- Email: [email protected]
Modelling and computer simulation for the manufacture by powder HIPing of blanket shield components for ITER
Fusion Engineering and Design 82 (2007) 2001–2007
Modelling and computer simulation for the manufacture by powder HIPing of blanket shield components for ITER O. Gillia b,∗ , B. Boireau a , C. Boudot a , A. Cottin a , P. Bucci b , F. Vidotto b , J.-M. Leibold b , P. Lorenzetto c a
AREVA NP Technical Centre Porte Magenta 1 rue B. Marcet, BP 191, 71200 Le Creusot Cedex, France b CEA/Grenoble DRT/LITEN, 17 rue des Martyrs, 38054 Grenoble Cedex 09, France c EFDA Close Support Unit, Boltzmannstr. 2, D-85748 Garching, Germany Received 28 July 2006; received in revised form 19 March 2007; accepted 19 March 2007 Available online 11 May 2007
Abstract Modelling and computer simulation have been developed in order to assist the hot isostatic pressing (HIP) fabrication of a shield prototype for the ITER blanket. Problems such as global bending of the whole part and deformations of tubes in their powder bed are addressed. It is important that the part does not bend too much. It is important as well to have circular shape of the cooling tube after HIP. For simulation purposes, the behaviour of the different materials is modelled. Although the modelling of the massive stainless steel behaviour is not neglected, the most critical modelling is about the stainless steel powder. For this study, a thorough investigation on the basic powder behaviour has been performed with some in situ HIP dilatometry experiments. These experiments have allowed the identification of a compressible viscoplastic model: improved Abouaf model by taking into account some strain hardening of the powder material. Some other important modelling side effects such as coupling of thermal properties of the powder with density are also taken into account. Validity of the modelling has been assessed with several fabricated partial scale mock-ups in terms of global shape changes with 3D simplified FEM mesh and local deformations of the tubes with 2D detailed FEM mesh. The simulation has also been used as a tool to study some particular local configurations of tube embedded in powder when designing rear side of the shield prototype. © 2007 Elsevier B.V. All rights reserved. Keywords: Shield blanket module; Modelling; HIP; Powder
1. Introduction
∗
Corresponding author. Tel.: +33 4 38 78 62 07; fax: +33 4 38 78 58 91. E-mail address: [email protected] (O. Gillia). 0920-3796/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2007.03.037
In components of blanket modules for ITER, intricate cooling networks are needed in order to evacuate all heat coming from the plasma. Hot isostatic pressing (HIP) technology is a very convenient method to
2002
O. Gillia et al. / Fusion Engineering and Design 82 (2007) 2001–2007
produce near net shape components with complex cooling network through massive stainless steel parts by bonding together tubes inserted in grooves machined in bulk stainless steel. Powder is often included in the process so as to release difficulties arising with gaps closure between tube and solid part or between several solid parts. However, inserting powder in the assembly means densification, i.e. volume change of powder during the HIP cycle. This leads to global and local shape changes of HIPed parts. In order to control the deformations, modelling and computer simulation are used. This simulation technique has already been used to model fusion components [1]. This paper presents improvement in terms of a better experimental knowledge on 316LN powder densification and modelling the thermal properties of the powder. The simulation associated to the shield manufacturing aims at two objectives: (1) to predict the final shape of the HIPed shield to check whether the deformations are reasonably low and to emit recommendations on the way to counteract too large deformations; (2) to help the designer to draw the rear face details for guiding cooling pipes in the powder. The tubes should not deform too much during HIPing both to avoid their failure and to keep an acceptable circular shape because of non-destructive examination requirement. Generally, 3D simulations with rough geometry model are performed in order to address objective (1) and 2D finer models to address objective (2), but it has been revealed that details from point (2) can have significant influences on global shapes changes. In the following, the model and equations are presented then the parameter identification is described. Other hypothesis introduced in the simulation are also detailed, particularly how non-stationary thermal effects are handled. Then some applications are presented and discussed. 1.1. Modelling Modelling HIP cycle requires the knowledge of the materials behaviour in the 20–1100 ◦ C temperature range. A sufficiently extended experimental database and a theoretical law are needed. This part describes
