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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

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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

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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

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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).

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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.

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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.

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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.

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