Modelling microstructural and mechanical
properties of ferritic ductile cast iron
P. Donelan
It is well known that the mechanical properties of ductile cast iron (DCI ) depend on its microstructure, and that the
microstructure depends on the properties of the melt and the cooling conditions during casting. There have been
many studies of the individual elements of the process of casting DCI, but as yet there have been very few examples
of modelling the entire process to predict cooling rates, microstructure, and mechanical properties, particularly for
large castings. The present paper describes a method of modelling the microstructural and mechanical properties of
ferritic DCI, and applies the methods to the case of a large (13 t) thick walled (300 mm thickness) casting. The
microstructure calculated includes nodule count, nodularity, ferrite grain size, and percentage ferrite. The mechanical properties calculated include yield stress, tensile strength, elongation, and static upper shelf fracture toughness
(J and K ). The calculated results compare well with those of a test casting.
MST/4243
1C
JC
T he author is with Ove Arup and Partners, 13 Fitzroy Street, L ondon W 1P 6BQ, UK, and is currently seconded to the Japan
Research Institute, 16 Ichibancho, Chiyoda-ku, T okyo 102, Japan. He can be contacted by email at pat.donelan@arup.com.
Manuscript received 30 October 1998; accepted 29 October 1999.
` 2000 IoM Communications L td.
Introduction
In the past 10 years there has been great interest in
computer modelling of the casting process, for its potential
to increase product quality and reduce rejection rates and
delivery times. Currently, such modelling techniques are
mainly used to predict defects, and this allows methods
which give rise to defect free castings to be developed with
less trial and error. However, modelling to predict microstructural and mechanical properties is at an earlier state
of development than modelling to predict defects.
Specifications of castings for general use normally require
that the microstructural and mechanical properties of either
separate or cast-on testpieces satisfy certain minimum
properties. In order to be suitable for use in high integrity
applications, thick walled ferritic ductile cast iron (DCI)
must satisfy microstructural as well as mechanical property
requirements measured in the casting itself. Such requirements typically include:
(i) minimum tensile properties1–3
(ii) pearlite content ∏20%,1,3 or ‘predominantly ferritic matrix’2
(iii) graphite nodularity 70%,3 or ‘no chunky graphite
and no compacted graphite’.1 (Reference 3 specifies
70% nodularity when measured in accordance with
the Japan Foundrymen’s Society (JFS) method,4
which is approximately equivalent to 80% when
measured in accordance with the ISO 945 method,5
see discussion in Ref. 6).
The location on the casting for testing these properties is
subject to agreement between the supplier and purchaser.
As the microstructure and mechanical properties are
functions of the cooling rates during manufacture, these
properties will vary throughout the casting. This raises the
question of where to measure these properties, i.e. where in
the casting are the worst properties to be found.
The present paper first presents a review of the current
state of the art in modelling the microstructural and
mechanical properties of ferritic DCI. Aspects which have
not been well covered in previous work are identified, and
the specific objectives of the present work are stated. A
method for calculating the microstructure and mechanical
properties of DCI from cooling rates during casting is then
presented. These cooling rates can be obtained from
ISSN 0267–0836
a computer thermal analysis of the casting process. The
microstructural properties considered are nodule count
(number of graphite nodules per mm2), nodularity (percentage of nodules which are spherical in form), ferrite grain
size, and percentage pearlite. The mechanical properties
considered in the present paper are yield stress, tensile
strength, elongation, and static upper shelf fracture toughness J and K . The method is then illustrated for the
1C
JC
case of a 13 t, 300 mm thick DCI casting containing
3·5 wt-%C, 1·8 wt-%Si, and 0·2 wt-%Mn, for which test
results of all the relevant parameters are available. The
computer results are compared with those of the test casting.
REVIEW OF STATE OF THE ART
Computer simulation of the casting process at its simplest
consists of thermal analysis of the flow of heat from the
melt to the mould to obtain the temperature–time history
of the solidifying melt. By appropriately specifying the
liquidus and solidus temperatures, specific and latent heats,
etc., good agreement between calculated and measured
temperatures within a casting can be obtained. If the initial
temperature distribution needs to be known more accurately then it may be necessary to analyse the pouring
phase of the casting process using a fluid flow code. As the
casting cools down differential shrinkage between the
casting and the mould causes gaps to form, thereby
increasing the resistance to flow of heat between the casting
and mould. To model this correctly may require a coupled
thermal–mechanical analysis. Typical applications of such
analyses are described below.
