Advanced solutions for virtual process modelling: application to steel ingot manufacturing from casting to open-die forging

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1 Advanced olution for virtual proce modelling: application to teel ingot manufacturing from cating to open-die forging JAOUEN Olivier 1,a, COSTES Frédéric 1,b, SAAD Ali 1,c and LASNE Patrice 1,d DUCLOUX ichard 1,e *, 1 TANSVALO SA Parc de Haute Technologie 694 avenue Dr Maurice Donat Mougin Cedex France a olivier.jaouen@tranvalor.com, b frederic.cote@tranvalor.com, c ali.aad@tranvalor.com, d patrice.lane@tranvalor.com, e richard.ducloux@tranvalor.com Keyword: fluid-tructure model, turbulent flow, egregation, grain tructure, cellular automata (cafe), complete manufacturing proce chain, ingot cating & open-die forging imulation, heat treatment. Abtract. The health of forged component depend on the quality of the emi-product previouly iued from cating proce. In that context, a numerical imulation tool able to mater material characteritic from initial cating to the final forming proce would be of a great interet for teel maker and forging manufacturer. Thi i the purpoe of the preent paper. Nowaday, it i well known that ingot defect like hot tear or crack are rooted in the very beginning of the olid hell birth. Damage are reulting from the competition between the hydrotatic preure occurring within the turbulent flow in the liquid zone and tenile tre combined with a train tate occurring while the kin olidifie. In addition, the thermal energy pulled-out from the cat-metal product into the mold ha a huge impact on the hell thickne. Thi thermal energy i alo affected by the gap growth iued from the hrinkage of the olidified together with the deformation of the mold contituent. Numerically peaking, the fluid/tructure model i one of the mot appropriate method to take into conideration all thee phenomena through an accurate way. Indeed, a tandard CFD method doe not repreent the olid behaviour, o that the tree, train and gap evolution due to the hell hrinkage are not reachable. On the other hand, a ingle tandard FEA model cannot repreent accurately the liquid behaviour. In a firt part, thi paper decribe a new 3D fluid/tructure model involving the turbulent fluid flow and the olid contitutive equation. The management of the liquid time tep allowing high velocity motion into the liquid phae of the alloy coupled with the olid time tep dealing with the olid phae and the correponding low motion i hown. Moreover, the fluid-tructure model i well adapted to localize egregation epecially when uing quality input data delivered by thermodynamic databae. An applicative example with an ingot cating conidering the coupling with the deformation of the mold i preented. On top of that, the example include grain tructure calculation reulting from a CAFE method coupled with the cooling of alloy. It alo illutrate the impact of a top powder defined a a deformable body and therefore able to follow the hrinkage of the ingot top urface. The exothermic reaction i conidered a well in order to etimate it impact on the cooling time and the final quality of the cat-metal product. In a econd part, the paper decribe the benefit of imulating the complete manufacturing chain from initial cating to open-die forging and final quenching. A direct data tranfer from cating to forging i performed between the imulation tool. All reult from the cating tage are o conidered into the forging model. Both cating & forging model are fully compatible. Hence, there i not any lo of data in the tranition tep and the forging proce imulation launch i een a a imple retart tep from the cating imulation. In that context, data like global hape, poroitie,

