web.mst.eduweb.mst.edu/~lekakhs/webpage Lekakh/Articles/2017 Comminication.pdfThe melt was treated...
Transcript of web.mst.eduweb.mst.edu/~lekakhs/webpage Lekakh/Articles/2017 Comminication.pdfThe melt was treated...
1 23
International Journal of Metalcasting ISSN 1939-5981Volume 11Number 4 Inter Metalcast (2017) 11:743-748DOI 10.1007/s40962-016-0128-1
Communication: Characterization ofSpatial Distribution of Graphite Nodules inCast Iron
Simon N. Lekakh
1 23
Your article is protected by copyright and
all rights are held exclusively by American
Foundry Society. This e-offprint is for personal
use only and shall not be self-archived
in electronic repositories. If you wish to
self-archive your article, please use the
accepted manuscript version for posting on
your own website. You may further deposit
the accepted manuscript version in any
repository, provided it is only made publicly
available 12 months after official publication
or later and provided acknowledgement is
given to the original source of publication
and a link is inserted to the published article
on Springer's website. The link must be
accompanied by the following text: "The final
publication is available at link.springer.com”.
COMMUNICATION: CHARACTERIZATION OF SPATIAL DISTRIBUTION OF GRAPHITENODULES IN CAST IRON
Simon N. LekakhMissouri University of Science and Technology, Rolla, MO, USA
Copyright � 2016 American Foundry Society
DOI 10.1007/s40962-016-0128-1
Abstract
Important properties of cast iron, such as fatigue strength,
wear resistance, and low-temperature toughness, relate to
spatial distribution of graphite nodules. Characterization
of spatial distribution can also provide insight into the
solidification sequence in casting. An automated SEM/EDX
analysis was utilized to distinguish graphite nodules from
other structural features (pores and inclusions). The two-
dimensional near-neighbor distance (NND) between nod-
ule centers was calculated for three equal sets of nodule
diameters (small, medium, and large) in each cast iron.
Comparison of measured spatial distributions and ideal
random distribution was executed by plotting the mean and
variance ratios of NND on a spatial distribution quadrant.
This method was used to clarify clustering or ordering
tendencies of graphite nodules in studied cast irons. The
suggested procedure was used to verify the effects of
inoculation and the cooling rate on spatial distribution of
graphite nodules. Inoculation of sand casting increased
nodule counts, decreased mean NND, and eliminated
clustering of small graphite nodules precipitated at the
solidification end. Intensive surface cooling of a continu-
ously cast bar significantly increased nodule count near the
external surface and decreased NND without changing
spatial distribution. The suggested analysis can be used as
a tool for cast iron quality control and process
development.
Keywords: cast iron, structure, graphite nodule, spatial
distribution
Dimensional Distribution of Graphite Nodules
The morphology of individual graphite nodules and its
spatial distribution in cast iron are both important structural
parameters in judging the casting properties. The graphite’s
shape, size, and quantity are determined by applying dif-
ferent algorithms and rules for digital images of the
structure.1–3 These methods are mainly used for quantita-
tive representation of the graphite phase morphology and
for the qualitative classification of a cast iron structure.
Digital optical metallography is a commonly used method
for the determination of cast iron structures; however, this
method presents several problems, two of which are
important for cast iron characterization:
1. Distinguishing microstructure features by optical
contrast, for example, large graphite particles from
micropores or small graphite particles from non-
metallic inclusions. To partially solve this problem,
a 2- to 5-lm threshold is used to cut off the possible
effect of inclusions and artifacts related to limiting
optical resolution. Application of an automated
scanning electron microscopy/energy dispersive
X-ray (SEM/EDX) method for analysis of cast iron
structure resolves these limitations.4–7 An auto-
mated SEM/EDX method has high resolution, and
chemistry of features can be determined for its
classification. Optimized settings of an automated
SEM/EDX analysis for specific applications were
discussed.8 Figure 1 illustrates the possibility of
distinguishing nonmetallic inclusions from small
graphite nodules using this method.7 A total of 2000
features were counted for the specimen, and a
search area was divided into 4 electronic fields with
high precision of field ‘‘stitching.’’
