FE Modelling of Investment Casting of a High Pressure Turbine Blade Under Directional Cooling

Transcription

1 FE Modelling of Investment Casting of a High Pressure Turbine Blade Under Directional Cooling S.M. Afazov*, A.A. Becker and T.H. Hyde Department of Mechanical, Materials and Manufacturing Engineering, University of Nottingham, Nottingham NG7 2RD, UK. * shukri.afazov@nottingham.ac.uk Received 3 June 2010; accepted 6 October 2010; available online 1 March Abstract This paper presents finite element (FE) simulation of an investment casting of a highpressure turbine blade (HPTB) under directional cooling. The main focus of the simulation is to highlight the difficulties of modelling the casting process and the prediction of the temperature field and residual stresses. The temperature field and the residual stresses are predicted for two withdrawal velocities. The simulation is performed in a sequential thermo-mechanical FE analysis (FEA). First, a thermal analysis is performed where the heat transfer is achieved by cavity radiation and view factor calculations. Mechanical analysis is then performed based on the temperature history from the thermal analysis. Keywords: FEA, investment casting, directional cooling, residual stresses, high-pressure turbine blade 1. Introduction The investment casting process involves the following steps. First, a wax model of the casting is prepared by injecting molten wax into a metallic mould. Next, the investment shell is produced by dipping the model into ceramic slurries. This operation is repeated until the shell thickness is adequate. Finally, the mould is baked to build up its strength. The first step involves a temperature just sufficient to melt out the wax. Further steps at high temperature are employed to fire the ceramic mould [1]. The ceramic slurries are sprinkled with coarse refractory stucco and dried. The purpose of the stucco is to minimise drying stresses in the coatings by presenting a number of stress concentration centres, which distribute and hence reduce the magnitude of the local drying stress. The second main purpose of the stucco is to present a rough surface, thus facilitating a mechanical bond between the primary coating and the back-up or secondary investment [2]. It has been found that the creep properties are improved markedly when directional solidification is used. After pouring, the casting is withdrawn at a controlled rate from the furnace. A speed of a few inches per hour is typical so that the solid/liquid interface progresses gradually along the casting, beginning at its base. This has the effect of producing large columnar grains, which are elongated in the direction of withdrawal, so that transverse grain boundaries are absent. In a variant of this process, the grain boundaries are removed entirely. Most typically, this is achieved by adding a grain selector in the form of a spiral [1]. A number of studies, carried out in the directional solidification of nickel-based blade castings, have mainly focused on investigation of the dendrite (crystal) growth and the microstructure [3-8]. 1

2 Despite the large volume of work conducted in investment casting under directional cooling, there are limited publications in FE modelling of the process, especially when complex 3D geometries such as the HPTB and built-up residual stresses are considered. The objectives of this study are to create a robust thermo-mechanical FE model with the capability of simulating an investment casting process of HPTB under directional cooling in a Bridgman furnace and predict the temperature field and the residual stresses. To achieve these objectives, many variables need to be taken into account. Generally, this can increase the complexity of the FE model where convergence difficulties can be observed. This study shows the methodology and highlights key issues and difficulties in FE modelling of the complex 3D geometry of the HPTB subjected to investment casting under directional cooling. 2. Process definition The directional solidification process is widely used in the aerospace industry for casting turbine blades with nickel-based alloys. Typically, the directional solidification process is achieved in a Bridgman furnace in the following sequence: The mould is placed on a water-cooled copper chill. The mould is placed into an induction-heated vacuum Bridgman furnace and heated by radiation above the liquidus temperature of the cast alloy. The liquid is poured into the mould. After the mould filling has finished, the mould and the casting are left for some time in the furnace to equalise the temperature of the mould and the casting. The mould with the liquid inside is withdrawn from the hot to the cold chamber of the Bridgman furnace where the directional solidification is achieved. This allows the dendrites (crystals) to start growing in the direction opposite to the withdrawal direction. The dimensions, maximum temperature, the travelling length, etc. of the Bridgman furnaces are designed according to the casting geometry and the casting material. For example, copper chill plate of the casting furnace at Rolls-Royce plc, Derby, UK has diameter of 140 mm [1]. This size is sufficient for five HPTB for a civil jet engine to be produced simultaneously. 3. FE model The investment casting process is simulated in a sequential thermo-mechanical analysis. First, the thermal analysis is carried out to obtain the temperature field of the model. Next, a mechanical analysis is performed to predict the residual stresses based on the temperature history from the thermal analysis Geometry and mesh Representative geometries of the furnace, cast and mould shell are created using SolidWorks package [9]. Figure 1 shows the FE model of the mould, cast and furnace. First, the furnace and the cast are modelled. The mould is then modelled by using the outer surface of the cast and creating a shell with a representative thickness. Jones and Yuan [2] used ceramic shell thickness achieved for polymer-modified and fibremodified shell systems of 4.6 mm and 5.31 mm respectively to investigate the strength, fired permeability and surface fracture of the shell. However, due to the complexity of the cast geometry, a mould shell thickness of 0.75 mm is achieved with the SolidWorks CAD package. This was mainly because of the spiral shape, which is connected to the bottom part of the cast and the small radii of the cast geometry. To overcome this 2

