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Single-crystal components made of nickel base superalloys contain pores after casting and homogenization heat treatment. Hot isostatic pressing (HIP), which is carried above the γ' -solvus temperature of the alloy, is industrially applied to reduce porosity. A modeling of HIP based on continuously distributed dislocations is developed in a 2D setting. Glide and climb of straight-edge dislocations, as well as vacancy diffusion, are the deformation mechanisms taken into account.
Thereby, dislocation glide is controlled by dragging a cloud of large atoms, and climb is controlled by vacancy diffusion. Relying on previous investigations of the creep behavior at HIP temperatures, it is assumed that new dislocations are nucleated at low-angle boundaries (LAB) and move through subgrains until they either reach the opposite LABs or react with other dislocations and annihilate.
Vacancies are created at the pore surface and diffuse through the alloy until they are either consumed by climbing dislocations or disappear at the LABs. The field equations are solved by finite elements. It is shown that pore shrinking is mostly controlled by vacancy diffusion as the shear stresses at the LABs are too low to
nucleate a sufficient amount of dislocations.
Porosity in single-crystal nickel-base superalloys is removed by hot isostatic pressing (HIP) at temperatures above gamma’-solvus where the material is very soft and ductile. For example, single-crystal nickel-base superalloy CMSX-4 is HIPed at temperature 1288 °C, which is slightly higher than the gamma’-solvus temperature of this alloy equal to about 1280 °C. It is assumed that pore shrinking during HIP is mostly due to dislocation creep. Such a modelling of HIP of CMSX-4 was started in our group on the base of results of creep tests of [001] single-crystals at 1288 °C [1]. However, it was found later [2] that the alloy CMSX-4 shows very strong creep anisotropy at 1288 °C. Therefore, for calibration of the creep law, creep tests of different orientations under different stress levels are required at the HIP temperature. This was the main task of present work. Single-crystals of CMSX-4 of axial orientations [001], [011], [123] and [111] were cast by VIAM Moscow and tested by BAM Berlin under creep conditions at 1288 °C and stress levels between 4 MPa and 16 MPa. At all stress levels, the creep rate increases by an order of magnitude when changing the orientation from [001] to [111] with [011] and [123] orientations in between. Such a character of creep anisotropy corresponds to the orientation dependence of the Schmid factor for octahedral glide.
The crystal viscoplasticity model developed in [1] was improved to better represent the time induced softening observed during creep. The creep tests for different stresses and orientations as well as pore closure were simulated. The results of pore closure simulation are compared with measurements of porosity decrease during Hiping.
The large number of TEM investigations and the regular microstructure
of single-crystal nickel-base superalloys has boosted the development of a number of physically motivated constitutive laws. In contrast to the more phenomenological models discussed in the next chapter, these models use dislocation densities as internal variables. Obvious advantages are that the computed densities can be compared to TEM observations and the Deformation mechanisms can be easier translated into mathematical equations.
A γ-analogue of the superalloy CMSX-4 that does not contain the strengthening γ′ -phase and only consists of the γ-solid solution of nickel has been designed, solidified as single-crystals of different orientations, and tested under creep conditions in the temperature range between 1150 and 1288 °C. The tests have revealed a very high creep anisotropy of this alloy, as was previously found for CMSX-4 at supersolvus temperature of 1288 °C. This creep anisotropy could be explained by the dominance of 〈011〉{111} octahedral slip. Furthermore, the analysis of the creep data has yielded a high value of the creep activation energy, Qc≈442 kJ/mol, which correlates with the high activation energy of Re diffusion in Ni. This supports the hypothesis that dislocation motion in the γ-matrix of Re-containing superalloys is controlled by the diffusion of the Re atoms segregating at the dislocation core. The Norton stress exponent n is close to 5, which is a typical value for pure metals and their alloys. The absence of γ′ -reprecipitation after high-temperature creep tests facilitates microstructural investigations. It has been shown by EBSD that creep deformation results in an increasing misorientation of the existing low angle boundaries. In addition, according to TEM, new low angle boundaries appear due to reactions of the a/2 〈011〉 mobile dislocations and knitting of new networks.
Single crystal superalloys usually contain pores of sizes 5-10 micro-m after casting and heat treatment. These pores can be reduced under compression by combined creep and diffusion in a subsequent treatment called Hot Isostatic Pressing (HIP). The paper presents a methodology to simulate pore shrinkage under HIP conditions in two dimensions (2D).
At the scale of the pores, which is also the scale of the sub-grains (<50 micro-m) the dislocation sources cannot be assumed to be homogeneously distributed. Thus, the applicability of classical crystal plasticity is questionable. In this case, the transport of dislocations under an applied stress from the location where they are nucleated must be explicitly modelled. This is done by solving the transport equations for the dislocation densities and the elasticity equations in 2D. The dislocations are assumed to be nucleated at Low Angle Boundaries. They glide or climb through the sub-grains with a stress dependent velocity.
The transport equations are solved by the Flux-Corrected Transport method, which belongs to the predictor-corrector class of algorithms. In the first step, an artificial diffusion is introduced, which suppresses spurious oscillations of the solution. In a second step, the solution is corrected in such a way that no additional extremes appear and that the extremes do not grow. The algorithm is validated by simulating the transport of simple distributions with a constant velocity field.
With the dislocation velocities and the computed dislocation densities, the inelastic shear rate at the slip system level is computed by integrating the Orowan equation. In the 2D-setting, three slip systems are considered. The contributions of these slip systems are summed up to obtain the total inelastic strain rate. Dislocation glide and climb and the coupling of climb with vacancies diffusion are considered.
