K. ZELI^, M. GODEC: NUCLEATION AND GROWTH OF EUTECTIC CARBIDES IN AISI D2 TOOL STEEL ...
515–520
NUCLEATION AND GROWTH OF EUTECTIC CARBIDES IN AISI
D2 TOOL STEEL MODIFIED BY RARE EARTH ELEMENTS:
EXPERIMENTAL AND MODELLING APPROACHES
NUKLEACIJA IN RAST EVTEKTI^NIH KARBIDOV V ORODNEM
JEKLU TIPA AISI D2, MODIFICIRANEM Z ELEMENTI REDKIH
ZEMELJ: EKSPERIMENTALNI IN MODELSKI PRISTOPI
Klemen Zeli~
1
, Matja` Godec
2
1
University of Ljubljana, Faculty of Mechanical Engineering, Laboratory for Internal Combustion Engines and Electromobility, A{ker~eva 4,
1000 Ljubljana, Slovenia
2
Institute of Metals and Technology, Physics and Chemistry of Materials Department, Lepi pot 11, 1000 Ljubljana, Slovenia
klemen.zelic@fs.uni-lj.si
Prejem rokopisa – received: 2018-02-15; sprejem za objavo – accepted for publication: 2018-09-10
doi:10.17222/mit.2018.024
AISI D2 tool steel from the group of cold work tool steels was modified by rare earth elements (REEs). Small additions of the
REEs to the steel melt led to the changed chromium eutectic carbides morphology in the steel as-cast microstructure. REEs
impact on nucleation and growth of eutectic carbides in AISI D2 tool steel was investigated by simulation. In order to simulate
eutectic reaction phase, field model was build. Dynamic partial differential equation system of the phase field model was solved
by finite volumes method. Parameters of the model were determined by comparison between non-modified and rare earth (RE)
modified AISI D2 tool steel samples, characterized by scanning electron microscopy (SEM) imaging, energy dispersive X-ray
spectroscopy (EDS) and classical chemical analysis. Beside general morphological change of eutectic carbides from lamellar to
globular due to RE modification, our model is capable of explaining small eutectic carbide morphological features. From the
results nucleation and growth mechanisms of eutectic phase in RE modified AISI D2 steel can be concluded.
Keywords: AISI D2 tool steel, nucleation, phase field modeling
Jeklo tipa AISI D2 iz skupine orodnih jekel za delo v hladnem smo modificirali z elementi redkih zemelj. Majhni dodatki
elementov redkih zemelj v talino so povzro~ili spremembo morfologije evtekti~nih kromovih karbidov v liti mikrostrukturi
jekla. Za preu~evanje vpliva redkih zemelj na nukleacijo in rast evtekti~nih karbidov v jeklu AISI D2 smo izdelali simulacijo
evtekti~ne reakcije. Za izdelavo simulacije smo uporabili modelski pristop faznega polja. Sistem dinami~nih parcialnih
diferencialnih ena~b modela smo re{ili z metodo kon~nih volumnov. Parametre modela smo dolo~ili s primerjavo vzorcev jekla
z dodatkom redkih zemelj in brez. Za karakterizacijo so bile uporabljene tehnike slikanja z vrsti~nim elektronskim
mikroskopom (SEM), disperzivna energijska spektroskopija X-`arkov (EDS) ter klasi~na kemijska analiza. Poleg splo{ne
spremembe morfologije evtekti~nih karbidov zaradi modifikacije iz lamelarne v globularno je predstavljeni model sposoben tudi
opisa lokalnih posebnosti morfologije evtekti~nih karbidov v modificiranem jeklu. S pomo~jo rezultatov modela lahko dobro
razlo`imo mehanizme nukleacije in rasti evtekti~nih karbidov v jeklu tipa ASIS D2, modificiranem z elementi redkih zemelj.
Klju~ne besede: AISI D2 orodno jeklo, nukleacija, modeliranje faznega polja
1 INTRODUCTION
AISI D2 steel from the group of cold-work tool steels
is used when wear resistance is important, such as
blanking, forming dies and thread-rolling dies, cutting
tools, stamping, woodworking and molding tools for
plastics.
