The control of the final quality of a forged product requires a perfect knowledge of the history and the quality of the initial casted ingot. Reach a final piece matching the specifications required to locate and analyze potential casting defects in the optimization of forging operations. Thus, monitoring of casting defects and their evolution in forging operations would allow to fully control the quality of formed products. In this context, a new package mixing both casting and a forging simulation module was created. This paper presents the new model to simulate the creation and evolution of casting defects and to follow them in forming operation
5 June, 2012 Brüssel-Saal Ingot Casting – Simulation 1 ICRF 1 st International Conference on Ingot Casting, Rolling and Forging 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: [email protected]Key Words 3D finite elements, ingot casting, open die forging, hot tearing, porosities, thermo-mechanical coupling, heat transfers Abstract The control of the final quality of a forged product requires a perfect knowledge of the history and the quality of the initial casted ingot. Reach a final piece matching the specifications required to locate and analyze potential casting defects in the optimization of forging operations. Thus, monitoring of casting defects and their evolution in forging operations would allow to fully control the quality of formed products. In this context, a new package mixing both casting and a forging simulation module was created. This paper presents the new model to simulate the creation and evolution of casting defects and to follow them in forming operation. Introduction The microstructure and grain sizes of a casted ingot are generally not compatible with the characteristics of the final part. In addition, internal porosities may be created during the casting of the ingot. The microstructure and the closure of porosities are in first approximation related to local deformation in the forged part. So that, the final quality of a forged product is fully depending of the casted ingot from which it originated. Hence, controlling the health of the initial ingot, or at least, knowing the location of the defects like porosities, cracks, etc. is essential for the caster. Same, being able to follow defects in the forging process represents a strong advantage for the forger. In the process of ingot casting, the first solidified zones occur mush before the end of the pouring and the liquid areas remain present even well after the end of the filling step. For sure, behavior of the different metal phases is fully coupled during the process. It appears that defects like porosities, cracks or hot tears take place in the brittle temperature range (BTR) of the alloy from the strains, stresses and distortions occurring at the first instants of solidification. Depending on the tonnage, solidified areas at the end of the pouring of ingots can represent up to 30% to 40% (Figure 1) of the total mass. Hence, it is easy to imagine that, defects are already present at that stage in such amount of transformed shell. Within this framework, thermo- mechanical modeling is of interest for steel makers. It can be helpful in the adjustment of the different process parameters in order to improve casting productivity while maintaining a satisfying product quality. However, optimization of the parameters requires a quite complex model that delivers very precise responses. Indeed, it is necessary to take 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 the solidification. Once the defects are trapped in the casting process, being able to follow them through the forging operations is really interesting. Not only tracking them, but also estimating the size of the voids in case of porosities or cracks is of interest. This can be allowed by a specific model initialized by results issued from casting and depending on strains and stresses occurring during the open die forging operations. In this paper, Thercast, software dedicated to the simulation of metal solidification is firstly presented. The thermo-mechanical models developed in this software are presented. The way of taking into account the coupling between metal and molds during solidification is shown. A model of determination of the liquid and mushy zones’ constituted equation parameters is developed. Secondly, the direct transfer of Thercast results into Forge and the model of evolution of the defects are shown. Applications on casted and forged ingot are finally illustrated.
ICRF 1st International Conference on Ingot Casting, Rolling and Forging 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
3D finite elements, ingot casting, open die forging, hot tearing, porosities, thermo-mechanical coupling, heat transfers
Abstract
The control of the final quality of a forged product requires a perfect knowledge of the history and the quality of the initial casted ingot. Reach a final piece matching the specifications required to locate and analyze potential casting defects in the optimization of forging operations. Thus, monitoring of casting defects and their evolution in forging operations would allow to fully control the quality of formed products. In this context, a new package mixing both casting and a forging simulation module was created. This paper presents the new model to simulate the creation and evolution of casting defects and to follow them in forming operation.