the equations used to model the behaviours of massive stainless steel and stainless steel powder under HIP conditions. 1.2. Modelling the solid part behaviour during the HIP cycle The modelling of the behaviour of massive (dense) material such as shield 316LN core or container, tooling or tubes, is quite usual; we simply use a viscoplastic law. A Ph.D. by Martinez [2] is profitable in that field, since it gives a viscoplastic law for massive 316LN. The modelling of the behaviour is achieved by a classical Chaboche law incorporating isotropic and kinematical hardening. These many parameters require quite an important set of experiments such as tensile tests with relaxation and cyclic loading to be identified. This law is obviously more sophisticated than required for the simulation of the HIP since our aim is to model the monotonic heating phase of the cycle when the powder densifies. 1.3. Modelling the powder behaviour during the HIP cycle In the field of modelling powder behaviour during HIP, CEA Grenoble benefits from several Ph.D. Thesis and a considerable work done at Grenoble (INPG, UJF, CEA) [3–5]. However, the law used in this study has not exactly the same expression as commonly used. The usual Abouaf’s law has been slightly modified, it is upgraded with taking into account some isotropic hardening. This modification was motivated by the fact that, for a 316LN powder material, a law without any isotropic hardening gives very poor results when trying to adjust the parameters on classical tensile tests under 800 ◦ C. We place ourselves in the frame of the theory of generalised standard material in which the viscous pseudo-potential Ω depends only on the positive part of the viscous stress Ω(σvp ). In the case of the present work, the viscous stress is written: σvp = σeq (σ, ρ) − R(p)
(1)
where p is the hardening variable and ρ is the instantaneous relative density of the material. The equivalent
O. Gillia et al. / Fusion Engineering and Design 82 (2007) 2001–2007
stress is written: σeq (σ, ρ) = f (ρ)I12 + 23 c(ρ)J22
Table 1 HIP cycle used for manufacturing the shield blanket component
(2)
where I1 = tr[σ], J22 = tr[σ 2 ] and σ are the deviatoric stress tensor. f(ρ) regulates the compressible behaviour of the material and c(ρ) regulates the deviatoric behaviour of the material. Let us remark that the physics requires that f(ρ) → 0 and c(ρ) → 1 when ρ → 1 so we tend to the classical Von Mises equivalent stress when approaching a dense material. The potential is chosen to be the extension of the Norton’s law (namely Odqvist law) which we write as: σvp (ρ) n(T )+1 1 Ω(σvp ) = (3) n(T ) + 1 K0 (T ) where n(T) and K0 (T) are the parameters. The derivation of the potential with respect to the dual variables gives the viscoplastic strain rate tensor: σeq − R n f × I1 × I + (2/3)c × σ ε˙ vp = (4) K0 σeq We have now to provide some evolution law for the internal variables R and ρ. R will vary according to: R(p, T ) = RMAX − (RMAX − KK) e−BR×p
2003
(5)
and, due to mass conservation, ρ will vary according to: ρ˙ (6) = −tr[˙εvp ] ρ The parameters of the model are thus RMAX(T), KK(T), BR(T), n(T), K0 (T) and f(ρ), c(ρ). Let remark that this law is advantageous in the sense that it decouples the dependence on the temperature and on the relative density. It is thus very practical to assume that the parameters of the viscous law (RMAX(T), KK(T), BR(T), n(T), K0 (T)) can be experimentally determined on the dense massive material during tensile tests. The f(ρ) and c(ρ) parameters are determined subsequently on porous samples with the help of in situ dilatometry experiments.
Time (h)
Temperature (◦ C)
Pressure (bar)
0 4 8 16
20 1100 1100 20
0 1400 1400 0
For the porous properties of the f(ρ) function has been adjusted on a densification curve from the result of in situ dilatometry experiments. The HIP cycle used to identify the parameter is the same as the one retain for the HIP of real components. It is given in Table 1. The function c(ρ) can be adjusted on compression tests results performed on samples from interrupted HIP cycles that are not available at the moment. Consequently, another function s(ρ) linked to c(ρ) has been adjusted on the bended shape of a trial small mock-up SEMU0 which dimension, FEM mesh and deformed shape are presented in Fig. 1. Fig. 2 shows the good accuracy obtain after fitting the function s(ρ) on the shape of SEMU0 component. 1.5. Thermo-elastic parameters To finalize the models, the thermo-elastic parameters are needed. All the thermo-mechanical parameters of dense materials are taken from ref. [6]. For the powder, the variation with ρ is needed. This introduces thermo-mechanical coupling: the Young’s modulus depends on temperature and relative density and the thermal parameters depends on temperature and density as well. The Young’s modulus depends on relative
1.4. Model parameters identification for the powder For the bulk dense material, the law has been identified on different tensile tests.