Prediction of defects in castings
The most reliable way of predicting a defect in a casting is
when the analysis predicts that an area of liquid is
completely surrounded by solid. In that case a shrinkage
cavity will form. Other formulae can also be applied using
the output of a thermal analysis (see Ref. 7 for further
details). The occurrence of inverse V segregation in large
castings can also be predicted using these techniques.8,9
Modelling of fluid flow during the pouring phase of
casting is also used to predict the occurrence of defects.10
For example the last place to be filled is frequently the
location of defects, and this method is capable of identifying
such locations.
Materials Science and Technology
March 2000
Vol. 16 261
262 Donelan Modelling properties of ferritic ductile cast iron
Design of casting method
Calculation of microstructural and mechanical
properties
A lot of research has been carried out in this area, however
by virtue of its complexity practical application to real
foundry problems is less developed. Good reviews of the
state of the art in this area can be found in Refs. 11 and 12.
Application to industrial castings is still relatively scarce,
but examples can be found in Refs. 13 and 14. These
examples are small automotive DCI castings. The mechanical properties calculated were hardness and yield stress,
and the results were presented as contour diagrams.
Reasonable agreement between analysis and test results
was obtained.
Work published to date has been limited in a number of
important ways including
(i) the castings have all been relatively thin walled. For
a thick walled DCI casting, phenomena such as
fading and loss of nodularity owing to the longer
solidification time become more significant
(ii) not all the important mechanical properties have
been considered, e.g. elongation, ultimate tensile
strength, and fracture toughness.
It was the objective of the present work to carry out
modelling of a thick walled ferritic DCI casting, taking into
account fading and loss of nodularity, to ultimately
calculate the mechanical properties (yield stress, ultimate
tensile strength, elongation, and fracture toughness).
Nodule count
In the literature on modelling of DCI, the nodule count is
normally obtained from a coupled thermal–microstructure
analysis of the process of solidification. Such an analysis
calculates the undercooling of the melt below the eutectic
solidification temperature, from which the nodule count is
obtained. However, in cases where the cooling rates at the
eutectic solidification temperature are low (in the case
considered the maximum is less than 10 K min−1) and
where inoculation is used to increase the nodule count, the
amount of undercooling is very small (<1 K) and a method
of calculating nodule count which does not require coupled
thermal–microstructure analysis can be used. This greatly
simplifies the computing effort required, and allows nonspecialist commercial thermal analysis codes to be used.
This approach was used in the work described in the
present paper.
There are three phenomena to be considered in calculating the nodule count: nucleation, growth, and fading.
Nucleation is the formation of nuclei of graphite in the
molten iron as it starts to solidify, growth is the growth of
these particles during the solidification process, and fading
is the reduction in the number of nuclei with time during
solidification.
NUCLEATION
The rate of nucleation can be obtained from Oldfield’s
equation15 or some variation of it
N=ADT 2 . . . . . . . . . . . . . . . (1)
where N is the number of nuclei per unit volume, DT is
the degree of undercooling, i.e. the difference between the
eutectic solidification temperature and the actual temperature of the melt, and A is the empirical coefficient,
determined experimentally for the melt being used.
Materials Science and Technology March 2000
Vol. 16
Nodules/mm2
Using the thermal analysis tool it is possible to choose the
most effective casting method which produces a sound
casting, with fewer expensive trial castings.