Introduction The microstructure and grain sizes of a
casted ingot are generally not compatible with the characteristics of the final part. In addition, internal porosities may be created during the casting of the ingot. The microstructure and the closure of porosities are in first approximation related to local deformation in the forged part. So that, the final quality of a forged product is fully depending of the casted ingot from which it originated. Hence, controlling the health of the initial ingot, or at least, knowing the location of the defects like porosities, cracks, etc. is essential for the caster. Same, being able to follow defects in the forging process represents a strong advantage for the forger. In the process of ingot casting, the first solidified zones occur mush before the end of the pouring and the liquid areas remain present even well after the end of the filling step. For sure, behavior of the different metal phases is fully coupled during the process. It appears that defects like porosities, cracks or hot tears take place in the brittle temperature range (BTR) of the alloy from the strains, stresses and
distortions occurring at the first instants of solidification. Depending on the tonnage, solidified areas at the end of the pouring of ingots can represent up to 30% to 40% (Figure 1) of the total mass. Hence, it is easy to imagine that, defects are already present at that stage in such amount of transformed shell. Within this framework, thermo-mechanical modeling is of interest for steel makers. It can be helpful in the adjustment of the different process parameters in order to improve casting productivity while maintaining a satisfying product quality. However, optimization of the parameters requires a quite complex model that delivers very precise responses. Indeed, it is necessary to take 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 the solidification. Once the defects are trapped in the casting process, being able to follow them through the forging operations is really interesting. Not only tracking them, but also estimating the size of the voids in case of porosities or cracks is of interest. This can be allowed by a specific model initialized by results issued from casting and depending on strains and stresses occurring during the open die forging operations.
In this paper, Thercast, software dedicated to the simulation of metal solidification is firstly presented. The thermo-mechanical models developed in this software are presented. The way of taking into account the coupling between metal and molds during solidification is shown. A model of determination of the liquid and mushy zones’ constituted equation parameters is developed. Secondly, the direct transfer of Thercast results into Forge and the model of evolution of the defects are shown. Applications on casted and forged ingot are finally illustrated.
ICRF 1st International Conference on Ingot Casting, Rolling and Forging 2
An original mixed thermo-mechanical model
Thercast is a commercial numerical package for the simulation of solidification processes: shape casting (foundry), ingot casting, and direct-chill or continuous casting. A 3D finite element thermo-mechanical solver based on an Arbitrary Lagrangian Eulerian (ALE) formulation is used.
Figure 1: State of solidification of a small ingot (~300kg) just after the end of pouring – high percentage of already solidified material
Thermal model
The thermal problem treatment is based on the resolution of the heat transfer equation, which is the general energy conservation equation:
))(.()( TTdtTdH
(1),
where T is the temperature, (W/m/°C) denotes the thermal conductivity and H (J) the specific enthalpy which can be defined as:
)()()()()(0
s
T
Tlp TLTgdCTH (2),
0T (°C) is an arbitrary reference temperature,
(kg/m3) the density, sT (°C) the solidus temperature,
pC (J/kg/°C) the specific heat, lg the volume
fraction of liquid, and L (J/kg) the specific latent heat of fusion. In the one-phase modelling, )(Tgs is
previously calculated using the micro-segregation model PTIMEC_CEQCSI [8].
The boundary conditions applied on free surface of the mesh of the metal could be of classical different types:
average convection: )(n. extTThT where h (W/m²/°C) is the heat transfer coefficient, and extT is the external temperature
radiation: )(n. 44extstef TTT ,
where is the steel emissivity, stef is the Stephan – Boltzmann constant.
external imposed temperature: impTT .
external imposed heat flux: impT n.
n denotes the outward normal unit vector.
At part/molds interface, heat transfers are taken into account with a Fourier type equation:
)(1n. moldeq
TTR
T (3),
where moldT is the interface temperature of the mold
and eqR (W/m²/°C) 1 , the heat transfer resistance
that can depend on the air gap and/or the local normal stress, as presented below:
011
1
0)11,1min(
1
0
0
airseq
airs
radair
eq
eifR
RR
R
eifR
RRR
R
(4),
where air
airair
eR
and
s
ss
eR
with aire and se
respectively the air gap and an eventual other body
(typically slag) thickness and air and s the air and
the eventual other body thermal conductivity. 0R is a
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stress n , A and m being the parameters of the
law.
Mechanical model
At any time, the mechanical equilibrium is governed by the momentum equation:
0. γgσ ,
where σ is the Cauchy stress tensor, g is the gravity vector, and γ is the acceleration vector.