Fig. 1. One-fourth of the deformed geometry and FEM mesh of the SEMU0 mock-up.
2004
O. Gillia et al. / Fusion Engineering and Design 82 (2007) 2001–2007
Fig. 2. Shape of the SEMU0 on its symmetrical plane along its longer dimension after adjusting the c(ρ) parameter.
Fig. 3. Normalized thermal diffusivity (h(ρ)/ρ) vs. relative density.
2. Applications density ρ through the equation: E(ρ, T ) = E(T )(0.1 + 0.9ρ12 )
(7)
This expression adjusts on results obtain on cold compacted samples in ref. [7]. In the case of large parts such a shield blanket, the non-stationary thermal effects during HIP are quite important. They can result in strong non-homothetic thermal deformation of the component and/or densification delays in some powder zones. In the powder, the conductivity k varies with relative density as well as the density of the material d whereas we chose that the heat capacity c does not vary. This is expressed by: k(ρ, T ) = kd (T )h(ρ) c(ρ, T ) = cd (T )
2.1. Simulation of the bending of a small elementary mock-up The model was applied to a fabricated SEMU6 mock-up. This mock-up includes a tube placed in a groove, and guided between two 316LN blocks at a point. Its shape is visible in Fig. 4. The 3D FEM model built assumes a simple two layers geometry, 100 mm of dense 316LN and 70 mm of powder encapsulated in a 2 mm thick 304L container. Fig. 4 shows the results of the simulation compared to the shape measured on fabricated component. Although the simulated bending does not fit perfectly the experimental profile, the results is acceptable if we consider that all the details of the inserted tube in a groove and the two blocks are not taken into account in the simulation. This explains why the shape of the fabricated part is not symmetrical.
(8)
d(ρ, T ) = dd (T )ρ where the subscript “d” denotes the property of the dense material and h(ρ) is a function of the relative density in the range [0:1]. Logically, the density d(ρ) depends linearly on the relative density. Argento [5] has proposed an expression for h(ρ) which is shown in Fig. 3. The adopted law retained for the completion of this study is an approximation of Argento’s law specially adapted around the initial density in order to avoid numerical problem arising when ρ tends to the initial density ρ0 = 0.67.
2.2. Application to the control of tube shape after HIP The rear face design consists in tubes placed in a powder bed. It also includes some grooves (narrow) and channels (large) in which tubes and powder are introduced. The simulation has been used in order to help the design of the rear face details. Fig. 5 shows the simulation of small elementary mock-ups on several configurations of a tube inserted in powder and groove. The dark zone emphasizes the powder shape after densification (no porosity left). The important deformation
O. Gillia et al. / Fusion Engineering and Design 82 (2007) 2001–2007
2005
Fig. 4. SEMU6, comparison between simulated bending and fabricated mock-up.
of the container is also visible. The simulation thus permits to precisely anticipate the volumetric shrinkage of the initial container in order to adjust its initial dimensions keeping in mind that the less powder the better. It appears that the tube shape is quite sensible to its position into a groove. The tube is quite ovoid when placed in a deep groove. Let remark as well that the presence of a deep groove generates a strong deformation of the whole part, the loss of volume when the powder densifies between the two walls of the groove
produces strong forces that are able to close the groove even though the global stiffness of the mock-up seems quite high. Another simulation is presented in Fig. 6. This example underlines the influence of the presence of a deep channel in an axi-symmetric part. At the end of the HIP, the part with a channel full of powder exhibits a strong bending deformation. As stated before, this is
Fig. 5. Deformed shape of several configurations of tubes placed in grooves.
Fig. 6. Influence of a large powder channel on global shape bending, without and with a dense insert of 316LN.