Cooling Rate at Eutectic Temperature, K min_1
1 Relationship between cooling
temperature and nodule count
rate
at
eutectic
NODULE GROWTH
During solidification the graphite nodule becomes surrounded by austenite, and the rate of growth of the nodule
becomes a function of the rate of diffusion of carbon from
the melt through the austenite to the growing nodule. This
can be obtained from the equation of Su et al.16
Dc (C −C )R
dR
c al
ag g
a=
. . . . . . . . (2)
dt
(R −R )R (C −C )
a
g a la
al
where R is the radius of the austenite shell (m), Dc is the
a
c
diffusion coefficient of carbon in austenite (m s−1), R is
g
the radius of the graphite nodule (m), C is the carbon
al
concentration of the austenite at the liquid boundary
(wt-%), C is the carbon concentration of the austenite at
ag
the graphite boundary (wt-%), and C is the carbon
la
concentration of the liquid at the austenite boundary
(wt-%). The values of C , C , and C can be obtained
al ag
la
from the phase diagram of the alloy under consideration.
In the present work the phase diagrams were calculated
using the Thermo-Calc17 computer program.
The nodule count, uncorrected for fading, is obtained
by solving the above two equations simultaneously. The
equations to be solved are18
P AP B
t dN
t dR 3
a dt
dt
dt
0
t
f =1−exp(−V )
V=
4p
3
Q=L
df
dt
H
. . . . . . . (3)
where V is the volume fraction of solid, f is the volume
fraction of solid corrected for cell to cell impingement, Q is
the rate of release of latent heat, t is time, and L is the
latent heat of DCI ( kJ kg−1).
During solidification the undercooling increases until at
a certain point the rate of latent heat release is greater than
the rate of heat loss, at which point the temperature starts
to rise. At this point no further nodules are assumed to
form, and the nodule count is obtained from the maximum
undercooling calculated.
In order to decouple the thermal analysis from the
microstructure analysis the set of equations (3) is repeatedly
solved for different cooling rates at the eutectic temperature,
from which the relationship between cooling rate and
nodule count is obtained. Figure 1 shows the results of
solving the set of equations (3) for the DCI in the present
study for a range of cooling rates at the solidification
temperature. It should be noted that, as these results
were derived using an empirical coefficient which is only
appropriate to the melt used in the test casting, these
results are not generally applicable to other castings.
Provided the undercooling is sufficiently small so that it
does not significantly affect the initial cooling rate, this
relationship may be used with the results of a simple
thermal analysis of the casting process to obtain the nodule
count (uncorrected for fading).
FADING
Fading is the reduction in the number of locations within
the melt which can potentially act as nuclei for the
formation of graphite. The extent of this phenomenon
depends on the type of inoculant used, but in general there
is an exponential decrease in the nodule count with time.
To correct for this effect, the nodule count from Fig. 1
should be multiplied by exp(−t/t*), where t is the time
between inoculation and the start of the solidification
reaction, and t* is a parameter dependant on the type of
inoculant used.19 This correction is particularly important
for thick walled castings, for which the time between
pouring and solidification is relatively long and fading
becomes significant.
Nodularity
As mentioned above in the ‘Introduction’, nodularity N∞ is
a method of classifying the graphite form of cast iron. In
the Japan Foundrymen’s Society (JFS) method4 nodules
are classified into five different types, types I to V. Types
IV and V are the desirable forms and nodularity N∞ is
JFS
calculated from the formula
(0+N +0·3N +0·7N +0·9N +N )100
I
II
III
IV
V
(N +N +N +N +N )
I
II
III
IV
V
where N is the number of type i nodules.
i
In the ISO 945 method5 nodules are classified into six
types, type I to VI. Types V and VI are the desirable forms.