1
Due to the high carbon and chromium contents,
large eutectic chromium carbides form during the
solidification. Carbides in the as-cast microstructure are
undesirable because they are points where cracks initiate
during the steel’s post processing (usually forging).
Thus, it is important to investigate ways in which we can
control the process of casting and solidification, for
example, by using small amounts of modifying agents
(different chemical elements) that are added to the
molten steel in order to influence the microstructure
during solidification.
2
In later years, modification of melt by rare earth
elements (REEs) prior to casting showed good potential
for influencing morphology of eutectic carbides in
as-cast microstructure of high – chromium high – carbon
tool steels. Investigations show that shape, size, mor-
phology and type of eutectic carbide can be modified by
rare earth (RE) additions.
3–10
Even though a lot of successful experimental exe-
cutions of eutectic carbide modification in high – chro-
mium high – carbon tool steels by REEs exist in
literature,
3–13
governing mechanisms of eutectic carbide
modification are not well understood. There are four
different possible explanation proposed in literature. Li
et al.
8
proposed the first explanation that was later also
used by Fu and Xing
5
and Qu et al.
6
According to this
explanation, segregations of REEs to the melt during
solidification enrich the melt at the tips of the growing
dendrites. This brings high compositional undercooling,
Materiali in tehnologije / Materials and technology 52 (2018) 5, 515–520 515
UDK 66.017:669.14:544.015.33:546.65 ISSN 1580-2949
Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 52(5)515(2018)

which promotes the branching of dendrites and conse-
quently refined eutectic carbides in interdendritic re-
gions. Second possible explanation of the eutectic
carbide modification by REEs was also proposed by Li
et al.
8
It states that segregations of REEs to the melt
during solidification result in the reduced carbon activity
in the remaining melt. This further leads to the initiation
of eutectic reaction at higher solid (austenite) ratios.
Dendrite arm spacing is reduced this way and eutectic
carbides solidified in interdentdritic spaces are refined.
Third possible explanation that is also capable of ex-
plaining change in carbide type due to RE modification
states that modification of non-metallic inclusions by
REEs in the melt is responsible for the carbide change.
4,7
According to this theory RE modified non-metallic
inclusions act as efficient heterogeneous nuclei for the
eutectic carbides. Consequently, morphology, size and
type of eutectic carbides is changed in comparison to
non-modified steel. In our previous work
11–13
we pro-
posed new possible mechanism that explains change in
morphology of eutectic carbides in AISI D2 tool steel.
The change in morphology of eutectic carbides is the
result of oxygen and sulfur depletion in the melt, due to
REEs high affinity to those two elements. Their theory is
firmly supported also by modelling of eutectic reaction
and not only experimental observation.
Investigation presented in this paper shows important
contribution to the clarification of which of four possible
explanations is more likely to be true. It is focused only
on nucleation of eutectic reaction by RE modified
non-metallic inclusions and their effect on growth of
eutectic carbides. Investigation was conducted in two
phases. First phase includes successful experimental
execution of AISI D2 tool steel modification and the
second phase is committed to phase field modeling of
eutectic reaction,
14–18
that provides good insight in the
governing mechanisms.
The original contribution of this paper arises from the
fact that independency of eutectic carbide morphology in
cold work tool steel on non-metallic inclusion type was
proved beyond doubt for the first time. With the connec-
tion between experimental and modeling observations it
was proved that RE modified non-metallic inclusions in
AISI D2 tool steel modified by REEs are not the reason
for the change in morphology of Cr
7
C
3
eutectic carbides.
2 EXPERIMENTAL PART
2.1 Sample Preparation
AISI D2 tool steel was melted in open induction
furnace. It was cast in five cylindrical metallic molds to
obtain five 4 kg ingots with 8 cm diameter and height of
approximately 10 cm. Small additions of rare earth
elements (REEs) in the form of Ce mischmetal (Table 1)
were introduced in the melt prior to last three ingots
casting. All ingots were cast under the same conditions.
This way comparable ingots of non-modified and RE
modified AISI D2 tool steel were obtained. Samples
were cut out of ingots by water jet slicer. Since micro-
structural differences between samples from all ingots
were independent of the spatial position of sample in
ingot, only samples from geometrical center of ingots are
presented in this paper. Result section of this paper
includes only the comparison between samples form first
and fifth casted ingot, since differences between this two
samples are the most significant. Samples were further
prepared for microscopy by grinding, polishing and
etching.