2006
O. Gillia et al. / Fusion Engineering and Design 82 (2007) 2001–2007
Fig. 7. Mesh and deformed shape of a 3D model of the shield blanket component after simulation of the HIP process. Only half of the shield is simulated. Dark zones corresponds to high vertical displacement. Numbers 0–5 locates the castellations.
due to the local change of volume of the powder in the channel. A comparison with a simulation done with a massive 316LN insert placed in the channel permits to estimate the part of the bending due to the channel compared to the bending due to the presence of powder above a flat thick solid 316LN base. This example sets that details such as channels have to be taken into account in the modeled geometry when wanting to simulate global shape changes of components. 2.3. Application to the prediction of shape changes of the shield blanket The shield blanket is composed by a solid (dense) 316LN base drilled with a set of parallel hole terminated by water boxes ensuring water distribution
Fig. 8. Cut at 2/3 of shield blanket component length showing temperature gradients during the HIP cycle (t = 3 h 20 min).
between holes. Some cuts (castellations) are made between the holes from the front side. On the back face of this component, a more complex cooling circuit has been designed. It is obtain by tubes embedded in powder. During HIP, due to powder densification, the shield is expected to bend. A simulation tacking into account the geometry machined in the bulk 316LN base has been performed. Fig. 7 shows the shape of the shield blanket component after simulation of the HIP. The sagging of the container on the back side is clearly visible where channels are deeper (dark zones). The curves presented in Fig. 9 are showing the evolution of the bending and of the castellation apertures during HIP. Their shape is somehow complicated. This is mainly due to non-stationary thermal effects coupled with complex densification process. Fig. 8 shows for instance the thermal field when external temperature
Fig. 9. Evolution of the bending and the castellation aperture during HIP cycle.
O. Gillia et al. / Fusion Engineering and Design 82 (2007) 2001–2007
is 865 ◦ C. At low density, the powder conduction is poor, so that temperature gradients are enhanced. Consequently, all the powder zones does not densify the same way. The evolution curves of the bending clearly show that the expected bending is not uniform along the shield (points 1–3 does not give the same bending), this depends on the powder arrangement on the rear face design. The aperture of the castellations has also been monitored in the middle of the component. It appears that the central castellations (1–3) are opening more than the other, with a much higher value for castellation 0. If the castellation slits are bonded at their extremities, the central aperture of the castellation (1–3) is significantly diminished. The bending is also strongly lowered.
3. Conclusion The modelling have been advantageneously used when designing the geometry of the shield blanket’s rear face incorporating tubes embedded in powder. Two aspects have been addressed: controlling the shape changes of the global component during the HIP cycle and guiding the way tubes are placed into the powder bed. Validations took place on several small elementary mock-ups and on a partial full-scale mock-up. The manufacturing of the complete shield blanket component will take place in a few weeks. This will provide the final validation of the model.
2007
Acknowledgements This work, supported by the European Communities under the contract EFDA/03-954 was carried out within the framework of the European Fusion Development Agreement. The views and opinions expressed herein do not necessarily reflect those of the European Commission. References [1] G. Le Marois, L. Federzoni, P. Bucci, P. Revirand, HIP technologies for fusion reactor blankets fabrication, Fusion Eng. Des. 49–50 (2000) 577–583. [2] M. Martinez, Jonction 16MND5-Inconel 690-316LN par soudage-diffusion—Elaboration et calcul des contraintes r´esiduelles de proc´ed´e, Ph.D., Ecole des Mines de Paris, 1999. [3] M. Abouaf, Mod´elisation de la compaction de poudres m´etalliques fritt´ees, Approche par la m´ecanique des milieux continus, Ph.D., Universit´e Joseph Fourier, Grenoble I, Grenoble (France), 1985. [4] O. Bouaziz, Mod´elisation thermom´ecanique du comportement d’une poudre d’acier inoxydable—Application a` la mise en forme par CIC, Ph.D., Universit´e Joseph Fourier, Grenoble I, 1997. [5] C. Argento, Mod´elisation du comportement thermique et m´ecanique des poudres m´etalliques, Ph.D., Universit´e Joseph Fourier, Grenoble I, 1994. [6] Material Properties Handbook—ITER Document S 74 RE 1, ITER-AA03-3112, 2003. [7] P. Mosbah, Etude exp´erimentale et mod´elisation du comportement de poudres m´etalliques au cours du compactage en matrice ferm´ee, Ph.D., Universit´e Joseph Fourier, Grenoble I, 1995.