2. Any analysis (optical or SEM) from a random
polished section provides only two-dimensional
structure characterization of the true three-di-
mensional geometry. The counted small graphite
circles in the two-dimensional analysis present a
International Journal of Metalcasting/Volume 11, Issue 4, 2017 743
Author's personal copy
sum of small spherical nodules and the cuts of
larger spheres. Therefore, the two-dimensional
data need to be converted into the real volume
distribution of graphite nodules. Fortunately, for
spherical particles, it is possible to computation-
ally restore true three-dimensional graphite nod-
ule (spheres) size distributions from two-
dimensional measurements of graphite sections
(circles) by applying different computational
algorithms.5,9,10 The obtained three-dimensional
distributions of graphite nodules showed a pos-
sibility of bimodal diameter distributions.7,10,11
However, it is not possible to restore the real
three-dimensional (X, Y, Z) spatial distribution
from two-dimensional (X, Y) graphite nodule
coordinates obtained from a random section.
Spatial Distribution of Graphite Nodules
Important properties of cast iron, such as fatigue strength,
wear resistance, and low-temperature toughness, relate to
the spatial distribution of graphite nodules. Characteri-
zation of the graphite nodule spatial distribution can also
provide insight into casting solidification.12 For example,
fractal analysis was used for the determination of ‘‘lacu-
narity’’—a measure of non-uniformity filled space by
nodules which was affected by prime austenite and gra-
phite solidification modes. The methods of evaluation of
spatial distributions of secondary phases have been
developing during the last half century since the first
digital microscopes became available.13–16 The Voronoi
tessellation method is used to visualize a spatial distri-
bution of graphite nodules.15 The Voronoi tessellation
divides a n-dimensional space into convex n-dimensional
Voronoi polytopes that fill space without overlap.
According to the definition of Voronoi tessellation, a
Voronoi cell associated with a nucleus P in space contains
all points in that space that are closer to P than any other
nucleus. These methods provide information about a
specific space associated with each particle, and they are
widely used in modeling different structures. However,
the tessellation methods are seldom applied for the anal-
ysis of graphite nodules12 because of its relative com-
plexity and difficulties with interpretation of the result in
everyday foundry practice.
In this study, the center of each nodule was defined in an
automated SEM/EDX analysis of polished section using an
8-sword raster at high magnification, and the ‘‘center-to-
center’’ near-neighbor distance (NNDC) was calculated
without considering nodule diameters. Typically, 2000
nodules were counted in each sample using several ‘‘stit-
ched’’ electronic fields. Obtained from an automatic SEM/
EDX analysis, ‘‘clean’’ graphite nodule data were digitized
and ImageJ 2 software was used to build Voronoi tessel-
lations.17 A practical method to interpret a spatial distri-
bution of graphite nodules in castings is suggested. In each
case, graphite nodules were sorted by diameter and after
that were divided into three equal by nodule number
classes: small, medium, and large. A set of NNDC was
calculated for each class. It was done to assess the solidi-
fication sequence assuming that early nucleated nodules
would be larger in diameter than nodules nucleated at the
solidification end. The experimental NNDC distributions of
graphite nodules were compared to the near-neighbor dis-
tance for virtual randomly distributed points using
methodology.15 For randomly generated large number of
XiYi points per unit area (N[ 1000), a mean NNDR
equals15:
MR ¼ 0:5N�0:5 Eqn: 1
and the expected variance (VR) is given by:
VR ¼ 4 � pð Þ= 4pNð Þ Eqn: 2
Based on ratios of experimentally observed (index ‘‘C’’)
and expected from random distribution (index ‘‘R’’) means
(Q = MC/MR) and variances (R = VC/VR), it is possible to
distinguish between random set (Q * 1, R * 1), short-
range ordered set (Q[ 1, R\ 1), cluster set (Q\ 1,
R\ 1), and set of cluster with a superimposed background
of random points (Q\ 1, R[ 1).15 A spatial distribution
quadrant was suggested in this communication to present
different possible structures. Figure 2 illustrates the
different computationally generated virtual distributions
of points (random, ordered, clustered, and combination of
clusters with random) in the unit area and calculated for
them Q and R ratios using Eqns. 1 and 2.
Results and Discussion
In this communication, the application of described spatial
distribution analysis was done for two cases.
1
10
100
0 10 20 30 40 50 60 70 80
Freq
uenc
y, 1
/mm
2
2D nodule diameter, µm
Inclusions
Graphite
Total
Figure 1. Two-dimensional diameter distributions ofnonmetallic inclusions and graphite nodules obtainedfrom automated SEM/EDX analysis.7
744 International Journal of Metalcasting/Volume 11, Issue 4, 2017
Author's personal copy
Case 1 describes the effect of a cooling rate on graphite
nodule spatial distribution. This effect was verified using
continuously cast, large-diameter bars (200 mm) made
from a near-eutectic composition un-alloyed ferritic–pear-
litic ductile iron. The melt was treated with FeSiMg and
inoculated with FeSiBa before being poured into the
launder of a continuous cast machine. Samples were taken
at two radial locations: (1) near surface, where the melt was
rapidly cooled in contact with a water-cooled graphite
mold, and (2) from the middle of the cast bar, where ductile
iron slowly solidified from the liquid core outside the mold.