The resolution of the equilibrium equations from the inelastic strains turned out to be prone to numerical instabilities. As an alternative, the stresses are directly computed from the distribution of geometrically necessary dislocations following the method presented in. The resulting boundary value problem is solved by the Least-Square Finite Element method.
Examples of simulations are presented for a representative region under creep tension and for a pore shrinking under external pressure.
A constitutive model for the mechanical behaviour of single crystal Ni-base superalloys under high temperature conditions has been developed in the framework of a Cooretec project in cooperation with Siemens AG, MTU Aero Engines AG and University Bayreuth. In addition to the conventional material properties e.g. elastic constants, the model requires the parameters of the initial microstructure as an input. Thus, the γ’-precipitate size and the channel width of the γ-matrix were obtained from SEM micrographs. The model uses the slip system theory and describes the movement, multiplication and annihilation of dislocations in the channels. Furthermore, the cutting of precipitates is another mechanism contributing to the plastic flow. The evolution of the morphology due to rafting and its effects on the deformation have been implemented according to. The kinematic hardening is introduced as a stress tensor to realistically represent the strain hardening of arbitrary oriented single crystals.
The mechanical behaviour of single crystal specimens has been experimentally investigated in tension tests at different strain rates and in creep tests under various loads. The constitutive model has been calibrated based on the experimental data for temperatures of 950°C and 850°C and the [001] and [111] crystallographic orientations.
Finally, a micromechanical model was created to simulate the creep response of additive manufactured polycrystalline structures. An EBSD image is taken to obtain the grain geometry and their respective orientation. The grain boundaries are discretised using cohesive elements, whereas the single crystal model was applied to each grain in the representative volume. The polycrystal model is generated using Dream3D, NetGen and other software previously developed at the BAM.
The creep behavior of single-crystals of the nickel-base superalloy CMSX-4 was investigated at 1288°C, which is the temperature of the hot isostatic pressing (HIP) treatment applied to this superalloy in the industry. It was found that at this super-solvus temperature, where no Gamma’-strengthening occurs, the superalloy is very soft and rapidly deforms under stresses between 4 and 16 MPa. The creep resistance was found to be very anisotropic, e.g. the creep rate of [001] crystals was about 11 times higher than that of a [111] crystal. The specimens of different orientations also showed a very different necking behavior. The reduction of the cross-section area psi of [001] crystals reached nearly 100%, while for a [111] crystal psi=62%. The EBSD analysis of deformed specimens showed that despite such a large local strain the [001] crystals didn’t not recrystallize, while a less deformed [111] crystal totally recrystallized within the necking zone. From the shape of deformed specimens and TEM investigations it was concluded that the main strain contribution resulted from <011> {111} octahedral slip.
The creep behavior of single crystals of the nickel-based superalloy CMSX-4 was investigated at 1288 °C, which is the temperature of the hot isostatic pressing treatment applied to this superalloy in the industry. It was found that at this super-solvus temperature, where no gammaPrime-strengthening occurs, the superalloy is very soft and rapidly deforms under stresses between 4 and 16 MPa. The creep resistance was found to be very anisotropic, e.g., the creep rate of [001] crystals was about 11 times higher than that of a [111] crystal. The specimens of different orientations also showed a very different necking behavior. The reduction of the cross-sectional area psi of [001] crystals reached nearly 100 pct, while for a [111] crystal psi = 62 pct. The EBSD analysis of deformed specimens showed that despite such a large local strain the [001] crystals did not recrystallize, while a less deformed [111] crystal totally recrystallized within the necking zone. The recrystallization degree was found to be correlated with deformation behavior as well as with dwell time at high temperature. From the analysis of the obtained results (creep anisotropy, stress dependence of the creep rate, traces of shear deformation, and TEM observations), it was concluded that the main strain contribution resulted from <01-1>{111} octahedral slip.
Les aubes de turbines à gaz utilisées en particulier pour les turboréacteurs de l’aéronautique sont élaborées par fonderie en superalliage monocristallin à base de nickel. Le procédé de fonderie, ainsi que les traitements thermique d’homogénéisation réalisés à très haute température, induisent la présence de pores au sein des pièces qui affectent les propriétés mécaniques et la durée de vie des aubes. Afin de réduire cette porosité les motoristes effectuent un traitement de compression isostatique à chaud (CIC) au cours duquel la porosité diminue par fermeture des pores. Afin de mieux comprendre les mécanismes impliqués au cours du traitement de CIC, nous avons lancé un programme de recherche dans le cadre du projet ERA-Net MICROPORE. La modélisation par champ de phase des mécanismes en jeu est présentée au cours de ce colloque. Nous présentons dans cette affiche un des volets de la caractérisation expérimentale du projet.
Des échantillons de superalliage CMSX4 sont observés après traitement de mise en solution et CIC sous 103 MPa à 1288°C pour différentes durées. Les pores présents sont caractérisés par microscopie électronique à balayage (MEB) afin de suivre l’évolution du taux de porosité au cours du traitement. Une caractérisation plus détaillée de pores partiellement refermés est menée par MEB et grâce à la diffraction des électrons rétrodiffusés (EBSD). Une vision tridimensionnelle de ces défauts est obtenue par des coupes métallographiques effectuées par découpe ionique (FIB).
Le projet ERA – Net MICROPORE est financé en Allemagne par la DFG (projects EP 136/1-1 and FE933/2-1) et en France par l’ANR (projects ANR15-MERA-000-03 and ANR15-MERA-0003-04).