This document presents a new 3D simulation model for casting and forging ingots. It combines casting and forging simulation modules to track defects from casting through forging operations. The model uses finite element analysis to simulate heat transfer, fluid flow, and mechanical behavior during solidification and forging. Simulation results can provide insight into defect formation during casting and how defects evolve during subsequent forging to help optimize process parameters and improve final product quality.

1. 5 June, 2012 Brüssel-Saal Ingot Casting – Simulation 1
A new 3D simulation model for complete chaining casted and forged ingot
Olivier Jaouen(1), Frederic Costes and Patrice Lasne
TRANSVALOR, Parc de Haute Technologie – Sophia Antipolis,
694, Av du Dr Maurice Donat, 06255 Mougins, Cedex, France
(1)
Contact Author: olivier.jaouen@transvalor.com
Key Words
3D finite elements, ingot casting, open die forging, hot tearing, porosities, thermo-mechanical coupling,
heat transfers
Abstract distortions occurring at the first instants of
solidification. Depending on the tonnage, solidified
The control of the final quality of a forged product areas at the end of the pouring of ingots can
requires a perfect knowledge of the history and the represent up to 30% to 40% (Figure 1) of the total
quality of the initial casted ingot. Reach a final piece mass. Hence, it is easy to imagine that, defects are
matching the specifications required to locate and already present at that stage in such amount of
analyze potential casting defects in the optimization transformed shell. Within this framework, thermo-
of forging operations. Thus, monitoring of casting mechanical modeling is of interest for steel makers. It
defects and their evolution in forging operations can be helpful in the adjustment of the different
would allow to fully control the quality of formed process parameters in order to improve casting
products. In this context, a new package mixing both productivity while maintaining a satisfying product
casting and a forging simulation module was created. quality. However, optimization of the parameters
This paper presents the new model to simulate the requires a quite complex model that delivers very
creation and evolution of casting defects and to follow precise responses. Indeed, it is necessary to take
them in forming operation. into account together liquid, mushy and solid areas in
a coupled model. In addition, at each instant and
locally, the air gap should be taken into account for
its influence on the heat transfers between metal
shell and molds that dramatically change throughout
Introduction the solidification. Once the defects are trapped in the
casting process, being able to follow them through
The microstructure and grain sizes of a
the forging operations is really interesting. Not only
casted ingot are generally not compatible with the
tracking them, but also estimating the size of the
characteristics of the final part. In addition, internal voids in case of porosities or cracks is of interest.
porosities may be created during the casting of the
This can be allowed by a specific model initialized by
ingot. The microstructure and the closure of
results issued from casting and depending on strains
porosities are in first approximation related to local and stresses occurring during the open die forging
deformation in the forged part. So that, the final
operations.
quality of a forged product is fully depending of the
casted ingot from which it originated. Hence,
In this paper, Thercast, software dedicated to
controlling the health of the initial ingot, or at least,
the simulation of metal solidification is firstly
knowing the location of the defects like porosities,
presented. The thermo-mechanical models
cracks, etc. is essential for the caster. Same, being
developed in this software are presented. The way of
able to follow defects in the forging process
taking into account the coupling between metal and
represents a strong advantage for the forger. In the
molds during solidification is shown. A model of
process of ingot casting, the first solidified zones
determination of the liquid and mushy zones’
occur mush before the end of the pouring and the
constituted equation parameters is developed.
liquid areas remain present even well after the end of
Secondly, the direct transfer of Thercast results into
the filling step. For sure, behavior of the different
Forge and the model of evolution of the defects are
metal phases is fully coupled during the process. It
shown. Applications on casted and forged ingot are
appears that defects like porosities, cracks or hot
finally illustrated.
tears take place in the brittle temperature range
(BTR) of the alloy from the strains, stresses and
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2. 5 June, 2012 Brüssel-Saal Ingot Casting – Simulation 1
An original mixed thermo- The boundary conditions applied on free
mechanical model surface of the mesh of the metal could be of classical
different types:
Thercast is a commercial numerical package
for the simulation of solidification processes: shape
casting (foundry), ingot casting, and direct-chill or
 average convection:  T .n  h(T  Text )
continuous casting. A 3D finite element thermo- where h (W/m²/°C) is the heat transfer
mechanical solver based on an Arbitrary Lagrangian coefficient, andText is the external
Eulerian (ALE) formulation is used.
temperature
4
radiation:   T .n   stef (T
4
  Text ) ,
where  is the steel emissivity,  stef is the
Stephan – Boltzmann constant.
 external imposed temperature: T  Timp .
 external imposed heat flux:  T .n   imp
n denotes the outward normal unit vector.