The graphite nodule count was 420 mm-2 for the near-
surface-located specimen and 93 mm-2 for the specimen
taken from the bar center. The Voronoi tessellations for the
near-wall and the center structures are shown in Figure 3.
The nodule density populations and Voronoi cells differ for
these structures.
For each specimen, nodules were sorted into three groups
(small, medium, and large) with an equal number of nod-
ules in each group. After that, NNDC was calculated for
each group and compared to the theoretical outcome for
random distribution assuming the same nodule number in
both cases (Figure 4). Two differences can be mentioned;
the mean NNDC of the surface specimen was half that of
the specimen from the center of the bar (red arrows), and
Figure 2. A spatial distribution quadrant with different virtual structural distributions and calculatedmean NND (Q) and variance (V) ratios for these structures (black points).
Figure 3. Voronoi tessellations of graphite nodule distribution in 800 continuously cast bar: (a) nearthe center and (b) near surface (1 mm2 area).
International Journal of Metalcasting/Volume 11, Issue 4, 2017 745
Author's personal copy
the former structure had larger departures of spatial dis-
tributions from a random distribution.
A suggested spatial distribution quadrant (Figure 5) char-
acterizes the nodule graphite structure using only one point
with coordinate X (ratio of means of experimental to ran-
dom NND) and Y (ratio of variances). These two numbers
represent a possible departure of random structure from
ordered of clustered spatial distributions. In this particular
case, small graphite nodules had the tendency of clustering,
while larger nodules had a more ordered spatial configu-
ration. High cooling rates had no significant effect on the
type of spatial distributions of nodules.
Case 2 describes the effect of inoculation on the graphite
nodule spatial distribution in two laboratory produced keel
blocks with 15 mm wall thickness from hypo-eutectic
pearlitic ductile iron treated in the ladle by FeSiMg. The
first casting was poured without additional inoculation
(‘‘base’’ ductile iron), and the second one was treated by
Ba- and Ca-bearing FeSi inoculant (‘‘inoculated’’). Inocu-
lation had a large effect on the graphite nodule number per
unit of area (167 mm-2 in base vs. 306 mm-2 in inocu-
lated irons). The Voronoi tessellations for the base and the
inoculated structures are shown in Figure 6. Both the
nodule density populations and Voronoi cells differ sig-
nificantly for these structures.
The same procedure of nodule classification into three
equal groups (small, medium, and large) for each specimen
was used to calculate the NNDC distributions (Figure 7).
Ductile iron inoculation slightly decreased a mean value of
(a) (b)
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200
Prob
abili
ty
NND, micron
Small
Medium
Large
Random
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200
Prob
abili
ty
NND, micron
Small
Medium
Large
Random
Figure 4. Spatial distributions of graphite nodules in 800 diameter continuously cast bar: (a) nearsurface and (b) near the center.
Figure 5. Spatial distribution quadrant for graphite nodules in two specimens (rapidcooled near surface and slow cooled from center) of 800 diameter continuously castbar.
746 International Journal of Metalcasting/Volume 11, Issue 4, 2017
Author's personal copy
Figure 6. Voronoi tessellations of graphite nodule distribution in keel-block sand castings: (a) baseand (b) inoculated ductile irons (1 mm2 area).
(a) (b)
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200
Prob
abili
ty
NND, micron
Small
Medium
Large
Random
0
0.2
0.4
0.6
0.8
1
0 50 100 150 200
Prob
abili
ty
NND, micron
Small
Medium
Large
Random
Figure 7. Spatial distributions of graphite nodules in keel-block sand castings (a) base (b) inoculated ductile irons.
Figure 8. Spatial distribution quadrant for graphite nodules in base and inoculatedkeel blocks produced in sand molds.
International Journal of Metalcasting/Volume 11, Issue 4, 2017 747
Author's personal copy
NNDC while having a large effect on the shape of the
curves which reflected changes in the type of spatial
distribution.
These changes are presented in the spatial distribution
quadrant (Figure 8). In the base casting, the small graphite
nodules had cluster superimposed on random distribution,
while the medium-size nodules had near-random distribu-
tion; also, the large nodules exhibited ordering tendency.