Table 1: Chemical composition of Ce mischmetal
Element Ce La Nd Pr
w/% 45–55 20–35 12–20 5–8
2.2 Characterization
All characterization was done on the as-cast
condition of the AISI D2 tool steel. The chemical com-
position of the samples was determined by wet chemical
analysis (Table 2). Content of silicon was determined
gravimetrically, content of carbon was analyzed with
ELTRA CS-800, and all other elements were analyzed
with optical emission spectrometry with inductively
coupled plasma (ICP-OES) on Aglient 720. The results
of the analysis are presented in Table 2, where the
chemical compositions of both ingots are shown.
Microstructure investigations were performed with a Jeol
JSM – 6500F field emission scanning electron micro-
scope (SEM) with secondary and backscattered electron
detectors. Type of non-metallic inclusions in the samples
was determined by energy-dispersive X-ray spectroscopy
(EDS) on SEM. Positions and distribution of RE
containing non-metallic inclusions were investigated by
backscattered electron imaging (BEI) on SEM. Type of
inclusions in both samples were determined by electron
backscattered diffraction (EBSD) technique on SEM.
EBSD measurements showed that type of eutectic
carbides in both samples is Cr
7
C
3
. The microstructure
consists of martensite and carbides.
K. ZELI^, M. GODEC: NUCLEATION AND GROWTH OF EUTECTIC CARBIDES IN AISI D2 TOOL STEEL ...
516 Materiali in tehnologije / Materials and technology 52 (2018) 5, 515–520
Table 2: Chemical composition of non-modified and RE modified AISI D2 tool steel
Element C Si Mn Cr Cu Ni Mo V Ce La Nd Pr Fe
Non-mod. 1.42 0.23 0.21 10.1 0.08 0.17 0.60 0.75 ////B a l
RE mod. 1.41 0.22 0.21 10.3 0.08 0.17 0.59 0.80 0.013 0.008 0.005 / Bal

3 MODELLING
Nucleation and growth of eutectic carbides in AISI
D2 tool steel was modelled by phase field approach.
19
Since three phases are present in the system at the tem-
perature of eutectic reaction (liquid, austenite and Cr
7
C
3
carbide), two order parameters of phase field are needed
for the description of eutectic reaction. Free energy
density was minimized for obtaining dynamic equations
by Lagrange formalism.
20
Obtained system of partial
differential equations was discretized on two dimen-
sional domain (50 x 50 control volumes) by finite vol-
ume method. Discretized dynamic equations of the
system were solved by Newton-Raphson method as des-
cribed in Numerical recipes in C.
21
Results of simula-
tions were presented as two dimensional plots of the
phase field time evolution. Detailed description of used
phase field model can be found is described in our
previous papers.
11,13
3.1 Nucleation
In order to model heterogeneous nucleation of the
eutectic carbides in AISI D2 tool steel, non-metallic
inclusions were introduced to the model. During simu-
lation of melt cooling such non-metallic inclusions act as
heterogeneous nuclei either for eutectic carbides or
austenitic phase. Non-metallic inclusions were intro-
duced to the model as the fourth existing phase in the
system that is not affected by temperature but participate
in the reaction only by surface interactions with other
three phases (liquid, austenite and Cr
7
C
3
carbide). The
introduction of additional surface to the system neces-
sarily calls for two additional boundary conditions. First
boundary condition that was used on the surface of
nonmetallic inclusion prohibits any flux of carbon from
melt to the bulk of inclusion. This boundary condition
was implemented by setting chemical potential gradient
at the surface of non-metallic inclusion to zero. Second
boundary condition on the surface of non-metallic inclu-
sion was much less trivial. Natural boundary condition
was used,
20,22
that describe the connection between non
dimensional molarity of carbon and surface free energy
between inclusion and melt:
nc
c
  ∇=
∂
∂
(1)
 n is the unit vector normal to the surface of the
inclusion, ∇ is gradient operator, c is non dimensional
molarity of carbon,  is gradient penalty coefficient and
 denotes surface free energy of interphase between
non-metallic inclusion and surrounding phase. Function
 (c) is the one determining the type of non-metallic
inclusion. Linear interpolation was used for the evalu-
ation of function  (c) between two boundary values of
surface free energy of austenite/inclusion and carbide/
inclusion interfaces. Positive slope of  (c) in the model
leads to the carbon enrichment of the melt in the close
surroundings of non-metallic inclusion and consequent-
ially nucleation of carbide. Negative slope of (c) results
in the depletion of carbon in the non-metallic inclusion
surroundings and consequently austenite is nucleated.
