Full Text - Journal of Metallurgical Engineering

www.me‐journal.org Journal of Metallurgical Engineering (ME) Volume 3 Issue 3, July 2014 doi:10.14355/me.2014.0303.02 Image Analysis as an Applicative Mean of Indentation Depth Determination M. Azami Ghadikolaei2,1, M. Naderi1, K. Sardashti3, M. Iranmanesh4 Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Hafez 1
Ave.424, Tehran, Iran Department of Materials Science and Engineering, Sharif University of Technology, Azadi Ave, Tehran, Iran 2
Advanced Materials and Processes Program (MAP), University of Erlangen‐Nürnberg, Martens st.5‐7, Erlangen, Germany 3
Department of Marine Engineering, Amirkabir University of Technology, Hafez Ave.424, Tehran, Iran 4
Corresponding author: Milad Azami Ghadikolaei Tel: +98‐0123‐3232478, E‐mail: Milad.azami.sut@gmail.com 1
Received 14 July, 2013; Accepted 31 July, 2013; Published 9 June, 2014 © 2014 Science and Engineering Publishing Company Abstract useful information concerning elastic and plastic deformation, Young modulus, fatigue and creep A practical noncontact technique has been developed behavior of the material examined [3‐6]. with the purpose of estimating depth of residual impressions remained after serial indentation. A simple image‐processing step was employed to analyze the pictures of indentation points obtained by conventional photography at close distances. Brightness levels of the indents that were obtained by the image analysis have been correlated with penetration depths, based on the inverse‐square light attenuation law. For a single indent, the penetration depth estimated by the suggested brightness‐depth correlation has been compared to the real depth measured by AFM. The deviation level of below 5% suggests that this technique can be a viable alternative to current expensive depth sensing methods. Keywords Serial Indentation; Depth Measurement; Image Analysis Introduction
Hardness testing is one of the most common tests done to evaluate behavior of materials. Apart from the hardness values, depth of the impressions formed contain useful information concerning mechanical behavior of the tested materials. Normally, depth measurement can be implemented by in situ and ex situ depth sensing. In situ techniques employs high resolution instruments that can continuously monitor the loads and displacements experienced by the indenter through the thorough course of loading and unloading[1, 2]. Resulting load–displacement curves may provide 104 In situ techniques require high accuracy, complex and expensive instruments to measure displacement of indenter concurrent to loading. Therefore, in situ techniques are suggested to be replaced by ex situ depth sensing that can be implemented by using piezoelectric probes [7] or 3D‐imaging laser interferometry [8] to scan residual impressions. Nevertheless, such techniques require long testing times and elaborate instrumentation sets. Ex situ depth measurement can be simplified by means of a combination between scanning hardness testing and image analysis [9]. Objective of this work is to introduce a simple and accurate technique to estimate depth of indents by employing inverse‐square light attenuation law [10]. Through fitting of experimentally‐derived depth and light intensity values in attenuation equation respective constants were obtained. Accuracy of the equation was then examined by comparing the estimated and real indentation depths through AFM investigation of a single indent. Materials and Methods
As the indentation sample, an austenitic A 321 stainless steel block of 2cm×2cm ×4cm in dimension, was first grinded and polished carefully through conventional metallographic techniques and then Journal of Metallurgical Engineering (ME) Volume 3 Issue 3, July 2014 www.me‐journal.org
underwent the serial indentation technique developed by Naderi et al. in RWTH Aachen[11]. The measurement was implemented in Vickers scale with 10 N loading on a measurement area of 7.29 mm2, comprising 100 indentation points of 0.3 mm in distance. Using a conventional photography camera equipped with a 100‐macro lens, images of measurement area were obtained at approximately 10 mm‐distances from the sample’s surface. The images were then analyzed by OriginLab 8.0 software and brightness profiles were acquired in form of both linear profiles and colored contour graphs. Relative brightness values assumed to be linearly correlated with reflected light intensity were connected to penetration depths. The constants of the suggested equation were finally found through curve fitting. To confirm experimentally the predictions of the resulting equation, real penetration depth for a single indent has been found by AFM microscopy. Measured penetration depth was compared to correlation result for the same indent and a measure of the relation’s errors has been obtained. Results and Discussions
