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7/31/2019 Manuscript Local Plastic Deformation-Suban_Cvelbar_Bundara-Recenzirano
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Digital imaging analysis of microstructures as a tool to identify local plastic deformation
Marjan Suban, Robert Cvelbar, Borut Bundara
Institute of metal constructions, Mencingerjeva 7, 1001 Ljubljana, Slovenia
Abstract:This paper presents a methodology to detect plastic deformation on micro level. The analysis
is based on statistical data describing the morphological and crystallographic textures of a
sample microstructure. This data was obtained from an optical microscopy using digital
imaging analysis. Important parameters necessary to describe a microstructure were identified
as grain size and grain orientation distributions. Change in weighted product of these two
parameters, grain size as area of grain and grain orientation as moment of inertia of grain can
represent a measure to identify plastic deformation on small area. Demonstration of
applicability was performed on a real object as part of ruptured pipe failure analysis in
thermal power plant boiler. Presented analysis leads to the fast identification of the local
plastic deformation and in a case of periodical analysis of the same sample can even be used
as a measure to identify creeping.
Keywords:
digital imaging analysis, plastic deformation, grain orientation, local deformation analysis
1 INTRODUCTION
The quantification of material microstructure is important for the evaluation state of the
material and some of its properties. Many properties of the material are strongly influenced by
size and shape of the grains. Observations of changes in geometric features of grains may be
quantified by image analysis. Microscopy is powerful non-invasive tool for studying material
microstructure, especially if complemented with image analysis.The paper presents the possibilities of evaluation of plastic deformation based on
microstructural grain layouts. Contrary to other researchers work, our methodology of grain
shape and orientation evaluation is based on moments of inertia of individual grains. When a
load is applied to a material, it will cause the material to change shape. Observed effects of
the deformation process on material microstructure using optical microscopy can be evidently
seen on Fig. 1. Changes in microstructure can be easily described on grain level by using
three parameters: change in grain area, shape (elongation) and orientation. New proposed
methodology to evaluate these three parameters is presented in the following sections.
1.1 Digital imaging
There are many imaging techniques available for viewing microstructure in 2D and thus
useful in collecting images on each cross section. These imaging methods include techniques
like secondary electron (SE), back-scattered electron (BSE), ion-induced secondary electron
(ISE) and electron back-scatter diffraction (EBSD) (see Fig. 2). While each method generates
an image in 2D, there are significant issues with some of the techniques [2].
Many laboratories are unfortunately limited to use optical microscopy as essential and only
available method for microstructures evaluation. If grain boundaries are very clearly defined,
computer programs could be written to take higher dimensional measurements (area and
shape measurements) on digital images, but often many grain boundaries are hard to
distinguish. Current state of optical recognition software offers many tools to improve image
resolutions, so that grain boundaries can be easily recognized.
7/31/2019 Manuscript Local Plastic Deformation-Suban_Cvelbar_Bundara-Recenzirano
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Figure 1: Microstructures of the C-Mn steel (a) initial state; (b) microstructure
after deformation [1]
Figure 2: Analysis of microstructure (a) optical microscopy, (b) secondary
electron microscopy image, (c) EBSD [3]
1.2 Quantitative Characterization
Quantitative characterization is an obvious tool for researchers to use when attempting to
develop a relationship between microstructure and properties. As a result of many studies
numerous different methods and rules have been developed. In reality the application of the
characterization greatly dictates the nature of the measurement technique chosen. Oftenmeasurements are performed only in 2D using optical microscopy and digital imaging. In
order to maximize the value of the data, microstructural quantification should be designed
effectively. Almost infinite number of parameters and correlations can be used to describe
microstructure, but just some of these parameters are actually important.
Measurement of grain size is the most used method of all techniques for quantifying
microstructural features. It is known that the grain size of a polycrystalline material is
extremely important in determining its properties. Various properties exhibit correlation with
grain size, such as: yield stress, ductility, and hardness [4]. Generally grain size is measured
as an average scalar value such as intercept length, grain area or grain volume [5].
1.3 Grain shape and principle axis orientationThe shape of grains is likely to be of major significance in a number of applications, but
irregular geometries of grains in a polycrystalline microstructure make grain shape a difficult
parameter to quantify. The difficulty lies in the need for the data to measure the true grain
shape. Usually a number of simplifying assumptions were made.