The boundary values and consequently the slope of  (c)
surface free energy depends on the crystallographic
misfit between crystal lattices of two phases forming the
interface. According to the misfit of crystal lattice we
divided inclusions in two groups. The first one that
show lower crystallographic misfit when forming
interface with austenite in comparison to Cr
7
C
3
carbide
(∂∂  /c < 0) and second type opposite (∂∂  /c > 0). Non-
metallic inclusions of the first type are better hetero-
geneous nuclei for the austenite phase and second type
non-metallic inclusions nucleate Cr
7
C
3
carbide more
efficiently than austenite. This way simulations enabled
good insight in the nucleation process of eutectic
reaction on different types of non-metallic inclusions
that were present in the melt.
4 RESULTS AND DISCUSSION
Investigation of effect of non-metallic inclusions was
done by comparison between experimental and modeling
results. Figure 1 shows comparison between SEM BEI
K. ZELI^, M. GODEC: NUCLEATION AND GROWTH OF EUTECTIC CARBIDES IN AISI D2 TOOL STEEL ...
Materiali in tehnologije / Materials and technology 52 (2018) 5, 515–520 517
Figure 1: SEM BEI of Cr
7
C
3
eutectic carbide in: a) non-modified
as-cast AISI D2 tool steel and b) RE modified as-cast AISI D2 tool
steel

micrographs of non-modified and RE modified AISI D2
tool steel.
11,13
From Figure 1 it can be seen that RE modification
affects the morphology of eutectic carbides in AISI D2
tool steel as-cast microstructure. Whether or not the
REEs containing non-metallic inclusions are responsible
for such morphological differences was tested in few
different ways. Positions of REEs containing non-metal-
lic inclusions were measured first. Since REEs have by
far largest atomic weight among all elements present in
the samples they appear bright on the SEM BEI micro-
graphs. The first proof that REEs containing non-metal-
lic inclusion does not influence the morphology of eutec-
tic carbides arises from the fact that no such inclusions
were found inside the eutectic region in as-cast micro-
structure of RE modified AISI D2 tool steel even after
investigation of large number of samples. Figure 2 show
two SEM BEI micrographs that show typical positioning
of REEs containing non-metallic inclusions in RE modi-
fied samples (bright spots in images). They are always
found inside the matrix of steel.
Type of non-metallic inclusions in samples were
determined by EDS measurements on SEM. The EDS
spectra and detailed discussion of the EDS results can be
found in our previous work.
12
Beside Al
2
O
3
an MnS
non-metallic inclusions that were found in non-modified
samples, complex oxy-sulfide RE
2
O
2
S inclusions were
found in RE modified samples (bright spots in Figure 2).
Such inclusions were expected due to the high affinity of
REEs to oxygen and sulfur. The only difference regard-
ing non-metallic inclusion between non-modified and
RE modified samples therefore is appearance of RE
2
O
2
S
in RE modified samples. This finding is in good agree-
ment with Hamidzadeh et al.
7
Second factor supporting the theory that REEs con-
taining non-metallic inclusions do not influence final
morphology of eutectic carbide in RE modified AISI D2
tool steel arises from the simulations presented in Fig-
ure 3. Figure 3 show two cases. Nucleation of eutectic
reaction in CASE 1 occurred on non-metallic inclusion
which crystal lattice shows lowest misfit with Cr
7
C
3
eutectic carbide crystal lattice in comparison to austenite
crystal lattice (type 2 inclusion). Simulation of solidifi-
cation in CASE 2 was nucleated on non-metallic inclu-
sion that shows lowest misfit of crystal lattice with the
austenite in comparison to carbide (type 1 inclusion).