Modelling and computer simulation for the manufacture by powder HIPing of blanket shield components for ITER O. Gillia b,∗ , B. Boireau a , C. Boudot a , A. Cottin a , P. Bucci b , F. Vidotto b , J.-M. Leibold b , P. Lorenzetto c a
AREVA NP Technical Centre Porte Magenta 1 rue B. Marcet, BP 191, 71200 Le Creusot Cedex, France b CEA/Grenoble DRT/LITEN, 17 rue des Martyrs, 38054 Grenoble Cedex 09, France c EFDA Close Support Unit, Boltzmannstr. 2, D-85748 Garching, Germany Received 28 July 2006; received in revised form 19 March 2007; accepted 19 March 2007 Available online 11 May 2007
Abstract Modelling and computer simulation have been developed in order to assist the hot isostatic pressing (HIP) fabrication of a shield prototype for the ITER blanket. Problems such as global bending of the whole part and deformations of tubes in their powder bed are addressed. It is important that the part does not bend too much. It is important as well to have circular shape of the cooling tube after HIP. For simulation purposes, the behaviour of the different materials is modelled. Although the modelling of the massive stainless steel behaviour is not neglected, the most critical modelling is about the stainless steel powder. For this study, a thorough investigation on the basic powder behaviour has been performed with some in situ HIP dilatometry experiments. These experiments have allowed the identification of a compressible viscoplastic model: improved Abouaf model by taking into account some strain hardening of the powder material. Some other important modelling side effects such as coupling of thermal properties of the powder with density are also taken into account. Validity of the modelling has been assessed with several fabricated partial scale mock-ups in terms of global shape changes with 3D simplified FEM mesh and local deformations of the tubes with 2D detailed FEM mesh. The simulation has also been used as a tool to study some particular local configurations of tube embedded in powder when designing rear side of the shield prototype. © 2007 Elsevier B.V. All rights reserved. Keywords: Shield blanket module; Modelling; HIP; Powder
1. Introduction
∗
Corresponding author. Tel.: +33 4 38 78 62 07; fax: +33 4 38 78 58 91. E-mail address: [email protected] (O. Gillia). 0920-3796/$ – see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.fusengdes.2007.03.037
In components of blanket modules for ITER, intricate cooling networks are needed in order to evacuate all heat coming from the plasma. Hot isostatic pressing (HIP) technology is a very convenient method to
2002
O. Gillia et al. / Fusion Engineering and Design 82 (2007) 2001–2007
produce near net shape components with complex cooling network through massive stainless steel parts by bonding together tubes inserted in grooves machined in bulk stainless steel. Powder is often included in the process so as to release difficulties arising with gaps closure between tube and solid part or between several solid parts. However, inserting powder in the assembly means densification, i.e. volume change of powder during the HIP cycle. This leads to global and local shape changes of HIPed parts. In order to control the deformations, modelling and computer simulation are used. This simulation technique has already been used to model fusion components [1]. This paper presents improvement in terms of a better experimental knowledge on 316LN powder densification and modelling the thermal properties of the powder. The simulation associated to the shield manufacturing aims at two objectives: (1) to predict the final shape of the HIPed shield to check whether the deformations are reasonably low and to emit recommendations on the way to counteract too large deformations; (2) to help the designer to draw the rear face details for guiding cooling pipes in the powder. The tubes should not deform too much during HIPing both to avoid their failure and to keep an acceptable circular shape because of non-destructive examination requirement. Generally, 3D simulations with rough geometry model are performed in order to address objective (1) and 2D finer models to address objective (2), but it has been revealed that details from point (2) can have significant influences on global shapes changes. In the following, the model and equations are presented then the parameter identification is described. Other hypothesis introduced in the simulation are also detailed, particularly how non-stationary thermal effects are handled. Then some applications are presented and discussed. 1.1. Modelling Modelling HIP cycle requires the knowledge of the materials behaviour in the 20–1100 ◦ C temperature range. A sufficiently extended experimental database and a theoretical law are needed. This part describes