Result of the initial scanning hardness has been tabulated in Table 1. The minimum and maximum hardness that have been measured are 360 HV and 492 HV and the average over 100 indentation points is 440 HV. Assuming negligible amounts of elastic deformation throughout the indentation process, the penetration depths has been estimated by the main equation that relates hardness to indentation load and depth as [12]: d=0.062×(F/HV)1/2 (1) Where in F is the indentation load in N, d is penetration depth in mm and HV is the magnitude of Vickers hardness. The equation is established to predict indents depth at 10N indentation load for test wherein specimen’s thickness is at least ten times thicker than indentation depth. Through applying Eq.1 to hardness value for each indentation point, respective penetration depth has been obtained (Table1). Grayscale image of the test area, taken at a normal angle to the sample surface is illustrated in Figure 1 with brightness variation graphs along the yellow perpendicular lines, on the top and right sides of the image (30002 Lux for the shown indent). Brightness is expressed in Lux (Lx) unit that accounts for illuminance with considering the reflect‐ ing sample surface as a distinct illumination source. Indentation points appear in form of white bright points lying in a dark gray matrix, which represents the intact zone in the scanned area. The contrast in brightness can be explained by the difference between the indents and TABLE 1. HARDNESS MAGNITUDES IN 10×10 POINTS SCANNING ZONE FOR INDENTATION DISTANCE OF 0.3 MM. Hardness [HV10] and Penetration Depth [d(μm)]
X Y 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 419 9.578 360 10.333 460 9.141 394 9.877 463 9.112 416 9.613 453 9.212 432 9.433 449 9.253 479 8.958 384 10.005
376 10.111
443 9.315 426 9.499 455 9.191 446 9.284 470 9.044 471 9.034 434 9.411 449 9.253 414 9.636 410 9.683 429 9.466 441 9.336 444 9.305 453 9.212 464 9.102 453 9.212 455 9.191 482 8.93 387 9.966 397 9.84 425 9.51 443 9.315 469 9.053 454 9.202 452 9.222 466 9.082 440 9.347 443 9.315 384 10.005
403 9.767 441 9.336 462 9.122 448 9.263 459 9.151 478 8.968 453 9.212 447 9.273 475 8.996 403 9.767 418 9.59 455 9.191 420 9.567 448 9.263 473 9.015 441 9.336 438 9.368 476 8.986 461 9.131 404 9.754 402 9.779 441 9.336 447 9.273 475 8.996 487 8.884 473 9.015 446 9.284 459 9.151 476 8.986 393 9.89 385 9.992 411 9.671 446 9.284 425 9.51 474 9.005 452 9.222 492 8.839 448 9.263 446 9.284 372 10.165 424 9.522 405 9.742 458 9.161 406 9.73 488 8.875 415 9.624 464 9.102 464 9.102 468 9.063 390 9.928 418 9.59 406 9.73 475 8.996 416 9.613 452 9.222 458 9.161 440 9.347 459 9.151 441 9.336 HV10
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d
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105 www.me‐journal.org Journal of Metallurgical Engineering (ME) Volume 3 Issue 3, July 2014 their intact matrix in reflection of light received from sample’s surrounding. In addition, deviations from the desired indentation pattern can be inspected in some regions with observation of extra indentation points within the standard 0.3‐mm spacing. However, the data related to those points have been neglected in further steps of calculations. In order to facilitate the process of finding the maximum Lx for each indent, the colored 2D brightness contour map can be very helpful. As a result, the brightness variation in the vicinity of single indents was shown in Fig. 2. Central point of the majority of indents is colored in yellow which represents the maximum Lx. The intact surface is covered by the dark blue color reflecting light intensity of 0 to 8750 Lx. Nonetheless, in most of areas surrounding the indents, as being slightly affected by indenter compressive force, relatively higher light reflection intensity (from 8750 to 17500 Lx) has been detected through the light blue color contours. FIGURE 1. GRAYSCALE PICTURE OF THE HARDNESS SCANNING AREA WITH LIGHT INTENSITY GRAPHS OVER THE VERTICAL AND HORIZONTAL MEASURE LINES. FOR PRESENTED INDENT, THE MAXIMUM LX IS 30002, SHOWN IN Z‐VALUE BOX. FIGURE 2. COLORED CONTOUR MAP OF BRIGHTNESS WITH VERTICAL AND HORIZONTAL MEASURE RULERS AND THE RESPECTIVE BRIGHTNESS VARIATIONS ALONG THEM. FOR PRESENTED INDENT, THE MAXIMUM LX IS 50903, SHOWN IN Z‐VALUE BOX. 106 Journal of Metallurgical Engineering (ME) Volume 3 Issue 3, July 2014 www.me‐journal.org