Even though simulations of solidification in both cases
were nucleated by different crystallographic types of
non-metallic inclusions, both simulations ended in the
K. ZELI^, M. GODEC: NUCLEATION AND GROWTH OF EUTECTIC CARBIDES IN AISI D2 TOOL STEEL ...
518 Materiali in tehnologije / Materials and technology 52 (2018) 5, 515–520
Figure 2: Position of RE
2
O
2
S non-metallic inclusions in RE modified
AISI D2 tool steel as-cast microstructure
Figure 3: Simulation of nucleation and growth of eutectic carbides in
RE modified AISI D2 tool steel. CASE 1 (Figures 3a to 3e)s h o w
growth of carbides nucleated on non-metallic inclusion of second
type. CASE 2 (Figures 3f to 3j) show growth of carbides nucleated on
non-metallic inclusion of first type. White color represents liquid
phase (melt), blue color austenite and red color Cr
7
C
3
carbide.

same morphologic type of eutectic carbide – globular
eutectic. This shows that final morphology of eutectic
carbide is independent of the type of nucleation sites.
Independency of final microstructure on type of
nucleation sites can also be seen from Figure 4. Simu-
lation presented in Figure 4a was started by nucleation
on non-metallic inclusion of the second type (effective
austenite nucleation site). Figure 4a shows that nucle-
ation on the non-metallic inclusion that effectively
nucleate only austenite phase, resulted in the growth of
carbide globule. Globule has a shape of toroid since the
first phase that grows in the center of globule is auste-
nite. Carbon enrichment of the melt in the close sur-
rounding leads to the carbide growth around the small
austenite core. Very similar morphological features were
found in experiment on SEM SEI (Figure 4b). The fact
that simulation show carbide globule growth from auste-
nite nucleation site additionally proves that final mor-
phology of eutectic carbides is independent of nucleation
sites type. Carbide morphological features found in SEM
BEI, presented in Figure 4b, support conclusions made
on the basis of simulation well since they provide
additional validation of our model.
5 CONCLUSIONS
With the connection between modeling and experi-
mental approaches to the RE modification of AISI D2
tool steel investigation, effects of different types of
non-metallic inclusion on nucleation and growth of
Cr
7
C
3
eutectic carbides during solidification were
studied. It was showed that RE containing non-metallic
inclusions in RE modified AISI D2 tool steel do not
influence the final morphology of eutectic carbides in the
as-cast microstructure. The final morphology of eutectic
carbides turned out to be independent of the type of
nuclei, that initiated eutectic reaction.
Acknowledgment
The authors acknowledge the financial support from
Slovenian Research Agency (ARRS) (research core
funding no. P2-0132). K. Z. acknowledges the ARRS for
the provision of Young Research funding for his PhD.
6 REFERENCES
1
A. C. Reardon, Metallurgy for the non-metallurgist, ASM Inter-
national, 2011
2
G. Krauss, Steels: processing, structure, and performance. ASM
International, 2015
3
J. Yang, D.-n. Zou, X.-m. Li, Z.-z. Du, Effect of rare earth on
microstructures and properties of high speed steel with high carbon
content, Journal of Iron and Steel Research, International, 14 (2007)
1, 47–59, doi: 10.1016/S1006-706X(07)60011-9
4
X. Zhou, X. Yin, F. Fang, J. Jiang, W. Zhu, Influence of rare earths
on eutectic carbides in AISI M2 high speed steel, Journal of Rare
Earths, 30 (2012) 10, 1075–1078, doi:10.1016/S1002-0721(12)
60181-1
5
H. Fu, J. Xing, A study of modification of M2 cast high speed steel,
Materialwissenschaft und Werkstofftechnik, 35 (2004) 9, 578–581
6
M. Qu, Z. Wang, H. Li, Z. Lv, S. Sun, W. Fu, Effects of mischmetal
