manuscript local plastic deformation-suban_cvelbar_bundara-recenzirano

7/31/2019 Manuscript Local Plastic Deformation-Suban_Cvelbar_Bundara-Recenzirano

1/6

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.


2/6

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


3/6

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


4/6

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


5/6

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)


6/6

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

manuscript local plastic deformation-suban_cvelbar_bundara-recenzirano

Documents