Establishment of a correlation between brightness and indentation depth requires attribution of a single magnitude for brightness to each indent. This has been achieved by setting the intersection of two yellow measure lines at indentation each point manually and record the highest brightness achieved. To correlate the brightness with depth we use the basic physical namely inverse‐square law that illuminance (Lx) is inversely proportional to square of light travelling distance as [11]: Lx = cd‐2+b (2) Where d is the indentation depth and c is the proportionality constant. Another constant is b that accounts for the fixed distance of the lens from the sample surface. To fit the data for penetration depth (d) and illuminance (Lx acquired from Figure 2 for each indents) in inverse‐square law, we rewrite Eq.2 as: Lx= m + n × (10000/d2) (3) Which relates 10000.d‐2 as a multiple of depth to light intensity. Subsequently, the values for illuminance and inverse‐square of depth have been fitted by linear curve fitting to Eq.3 as shown in Figure 3. As result shows, m and n are equal to 61909.55 and 17.63, respectively. Error level of the suggested light intensity‐depth equation had to be determined by means of AFM precise depth measurement. Figure 4a illustrates the 2D depth map of the indent located at the 9th row and 6th column of the 10 × 10 indent matrix, resulted from AFM measurements. According to the pale orange color of indent’s surrounding area compared to the black color of central tip, the indentation depth can be estimated at 7 or 8 μm. FIGURE 3. GRAPHIC REPRESENTATION OF LINEAR CURVE FITTING OF LIGHT INTENSITY OVER 10000.d ‐2 SHOWING DATA POINTS FIT WELL TO A LINEAR BEHAVIOR SHOWN BY RED LINE. THE GRAPH SHOWS NO LARGE DEVIATION FROM LINEAR BEHAVIOR. FIGURE 4. AFM MEASUREMENT RESULTS IN FORM OF a) 2D HEIGHT MAP OF THE SINGLE INDENT AT 9th ROW AND 6th COLUMN, A) VERTICAL DISPLACEMENT TRACK OF THE PROBE THROUGH SCANNING OF THE INDENT. 107 www.me‐journal.org Journal of Metallurgical Engineering (ME) Volume 3 Issue 3, July 2014 On the other hand, exact depth is calculated using the SPM software to monitor the vertical displacement of the AFM probe throughout scanning of the indent (Figure 4b). The difference in height between deepest and edge points that are specified by the two red cursors, is 8.49 μm. This height difference of 8.49 μm is an equivalent to the indentation depth. The indentation depth obtained by inserting the corresponding illuminance of the investigated indent (64210 lx) into Eq.3 is 8.75 μm that exhibits a 3.06% deviation from the AFM‐resulted depth. Therefore, the correlation error is in an acceptable margin and its application is encouraged. Regarding the inverse proportionality of Vickers hardness to square of indent base square diagonal and the linear dependency of penetration depth on diagonal length, a linear equation similar to Eq.2 has been established to correlate hardness with illuminance. The average base square diagonal found by AFM measurements was 60.15 μm. The resultant hardness magnitude was 522 HV from which the hardness value predicted by the respective linear equation (501 HV) showed approximated deviation of 4%. relative to true depth found by AFM measurements. Therefore, this simple procedure offers a technically feasible and precise route to determine the depth of impressions formed by indentation. REFERENCE
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In this paper a quick, inexpensive and simple technique to obtain indentation depth has been introduced. Serial indentation was done for a hundred points and a conventional camera, equipped with a 100 micro lens, took picture of the indentation surface at close distances. The picture is analyzed by image analysis and a single light intensity value is assigned to each indent. Finally, a linear equation that correlates brightness (illuminance) with indenter penetration depth has been suggested. The resultant values showed errors of below %5 108 [9]
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