Inoculation significantly eliminated clustering of small
graphite nodules. This can be a result of effective hetero-
geneous nucleation of graphite nodules during whole
solidification period including forming a second nucleation
wave which was described by the author.7,11 Continuous
graphite nodule nucleation will restrict the growth of large
austenite dendrites and decrease the clustering tendency of
small graphite nodules formed at the end of solidification.
Conclusions
Comprehensive characterization of the structure of nodular
cast iron offers two advantages; the characterization results
can be used for casting quality control, and useful casting
solidification kinetics could be extracted. The microstruc-
ture characterization parameters which are used today
mainly describe graphite morphology (shape, size, and
number of graphite particles) as well as a metal matrix
structure (ferrite/pearlite ratio for example). These methods
were originally described by Saltikov,18 De Hoff,19 and the
other authors.
In this communication, the analysis of the spatial distri-
bution of graphite nodules was discussed as an additional
tool for complex structure characterization. The center-to-
center near-neighbor distance was used as a parameter for
the global characterization of the type of spatial distribu-
tion which can be related to a nucleation event during
solidification. The other parameter, surface-to-surface near-
neighbor distance can also be used to characterize the local
spatial distributions and link to crack propagation during
failure and material’s properties.20 The suggested practical
method for presentation of graphite nodule spatial distri-
bution is based on plotting spatial quadrants with coordi-
nates related to the ratio of measured NND to NND of
randomly distributed particles. This method was used to
characterize clustering or ordering tendencies. It was
shown that the cooling rate and inoculation have significant
effects on the type of graphite nodule spatial distribution.
The results can be used for analysis of the solidification
sequence and for casting quality control.
REFERENCES
1. ISO 945, Microstructure of cast irons—test method for
determining nodularity in spheroidal graphite cast
irons
2. A. De Santis, O. Di Bartolomeo, D. Iacoviello, F.
Iacoviello, Int. J. Comput. Vis. Biomech. 1(2),
203–213 (2008)
3. P. Prokash, V. Myrti, P. Hiremath, Int. J. Adv. Sci.
Tech. 29, 31–40 (2011)
4. S. Lekakh, J. Qing, V. Richards, K. Peaslee, Trans.
Am. Found. Soc. 121, 419–426 (2013)
5. S. Lekakh, V. Thapliyal, K. Peaslee, in AISTech Pro-
ceedings (2013), pp. 1061–1068
6. S. Lekakh, M. Harris, Int. J. Metal Cast. 8(2), 41–49
(2014)
7. S. Lekakh, B. Hrebec, Int. J. Metal Cast. 10(4),
389–400 (2016)
8. M. Harris, O. Adaba, S. Lekakh, R. O’Malley, V.
Richards, in AISTech Proceedings (2015),
pp. 3315–3325
9. C. Basak, A. Sengupta, Scr. Mater. 51, 255–260 (2004)
10. K.M. Pedersen, N.S. Tiedjie, Mater. Charact. 59,
1111–1121 (2008)
11. S. Lekakh, ISIJ Int. 56(5), 812–818 (2016)
12. K.V. Makarenko, Met. Sci. Heat Treat. 51(11–12),
235–238 (2009)
13. P.P. Bansal, A.J. Ardell, Metallography 5, 97–111
(1972)
14. V. Benes, R. Lechnerova, L. Klebanov, M. Slamova,
P. Slama, Mater. Charact. 60, 1067–1081 (2009)
15. W.A. Spitzig, J.R. Kelly, O. Richmond, Metallography
18, 235–261 (1985)
16. S. Kumar, S. Kurtz, Mater. Charact. 31, 55–68 (1993)
17. ImageJ 2 software, http://imagej.net/ImageJ2
18. S. Saltykov, Stereometric Metallography, 2nd edn.
(Metallurgizdat, Moscow, 1958)
19. R. De Hoff, Quantitative Metallography in Techniques
of Metals Research, vol II, Part 1 (Interscience, New
York, 1968)
20. L. Morales-Hernandez, A. Herrera-Navarro, F. Man-
riquez-Guerrero, H. Peregrina-Barreto, I. Terol-Vil-
lalobos, in International Symposium on Mathematical
Morphology and Its Applications to Signal and Image
Processing ISMM 2011, pp. 461–471. doi:
10.1007/978-3-642-21569-8_40
748 International Journal of Metalcasting/Volume 11, Issue 4, 2017
Author's personal copy