3 limitation, it is assumed that the shell thickness can be simulated by decreasing the coefficient of thermal conductivity for the mould material. This assumption is based on the fact than the mould shell thickness is modelled as a constant for the entire mould and the heat transfer is linear through the thickness due to the temperature-independent thermal conductivity coefficient of the mould material used in this study. Based on this assumption, the shell thickness of 5 mm is effectively modelled by decreasing the coefficient of thermal conductivity by times. It should be noted that this assumption could affect the heat transfer process and the built-up residual stresses respectively. The water-cooled chill plate diameter is chosen to be 140 mm, where a shell cluster assembly of five blades can be placed on it [1]. The furnace geometry is approximated based on the shell cluster assembly dimensions and the design of the Bridgman furnace [8]. Due to cyclic symmetry, only one fifth of the furnace and the cluster assembly are modelled. The furnace cast and mould shell geometries are meshed in the ABAQUS FE package [10]. Four node linear tetrahedron elements are used for the mesh of the cast, mould and copper chill. The mould is meshed with one layer of tetrahedron elements with size of the 0.75 mm. It is important to mention that meshing the mould with more than one layer of elements can predict more accurately the temperature field, but to achieve this, specialised meshing algorithms must be employed. The furnace and the holder are meshed with eight node linear hexahedron elements. The cast mesh used for the thermal analysis has 22,164 elements, while the cast mesh for the mechanical analysis has 42,946 elements. A more refined mesh is created for the mechanical analysis in order to predict more accurately the residual stresses while the number of the elements for the mesh in the thermal analysis is kept smaller due to the complexity of the thermal model which requires significant amount of computational time. Figure 1: FE model of the mould, cast and furnace 3