Similar to the calculation of grain size, the determination of grain shape has been greatly
aided by EBSD maps. The boundaries of each grain can clearly be found and measured by
identifying local changes in orientation. The problem can occur when two neighboring grains
have the same orientation. The image analyzer can consider these two grains as one grain that
could lead to the error in grain size and shape. Difference between quantifying grain shape
and grain size is in the inability to clearly describe shape. Grain area is a relatively
straightforward measurement yielding a scalar value, while shape really needs to be describedby local curvatures, which becomes more complicated and requires higher order mathematical
7/31/2019 Manuscript Local Plastic Deformation-Suban_Cvelbar_Bundara-Recenzirano
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descriptors. It is most commo
as ellipse. In this case, quant
equivalent ellipse major Emax
area of approximated ellipse.
represents measure of grain
relationship, with a value inwhile a very narrow elongated
In addition, many shape desc
a dimensionless value like
length/fiber length (curl) [6],
such as moments of inertia, c
orientation.
The principal axes orientation
the global coordinate system
principal axes orientation, w
crystal lattice (crystallographi
of ellipse, orientation is preseaxis x to the axis of lowest m
Figure 3: Schema
equival
2 METHODOLOGY
Generally, the microstructure
and noise that are developed
attain higher grain-segmentat
tools of digital imaging with
grains, excluding border grai
differentiation between indiv
distinguished then the next stanalysis or Blob analysis in N
imaging and calculation. Blo
dimensional shapes within a r
grains, location, shape, area, p
As one of main result from
area, which is a property of a
section areas to bending and
The moments of inertia for an
computed in a generic way
Equations marked as 1, 2 and
xi and yi represents distance f
area of this triangle.
in everyday work to use simple objects to
ification of grain shape is done by calculati
and minor axis Emin, where the area of grain
Ratio of minor axis of the equivalent ellip
oundness. Roundness is a measurement of
he range from 0 to 1. A perfect round graigrain has roundness near to 0.
iptors involve combining groups of size par
length/width (aspect ratio), area/convex
which can be sometimes ambiguous. Some
an do an adequate or better job of expressi
quantifies the orientation of the grains princ
of cross section. It is important to disti
ich is the orientation referring to the prin
c) orientation, which is usually determined
nted as angle measured counterclockwisement of inertia x1, as shown on Fig. 3
ic representation of the grains appro
nt ellipse
images suffer from defects of improper ill
at the time of sample preparation. First st
ion accuracy. RGB microstructure image w
inal goal to achieve image without noise, w
ns. This is also the most important step o
idual grains in the microstructure. If grain
ps of methodology are purposeless. Applicational Instruments IMAQ Vision software
analysis is the process of detecting and ana
egion of the image. It can provide informati
erimeter, and orientation of grains.
nalyzing software is moment of inertia or
cross section and can be used to predict the
deflection around an axis that lies in the cr
y cross section defined as a simple polygon
by summing contributions from each seg
3 can be used to calculate moments of inerti
rom origin to elementary triangle center poi
escribe shape such
on of the length of
is equivalent to the
e to its major axis
the length width
n has roundness 1,
ameters to generate
rea (solidity) and
scalar parameters,
ng grain shape and
ipal axes relative to
guish between the
cipal axes and the
y EBSD. In a case
from the horizontal
imation by their
umination, artifacts
ge is important to
as processed using
ith set of individual
f analysis to reach
s were not clearly
tion called Particleas used for digital
lyzing distinct two-
n about number of
second moment of
resistance of cross
ss-sectional plane.
n x-y plane can be
ent of a polygon.
, where parameters
nt and ai represents
7/31/2019 Manuscript Local Plastic Deformation-Suban_Cvelbar_Bundara-Recenzirano
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2
From this values which reprprinciple axis x1-y1 can be cal
,
In this case Ix1 represent the
value. The roundness of the g
range from 0 (extremely elon
The angle of rotation of coord
using Eq. 6. It is used as a par
of angle is needed to transf
for angle 1o
is almost equal as
atan
3 EXPERIMENTAL R
For the experimentation we
austenitic stainless steel at v
images were obtained from
austenitic stainless steel and st
Figure 4: Schemacalculat
2 sents moment of inertia for x-y axis, moulated (for axis presentation see Fig. 3).
minimum eigenvalue of moment of inertia
ain can be then calculated using ratio of the
ated grain) to 1 (round grain).
inate system around the grain center of mass
meter to quantify orientation of the individu
rm angles range from 0 180o
to 0 90o
(e.
for 179o).
