THERCAST: A new 3D simulation model for complete chaining casted and forged ingot

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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

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THERCAST: A new 3D simulation model for complete chaining casted and forged ingot

  1. 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, solidifiedThe control of the final quality of a forged product areas at the end of the pouring of ingots canrequires a perfect knowledge of the history and the represent up to 30% to 40% (Figure 1) of the totalquality of the initial casted ingot. Reach a final piece mass. Hence, it is easy to imagine that, defects arematching the specifications required to locate and already present at that stage in such amount ofanalyze 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. Itdefects and their evolution in forging operations can be helpful in the adjustment of the differentwould allow to fully control the quality of formed process parameters in order to improve castingproducts. In this context, a new package mixing both productivity while maintaining a satisfying productcasting and a forging simulation module was created. quality. However, optimization of the parametersThis paper presents the new model to simulate the requires a quite complex model that delivers verycreation and evolution of casting defects and to follow precise responses. Indeed, it is necessary to takethem 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 onlycasted ingot are generally not compatible with the tracking them, but also estimating the size of thecharacteristics 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 byingot. The microstructure and the closure of results issued from casting and depending on strainsporosities are in first approximation related to local and stresses occurring during the open die forgingdeformation in the forged part. So that, the final operations.quality of a forged product is fully depending of thecasted ingot from which it originated. Hence, In this paper, Thercast, software dedicated tocontrolling the health of the initial ingot, or at least, the simulation of metal solidification is firstlyknowing the location of the defects like porosities, presented. The thermo-mechanical modelscracks, etc. is essential for the caster. Same, being developed in this software are presented. The way ofable to follow defects in the forging process taking into account the coupling between metal andrepresents a strong advantage for the forger. In the molds during solidification is shown. A model ofprocess 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 intothe filling step. For sure, behavior of the different Forge and the model of evolution of the defects aremetal phases is fully coupled during the process. It shown. Applications on casted and forged ingot areappears 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 ICRF 1st International Conference on Ingot Casting, Rolling and Forging 1
  2. 2. 5 June, 2012 Brüssel-Saal Ingot Casting – Simulation 1 An original mixed thermo- The boundary conditions applied on freemechanical model surface of the mesh of the metal could be of classical different types: Thercast is a commercial numerical packagefor the simulation of solidification processes: shapecasting (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 transfermechanical solver based on an Arbitrary Lagrangian coefficient, andText is the externalEulerian (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), ReqFigure 1: State of solidification of a small ingot(~300kg) just after the end of pouring – highpercentage 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 onthe resolution of the heat transfer equation, which is  1the 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 enthalpywhich 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 andT0 (°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 surfaceC p (J/kg/°C) the specific heat, g l the volume 1 1  1   moldfraction 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 ) 2previously calculated using the micro-segregation with  mold the emissivity of the mold, R  1 A n mmodel PTIMEC_CEQCSI [8]. a heat resistance taking into account the normal ICRF 1st International Conference on Ingot Casting, Rolling and Forging 2
  3. 3. 5 June, 2012 Brüssel-Saal Ingot Casting – Simulation 1stress  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 likelaw. 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 isgoverned 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 ratewhere 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   lgravity 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 thebehaviors of liquid and solid metal is realized by a parameters:clear distinction between constitutive equationsassociated to the liquid, the mushy and the solid  g l ,cohe the liquid fraction at coherencystates. In order to fit the complex behavior of temperaturesolidifying alloys, a hybrid constitutive model isconsidered. 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 usedthermo-Newtonian (respectively thermo-viscoplastic,VP) fluid. In the solid state, the metal is assumed to For g l the liquid fraction taken in the intervalbe thermo-elastic-viscoplastic (EVP) (Figure 2). Solidregions are treated in a Lagrangian formulation, while g l ,cohe , g l , susp liquid regions are treated using ALE [9]. Moreprecisely, a so called, transient temperature orcoherency 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 interestedreader 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 rheologicalbehavior of the different phases of the metal insolidification conditions Defects criteria Precise prediction of defects like macro- In such a model, physical data, hence porosities and/or hot tears is quite appreciated bynumerical data, take values in a huge range, from steel makers. Several hot tear criteria are presentsome Pa to hundreds of GPa. If getting data at low throughout literature. Some are based on thermaltemperatures is quite usual, it is not the case for the considerations, others are fed with stresses, strainhigh temperatures closed to solidus and above. From and/or strain rate. In [5] the conclusion of the authors ICRF 1st International Conference on Ingot Casting, Rolling and Forging 3
  4. 4. 5 June, 2012 Brüssel-Saal Ingot Casting – Simulation 1tends to prove that the criterion of Yamanaka et al [6]is pertinent to forecast location of hot tears insolidification conditions. The expression of thiscriterion is the following: c   ˆdt (11) BTR  ….        whereBTR is the Brittle Temperature Range definedwhen g l  0 , typically 0  g l  0.1 , introduced by ˆWon et al [7] and  represents a norm associated to the damaging components of the strain rate tensor,expressed in tensile stress axis orthogonally of thecrystal growth direction [5]. The critical value cdepends on steel composition. However, Yamanakaintroduced, by experimental observations, a thresholdvalue 2% of the criterion above which, the odds of hottears creation are high. Modelling experience tendsto show that the same criterion applied with a lowerthreshold, 0.5%, gives distribution that fits quite wellthe macro-porosities evolution in solidificationconditions.   