2 egregation ditribution iued from the cating are accounted in the forging proce in order to fully monitor the hitory and their impact on the final product health. The modelling of the forging tage allow etimating the efficiency of the manufacturing proce with regard to the cloure of poroitie and the tracking of egregation. In addition, the carbon rate concentration coming from the cating tage and tranferred into the ubequent forging tage will impact the olid phae change occurring in the final quenching operation. The imulation of thi phenomenon i poible conidering an appropriated heat treatment model baed on TTT diagram which depend on the local carbon concentration. Finally, thi paper demontrate how teel maker and forging manufacturer can take benefit of full compatible proce modelling oftware in order to imulate the entire the forming chain from raw material to final end-uer product. Introduction The heavy indutry, petrochemical and/or the nuclear, ue largely the hell a high preurized container. Thee hell are obtained after a equence of multiple operation that may involve different method. The equence can tart from olid ingot. It can alo aemble rolled and welded heet metal, or can ue hollow ingot. Compared to the other method, the equence tarting from hollow ingot preent certain advantage. Indeed, in that context, a oppoed to the method uing rolled and welded heet, the final product that i one piece avoid weaknee in welded area. On the other ide, on the contrary to the proce tarting from a full ingot, it gain a crewing operation. In addition, ince the poroitie are in the core of the hell and not at kin area, they can be better controlled way during the becking operation yielding a better quality product. The final egregation ditribution are till eaier a lot to anticipate. However, in pite of all thee advantage, all i not perfect in thi model. Indeed, by it hollow nature, in order to obtain the requeted qualitie of the final product, the olidification of the ingot mut be perfectly matered. Thu, a pecific and complex cooling i applied to the inner wall of the ingot aiming at obtain ymmetrical characteritic between it inner and outer wall. Thi can be yielding from controlled circulation of water or blown freh. In order to fully carry out all of thi chain, a imulation tool can be of great help in thi proce. It allow optimizing the cooling time, to regulate the inner cooling or to etimate the intern tructure. Moreover, it can be helpful in the forging operation in the determination of the equence of troke, and many thing ele. However thi involve the capability to imulate the entire equence of different operation from the ingot cating to the heat treatment paing through the mandrel drawing. In thi paper a numerical model able to perform the imulation of all thee ucceive operation i preented. It how the perfect and natural chaining between an ingot cating imulation oftware and an open die forging oftware. Through a dedicated example, the author how how the pecific condition of cooling of the ingot are taken into account through the implementation of thermomechanical interface boundary condition. The impact of gap on temperature change and the revere effect on the ingot hape are particularly highlighted. They illutrate the ame, how poroitie and egregation are on the one hand determined by the cating oftware and on the other hand, naturally tranferred to forging oftware. Thu, the monitoring of their evolution and their impact on the mechanical behavior and on the tructure of the final product i perfect. Mandrel drawing and becking operation are hown including the example of the cloure of poroitie. At end, the ditribution of local egregation i taken into account in order to illutrate the impact of phae change during the heat treatment operation. Finally, thi article preent the trategic interet of a imulation tool capable of predicting the overall proce of making a hell from a hollow ingot for cating ingot, cooling and it forging. Author propoe a coupling between the two product to have an advanced numerical uite for the deign of uch component. Thi coupling will allow to produce part meeting the requirement of high level of nuclear and petrochemical indutrie a well a to limit the actual tet repreenting a ignificant material aving regarding the volume and ma of the part involved.

3 Ingot cating Mandrel drawing Becking Heat Treatment Machining Fig 1: Example of the making chain of a hell from hollow ingot. Final part i obtained after cating of a hollow ingot, mandrel drawing operation, then becking operation. Heat treatment operation i not preented here, but could be alo performed Cae context The cae illutrated in thi article wa built internally from the knowledge of our engineering expert. Only the initial CAD file for ingot cating tep computation were provided by one of our indutrial partner. The material of the hell i 40CMD8. Dimenion of the initial ingot are preented Fig. 2. It weight i of 140 ton. The cating tep i a bottom pouring proce through a running ytem pited in 3 feeding gate (Fig. 4). The flow rate i et uch that the peed of the flow front repreent 100mm/min. The initial temperature i 1550 C. Once the ingot tripped out, the cut of the rier and the bottom yield a piece which height i 3 m. It will be tretched till 4 m at the end of the mandrel drawing proce. Ingot cating Mandrel drawing Fig 2: Dimenion of the cat ingot, and after the drawing and becking tep. Cating proce Fluid/Structure model The imulation of the cating proce require a pecific treatment of the different phae change of metal, liquid, muhy and olid, from the beginning of pouring to the end of olidification. By default, the cating oftware calculate evolution of temperature in the cat product and the different component of the cooling ytem, the mold, the cating plate, and other refractory or inulating cover powder, etc. Thi i performed uing a dedicated model. At any time, the mechanical equilibrium i governed by the general momentum equation:

4 . σ g γ 0. (1) where σ i the Cauchy tre tenor, g i the gravity vector, and γ i the acceleration vector. The very different behaviour of liquid and olid metal are conidered by a clear ditinction between contitutive equation aociated to the liquid, the muhy and the olid tate repectively. In order to fit the complex behaviour of olidifying alloy, a hybrid contitutive model i accounted. The liquid (repectively, muhy) metal i conidered a a thermo-newtonian (repectively thermovicoplatic, VP) fluid. In the olid tate, the metal i aumed to be thermo-elatic-vicoplatic (EVP). However, thi cheme ha a drawback. Indeed, the reolution i carried out in one hot, taking account the total range of temperature. Due to the limit of actual algorithm and hardware preciion, it cannot conider the correponding total magnitude of concerned vicoity. In order to deal with the very large range of the vicoity value involved within the olidification proce of the molten alloy, a two tep cheme i ued for the olving of (1). Hence, one tep, tep 1, i dedicated to the muhy and olid zone, the olid olver, and another one, tep 2, i in charge of the liquid and muhy zone, the liquid olver (Fig 3). Solid region are treated in a Lagrangian formulation, while liquid region are treated uing an ALE (Arbitrary Lagrangian Eulerian) method [2]. A o called, tranient temperature, or coherency temperature, i ditinguihing the two different behaviour. It i typically defined in between liquidu and olidu, and uually et cloe to olidu. Thermo-phyical parameter are etup uch that the continuity of behaviour i enured at tranient temperature. For more information, the intereted reader can refer to [3] to [5]. Under that context, two cae are poible. Option 1, the tranient temperature bound the two tep. The full coupling liquid/olid i enured by the control of liquid velocitie and preure with the olid correponding one at tranient temperature volume interface [6]. Option 2, an overlap within the muhy zone i alo available. Yield, both liquid olver and olid olver are applied on the total or partial range between liquidu and olidu (Fig. 3). In addition, any governing model can be aociated to each olver. In particular, turbulent fluid flow within the liquid zone of the metal i managed by the Navier-Stoke equation completed by LES term [7]. Fig 3: Schematic repreentation of the option 2 for the 2 tep algorithm. The high level of temperature for the tep 1 (Ttep1) i within the muhy zone range. Same, the low level of temperature for the tep 2 (Ttep2) i within the muhy zone, uch that Ttep 1> Ttep2. In cae of Ttep1 = Ttep2, it i imilar to the option 1. The choice of the two temperature Ttep1 and Ttep2 i depending on the tructure of the alloy within the muhy zone, typically, it can depend on the vicoity and/or the olid fraction and the compoition. In that cheme, the tep 2 of the algorithm i not only dealing with the liquid metal, but alo with the within the cavity till thi one i fulfilled. Thi i poible thank the ue of a level-et method.

5 Level-et repreent the ditance (t) to the interface (t) metal and ; it expreion i: ( x, t) dit( x, ( t)) in ( t) ( x, t) 0 on ( t) ( x, t) dit( x, ( t)) in / ( t) between fluid at time t, here liquid (2) where i the cavity pace, (t) i the pace occupied by the metal into the cavity, and / ( t) i the remaining pace, meaning the pace. Conidering definition (2), flow front of the metal i the 0 value io-urface of (t) [6], [7]. Thermal model The olving of the general energy equation drive heat tranfer: dh( T) dt.( ( T) T ) (3) where T i the temperature, which can be defined a: (W/m/ C) denote the thermal conductivity and H (J) the enthalpy T H( T) ( ) C ( ) d g ( T) L( T ) (4) T0 p l T 0 ( C) i an arbitrary reference temperature, (kg/m 3 ) the denity, T ( C) the olidu temperature, C p (J/kg/ C) the pecific heat, g l the volume fraction of liquid, and L (J/kg) the pecific latent heat of fuion. In the one-phae modeling, g l (T ) can be previouly calculated uing the microegregation model PTIMEC_CEQCSI [8] or reult from micro-egregation model that can be ued [9]. Cooling condition One of the difficultie in the cating of the hollow ingot i the cooling control. In particular, the cooling of the inner ide repreent a king of challenge. Indeed, in the end of the olidification, the intern tructure of the ingot mut be a ymmetric a poible compared to the outer ide. However, the building of the cooling ytem i rather aymmetric: the inner ide i a thin wall wherea the outer ide i a wide cat iron mold. Therefore, the difference of mold contitution between inner ide and outer ide ha impact on olidification. That very difference mut be balanced by the cooling condition. Thi require a perfect control of the inner cooling. Typically, what are uually conidered are either water channel or blowing. In our cae, freh blowing all over the urface of the inner wall ha been choen. Thi i carried out numerically peaking by a pecific heat tranfer coefficient, repreenting the blow effect (Fig. 5).