Nodularity N∞ is calculated from the formula
ISO
N +N
V
VI 100
N∞ =
ISO
VI
∑N
i
I
The percentage nodularity is a function of the eutectic
solidification time. There is very little quantitative published
research on the relationship between nodularity and
solidification time, only one paper was found20 from which
the following equation was derived
N∞ =
JFS
A B
N∞ =87·5 exp(−0·0539t) . . . . . . . . . (4)
JFS
where t is the time from start to finish of the eutectic
reaction in hours. Nodularity from the JFS method is
related to that from the ISO method using the equation6
N∞ =4·58+1·05N∞
ISO
JFS
. . . . . . . . . . (5)
Percentage ferrite and pearlite
The method of calculating the percentage ferrite and
pearlite followed that of Wessen.19 When the temperature
falls below the stable eutectoid temperature (around
750–800°C, depending on the composition of the iron)
austenite can decompose to ferrite. As the carbon content
of ferrite is much smaller than that of austenite the carbon released diffuses to the graphite nodules. The rate
of transformation is governed by the rate of diffusion of
carbon in ferrite, and the rate of incorporation of carbon
into the nodules. Wessen describes this transformation as a
three stage process as follows:
(i) formation of a complete ferrite shell around the
nodules
Modelling properties of ferritic ductile cast iron 263
Cooling Rate at Start of Eutectoid
Reaction, K s_1
Donelan
Nodules/mm2
2 Variation of ferrite percentage with nodule count and
cooling rate at start of eutectoid reaction
(ii) growth of the ferrite shell governed by the rate of
incorporation of carbon into the nodule
(iii) growth of the ferrite shell governed by the rate of
diffusion of carbon in ferrite.
In the present study problems were encountered in trying
to model the first stage. However, this first stage appears
to be a refinement, and the essentials of the process can be
captured with the second and third stages only. The growth
rate of ferrite in stage (ii) is given by
A B A B
4pR3
dIa (Cac −Cagr ) R 2
c
g exp
a m . . . . . (6)
= c
dt
(Cca −Cac ) R
3
c
c
a
and the rate of growth in stage (iii) is given by
dIa Cac −Cagr R Da
c
g C
= c
. . . . . . . . . . (7)
dt
Cca −Cac IaR
c
c
a
where Ia is the thickness of the ferrite shell (m), R is the
a
radius of the ferrite shell (m), R is the radius of the
g
graphite nodule (m), Da is the coefficient of diffusion of
C
carbon in ferrite (m s−1), m is the parameter describing the
rate at which carbon atoms can be incorporated on the
graphite surface (m s−1), Cac and Cagr are the carbon
c
c
concentrations (wt-%) of the ferrite at the austenite/ferrite
and ferrite/graphite boundaries, respectively, and Cca
c
is the carbon concentration of the austenite at the
austenite/ferrite boundary (wt-%). The values of Cac, Cagr,
c
c
and Cca are derived from the phase diagram for the alloy
c
in question.
When the temperature falls below the metastable eutectoid temperature (~30°C below the stable eutectoid
temperature, depending on the composition of the iron in
question) then pearlite starts to form from any remaining
austenite. The growth rate of pearlite is faster than that
of ferrite, and is given by (dR /dt)=kDT 2, where R is the
p
p
radius of the pearlite shell and k#9·4×10−10 (see Ref. 19).
In solving these equations it is necessary to take account
of segregation of silicon and manganese, and their effect on
the eutectoid temperatures. Segregation was calculated
using Scheil’s equation, together with partition coefficients
obtained from Boeri.21
The results for the iron in question are shown in Fig. 2.
The results are presented in the form of percentage ferrite
for a range of cooling rates at the eutectoid temperature
and nodule counts. By using these results to post-process
the temperature–time output from a thermal analysis of
the casting process the percentage ferrite and pearlite can
be obtained.
Ferrite grain size
No method of calculating ferrite grain size of DCI has been
found in the literature. However, from the data of Frenz
Materials Science and Technology
March 2000
Vol. 16
264 Donelan Modelling properties of ferritic ductile cast iron
Ferrite Grain Size, µm
(a)
(a)
(b)
Nodule Diameter, µm
3 Relationship between nodule diameter and ferrite
grain size from data in Ref. 22
(Table 5d in Ref. 22), it was found that ferrite grain size is
approximately equal to the nodule diameter multiplied by
1·6 (see Fig. 3). This result is applicable for both heat
treated and non-heat treated specimens. The results of
Yanagisawa23 are reasonably consistent with this for carbon
contents between 2–4 wt-%, but for carbon contents outside
this range the relationship does not appear to be valid.
Mechanical properties
There have been many studies of the relationship between
microstructural and mechanical properties of DCI.
However, in most cases only a limited range of microstructural parameters have been studied, so that the range
of application of the formulae deduced is rather limited.