ESULTS AND DISCUSSION
have used many microstructure images
arious resolutions (i.e. magnifications) & g
ptical microscopy. Sample of microstructu
eps of digital imaging are shown in Fig. 4.
ic representation of steps of digital imad result for one grain
(1)
(2)
(3)
ents of inertia for
(4)
hile Iy1 maximum
e two values and it
(5)
can be calculated
al grain. Correction
g. grain orientation
(6)
f low carbon and
rain shapes. These
e image (500x) of
ging and obtained
7/31/2019 Manuscript Local Plastic Deformation-Suban_Cvelbar_Bundara-Recenzirano
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On the right side of Fig. 5 results for examined sample from Fig. 4 are shown. From graph it
can be concluded that roundness of the grains in microstructure is around 0,46 and that
median of the grains orientation angle is approximately 15o, while average value is 21
o. In
short it can be said, grains are elongated in direction close to horizontal axis.
The results presented in Fig. 5-left show comparison between roundness calculated using ratio
of equivalent ellipse axis and roundness calculated using ratio of moment of inertia forprinciple axis. It is observed that second mentioned roundness is much more sensitive to grain
shape then the first one. The range of calculated results is also much wider, which is more
authentic description of real state.
Figure 5: Correlation between roundness and orientation angle (left) andcorrelation between differently calculated roundness (right)
4 CASE STUDY
For practical demonstration, two samples taken from ruptured steam pipe, marked as No. 2
and No. 4 (200x), were analyzed using described methodology. Average value of calculated
roundness using Eq. 5 for sample No. 4 is 0,4, while for sample No. 2 is 0,36. As it can be
seen from Fig. 6, grains are more elongated in a case of sample No. 4 than in other case.
Similar difference can also be found when observing grain orientation angle. Grain orientation
angle distribution for sample No. 4 is almost flat and median is 45o, which means that grains
how no tendency in orientation. In second case median of grain orientation angle is 64o, while
average value is 59o. This can also be observed from grains in microstructure on Fig. 6-right.
5 CONCLUSIONS
In this paper, a semi-automatic digital microstructure image analysis system to quantify the
microstructure is developed. As input in the analysis process, image obtained from optical
microscopy was used. In a calculation part of investigation, a moment of inertia was
introduced as a major parameter to quantify grain shape and orientation. The results obtained
by proposed method are reproducible and repeatable but can be misleading if differentiation
between individual grains in microstructure is not clear. Method demonstrates its accuracy
and its usefulness by comparing the computed values with other methods. Presented case
study on sample of ruptured steam pipe demonstrates its usefulness for laboratory and
industrial applications in the field of material investigations.
0
10
20
30
40
50
60
70
80
90
0 0,2 0,4 0,6 0,8 1
corr.
R
0
0,1
0,2
0,3
0,4
0,5
0,6
0,7
0,8
0,9
1
0 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 1
R(
ratio
Ix1
/I
y1)
R (eq. ellipse)
7/31/2019 Manuscript Local Plastic Deformation-Suban_Cvelbar_Bundara-Recenzirano
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No.4
Figure 6: Position
corresp
6 REFERENCES
1. R. Song, D. Ponge, D. Rits evolution during war4881-4892
2. M. Groeber, Developmenthe modeling of polycryst
3. S. Xia, B. Zhou, W. CheDistribution in Alloy 69
3016-3030
4. R. W. Armstrong, I. CPolycrystalline Aggregat
5. L. Ciupinski, B. Ralph,size, Materials Characteri
6. S. Ghosh, D. DimidukRelationships, 1
stEdition,
0
10
20
30
40
50
60
70
80
90
0 0,2 0,4 0,6
corr.
R
of samples No. 4 (left) and 2 (right) on r
nding microstructures and results of analysi
aabe, Texture evolution of an ultrafine grai
deformation and annealing, Acta Materi
t of an automated characterization-represent
alline materials in 3D, Diserrtation, Ohio Sta
n, Grain Cluster Microstructure and Grain
0, Metallurgical and materials transactions
dd, R. M. Douthwaite, N. J. Petch, Plas
s, Philosophical Magazine, 7 (1962), pp. 45-
K.J. Kurzydlowski, Methods for the chara
zation, 38 (1997), 3, 177-185
(Eds.), Computational Methods for Micr
Springer New York, 2011
0,8 1
0
10
20
30
40
50
60
70
80
90
0 0,2 0,4 0,6
corr.
R
No. 2
ptured steam pipe,
ed C-Mn steel and
lia, 53 (2005), 18,
tion framework for
te University, 2007
oundary Character
A, 40 (2007), 12,
ic Deformation of
58.
terization of grain
ostructure-Property
0,8 1