. The measurement results can also be used in the steady state tearing modelling and simulation applying the extended finite element method XFEM .
The steady state tearing was performed using the CT specimens with an electro-spark produced notch and with a fatigue crack. No important differences in the tearing resistances (slope dCTOD/da) between the fatigue precracked and the electro-spark notched specimens of the investigated steels have been observed. The tearing resistance achieved the maximum value in the interstitial free steel and the minimum value was observed in the ferrite-pearlite steel.
The authors would like to thank the Scientific Grant Agency of Ministry of Education, Science, Research and Sport of the Slovak Republic (grant number VEGA 1/0429/18).
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Cite this article as: Ľubomír Ambriško, Ladislav Pešek, Measurement of the steady state tearing in thin sheets using the contactless system, Metall. Res. Technol. 117, 310 (2020)
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