Taking into account the very different behaviors of liquid and solid metal is realized by a clear distinction between constitutive equations associated to the liquid, the mushy and the solid states. In order to fit the complex behavior of solidifying alloys, a hybrid constitutive model is considered. In the one-phase modelling, the liquid (respectively, mushy) metal is considered as a thermo-Newtonian (respectively thermo-viscoplastic, VP) fluid. In the solid state, the metal is assumed to be thermo-elastic-viscoplastic (EVP) (Figure 2). Solid regions are treated in a Lagrangian formulation, while liquid regions are treated using ALE [9]. More precisely, a so called, transient temperature or coherency temperature is used to distinguish the two different behaviors. It is typically defined between liquidus and solidus, and usually set close to solidus temperature. For more information, the interested reader can refer to [1], [2] and [3].
Figure 2 : Schematic representation of the rheological behavior of the different phases of the metal in solidification conditions
In such a model, physical data, hence numerical data, take values in a huge range, from some Pa to hundreds of GPa. If getting data at low temperatures is quite usual, it is not the case for the high temperatures closed to solidus and above. From
this finding, Bellet [4] has proposed an extrapolation model of the solid data to liquid data for fields like viscosity and strain rate sensitivity in case of viscoplastic behavior. The viscoplastic behavior is formulated with the well known power law:
mmTK 13)(
(5),
where is the von Mises flow stress, the equivalent plastic strain rate,T the temperature, K the viscoplastic consistency and m the strain rate sensitivity. It is to be noted that the Newtonian behavior is obtained in case of 1m and lK where l is the dynamic viscosity of the liquid. The model is aimed at defining K and m throughout the mushy zone divided in three intervals limited by the parameters:
cohelg , the liquid fraction at coherency temperature
susplg , the liquid fraction beyond which a suspension model is used
For lg the liquid fraction taken in the interval
susplcohel gg ,, ,
1)1)(()(
)()()(
,
1,,
cohell
susplcohell
gmgmgKgKgK
(6)
where cohelsuspl
lsuspl
gggg
,,
,
The values of K and m are continuous along the three intervals, so that, )0( lgK and
)0( lgm are deduced from the solid state
constitutive model and are taken at solid temperature or just below. The value of llg )1( is
taken a priori. Taking 0, cohelg and 1, susplg , the
model is summarized in (6).
Defects criteria
Precise prediction of defects like macro-porosities and/or hot tears is quite appreciated by steel makers. Several hot tear criteria are present throughout literature. Some are based on thermal considerations, others are fed with stresses, strain and/or strain rate. In [5] the conclusion of the authors
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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:
BTR
c dt ̂ (11)
where BTR is the Brittle Temperature Range defined when 0lg , typically 1.00 lg , introduced by
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.
Direct transfer to forging operations
Forge is a 3D simulation software dedicated to forging processes. Its range of applications is very large, from hot forging to cold forging. Open die forging process is one of them. The thermo-mechanical core of both Thercast and Forge software for solid metal behavior is similar (EVP). So that there is no loss of information in the transfer of data, as Forge can directly read results from Thercast. In addition, to ensure the continuity of behavior of the part between casting process and forging process, the material data file is exactly the same for Thercast simulation and Forge simulation.
In open die forging, material forming processes request many number of blows exceeding several hundreds. Moreover, the part is moved in rotation and/or translation between each blow. In order to define theses transitions, a specific automatic procedure has been implemented in the software. Reheating in the furnace is also available in the procedure. In order to be as close as possible to reality, the manipulator is simulated by boundary conditions imposing speed and/or effort on predefined zones on the part surface. Figure 3 illustrates sequence of cogging operations, the upsetting and different steps of the forging involving manipulations of the part between each one.
….
Figure 3 : Example of upsetting – beginning of a cogging operation. Each step involves manipulation of the part
Numerical simulation aims at predict the shape of the part during the process of metal forming. On the contrary of closed die forging, the final shape of the part does not correspond to the shape of the tool. Indeed, that depends on several parameters among them, it can be listed shape and kinetic of the tools, friction on the tools, behavior of the metal, temperature evolution, etc. Yield, numerical modelling can be a useful tool in evaluating the respective impact of each parameters and optimizing the forging. Many virtual tests are so possible in order to improve the internal structure of the metal. In particular, this is actually depending on the internal porosity distribution issued from casting process. Therefore, following the evolution of the porosities in the forging process is essential to predict the final quality of the forged part.