At part/molds interface, heat transfers are
taken into account with a Fourier type equation:
1
 T .n  (T  Tmold ) (3),
Req
Figure 1: State of solidification of a small ingot
(~300kg) just after the end of pouring – high
percentage of already solidified material where Tmold is the interface temperature of the mold
1
and R eq (W/m²/°C) , the heat transfer resistance
that can depend on the air gap and/or the local
Thermal model normal stress, as presented below:
The thermal problem treatment is based on
the resolution of the heat transfer equation, which is  1
the general energy conservation equation:  Req  1 1 1
 Rs if eair  0
 min( ,  )
 R0 Rair Rrad
dH (T )  (4),
 .( (T )T ) (1), 1
dt R   Rs if eair  0
 eq 1 1
 
where T is the temperature,  (W/m/°C) denotes the R R0

thermal conductivity and H (J) the specific enthalpy
which can be defined as:
e air es
where Rair  and Rs  with eair and es
T  air s
H (T )    ( )C p ( )d  g l (T ) L (Ts ) (2),
respectively the air gap and an eventual other body
T0
(typically slag) thickness and air and s the air and
T0 (°C) is an arbitrary reference temperature,  the eventual other body thermal conductivity. R0 is a
3
(kg/m ) the density, Ts (°C) the solidus temperature, nominal heat resistance depending on the surface
C p (J/kg/°C) the specific heat, g l the volume 1 1
 1
  mold
fraction of liquid, andL (J/kg) the specific latent heat roughness, Rrad 
of fusion. In the one-phase modelling, g s (T ) is
 stef (T 2  Tmold )(T  Tmold )
2
previously calculated using the micro-segregation with  mold the emissivity of the mold, R  1 A n
m
model PTIMEC_CEQCSI [8]. a heat resistance taking into account the normal
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3. 5 June, 2012 Brüssel-Saal Ingot Casting – Simulation 1
stress  n , A and m being the parameters of the this finding, Bellet [4] has proposed an extrapolation
model of the solid data to liquid data for fields like
law.
viscosity and strain rate sensitivity in case of
viscoplastic behavior. The viscoplastic behavior is
formulated with the well known power law:
Mechanical model
m 1
  K (T ) 3 m
 (5),
At any time, the mechanical equilibrium is
governed by the momentum equation:
where  is the von Mises flow stress,  the 
.σ  g  γ  0 , equivalent plastic strain rate, T the temperature, K
the viscoplastic consistency and m the strain rate
where σ is the Cauchy stress tensor, g is the sensitivity. It is to be noted that the Newtonian
behavior is obtained in case of m  1 and K   l
gravity vector, and γ is the acceleration vector. where  l is the dynamic viscosity of the liquid. The
model is aimed at defining K and m throughout the
Taking into account the very different mushy zone divided in three intervals limited by the
behaviors of liquid and solid metal is realized by a parameters:
clear distinction between constitutive equations
associated to the liquid, the mushy and the solid  g l ,cohe the liquid fraction at coherency
states. In order to fit the complex behavior of
temperature
solidifying alloys, a hybrid constitutive model is
considered. In the one-phase modelling, the liquid  g l , susp the liquid fraction beyond which a
(respectively, mushy) metal is considered as a suspension model is used
thermo-Newtonian (respectively thermo-viscoplastic,
VP) fluid. In the solid state, the metal is assumed to For g l the liquid fraction taken in the interval
be thermo-elastic-viscoplastic (EVP) (Figure 2). Solid
regions are treated in a Lagrangian formulation, while g l ,cohe , g l , susp 
liquid regions are treated using ALE [9]. More
precisely, a so called, transient temperature or
coherency temperature is used to distinguish the two  K ( g l )  K ( g l ,cohe ) K ( g l , susp )1

different behaviors. It is typically defined between  (6)
liquidus and solidus, and usually set close to solidus m( g l )   (m( g l ,cohe )  1)  1

temperature. For more information, the interested
reader can refer to [1], [2] and [3].
g l , susp  g l
where 
g l , susp  g l ,cohe
K and m are continuous
The values of
along the three intervals, so that, K ( g l  0) and
m( g l  0) are deduced from the solid state
constitutive model and are taken at solid temperature
or just below. The value of  ( g l  1)   l is
taken a priori. Taking g l ,cohe  0 and g l , susp  1 , the
model is summarized in (6).