4 3.2. Boundary conditions The thermal analysis is simulated by applying the following boundary conditions. A constant temperature of 1500 ºC is applied to the heating elements of the furnace, which represents the heat generation in the hot chamber of the furnace. A constant temperature of 20 ºC is applied to the cold water-cooled chamber of the furnace, which represents the circulated water in the water-cooled cold chamber. An initial temperature of 1500 ºC is applied to the mould, cast, baffles, insulation and the copper-chill. These temperatures are considered with the pouring temperature of the CMSX-4 alloy of 1500 ºC [7] and the fact that after pouring the mould and the casting are left for some time in the furnace to equalise their temperatures. Air convection is applied to the outside surfaces of the furnace using a convection coefficient of 20 W/m 2 K. Forced convection of 2500 W/m 2 K is applied to represent the water circulation inside the copper chill plate. Thermal contacts are defined between the following surfaces: (a) water-cooled chill plate and mould; (b) cast and mould; (c) cast and water-cooled chill plate. The same heat transfer coefficients (HTC), as in Ref. [7], are used in this study. HTC of 20 W/m 2 K is applied between contact surfaces (a), 200 W/m 2 K between surfaces (b) and temperature dependent HTC between surfaces (c). The heat transfer inside the furnace is achieved in vacuum, where the radiation is the dominant factor. Cavity radiation is defined between the internal furnace surfaces and the external surfaces of the mould and the holder. View factor calculations, with reflections in the cavity, are included. This is based on the work carried out by Johnson [11], which has been implemented in ABAQUS. Two withdrawal velocities are applied. Withdrawal velocity of 0.06 mm/s, typically used in this type of casting [7], is compared to a relatively fast withdrawal velocity of 0.6 mm/s. The fast withdrawal velocity is used to highlight the undesirable effects of the fast cooling. It is also used to compare the residual stresses field with the withdrawal velocity of 0.06 mm/s. The mechanical analysis is simulated by applying the following boundary conditions. All components of the model, except the cast, are constrained by applying zero displacements in all directions. The cast is constrained by applying zero displacements in the z direction on one of the surfaces of the cast feeder and zero displacements in the x and z direction on the edge of the cast feeder. Gravity is also applied to the cast. Frictionless contact is specified between contact surfaces (a), (b) and (c) Simulation sequence A thermal analysis followed by a mechanical analysis is carried out in the current FE simulation. The thermal analysis is performed in two steps. In the first step, the mould and the cast are withdrawn from the hot to the cold chamber. In the second step, when the mould and the cast are located entirely in the cold chamber, the furnace is switched off. This is achieved by deactivating the constant temperature of the heating elements. The mechanical analysis is performed in three steps. The first two steps use the temperature history of the thermal analysis. Due to the two different cast FE meshes used in the thermal and the mechanical analysis, a temperature interpolation is performed from the thermal to the mechanical mesh of the cast by using the built-in algorithms in ABAQUS [10]. A third step is applied to release the cast from the mould where the contact between the mould and the cast is deactivated Material properties The cast material is CMSX-4 single crystal nickel-based alloy. The mould material is Sand Silica. The Bridgman furnace materials are considered the same as is Ref. [12]: water-cooled chill plate (copper); heating element (molybdenum), insulation and baffle 4

5 (zirconia); water-cooled chamber and holder (stainless steel). The CMSX-4 alloy is an ultra high strength second-generation nickel-based single-crystal superalloy. Temperature dependent thermo-physical and mechanical material properties of CMSX- 4 are collected from the literature and summarised in Ref. [13] where the elastic modulus up to 1100 ºC and the yield stress up to 1090 ºC are used. An elastic modulus of 250 MPa and a yield stress of 7.5 MPa are applied at the mushy zone of the alloy, as recommended in Ref. [14]. The mushy zone is the range between the liquidus and the solidus temperature of the material, e.g C for CMSX-4. A material model with isotropic hardening is used in the current FE model. The material properties used for sand silica, copper, zirconia, molybdenum and stainless steel can also be found in Ref. [13]. 4. Results As mentioned before, two withdrawal velocities are investigated. A withdrawal motion of 240 mm is used for both withdrawal velocities. This means that for applied withdrawal velocities of 0.6 and 0.06 mm/s, the directional cooling step lasts 6.6 minutes and 66 minutes respectively. The computational time for the thermal and mechanical analyses is 27 days and 3 days respectively for the model with 0.06 mm/s. The analyses are performed on a UNIX system where one CPU is occupied. The high computational time in the thermal analysis is due to the high number of time increments required at the beginning of the thermal analysis when the equilibrium of the furnace needs to be achieved due to the applied initial temperature conditions. Also, the computational time for each increment is significantly large due to the complexity of the analysis. The following technique can be used to decrease the computational time in the thermal analyses. The actual thermal equilibrium of the furnace after applying the thermal boundary conditions can be obtained in a separate thermal analysis where the mould and cast are not considered. The temperature at all nodes are saved at the end of the analysis and used as an initial condition for the thermal analysis where the mould and the cast are considered and the withdrawal velocity is applied. This technique can save computational time when different casting conditions and parameters are investigated and many analyses are required. Figure 2(a) shows the temperature contour of the cast at a withdrawal motion of 144 mm for a withdrawal velocity of 0.6 mm/s. It can be seen that the temperature is different in the cross sections of the cast, except in the bottom part where the cooling is dominant by the water circulation in the copper chill plate. Generally, the temperature difference in the cross sections allows the dendrites (crystals) to grow in the direction opposite of the withdrawal direction. This creates stray grains in the blade, which is not desirable as investigated in Ref. [5]. Figure 2(b) shows the temperature versus the time for the two steps of the thermal analysis at six points of the cast. It can be seen that all nodes are in the mushy zone at the end of the directional cooling step except node F. This means that the cast arrives in the cold chamber as non-solid. This allows the formation of equiaxed grains during the entire cooling of the cast at step two where the effect of creating grain growth in the direction of solidification might not be achieved. Figure 3(a) shows the temperature contour of the cast at the same motion of 144 mm for a withdrawal velocity of 0.06 mm/s. It can be seen that the temperature is similar in the cross sections of the cast, which avoids the formation of stray grains in the blade. Figure 3(b) shows the temperature versus the time at the same six points from the cast. It can be seen that at the end of the directional cooling step, all six points are below the solidus temperature. The graded cooling of the cast can also be seen. This allows grain growth 5