the equations used to model the behaviours of massive stainless steel and stainless steel powder under HIP conditions. 1.2. Modelling the solid part behaviour during the HIP cycle The modelling of the behaviour of massive (dense) material such as shield 316LN core or container, tooling or tubes, is quite usual; we simply use a viscoplastic law. A Ph.D. by Martinez [2] is profitable in that field, since it gives a viscoplastic law for massive 316LN. The modelling of the behaviour is achieved by a classical Chaboche law incorporating isotropic and kinematical hardening. These many parameters require quite an important set of experiments such as tensile tests with relaxation and cyclic loading to be identified. This law is obviously more sophisticated than required for the simulation of the HIP since our aim is to model the monotonic heating phase of the cycle when the powder densifies. 1.3. Modelling the powder behaviour during the HIP cycle In the field of modelling powder behaviour during HIP, CEA Grenoble benefits from several Ph.D. Thesis and a considerable work done at Grenoble (INPG, UJF, CEA) [3–5]. However, the law used in this study has not exactly the same expression as commonly used. The usual Abouaf’s law has been slightly modified, it is upgraded with taking into account some isotropic hardening. This modification was motivated by the fact that, for a 316LN powder material, a law without any isotropic hardening gives very poor results when trying to adjust the parameters on classical tensile tests under 800 ◦ C. We place ourselves in the frame of the theory of generalised standard material in which the viscous pseudo-potential Ω depends only on the positive part of the viscous stress Ω(σvp ). In the case of the present work, the viscous stress is written: σvp = σeq (σ, ρ) − R(p)
(1)
where p is the hardening variable and ρ is the instantaneous relative density of the material. The equivalent
O. Gillia et al. / Fusion Engineering and Design 82 (2007) 2001–2007
stress is written: σeq (σ, ρ) = f (ρ)I12 + 23 c(ρ)J22
Table 1 HIP cycle used for manufacturing the shield blanket component
(2)
where I1 = tr[σ], J22 = tr[σ 2 ] and σ are the deviatoric stress tensor. f(ρ) regulates the compressible behaviour of the material and c(ρ) regulates the deviatoric behaviour of the material. Let us remark that the physics requires that f(ρ) → 0 and c(ρ) → 1 when ρ → 1 so we tend to the classical Von Mises equivalent stress when approaching a dense material. The potential is chosen to be the extension of the Norton’s law (namely Odqvist law) which we write as: σvp (ρ) n(T )+1 1 Ω(σvp ) = (3) n(T ) + 1 K0 (T ) where n(T) and K0 (T) are the parameters. The derivation of the potential with respect to the dual variables gives the viscoplastic strain rate tensor: σeq − R n f × I1 × I + (2/3)c × σ ε˙ vp = (4) K0 σeq We have now to provide some evolution law for the internal variables R and ρ. R will vary according to: R(p, T ) = RMAX − (RMAX − KK) e−BR×p
2003
(5)
and, due to mass conservation, ρ will vary according to: ρ˙ (6) = −tr[˙εvp ] ρ The parameters of the model are thus RMAX(T), KK(T), BR(T), n(T), K0 (T) and f(ρ), c(ρ). Let remark that this law is advantageous in the sense that it decouples the dependence on the temperature and on the relative density. It is thus very practical to assume that the parameters of the viscous law (RMAX(T), KK(T), BR(T), n(T), K0 (T)) can be experimentally determined on the dense massive material during tensile tests. The f(ρ) and c(ρ) parameters are determined subsequently on porous samples with the help of in situ dilatometry experiments.
Time (h)
Temperature (◦ C)
Pressure (bar)
0 4 8 16
20 1100 1100 20
0 1400 1400 0
For the porous properties of the f(ρ) function has been adjusted on a densification curve from the result of in situ dilatometry experiments. The HIP cycle used to identify the parameter is the same as the one retain for the HIP of real components. It is given in Table 1. The function c(ρ) can be adjusted on compression tests results performed on samples from interrupted HIP cycles that are not available at the moment. Consequently, another function s(ρ) linked to c(ρ) has been adjusted on the bended shape of a trial small mock-up SEMU0 which dimension, FEM mesh and deformed shape are presented in Fig. 1. Fig. 2 shows the good accuracy obtain after fitting the function s(ρ) on the shape of SEMU0 component. 1.5. Thermo-elastic parameters To finalize the models, the thermo-elastic parameters are needed. All the thermo-mechanical parameters of dense materials are taken from ref. [6]. For the powder, the variation with ρ is needed. This introduces thermo-mechanical coupling: the Young’s modulus depends on temperature and relative density and the thermal parameters depends on temperature and density as well. The Young’s modulus depends on relative
1.4. Model parameters identification for the powder For the bulk dense material, the law has been identified on different tensile tests.