Figure 2 : Schematic representation of the rheological
behavior of the different phases of the metal in
solidification conditions
Defects criteria
Precise prediction of defects like macro-
In such a model, physical data, hence
porosities and/or hot tears is quite appreciated by
numerical data, take values in a huge range, from
steel makers. Several hot tear criteria are present
some Pa to hundreds of GPa. If getting data at low
throughout literature. Some are based on thermal
temperatures is quite usual, it is not the case for the
considerations, others are fed with stresses, strain
high temperatures closed to solidus and above. From
and/or strain rate. In [5] the conclusion of the authors
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4. 5 June, 2012 Brüssel-Saal Ingot Casting – Simulation 1
tends to prove that the criterion of Yamanaka et al [6]
is pertinent to forecast location of hot tears in
solidification conditions. The expression of this
criterion is the following:
c   ˆdt (11)
BTR

….
whereBTR is the Brittle Temperature Range defined
when g l  0 , typically 0  g l  0.1 , introduced by
ˆ
Won et al [7] and  represents a norm associated to

the damaging components of the strain rate tensor,
expressed in tensile stress axis orthogonally of the
crystal growth direction [5]. The critical value c
depends on steel composition. However, Yamanaka
introduced, by experimental observations, a threshold
value 2% of the criterion above which, the odds of hot
tears creation are high. Modelling experience tends
to show that the same criterion applied with a lower
threshold, 0.5%, gives distribution that fits quite well
the macro-porosities evolution in solidification
conditions.
Figure 3 : Example of upsetting – beginning of a
cogging operation. Each step involves manipulation
Direct transfer to forging of the part
operations
Numerical simulation aims at predict the
Forge is a 3D simulation software dedicated shape of the part during the process of metal forming.
to forging processes. Its range of applications is very On the contrary of closed die forging, the final shape
large, from hot forging to cold forging. Open die of the part does not correspond to the shape of the
tool. Indeed, that depends on several parameters
forging process is one of them. The thermo-
among them, it can be listed shape and kinetic of the
mechanical core of both Thercast and Forge software
tools, friction on the tools, behavior of the metal,
for solid metal behavior is similar (EVP). So that there temperature evolution, etc. Yield, numerical
is no loss of information in the transfer of data, as modelling can be a useful tool in evaluating the
Forge can directly read results from Thercast. In respective impact of each parameters and optimizing
addition, to ensure the continuity of behavior of the the forging. Many virtual tests are so possible in order
part between casting process and forging process, to improve the internal structure of the metal. In
the material data file is exactly the same for Thercast particular, this is actually depending on the internal
simulation and Forge simulation. porosity distribution issued from casting process.
Therefore, following the evolution of the porosities in
In open die forging, material forming the forging process is essential to predict the final
processes request many number of blows exceeding quality of the forged part.
several hundreds. Moreover, the part is moved in
rotation and/or translation between each blow. In
order to define theses transitions, a specific Model of evolution of the porosities
automatic procedure has been implemented in the
software. Reheating in the furnace is also available in In order to predict the evolution of porosities
the procedure. In order to be as close as possible to in forging process simulation, there are mainly two
ways. The first one is to directly take voids account in
reality, the manipulator is simulated by boundary
very fine meshes. This is the most precise way, but
conditions imposing speed and/or effort on also quite costly in terms of CPU time. The second
predefined zones on the part surface. Figure 3 one is to initialize a specific field representing the
illustrates sequence of cogging operations, the presence of porosities and to follow the evolution of
upsetting and different steps of the forging involving the field under the forging operations. The
manipulations of the part between each one. localization of the porosities and the evolution of the
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5. 5 June, 2012 Brüssel-Saal Ingot Casting – Simulation 1
size respectively to the initial one are so available. boundary conditions and in the treatment on the
The model of evolution of the porosity volume can be feeding metal. Here ingot casting applications are
written as follow: focused.
  p  In case of ingot casting application, the
 t  K c   if p  0

pouring is piloted by the flow rate that can vary or not.