6 in the direction of solidification. In general, the predicted temperatures for the two withdrawal velocities are in line with the practical expectations. The developed FE model can be further used to investigate the influence of each variable on the temperature field of the casting process. Step 1 Step 2 Temperature (ºC) Solidus Temperature Liquidus Temperature Node A Node B Node C Node D Node E Node F (a) Time (h) Figure 2: Temperature results: (a) Temperature contour of the cast at motion of 144 mm for withdrawal velocity of 0.6 mm/s; (b) Temperature variation at nodes A, B, C, D, E and F versus the time for Step 1 (the model is withdrawn from the hot to the cold chamber of the furnace) and Step 2 (the model is located in the cold chamber of the furnace) (b) Step 1 Step 2 Temperature (ºC) Solidus Temperature Liquidus Temperature Node A Node B Node C Node D Node E Node F (a) Time (h) Figure 3: Temperature results: (a) Temperature contour of the cast at motion of 144 mm for withdrawal velocity of 0.06 mm/s; (b) Temperature variation at nodes A, B, C, D, E and F versus the time for Step 1 (the model is withdrawn from the hot to the cold chamber of the furnace) and Step 2 (the model is located in the cold chamber of the furnace) (b) 6

7 Figure 4 shows the Von Mises residual stress contours for the cast obtained for withdrawal velocities of 0.6 and 0.06 mm/s. The peak stress of 917 MPa is observed around the sharp corners for both models. It can be seen that the stresses in the lower part of the HPTB are higher at 0.6 mm/s compared to 0.06 mm/s. Figure 5 shows the Von Mises stresses obtained in the three steps of the mechanical analysis for both withdrawal velocities at six positions (see Figure 4). As mentioned before, the cast and mould are withdrawn from the hot to the cold chamber in step one, the furnace is switched off and the cluster is cooled to room temperature in step two, and finally the cast is released from the mould in step three where the residual stresses are obtained. Node A shows Von Mises stresses around MPa at step 3 for both withdrawal velocities. At the end of the cooling step two; the Von Mises stresses reach values of 900 MPa. High values are also observed for nodes B, C and D at step two. The final Von Mises stresses at step three for nodes B, C and D are slightly different. Higher Von Mises stresses (more than 8 times) are obtained for Nodes E and F at the withdrawal velocity of 0.6 mm/s compared to 0.06 mm/s when the cast is released from the mould. In general, the predicted residual stresses are lower at the withdrawal velocity of 0.06 mm/s compared to 0.6 mm/s After casting, the HPTB are machined and coated before being assembled onto the aeroengine. Another important issue in manufacturing the HPTB is its life cycles. The life mainly depends on the applied loads but also on the existing residual stresses in the HPTB. Similar to the work carried out by Afazov et al. [15], the predicted residual stresses from the developed FE model can be used to simulate the manufacturing chain of processes for producing the HPTB. The final residual stress state from the manufacturing chain can be used for estimating the life of the HPTB. The predicted residual stresses from the current FE model can also be used to predict potential crack initiations and failure based on the high stresses. (a) Figure 4: Von Mises residual stresses in MPa obtained at withdrawal velocities of: (a) 0.6 mm/s; (b) 0.06 mm/s (b) 7

