image analysis as an applicative mean of indentation depth determination

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

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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


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.


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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image analysis as an applicative mean of indentation depth determination

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