Where necessary, in the present work, formulae containing
a greater number of parameters and with a wider range of
application have been deduced using the results of a
number of separate studies.
It is important to realise that in most cases the
relationship between microstructural and mechanical properties is non-linear, but over a restricted range the
relationship is approximately linear. Thus, for example in
Ref. 22 it was found that different parameters determined
the mechanical properties when the pearlite content was
greater than ~20% and when it was less than ~20%. The
relationships given below are applicable to DCI meeting
the following criteria:
(i) predominantly ferritic matrix (pearlite content <20%)
(ii) nodularity (measured by JFS method)>70%
(iii) silicon content <4 wt%, manganese content <1%,
other alloying elements should be ‘relatively
insignificant’.
YIELD AND ULTIMATE TENSILE STRENGTH
In Ref. 22 formulae are presented which relate the yield
and ultimate tensile strength (UTS) of ferritic DCI to the
percentage silicon and pearlite. The effect of ferrite grain
size and carbon content is not taken into account. In
Ref. 24 carbon content and ferrite grain size are taken into
account but silicon content and pearlite quantity are not
considered. By combining both equations it is possible to
obtain relationships covering a wider range of variables as
follows
Yield stress (MPa)
Elongation
The following formula was obtained by combining formulae
from Venugopalan and Alagarsamy,25 which did not take
into account the effect of nodularity on elongation, and
Iwabuchi et al.,20 who studied the effect of nodularity on
elongation. The effect of nodularity was very non-linear,
and significant scatter was found. However, for nodularities
greater than 70% the relationship can be linearised
Elongation (%)=37·85−0·093H −0·8(95−N∞)
m
. . . . . . . . . (10)
where H is the composite matrix microhardness which is
m
given by
H =(H X +H X )/100 . . . . . . . . . (11)
m
f f
p p
where X is the ferrite content and H and H are the
f
f
p
hardness of ferrite and pearlite, respectively and are
calculated from the equations given below
H =64+44[%Si ]+9[%Mn]+114[%P]+10[%Cu]
f
+7[%Ni ]+22[%Mo]
. . . . . . . (12)
. . . . . (8)
. . . . . . (9)
This formula has been obtained by combining formulae
provided by Salzbrenner26 and Bhandhubanyong.27 The
UTS (MPa)
FRACTURE TOUGHNESS
=147+68·1[%Si]+1·77X
p
+26·7(1−0·0656[%C])d−0·5
where d is the ferrite grain size measured in micrometres,
the chemical compositions are measured in weight per cent,
and the pearlite composition X is measured in per cent.
p
Figure 4a shows the comparison between Frenz’s original
equation22 and his test results for yield strength, and Fig. 4b
shows the comparison between equation (8) and his test
results. It can be seen that the agreement is improved. A
similar improvement is obtained for ultimate tensile
strength.
H =249+26[%Si]+12[%Mn]+234[%P]
p
+16[%Cu]+17·5[%Ni ]+26[%Mo] . . (13)
=52+63·2×[%Si]+0·663X
p
+21·6(1−0·0656×[%C])d−0·5
4 Comparison of yield stress data from Ref. 22 and
calculated values using a equation in Ref. 22 and
b equation (8) in present study
Materials Science and Technology March 2000
Vol. 16
Donelan
Modelling properties of ferritic ductile cast iron 265
Temperature, °C
Thermocouple 3
Node 5233 temperature
(a)
Thermocouple 6
Node 5408 temperature
(b)
Time, s
6 Comparison of test and finite element results for
temperature–time history at a thermocouple 3 (centre
of base) and b thermocouple 6 (inside of wall)
5 Illustration of test casting and finite element model
work by Salzbrenner deliberately used high nodularity
specimens, and specimens were heat treated to remove any
pearlite. The work of Bhandhubanyong did not consider
the effect of nodule diameter
J
1C
( kJ m−2)=23·6+581×D
A
−0·5(95−N∞)−0·06X
p
−0·004×(N∞X )
. . . . . . (14)
p
where D is the average nodule diameter.
A
The static upper shelf fracture toughness K can be
JC
obtained from K =(EJ )0·5, where E is the Young’s
JC
1C
modulus of DCI.
