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http://www.me-journal.org/paperInfo.aspx?ID=9719 A practical noncontact technique has been developed 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.
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www.me‐journal.org Journal of Metallurgical Engineering (ME) Volume 3 Issue 3, July 2014
doi:10.14355/me.2014.0303.02
104
Image Analysis as an Applicative Mean of
Indentation Depth Determination M. Azami Ghadikolaei2,1, M. Naderi1, K. Sardashti3, M. Iranmanesh4
1Department of Mining and Metallurgical Engineering, Amirkabir University of Technology, Hafez
Ave.424, Tehran, Iran
2Department of Materials Science and Engineering, Sharif University of Technology, Azadi Ave, Tehran, Iran
3Advanced Materials and Processes Program (MAP), University of Erlangen‐Nürnberg, Martens st.5‐7, Erlangen,
Germany
4Department of Marine Engineering, Amirkabir University of Technology, Hafez Ave.424, Tehran, Iran
1 Corresponding author: Milad Azami Ghadikolaei Tel: +98‐0123‐3232478, E‐mail: [email protected]
Received 14 July, 2013; Accepted 31 July, 2013; Published 9 June, 2014
© 2014 Science and Engineering Publishing Company
Abstract
A practical noncontact technique has been developed
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
useful information concerning elastic and plastic
deformation, Young modulus, fatigue and creep
behavior of the material examined [3‐6].
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
105
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
1 419 384 414 387 384 403 404 393 372 390 HV10
9.578 10.005 9.636 9.966 10.005 9.767 9.754 9.89 10.165 9.928 d
2 360 376 410 397 403 418 402 385 424 418 HV10
10.333 10.111 9.683 9.84 9.767 9.59 9.779 9.992 9.522 9.59 d
3 460 443 429 425 441 455 441 411 405 406 HV10
9.141 9.315 9.466 9.51 9.336 9.191 9.336 9.671 9.742 9.73 d
4 394 426 441 443 462 420 447 446 458 475 HV10
9.877 9.499 9.336 9.315 9.122 9.567 9.273 9.284 9.161 8.996 d
5 463 455 444 469 448 448 475 425 406 416 HV10
9.112 9.191 9.305 9.053 9.263 9.263 8.996 9.51 9.73 9.613 d
6 416 446 453 454 459 473 487 474 488 452 HV10
9.613 9.284 9.212 9.202 9.151 9.015 8.884 9.005 8.875 9.222 d
7 453 470 464 452 478 441 473 452 415 458 HV10
9.212 9.044 9.102 9.222 8.968 9.336 9.015 9.222 9.624 9.161 d
8 432 471 453 466 453 438 446 492 464 440 HV10
9.433 9.034 9.212 9.082 9.212 9.368 9.284 8.839 9.102 9.347 d
9 449 434 455 440 447 476 459 448 464 459 HV10
9.253 9.411 9.191 9.347 9.273 8.986 9.151 9.263 9.102 9.151 d
10 479 449 482 443 475 461 476 446 468 441 HV10
8.958 9.253 8.93 9.315 8.996 9.131 8.986 9.284 9.063 9.336 d
www.me‐journal.org Journal of Metallurgical Engineering (ME) Volume 3 Issue 3, July 2014
106
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.
Journal of Metallurgical Engineering (ME) Volume 3 Issue 3, July 2014 www.me‐journal.org
107
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.
www.me‐journal.org Journal of Metallurgical Engineering (ME) Volume 3 Issue 3, July 2014
108
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%.
Conclusion
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
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.
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