 (8), Both air and metal are taken into account into the
  p  ingot. As presented, before theses phases are mainly
 K t  if p  0
 t
  treated with an ALE model, whereas the solid phase
is actualized following a Lagrangian scheme. Such a
scheme allows taking into account the solid shell of
where  is the volume of porosity, p the pressure, the ingot throughout the solidification. It means that
 equivalent stress, and  the strain rate. K c and
 the air gap can be caught as soon as it occurs even
though the filling stage is not achieved, in case of
K t are respectively the compression and tension solidification of the ingot skin. Hence, strong thermo-
mechanical coupling of all the domains in the cooling
p
coefficient of the law and is the triaxiality of system is applied via the heat transfers that are
 impacted between cooling metal and mold following
stresses. According to this model, the porosity size (4). Moreover, strain and stress being calculated in
will depends on the deformation with respect to the the solid zones while pouring, it is possible to
compression or tension stresses. forecast defects creation and evolution within the
mushy and solid shell of cooling metal. This is true
This model has been validated in comparison from stress and strain birth till the end of complete
to a direct computation where porosity has been solidification of the ingot using (7). Other kind of
meshed in a fine mesh. Figure 4 illustrates the results is the possibility to predict macro secondary
piping or shrinkage in case of local lack of exothermic
evolution of the meshed porosity shape and the
powder for example. Actually, a relevant state of
evolution of the volume of the porosity predicted by
stresses within the metal is predicted from the
the two models. This comparison allowed to coupling between VP and EVP models. This state
determine the respective values of K c and K t . yields a criterion providing the opening of the mushy
zone of the metal based on a specific analysis of the
localization of the liquid areas compared to the solid
zones. The secondary shrinkage results from the
mass conservation throughout the solidification of the
steel.
Small Ingot (1600kg)
A specific study has been launched on small
ingot (1600kg) casting. The aim of the study was to
calibrate exothermic powder used on the top of the
riser. The case simulates a lack of exothermic
Figure 4 : Comparison of evolution of the porosity powder effect on the ingot solidification.
volume predicted by (8) and by a direct simulation of
a meshed porosity (bottom). Shape evolution of Figure 5 illustrates the distribution of the
porosity in a direct simulation temperature (on the left) and the solidified skin (on
the right) of the ingot at the end of the filling. Even
In addition to porosities, Forge is able to take though the cases are not the same, this result is in
account the phenomena of recrystallization occurring good agreement with Figure 1. That illustrates the
during the forming process and after deformation. fact that solidification begins a long time before the
Also, the secondary growth of grains is modeled. end of pouring and the amount of solidified mass is
significant once the filling is achieved. In addition the
influence of the air gap on the temperature evolution
during the cooling process is relevant. Indeed, it
Applications appears that, in such small ingot, much before the
end of filling, air gap is created due to the shrink of
The model presented above can be applied the solidified skin of the ingot involving non
for ingot casting application or continuous casting continuous temperature distribution at ingot/mold
applications. The differences are mainly set in the interface.
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6. 5 June, 2012 Brüssel-Saal Ingot Casting – Simulation 1
location of porosities for the forging process (Figure
7, left high).
Figure 6 : global shape of the ingot after 3h10mn of
cooling. Note the air gap thickness and the free
surface shape. Note the secondary shrinkage (left).
Response of the hot tearing criterion in porosities
application. Standard results showing a low density
zone on the central axis of the ingot. (right).
The void resulting from the secondary shrinkage is
also taken into account. Figure 7 illustrates both the
evolution of porosities sizes and void shape under
Figure 5 : illustration of the temperature distribution at the strokes of the forging operation in the first pass.
the end of the pouring (top) and the corresponding At the end of the first pass, porosities are closed
solidification zones (bottom). Note the discontinuous according to the model (8), where as the void has
values of temperature at ingot/mold interface due to
been partially closed as shown by the white spots.
the HTC air gap dependency.
Figure 8 shows the shape of the part at the end of the
The global shape of the ingot after 3h10mn of second and the third passes. The void has been
cooling is presented Figure 6. The picture shows the almost completely closed. The white spots illustrate
effects of the bad calibration of the exothermic the self contact of the metal in the area of the void
powder: internal open shrinkage occurring. The that has been closed.
defect criterion with application of prediction of macro
porosities is illustrated on the right. The area of low
density in the lower part of the ingot is indicated by
the lowest values of the criterion while the macro
porosities, present just below the internal shrinkage,
are indicated by the highest values. The criterion
indicates that odds of getting hot tears are quite low
as the maximum values in this case do not reach the
critical threshold. Ingot skin getting solidified rapidly,
the cooling metal does not remain in the BTR long
enough under tensile stresses to create strain
yielding hot tears.
As presented above, the link between
Thercast and Forge is direct. Hence, results from the
model (7) can be directly transferred into Forge. This
is used in order to initialize parameters of the specific
model (8) aimed at predict the closure of porosities
that has been implemented in Forge. As per the
range of Yamanaka criterion model, a distribution of
porosities at the end of casting process is established
following 0.5% as a threshold. That initializes the
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7. 5 June, 2012 Brüssel-Saal Ingot Casting – Simulation 1
distribution of the ingot and molds at the end of
cooling phase and the air gap growth at ingot/molds
interface. In that case, the effect of the trunnions of
the cast iron mold is really visible through the
asymmetric distributions of the temperature and the
air gap.