In all the above mechanical property equations the
convention X =(100−X ) has been used, and nodularity
p
f
is measured according to the JFS Method.4 For this reason
it has been necessary to make an adjustment for Frenz’s
formulae,22 as his formulae are based on the convention
(%ferrite+%pearlite+%graphite)=100.
Validation of methodology
Validation of the methodology was carried out by:
(i) building a three-dimensional finite element model of
a large casting (~13 t)
(ii) carrying out thermal analysis to obtain the temperature–time histories at each point in the casting as
it solidified and cooled. The computer program used
was LS-DYNA3D28
(iii) applying the methodology to the calculated temperature–time history results to calculate microstructural and mechanical properties
(iv) comparing the analysis results with the test data.
CONSTRUCTION OF MODEL
Figure 5 shows a view of the finite element model of the
test casting. The test casting represents a quarter section of
the body of a container for transporting radioactive
material, which was produced for trial purposes. The wall
thickness is 300 mm. To get satisfactory mechanical properties the casting was produced using a permanent mould
on the outside and a sand mould on the inside. The finite
element model incorporated all these components and the
number of elements in the model was 4300.
One very significant problem in carrying out the analysis
is the fact that as the casting cools a gap opens up between
the casting and the mould, and this affects the heat transfer
coefficient between the mould and the casting. To obtain
satisfactory correlation between test and calculated temperature–time histories this fact must be taken into account.
A coupled thermal–mechanical analysis can calculate the
shrinkage of the casting and mould during cooling, and
from this calculate the change in the heat transfer coefficient
and feed this result into the next thermal analysis step.
However, this approach is very computer intensive and
difficult to do. In the present work, after investigating
several options, a thermal analysis alone was used with a
non-linear heat transfer coefficient between the mould and
the melt. The non-linear heat transfer coefficient was taken
from the literature.18
Figure 6 shows the comparison between the calculated
and measured temperature–time histories at two points in
the casting.
Results
The calculated temperature–time histories were postprocessed using the methodology described above, to
obtain the calculated microstructural and mechanical
properties. The results are shown in Fig. 7. The following
qualitative observations were made.
1. The overall distribution of nodule count is reasonable,
with a higher nodule count on the outside of the casting,
because of the higher solidification rate owing to the
permanent mould on this side.
Materials Science and Technology
March 2000
Vol. 16
266 Donelan Modelling properties of ferritic ductile cast iron
Nodules/mm2
Nodularity, %
(a)
(b)
Yield Stress, MPa
Ferrite, %
(c)
(d)
a nodule count; b nodularity; c percentage ferrite; d yield stress
7 Calculated microstructural and mechanical properties
2. The nodularity also shows a reasonable distribution,
being higher on the permanent mould side and lower on
the sand mould side, reflecting the difference in eutectic
solidification time.
Materials Science and Technology March 2000
Vol. 16
3. The casting is almost totally ferritic, owing to the long
cooling time in the eutectoid range. This example is
therefore not a good test to demonstrate the capability of
the model to correctly predict ferrite/pearlite levels.
Donelan
Modelling properties of ferritic ductile cast iron 267
UTS, MPa
(e)
Elongation, %
(f)
JIC toughness, kJ m_2
(g)
KJC toughness, MPa m1/2
(h)
e ultimate tensile strength; f elongation; g fracture toughness J ; h fracture toughness K
1C
JC
7 Calculated microstructural and mechanical properties (cont.)
4. Elongation increases with nodularity, and hence the
elongation is highest on the permanent mould side where
nodularity is highest.
5. The plots of upper shelf fracture toughness (J and
1C
K ) both show maxima in the central region where the
1C
thickness is greatest. This was initially a surprise, as this
Materials Science and Technology
March 2000
Vol. 16
268 Donelan Modelling properties of ferritic ductile cast iron
measure of the uncertainty in the analytical prediction. The
following observations were made.
1. Overall the level of agreement between test and
analysis results for nodule count is satisfactory. The nodule
count at the ‘outer wall’ was measured as 169 nodules per
mm2. It is not known how close to the surface this
measurement was taken. The nodule count calculated for
the node at the surface was 193 nodules per mm2, and the
next node in from the surface was 93 nodules per mm2.