8 Figure 5: Von Mises stresses obtained in three steps of the mechanical analysis for withdrawal velocities of 0.6 mm/s and 0.06 mm/s for Node A, Node B, Node C, Node D, Node E and Node F (see Figure 4) 5. Conclusions A thermo-mechanical FE simulation of investment casting of high-pressure turbine blade (HPTB) subjected to directional cooling in Bridgman furnace has been performed. The difficulties in modelling the process and key solutions have been pointed out. The simulation has been performed in sequential thermo-mechanical FEA where the simulation steps are described in detail. The thermal and mechanical FEAs have been performed for two withdrawal velocities of 0.6 mm/s and 0.06 mm/s. The temperature fields and the residual stresses have been predicted. Higher residual stresses have been determined in the lower thick part of the blade for the withdrawal velocity of 0.6 mm/s. The residual stresses in the rest of the blade have been found to be similar for both withdrawal velocities. In general, the predicted 8

9 residual stresses have been lower at the withdrawal velocity of 0.06 mm/s compared to 0.6 mm/s. The predicted residual stresses can be used in the life estimation of the HPTB. Also, the residual stresses can be considered in arriving at the most appropriate casting conditions. The predicted FE temperatures and residual stresses are in line with practical expectations. The FE model can be successfully used in investigating different casting parameters (e.g. shell thickness, withdrawal velocity, etc.) on the temperature field and the residual stress state of the HPTB. References [1] R Reed, 2006, The Superalloys Fundamentals and Applications, Cambridge University Press [2] S Jones, and C Yuan, 2003, Advances in shell moulding for investment casting, Journal of Materials Processing Technology, 135(2), PP [3] X Yang, H Dong, W Wang, and P Lee, 2004, Microscale simulation of stray grain formation in investment cast turbine blades, Material Science and Engineering A, 386(1-2), PP [4] N D Souza, M Newell, K Devendra, P Jennings, M Ardakani, and B Shollock, 2005, Formation of low angle boundaries in Ni-based superalloys, Material Science and Engineering A, , PP [5] N Hofmann, S Olive, G Laschet, F Hediger, J Wolf, and P Sahm, 1997, Numerical optimization of process control variables for the Bridgman casting process, Modelling and Simulation in Materials Science and Engineering, 5(23), PP [6] H Esaka, K Shinozuka, and M Tamura, 2005, Analysis of single crystal casting process taking into account the shape of pigtail, Material Science and Engineering A, , PP [7] P Carter, D Cox, C Gandin, and R Reed, 2000, Process modelling of grain selection during the solidification of single crystal superalloy castings, Materials Science and Engineering A, 280(2), PP [8] H Saari, J Beddoess, D Seo, and L Zhao, 2005, Development of directionally solidified γ-tial structure, Intermetallics, 13(9), PP [9] SolidWorks, 2009, User s guide [10] ABAQUS, 2009, Analysis User s Manual, Version [11] D Johnson, 1987, Surface to Surface Radiation in the Program TAU, Taking Account of Multiple Reflection, United Kingdom Atomic Energy Authority Report ND-R-1444(R) [12] H Saari, 1999, The processing of gas turbine engine hot section materials through directional solidification, Master s Thesis, Carleton University, Canada [13] S Afazov, 2009, Simulation of manufacturing processes and manufacturing chains by using FE techniques, PhD Thesis, University of Nottingham, Chapter 5 PP 92-96, [14] ProCast, 2007, User s Manual, ESI Group [15] S Afazov, S Nikov, A Becker, and Hyde TH, 2011, Manufacturing chain simulation of an aero-engine disk and sensitivity analyses of micro-scale residual stresses, International Journal of Advanced Manufacturing Technology, 52(1-4), PP