6 Fig 4: Illutration of the ingot hape. Note the three feeder gate. Thermal tranfer At ingot/mold interface : - Specific heat tranfer depending on the mold nature - Air gap/preure dependent heat tranfer Deformable exothermic powder follow the metal hrinkage Mechanical tranfer At ingot/mold interface: - Sticky liquid - Friction for muhy and olid phae At mold/mold interface : - Specific heat tranfer depending on the mold nature Blown freh cooling Fig 5: illutration of the configuration of computation. A ymmetry plan ha been ued in view of the geometry of the cating. To fully addre the evolution of the temperature through the variou ytem component cating, a fine meh i adapted in the inulating part uch a refractory and garnex part. Similarly, the part of the meh running ytem i refined to manage the flow. The variou mechanical and thermal boundary condition are indicated. They allow to take into account the interaction between the variou component of the cating ytem with one another and with ambient. The boundary condition applied on free urface of the meh of the different part of the cooling ytem are of claical different type: average convection: T n h( T T ) where h (W/m²/ C) i the heat tranfer. ext coefficient, and T ext i the ambient temperature 4 4 radiation: T.n tef ( T T ext ), where i the teel emiivity, tef i the Stephan Boltzmann contant. external impoed temperature: T Timp. external impoed heat flux: T. n n denote the outward normal unit vector. imp

7 At part/mold interface, heat tranfer are taken into account with a Fourier type equation: 1 T. n ( T Tmold ) (5) where T mold i the interface temperature of the mold and eq (W/m²/ C) 1, the heat tranfer reitance that can depend on the gap and/or the local normal tre, a preented below: eq eq min(, 0 1 rad ) if e 0 or eq if e 0 (6) where e and e with e and e repectively the gap and an eventual other body (typically mold powder) thickne and and the and the eventual other body thermal conductivity. 0 i a nominal heat reitance depending on the urface roughne, rad tef ( T T mold 2 mold 1 )( T T mold ) with mold the emiivity of the mold, A a heat 1 reitance taking into account the normal tre n, A and m being the parameter of the law. Through (5), (6), the full thermal/mechanical coupling within the cating ytem i enured. Indeed, the cooling of the olidifying alloy implie external hrinkage that create gap at ingot/mold interface. Thi gap behave a a local inulator and modifie heat exchange locally in time and pace between ingot and mold which in return modifie the cooling of the alloy and o the hrinkage. Thi i only poible becaue thermomechanical computation i performed and (5) i ued a boundary condition. An a priori input of heat tranfer coefficient doe not allow thi full coupling. Prediction of the defect and the tructure of the cat product The trength of the above thermo-mechanical model allow combining different cat product health prediction model. Indeed, to the liquid/muhy model i aociated a egregation model. To the muhy/olid model i aociated a crack/hot tear prediction model. Thi i poible thank to the full coupling between liquid and olid behavior conidered via the mix of the dedicated thermomechanical model that are olved in the two tep model above (Fig. 6,7,8,9 and 10). m n

8 Fig 6: illutration of the temperature ditribution in four different intant of the filling. The horizontal line indicate the level of metal in the mold. The arrow demontrate the movement of the liquid metal. Note the mold heating by the advancing metal during pouring. Fig. 7: Illutration of the final configuration of the calculation. One can notice the hape of the covering powder in the end of olidification which i deformed according to change in the free urface of the ingot. On the right, the final hape of the ingot with the primary hrinkage. The radial ymmetry of the ingot confirm that the cooling at inner ide wall of the cating ytem ha been calibrated and well controlled.

9 Fig. 8: illutration of the ditribution of the final temperature in the cating ytem. One can notice the non-continuity of the temperature at the interface between the ingot and the mold howing the recognition of the impact of the gap on heat tranfer. Indeed, the gap act a an inulator which low down the evacuation of the heat energy from the ingot to the mold reulting in a temperature difference at ingot/mold interface (5). The gap i particularly viible by the dark line that can be een at that very interface. Fig. 9: illutration of the evolution of carbon egregation at different time of proce. It may be noted that egregation begin a oon a the filling phae in liquid and muhy metal area. Fig. 10: Illutration of the ferrotatic preure in the liquid portion of the olidifying metal (left). The ditribution of preure in layer according to the height of the ingot (gravity direction) how that the behavior of the liquid portion of the metal i fully taken into account in the calculation. The thin line repreent the muhy zone eparating the liquid from the olid. Ditribution of the firt principal tre (right). Poitive value mainly how the tenile tate of the area. On the other hand, the abence of pace around the central leeve indicate that the ingot i contracted mainly around the leeve, a priori expected reult in thi configuration.