Hence in this case the analysis results bound the test result.
2. Nodularity shows a very good agreement between test
and analysis.
3. Figure 8a and b shows the comparison between test
and analysis for the yield stress and UTS, respectively. The
agreement is ‘fair’. The results suggest that there might be
some strengthening mechanism which is not contained in
the formulae for these properties.
4. The comparison of elongation is reasonable overall.
There is inherently a lot of experimental scatter in
elongation results. Also the effect of nodularity has been
conservatively taken into account in the formula for
elongation, with the result that the calculated result is
slightly lower than the test result.
5. The comparison of calculated and measured fracture
toughness is satisfactory.
(a)
(b)
8 Comparison of a yield stress and b ultimate tensile
strength calculated from finite element analysis
results and casting test data
area was expected, on intuition alone, to have the lowest
fracture toughness. After further research, however, it was
confirmed that the computer results were in fact correct.
Fracture toughness is a function of both nodule spacing
(fracture toughness increases with nodule spacing) and
nodularity (fracture toughness increases with nodularity).
The region with the maximum toughness has high nodule
spacing and relatively low nodularity. The dominant effect
is that of nodule spacing, so that the overall result is that
fracture toughness is high.
Table 1 and Fig. 8 show a quantitative comparison
between the analysis results and the test data. For the
microstructure only one test measurement at each point
was taken, but for mechanical properties there were either
two or three specimens tested at each location, so that a
measure of the inherent scatter in the results could be
obtained. Also, as the location of measurement of the
material properties is not known with great accuracy, the
properties calculated at two adjacent nodes are given, as a
Table 1 Comparison of analysis and test results
Parameter
Location
Test results
Analysis result
Nodule count,
mm−2
Outer base
Centre base
Outer wall
Centre wall
Inner wall
Outer base
Centre base
Outer wall
Centre wall
Inner wall
Outer base
Centre base
Inner base
Outer wall
Centre wall
Inner wall
Top
Outer wall
Centre wall
Inner wall
251
47
169
49
29
89
83
89
84
74
23, 23
22
18, 22
17, 18
17, 16
14, 12
83·3, 76·9, 88·5
74·1, 76·2, 78·9
88·7, 77·7, 90·2, 86·3
107·9, 97·8
178, 93
35
193, 93
36
34
87, 86
84
87
84
80
17·7, 16·9
14·8
12, 17·7
17, 17·1
14·4
11·4
82·74, 86·68
75·6, 84·65
95·87, 95·7
94·95, 95·26
Nodularity,
%
Elongation,
%
K
JC
MPa m1/2
Materials Science and Technology March 2000
Vol. 16
Discussion
As the process being modelled was rather complex it was
necessary at various stages to make simplifications in order
to be able to proceed. Notwithstanding this, however, the
results achieved were satisfactory. However, in many areas
there is scope for further improvement.
For routine use by a commercial foundry the method is
too time consuming at present. However, it is possible to
envisage an expert system for data preparation of the
model, which could take the chemical composition as input,
and produce all the necessary data input required by the
model. This would greatly reduce the overall time to obtain
a useful result.
Areas for future research include:
(i) further development of the model for austenite to
ferrite transformation
(ii) the relationship between nodularity and solidification time
(iii) the relationship between microstructure and
mechanical properties, in particular the effect of
nodularity has been poorly researched to date
(iv) development of expert systems which will speed up
data preparation and allow these models to be used
in a commercial environment
(v) more examples of test versus analysis are needed in
order to build up a better picture of the limitations
of the method and the confidence which can be
placed in the results.
Conclusion
A method for calculating the microstructure and mechanical
properties of a thick walled ferritic ductile cast iron casting
has been demonstrated to give satisfactory results, by
comparison with test data.
Acknowledgements
The author carried out this work while on secondment
to the Japan Research Institute Limited, Tokyo, on an
Donelan
Engineering Foresight Award from the Royal Academy of
Engineering.
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Materials Science and Technology
March 2000
Vol. 16