Model of evolution of the porosities
In order to predict the evolution of porosities in forging process simulation, there are mainly two ways. The first one is to directly take voids account in very fine meshes. This is the most precise way, but also quite costly in terms of CPU time. The second one is to initialize a specific field representing the presence of porosities and to follow the evolution of the field under the forging operations. The localization of the porosities and the evolution of the
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size respectively to the initial one are so available. The model of evolution of the porosity volume can be written as follow:
0
0
pifpKt
pifpKt
t
c
(8),
where is the volume of porosity, p the pressure,
equivalent stress, and the strain rate. cK and
tK are respectively the compression and tension
coefficient of the law and p
is the triaxiality of
stresses. According to this model, the porosity size will depends on the deformation with respect to the compression or tension stresses.
This model has been validated in comparison to a direct computation where porosity has been meshed in a fine mesh. Figure 4 illustrates the evolution of the meshed porosity shape and the evolution of the volume of the porosity predicted by the two models. This comparison allowed to determine the respective values of cK and tK .
Figure 4 : Comparison of evolution of the porosity volume predicted by (8) and by a direct simulation of a meshed porosity (bottom). Shape evolution of porosity in a direct simulation
In addition to porosities, Forge is able to take account the phenomena of recrystallization occurring during the forming process and after deformation. Also, the secondary growth of grains is modeled.
Applications
The model presented above can be applied for ingot casting application or continuous casting applications. The differences are mainly set in the
boundary conditions and in the treatment on the feeding metal. Here ingot casting applications are focused.
In case of ingot casting application, the pouring is piloted by the flow rate that can vary or not. Both air and metal are taken into account into the ingot. As presented, before theses phases are mainly 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 the ingot throughout the solidification. It means that the air gap can be caught as soon as it occurs even though the filling stage is not achieved, in case of solidification of the ingot skin. Hence, strong thermo-mechanical coupling of all the domains in the cooling system is applied via the heat transfers that are impacted between cooling metal and mold following (4). Moreover, strain and stress being calculated in the solid zones while pouring, it is possible to forecast defects creation and evolution within the mushy and solid shell of cooling metal. This is true from stress and strain birth till the end of complete solidification of the ingot using (7). Other kind of results is the possibility to predict macro secondary piping or shrinkage in case of local lack of exothermic powder for example. Actually, a relevant state of stresses within the metal is predicted from the coupling between VP and EVP models. This state 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 powder effect on the ingot solidification.
Figure 5 illustrates the distribution of the temperature (on the left) and the solidified skin (on the right) of the ingot at the end of the filling. Even though the cases are not the same, this result is in good agreement with Figure 1. That illustrates the fact that solidification begins a long time before the 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 appears that, in such small ingot, much before the end of filling, air gap is created due to the shrink of the solidified skin of the ingot involving non continuous temperature distribution at ingot/mold interface.
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Figure 5 : illustration of the temperature distribution at the end of the pouring (top) and the corresponding solidification zones (bottom). Note the discontinuous values of temperature at ingot/mold interface due to the HTC air gap dependency.
The global shape of the ingot after 3h10mn of cooling is presented Figure 6. The picture shows the effects of the bad calibration of the exothermic powder: internal open shrinkage occurring. The 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
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 the strokes of the forging operation in the first pass. At the end of the first pass, porosities are closed according to the model (8), where as the void has been partially closed as shown by the white spots. Figure 8 shows the shape of the part at the end of the second and the third passes. The void has been almost completely closed. The white spots illustrate the self contact of the metal in the area of the void that has been closed.
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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 8 : Shape of the part at the end of the second pass (top) and at the end of the third pass (bottom). A small volume of void is still remaining.
Average size ingot (24 tons)
Another example of chaining Thercast and Forge is presented here. This case is a 24 tons ingot bottom poured. The same procedure as above has been applied. Hence, after the filling and cooling of the casting process, the transfer to Forge has been achieved with the initialization of the porosities location. Figure 9 illustrates the temperature
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 9 : Temperature in the ingot and molds (on top) and air gap at ingot/molds interface (at the bottom). Note the non symmetrical distribution either on temperature or air gap due to the trunnions at cast iron molds outside.
Same, Figure 10 shows how the Yamanka criterion results from Thercast is initializing the porosities evolution model in Forge. The non symmetrical distribution is also visible on Yamanaka criterion results. After the first blooming, porosities have been closed a lot and only small voids remain localized at the central axis of the part. At the end of the second blooming, all porosities have been closed
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according to the model (8) (Figure 11, left). Figure 11 (right) illustrates the average grain size resulting.
Figure 10 : Yamanaka criterion result at the end of 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 criterion localizes hot tears.
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 porosities have been closed (bottom).
Conclusion
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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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.