Figure 7 : Chaining of casting simulation results to
forging simulation in order to follow the porosities
evolution. At the end of the first pass, porosities are
closed but secondary shrink is still partially opened.
Figure 9 : Temperature in the ingot and molds (on
top) and air gap at ingot/molds interface (at the
Figure 8 : Shape of the part at the end of the second bottom). Note the non symmetrical distribution either
pass (top) and at the end of the third pass (bottom). A on temperature or air gap due to the trunnions at cast
small volume of void is still remaining. iron molds outside.
Average size ingot (24 tons)
Same, Figure 10 shows how the Yamanka
Another example of chaining Thercast and criterion results from Thercast is initializing the
Forge is presented here. This case is a 24 tons ingot porosities evolution model in Forge. The non
bottom poured. The same procedure as above has symmetrical distribution is also visible on Yamanaka
been applied. Hence, after the filling and cooling of criterion results. After the first blooming, porosities
the casting process, the transfer to Forge has been have been closed a lot and only small voids remain
achieved with the initialization of the porosities localized at the central axis of the part. At the end of
location. Figure 9 illustrates the temperature the second blooming, all porosities have been closed
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8. 5 June, 2012 Brüssel-Saal Ingot Casting – Simulation 1
according to the model (8) (Figure 11, left). Figure 11
(right) illustrates the average grain size resulting.
Figure 11 : Residual porosity distribution at the end of
the first blooming, porosities haves been almost
completely closed (top). Average grain size at the
end of the second blooming. At this stage all
Figure 10 : Yamanaka criterion result at the end of porosities have been closed (bottom).
casting process in Thercast (top), at the beginning of
forging process in Forge (bottom). Note the non
symmetrical distribution also issued from the
trunnions impact, even on the skin, where the Conclusion
criterion localizes hot tears.
Thercast and Forge are both industrially
used. They allow determining the thermo‐
mechanical behavior of the cooling metal in ingot
casting and open die forging processes. On the one
hand, Thercast’s original model of treating the
solidifying metal, associated to specific boundary
conditions leads to forecast accurately the defects of
ingots. It permits to better understand the impact of
process parameters. On the other hand, Forge’s
specific model allows to follow the porosities
evolution throughout the multi‐pass cogging
operations. It gives a better understanding of the
internal structure of the forged part. With such
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9. 5 June, 2012 Brüssel-Saal Ingot Casting – Simulation 1
simulation tools, steel makers are able to control
and optimize their process. This example illustrates
how nowadays numerical models could be used in
the steel industry to improve the quality of
production and the productivity.
References
[1] O. Jaouen, Ph.D. thesis, Ecole des Mines de Paris,
1998.
[2] F. Costes, PhD Thesis, Ecole des Mines de Paris,
2004.
[3] M. Bellet et al., Proc. Int. Conf. On Cutting Edge
of Computer Simulation of Solidification and Casting,
Osaka, The Iron and Steel Institute of Japan, pp 173
– 190, 1999.
[4] M. Bellet, Simple consititutive models for metallic
alloys in the mushy state and around the solidus
temperature. Implementation in Thercast, Intern
report, CEMEF, Mines‐ParisTech, France
[5] O. Cerri, Y. Chastel, M. Bellet, Hot tearing in
steels during solidification – Experimental
characterization and thermomechanical modeling,
ASME J. Eng. Mat. Tech. 130 (2008) 1‐7.
[6] A. Yamanaka, K. Nakajima, K. Yasumoto, H.
Kawashima, K. Nakai, Measurement of critical strain
for solidification cracking, Model. Cast. Weld. Adv.
Solidification Processes V, M. Rappaz et al. (eds.),
TMS (1991) 279‐284.
[7] YM. Won et al., Metallurgical and Materials
Transactions B, volume 31B, pp 779 – 794, 2000.
[8] C. Li, B.G. Thomas, Maximum casting speed for
continuous cast steel billets based on submold
bulging computation, 85th Steelmaking Conf. Proc.,
ISS, Warrendale, PA (2002) 109‐130.
[9] M. Bellet, V.D. Fachinotti, ALE method for
solidification modelling, Comput. Methods
Appl. Mech. and Engrg. 193 (2004) 4355‐4381.
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