10 Connection with forging phae The imulation of the complete chain of the making proce involve that a lole tranfer between the cating and the forging tep i performed [10], [11], [12]. Only the fact that the two oftware are haring the ame core tructure enure uch a fully compatibility of reult. Thi tranfer operation between the two product i therefore imple and natural way. Thank to thi coupling between the cating oftware and the forging one, the reult at the end of olidification are tranferred to the calculation of forging to tart drawing pa with precie ditribution. In particular, the criteria for poroity, egregation and concentration of chemical element are paed to forging oftware. It i therefore undertood the value of uch a coupling in tracking development reulting from cating tep. For example, the prediction of poroity cloing in forging tep will rely on a tarting ditribution that i the end of cating calculation (Fig.11). Similarly, by tranferring concentration of chemical element, it will be poible to follow the carbon impoverihed and enriched area during all ubequent forging operation. For the treated cae, the tranfer operation will alo conit in cutting the rier and feed channel of the meh reulting from cating tep. Then all of the meh of the leeve (360 ) i performed by ymmetrization. Fig. 11: Example and reult tranferred from cating oftware to forging during tranition between the cating proce and the forging proce. On the left, area of high rik of preence of poroitie. On the right, the ditribution of the carbon concentration at the end of olidification Forging tep The incremental forging operation on the hollow ingot will allow to obtain the final geometry but alo to impart metallurgical and mechanical propertie to the piece. For example, one ha to enure that at the end of the forging poroitie will be cloed. Thee forging operation and their control therefore fall of great importance both in the quality and life of the final component and on the financial apect. Alo, it i eay to undertand the trategic invetment that repreent the numerical imulation a an aid to deign for the manufacture of thi type of product: validation of the et of troke, prediction of the number of heater, dimenional prediction, prediction of mechanical and metallurgical propertie. The hollow ingot will undergo two forging operation: a drawing operation on the mandrel to tretch from a length of 3m to 4m length while maintaining a certain thickne. Then an operation of becking to expand it diameter from 1800m to 2100m will be carried out. The drawing mandrel operation will alo help cloing the poroitie potentially preent at the end of olidification. Similarly to the cating oftware, the model ued in the forging oftware to repreent the material behavior i EVP. Thermal and mechanical phenomena are olved in a coupled manner. The drawing mandrel i compried of a ingle pa, and 114 hot are given. Between each hot piece undergoe either a rotation or a tranlation. Similarly, a becking pa of 240 hot i made

11 with a rotation of 20 of the ring between each blow. Given the high number of movement of the hell between hot, it i undertandable that the difficultie of the numerical imulation for thi type of proce will be to communicate effectively all thee movement to the workpiece; movement during which there i no platic deformation. Note that i generally true for all open die forging procee. Thi i actually poible in the forging oftware through the ue of a dedicated control file in which the detail of each pa the number of troke, movement and rotation of the part, the waiting time i pecified. The link between the drawing imulation reult and becking imulation i provided naturally through chaining operation. Thi enure the tranport of any thermo-mechanical hitory between the two tep of the forging proce. Fig. 12 how how the urface including area with high rik of the preence of poroitie, coming from cating proce (Fig 11, left), i evolving in different tage of tretching, in the beginning, during and at the end. Numerical imulation allow to check the cloure of poroitie during the forging operation. Fig. 12: Evolution of the area (blue area) with high rik of poroity during drawing. Note that poroitie are cloed at the end of tretching. Fig. 13: illutration of the evolution of equivalent platic train at 50% (left) and in the end of the drawing (right)