Figure 3 : Example of upsetting – beginning of a cogging operation. Each step involves manipulation Direct transfer to forging of the partoperations 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 shapelarge, 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 parametersforging process is one of them. The thermo- among them, it can be listed shape and kinetic of themechanical 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, numericalis no loss of information in the transfer of data, as modelling can be a useful tool in evaluating theForge can directly read results from Thercast. In respective impact of each parameters and optimizingaddition, to ensure the continuity of behavior of the the forging. Many virtual tests are so possible in orderpart between casting process and forging process, to improve the internal structure of the metal. Inthe material data file is exactly the same for Thercast particular, this is actually depending on the internalsimulation 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 finalprocesses 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. Inorder to define theses transitions, a specific Model of evolution of the porositiesautomatic procedure has been implemented in thesoftware. Reheating in the furnace is also available in In order to predict the evolution of porositiesthe 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 inreality, the manipulator is simulated by boundary very fine meshes. This is the most precise way, butconditions imposing speed and/or effort on also quite costly in terms of CPU time. The secondpredefined zones on the part surface. Figure 3 one is to initialize a specific field representing theillustrates sequence of cogging operations, the presence of porosities and to follow the evolution ofupsetting and different steps of the forging involving the field under the forging operations. Themanipulations of the part between each one. localization of the porosities and the evolution of the ICRF 1st International Conference on Ingot Casting, Rolling and Forging 4
  5. 5. 5 June, 2012 Brüssel-Saal Ingot Casting – Simulation 1size respectively to the initial one are so available. boundary conditions and in the treatment on theThe model of evolution of the porosity volume can be feeding metal. Here ingot casting applications arewritten 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 ofwhere  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 ofK t are respectively the compression and tension solidification of the ingot skin. Hence, strong thermo- mechanical coupling of all the domains in the cooling pcoefficient of the law and is the triaxiality of system is applied via the heat transfers that are  impacted between cooling metal and mold followingstresses. According to this model, the porosity size (4). Moreover, strain and stress being calculated inwill depends on the deformation with respect to the the solid zones while pouring, it is possible tocompression 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 completeto a direct computation where porosity has been solidification of the ingot using (7). Other kind ofmeshed 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 exothermicevolution of the meshed porosity shape and the powder for example. Actually, a relevant state ofevolution of the volume of the porosity predicted by stresses within the metal is predicted from thethe two models. This comparison allowed to coupling between VP and EVP models. This statedetermine 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 exothermicFigure 4 : Comparison of evolution of the porosity powder effect on the ingot solidification.volume predicted by (8) and by a direct simulation ofa meshed porosity (bottom). Shape evolution of Figure 5 illustrates the distribution of theporosity 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 inaccount the phenomena of recrystallization occurring good agreement with Figure 1. That illustrates theduring the forming process and after deformation. fact that solidification begins a long time before theAlso, 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 nonfor ingot casting application or continuous casting continuous temperature distribution at ingot/moldapplications. The differences are mainly set in the interface. ICRF 1st International Conference on Ingot Casting, Rolling and Forging 5
  6. 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 underFigure 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 closedsolidification zones (bottom). Note the discontinuous according to the model (8), where as the void hasvalues 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 beencooling is presented Figure 6. The picture shows the almost completely closed. The white spots illustrateeffects of the bad calibration of the exothermic the self contact of the metal in the area of the voidpowder: internal open shrinkage occurring. The that has been closed.defect criterion with application of prediction of macroporosities is illustrated on the right. The area of lowdensity in the lower part of the ingot is indicated bythe lowest values of the criterion while the macroporosities, present just below the internal shrinkage,are indicated by the highest values. The criterionindicates that odds of getting hot tears are quite lowas the maximum values in this case do not reach thecritical threshold. Ingot skin getting solidified rapidly,the cooling metal does not remain in the BTR longenough under tensile stresses to create strainyielding hot tears. As presented above, the link betweenThercast and Forge is direct. Hence, results from themodel (7) can be directly transferred into Forge. Thisis used in order to initialize parameters of the specificmodel (8) aimed at predict the closure of porositiesthat has been implemented in Forge. As per therange of Yamanaka criterion model, a distribution ofporosities at the end of casting process is establishedfollowing 0.5% as a threshold. That initializes the ICRF 1st International Conference on Ingot Casting, Rolling and Forging 6
  7. 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 toforging simulation in order to follow the porositiesevolution. At the end of the first pass, porosities areclosed 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 theFigure 8 : Shape of the part at the end of the second bottom). Note the non symmetrical distribution eitherpass (top) and at the end of the third pass (bottom). A on temperature or air gap due to the trunnions at castsmall 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 theForge is presented here. This case is a 24 tons ingot porosities evolution model in Forge. The nonbottom poured. The same procedure as above has symmetrical distribution is also visible on Yamanakabeen applied. Hence, after the filling and cooling of criterion results. After the first blooming, porositiesthe casting process, the transfer to Forge has been have been closed a lot and only small voids remainachieved with the initialization of the porosities localized at the central axis of the part. At the end oflocation. Figure 9 illustrates the temperature the second blooming, all porosities have been closed ICRF 1st International Conference on Ingot Casting, Rolling and Forging 7
  8. 8. 5 June, 2012 Brüssel-Saal Ingot Casting – Simulation 1according 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 allFigure 10 : Yamanaka criterion result at the end of porosities have been closed (bottom).casting process in Thercast (top), at the beginning offorging process in Forge (bottom). Note the non  symmetrical distribution also issued from thetrunnions impact, even on the skin, where the Conclusioncriterion 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  ICRF 1st International Conference on Ingot Casting, Rolling and Forging 8
  9. 9. 5 June, 2012 Brüssel-Saal Ingot Casting – Simulation 1simulation  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.  ICRF 1st International Conference on Ingot Casting, Rolling and Forging 9

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