Fig. 1. One-fourth of the deformed geometry and FEM mesh of the SEMU0 mock-up.
2004
O. Gillia et al. / Fusion Engineering and Design 82 (2007) 2001–2007
Fig. 2. Shape of the SEMU0 on its symmetrical plane along its longer dimension after adjusting the c(ρ) parameter.
Fig. 3. Normalized thermal diffusivity (h(ρ)/ρ) vs. relative density.
2. Applications density ρ through the equation: E(ρ, T ) = E(T )(0.1 + 0.9ρ12 )
(7)
This expression adjusts on results obtain on cold compacted samples in ref. [7]. In the case of large parts such a shield blanket, the non-stationary thermal effects during HIP are quite important. They can result in strong non-homothetic thermal deformation of the component and/or densification delays in some powder zones. In the powder, the conductivity k varies with relative density as well as the density of the material d whereas we chose that the heat capacity c does not vary. This is expressed by: k(ρ, T ) = kd (T )h(ρ) c(ρ, T ) = cd (T )
2.1. Simulation of the bending of a small elementary mock-up The model was applied to a fabricated SEMU6 mock-up. This mock-up includes a tube placed in a groove, and guided between two 316LN blocks at a point. Its shape is visible in Fig. 4. The 3D FEM model built assumes a simple two layers geometry, 100 mm of dense 316LN and 70 mm of powder encapsulated in a 2 mm thick 304L container. Fig. 4 shows the results of the simulation compared to the shape measured on fabricated component. Although the simulated bending does not fit perfectly the experimental profile, the results is acceptable if we consider that all the details of the inserted tube in a groove and the two blocks are not taken into account in the simulation. This explains why the shape of the fabricated part is not symmetrical.
(8)
d(ρ, T ) = dd (T )ρ where the subscript “d” denotes the property of the dense material and h(ρ) is a function of the relative density in the range [0:1]. Logically, the density d(ρ) depends linearly on the relative density. Argento [5] has proposed an expression for h(ρ) which is shown in Fig. 3. The adopted law retained for the completion of this study is an approximation of Argento’s law specially adapted around the initial density in order to avoid numerical problem arising when ρ tends to the initial density ρ0 = 0.67.
2.2. Application to the control of tube shape after HIP The rear face design consists in tubes placed in a powder bed. It also includes some grooves (narrow) and channels (large) in which tubes and powder are introduced. The simulation has been used in order to help the design of the rear face details. Fig. 5 shows the simulation of small elementary mock-ups on several configurations of a tube inserted in powder and groove. The dark zone emphasizes the powder shape after densification (no porosity left). The important deformation
O. Gillia et al. / Fusion Engineering and Design 82 (2007) 2001–2007
2005
Fig. 4. SEMU6, comparison between simulated bending and fabricated mock-up.
of the container is also visible. The simulation thus permits to precisely anticipate the volumetric shrinkage of the initial container in order to adjust its initial dimensions keeping in mind that the less powder the better. It appears that the tube shape is quite sensible to its position into a groove. The tube is quite ovoid when placed in a deep groove. Let remark as well that the presence of a deep groove generates a strong deformation of the whole part, the loss of volume when the powder densifies between the two walls of the groove
produces strong forces that are able to close the groove even though the global stiffness of the mock-up seems quite high. Another simulation is presented in Fig. 6. This example underlines the influence of the presence of a deep channel in an axi-symmetric part. At the end of the HIP, the part with a channel full of powder exhibits a strong bending deformation. As stated before, this is
Fig. 5. Deformed shape of several configurations of tubes placed in grooves.
Fig. 6. Influence of a large powder channel on global shape bending, without and with a dense insert of 316LN.