12 C=0,25 C=0,44 Fig. 14: Ditribution of carbon in the end of drawing (carbon-depleted zone correpond to the foot of the ingot and carbon-enriched zone correpond to the top of the hollow ingot) and conideration of offet curve TC. Along with the cloure of poroitie, Fig. 13 how the evolution of the equivalent platic train during the proce. It i intereting to remark that, if one would have conidered the proce tarting from a full ingot, the ituation would have been rather different from the preent one. Indeed, the proce would have requeted a crewing tep more. But, which would have been really different i the ditribution of poroitie at the beginning of the drawing tep localized cloed to the mandrel, almot at contact. Thi reult from initial ditribution into the full ingot that i at central axi. Now, if one conider the range of equivalent platic train Fig. 13 at mandrel contact area, it appear much lower than at intermediate level and much lower again than at outide urface. That mean that cloure of poroitie localized at mandrel contact area requet a much higher forging power than the one in the preent cae. Conequently, if it i poible to reach the ame level of final product quality tarting from a full ingot, that need more tep within the whole proce, like crewing tep and certainly machining proce, hence higher cot. Monitoring concentration map of different chemical element from the olidification phae and during the drawing operation i enured by the coupling between the two oftware. The ditribution of chemical element at the end of forging i determined o that allow a more accurate calculation of ubequent heat treatment operation. In thi repect, Fig. 14 how the ditribution of carbon in the end of drawing, after being initialized by the ditribution coming from cating phae (Fig 11, right), and the influence of the variation of the rate of carbon on the CCT diagram. A explained above, the automatic tranfer from drawing to becking i carried out through a numerical chaining. Then the becking tep i launched. Fig. 15 illutrate the ditribution of temperature during thi operation. Once the forging proce completed, heat treatment can be alo treated in the end of the becking operation, taking account the carbon ditribution, thi one being tranported all over the proce.

13 Fig. 15: Ditribution of temperature during the becking tep of the proce. Concluion THECAST, a cating oftware, and FOGE, a forging one, are both indutrially ued. They allow determining the thermo-mechanical behavior of the cooling metal in ingot cating and open die forging procee. Thi paper how the interet of coupling between the two oftware, which i a powerful tool a an aid in the deign of hell produced from hollow ring. Thi coupling provide a oftware olution to monitor the complete proce chain, the prediction of poroitie, egregation, concentration of chemical element during olidification to their evolution during the phae of forging. It give a better undertanding of the internal tructure of the forged part. Thi example illutrate how nowaday numerical model could be ued in the teel indutry to improve the quality of production and the productivity. Moreover, one how how the proce tarting from a hollow ingot in the hell making can be better than tarting from rolled and welded heet or full ingot. With uch imulation tool, teel maker are able to control and optimize their proce. Beide, thi tool i thu evolving. Indeed, it i continuouly enriched through the implementation of new model from applied reearch and adding new feature. eference [1] M. Bellet et al., Proc. Int. Conf. On Cutting Edge of Computer Simulation of Solidification and Cating, Oaka, The Iron and Steel Intitute of Japan, pp , [2] M. Bellet, V.D. Fachinotti, ALE method for olidification modelling, Comput. Method Appl. Mech. and Engrg. 193 (2004) [3] O. Jaouen, Ph D. thei, Ecole de Mine de Pari, [4] F. Cote, Ph D. thei, Ecole de Mine de Pari, [5] M. Bellet et al, Proc. Int. Conf. On Cutting Edge of Computer Simulation of Solidification and Cating, Oaka, The Iron and Steel Intitute of Japan, pp , [6] M. Bellet, O. Boughanmi, G. Fidel, A partitioned reolution for concurrent fluid flow and tre analyi during olidification: application to ingot cating, Proc. MCWASP XIII, 13th Int. Conf. on Modelling of Cating, Welding and Advanced Solidification Procee, Schladming (Autria), June 17-22, 2012, A. Ludwig, M. Wu, A. Kharicha (ed.), IOP Conference Serie 33 (2012) , 6 page [7] G. Françoi, Ph D. thei, Ecole de Mine de Pari, [8] N. Triolet et al, The thermo-mechanical modeling of the teel lab continuou cating: a ueful tool to adapt proce actuator, ECCC [9] A. Kumar, M. Zaloznik, H. Combeau,International Journal of Thermal Science, vol. 54, (2012) [10] Jean-Loup Chenot et al., Advanced Numerical method for F.E. Simulation of Metal Forming Proce

14 [11] Jean-Loup Chenot et al. Numerical Simulation and Optimization of the Forging Proce, ICFC Proceeding [12] Patrice Lane, Simulation in open die forging operation, Tranvalor internal report (2009)

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