addition on phase transformation and as-cast microstructure cha-
racteristics of m2 high-speed steel, Journal of Rare Earths, 31 (2013)
6, 628–633, doi:10.1016/S1002-0721(12)60332-9
7
M. A. Hamidzadeh, M. Meratian, A. Saatchi, Effect of cerium and
lanthanum on the microstructure and mechanical properties of AISI
D2 tool steel, Materials Science and Engineering: A, 571 (2013)
Supplement C, 193-198, doi:10.1016/j.msea.2013.01.074
8
Y. Li, Q.-C. Jiang, Y. Zhao, Z. He, X.-Y. Zhong, Influence of cerium
on solidification microstructure of M2 high speed steel, 18 (2000),
134–135
9
M. Wang, S. Mu, F. Sun, Y. Wang, Influence of rare earth elements
on microstructure and mechanical properties of cast high-speed steel
rolls, Journal of Rare Earths, 25 (2007) 4, 490–494
10
M. Boccalini, A. Correa, H. Goldenstein, Rare earth metal induced
modification of  -M2C,  -M6C and  -MC eutectics in as cast M2
high speed steel, Materials Science and Technology, 15 (1999)6 ,
621–626, doi:10.1179/026708399101506355
11
K. Zeli~, J. Burja, J. P. McGuiness, M. Godec, Effect of rare earth
elements on the morphology of eutectic carbides in AISI D2 tool
steels: experimental and modelling approaches, Scientific reports, 8
(2018) 1, doi:10.1038/s41598-018-27658-w
12
K. Zeli~, M. Godec, A modified mean-linear-intercept method for
distinguishing lamellar and globular eutectic carbides in metallo-
graphic samples, Mater. Tehnol., 52 (2018) 1, 83–87, doi:10.17222/
mit.2017.173
13
K. Zeli~, Effect of the rare-earth elements Ce, La, Nd and Pr on the
morphology of eutectic carbides in tool steels: experimental and
modelling approaches (doctoral dissertation), 2018
14
M. Ode, T. Suzuki, S. Kim, W. Kim, Phase – field model for soli-
dification of Fe-C alloys, Science and Technology of Advanced
K. ZELI^, M. GODEC: NUCLEATION AND GROWTH OF EUTECTIC CARBIDES IN AISI D2 TOOL STEEL ...
Materiali in tehnologije / Materials and technology 52 (2018) 5, 515–520 519
Figure 4: Comparison between simulation and SEM secondary electron image (SEI) of RE modified AISI D2 tool steel as-cast microstructure

Materials, 1 (2000) 1, 43–49, 2000. doi:10.1016/S1468-6996(99)
00004-2.
15
X.-l. Dong, H. Xing, K.-r. Weng, H.-l. Zhao, Current development in
quantitative phase-field modeling of solidification, Journal of Iron
and Steel Research, International, 24 (2017) 9, 865-878,
doi:10.1016/S1006-706X(17)30129-2
16
N. Moelans, B. Blanpain, P. Wollants, An introduction to phase-field
modeling of microstructure evolution, Calphad, 32 (2008)2 ,
268–294 doi:10.1016/j.calphad.2007.11.003
17
B. Nestler, A. A. Wheeler, Phase-field modeling of multi-phase
solidification, Computer Physics Communications, 147 (2002)1 ,
230–233, 2002, Proceedings of the Europhysics Conference on
Computational Physics Computational Modeling and Simulation of
Complex Systems, doi:10.1016/S0010-4655(02)00252-7
18
B. Böttger, G. J. Schmitz, B. Santillana, Multi-phase-field modeling
of solidification in technical steel grades, Transactions of the Indian
Institute of Metals, 65 (2012) 6, 613-615, doi:10.1007/s12666-
012-0169-y
19
N. Provatas, K. Elder, Phase-field methods in materials science and
engineering, John Wiley and Sons, 2011
20
H. Sagan, Introduction to the Calculus of Variations. Courier
Corporation, 1969
21
W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery,
Numerical recipes in C: the art of scientific computing, 2
nd
ed.,
Cambridge, 2007, 362-369
22
L. Gránásy, T. Pusztai, D. Saylor, J. A. Warren, Phase field theory of
heterogeneous crystal nucleation, Phys. Rev. Lett., 98 (2007)3 ,
doi:10.1103/PhysRevLett.98.035703
K. ZELI^, M. GODEC: NUCLEATION AND GROWTH OF EUTECTIC CARBIDES IN AISI D2 TOOL STEEL ...
520 Materiali in tehnologije / Materials and technology 52 (2018) 5, 515–520