2006
O. Gillia et al. / Fusion Engineering and Design 82 (2007) 2001–2007
Fig. 7. Mesh and deformed shape of a 3D model of the shield blanket component after simulation of the HIP process. Only half of the shield is simulated. Dark zones corresponds to high vertical displacement. Numbers 0–5 locates the castellations.
due to the local change of volume of the powder in the channel. A comparison with a simulation done with a massive 316LN insert placed in the channel permits to estimate the part of the bending due to the channel compared to the bending due to the presence of powder above a flat thick solid 316LN base. This example sets that details such as channels have to be taken into account in the modeled geometry when wanting to simulate global shape changes of components. 2.3. Application to the prediction of shape changes of the shield blanket The shield blanket is composed by a solid (dense) 316LN base drilled with a set of parallel hole terminated by water boxes ensuring water distribution
Fig. 8. Cut at 2/3 of shield blanket component length showing temperature gradients during the HIP cycle (t = 3 h 20 min).
between holes. Some cuts (castellations) are made between the holes from the front side. On the back face of this component, a more complex cooling circuit has been designed. It is obtain by tubes embedded in powder. During HIP, due to powder densification, the shield is expected to bend. A simulation tacking into account the geometry machined in the bulk 316LN base has been performed. Fig. 7 shows the shape of the shield blanket component after simulation of the HIP. The sagging of the container on the back side is clearly visible where channels are deeper (dark zones). The curves presented in Fig. 9 are showing the evolution of the bending and of the castellation apertures during HIP. Their shape is somehow complicated. This is mainly due to non-stationary thermal effects coupled with complex densification process. Fig. 8 shows for instance the thermal field when external temperature
Fig. 9. Evolution of the bending and the castellation aperture during HIP cycle.
O. Gillia et al. / Fusion Engineering and Design 82 (2007) 2001–2007
is 865 ◦ C. At low density, the powder conduction is poor, so that temperature gradients are enhanced. Consequently, all the powder zones does not densify the same way. The evolution curves of the bending clearly show that the expected bending is not uniform along the shield (points 1–3 does not give the same bending), this depends on the powder arrangement on the rear face design. The aperture of the castellations has also been monitored in the middle of the component. It appears that the central castellations (1–3) are opening more than the other, with a much higher value for castellation 0. If the castellation slits are bonded at their extremities, the central aperture of the castellation (1–3) is significantly diminished. The bending is also strongly lowered.
3. Conclusion The modelling have been advantageneously used when designing the geometry of the shield blanket’s rear face incorporating tubes embedded in powder. Two aspects have been addressed: controlling the shape changes of the global component during the HIP cycle and guiding the way tubes are placed into the powder bed. Validations took place on several small elementary mock-ups and on a partial full-scale mock-up. The manufacturing of the complete shield blanket component will take place in a few weeks. This will provide the final validation of the model.
2007
Acknowledgements This work, supported by the European Communities under the contract EFDA/03-954 was carried out within the framework of the European Fusion Development Agreement. The views and opinions expressed herein do not necessarily reflect those of the European Commission. References [1] G. Le Marois, L. Federzoni, P. Bucci, P. Revirand, HIP technologies for fusion reactor blankets fabrication, Fusion Eng. Des. 49–50 (2000) 577–583. [2] M. Martinez, Jonction 16MND5-Inconel 690-316LN par soudage-diffusion—Elaboration et calcul des contraintes r´esiduelles de proc´ed´e, Ph.D., Ecole des Mines de Paris, 1999. [3] M. Abouaf, Mod´elisation de la compaction de poudres m´etalliques fritt´ees, Approche par la m´ecanique des milieux continus, Ph.D., Universit´e Joseph Fourier, Grenoble I, Grenoble (France), 1985. [4] O. Bouaziz, Mod´elisation thermom´ecanique du comportement d’une poudre d’acier inoxydable—Application a` la mise en forme par CIC, Ph.D., Universit´e Joseph Fourier, Grenoble I, 1997. [5] C. Argento, Mod´elisation du comportement thermique et m´ecanique des poudres m´etalliques, Ph.D., Universit´e Joseph Fourier, Grenoble I, 1994. [6] Material Properties Handbook—ITER Document S 74 RE 1, ITER-AA03-3112, 2003. [7] P. Mosbah, Etude exp´erimentale et mod´elisation du comportement de poudres m´etalliques au cours du compactage en matrice ferm´ee, Ph.D., Universit´e Joseph Fourier, Grenoble I, 1995.