## 5 Werkstofftechnik

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- Superalloy (7) (entfernen)

#### Organisationseinheit der BAM

- 5.2 Experimentelle und modellbasierte Werkstoffmechanik (7) (entfernen)

Gas turbines are widely used for a variety of purposes including power generation, compression or as jet engines in aircrafts. The critical components of a gas turbine are the high-pressure turbine blades which operate under severe conditions. These include thermo-mechanical loadings over temperatures ranging from room temperature up to 1100°C.
While a large number of constitutive models for single crystals have been proposed, most applications are restricted to special loading scenarios, temperature range and deformation mechanisms. In particular, a number of models are focused on pure creep. Only a few papers consider application of both creep and fatigue. Applications of the constitutive models to long-term stress relaxation are even scarcer. The new model assumes deformation-induced softening and can properly reproduce the viscous behavior at different time scales.
The model has been calibrated with the uniaxial tests at 800°C and 950°C in [001], [011] and [111] specimens of a nickel-basis superalloy. The predicted creep, short- and long-term relaxation and cyclic tests are in reasonable agreement with the experimental observations.

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.

Data about the creep of metals and their alloys at temperatures close to the melting point are very limited. The reason is that most engineering alloys are used at temperatures below 0.6-0.8 of their melting point, so, investigation of creep at higher temperatures has usually no practical relevance. For some special applications however it is important, in our case hot isostatic pressing (HIP) of single-crystal turbine blades cast from nickel-base superalloys. In order to remove porosity the blades are HIPed at temperatures above GammaP-solvus where superalloy has no strengthening GammaP-phase and therefore is very soft. E.g., the company Howmet Castings hips the superalloy CMSX-4 at 1288°C, which corresponds to a homologous temperature of about 0.97=1561 K/1612 K (solidus temperature). Knowledge about the creep of CMSX-4 at this temperature and understanding of the creep mechanisms are necessary to model the kinetics of pore closure during HIP.
CMSX-4 single-crystals of [001] orientation and few single-crystals of different orientations, [011], [123] and [111], were tested under creep conditions at 1288°C in the stress range between 4 and 16 MPa. At this temperature which is above the GammaP-solvus (for CMSX-4 1280°C) the superalloy has single phase structure representing the Gamma-solid solution of nickel strengthened by solute atoms. On creep curves of CMSX-4 single-crystals of different orientations measured at 1288°C/10 MPa it is seen that despite such a high homological temperature, 0.97, CMSX-4 shows very high anisotropy of creep rate. The average creep rate of [001] single-crystal in the range 0-30% strain is about 11.5 time faster than that for [111], a ratio, which is even higher than at the practically relevant temperatures 750-1100°, see e.g.. Approximation the strain rate – stress dependence by the Norton power law gave a stress exponent n of about 6 which is an indication of dislocation creep. The specimen shape after testing, analysis of traces of plastic deformation by electron backscatter diffraction (EBSD) and transmission electron microscopy (TEM) investigations indicate on dislocation slip on the octahedral system <011>{11-1}.This result however does not support the current doctrine that at high temperatures creep of metals and alloys are climb controlled. It is concluded from the obtained results that even at such a high homologous temperature, 0.97, dislocation movement by slip is more preferable than by climb if only relatively week obstacles are present like solute atoms and low angle boundaries (LABs).
It is remarkable that under used testing conditions the necking and recrystallization behavior of differently oriented single-crystals is very different. E.g., the [001] single-crystal showed very large local strain during necking, Phi=99.8%, and no recrystallization (see Fig. 3a), while the [111] single-crystal small necking, Phi=62%, accompanied by recrystallization. Such a specific deformation and recrystallization has to be undestood.
The obtained creep data of CMSX-4 was introduced in a finite element model in order to simulate pore closure during commercial HIP at a temperature of 1288°C.

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).

The technological importance, the regularity of the microstructure and the complexity of the mechanical behavior of single crystal superalloys have motivated the development of a large number of mathematical models of the mechanical behavior of these alloys in the last two decades. While crystal viscoplasticity has proven to be an efficient framework to account for their anisotropy, several issues are still challenging. Indeed, most models consider that octahedral and cubic slip systems contribute to the largest part of the plastic deformation. However, the exact nature of cubic slip is still controversial and the precipitates can be sheared by <112> slip systems at intermediate temperatures, which largely influence the dependence of the flow rate on the orientation under creep conditions. Due to the different strengths of the matrix and the precipitates and the large volume fraction of the precipitate phase, a complex distribution of internal stresses exists, which can difficultly be captured by the conventional back stress models of plasticity. In addition, at high temperature, the microstructure degrades and the residual mechanical strength is reduced. The driving force for this microstructure degradation is intimately connected to the distribution of the internal stresses. As a result of this complexity, a large number of tests are usually required to fully characterize the mechanical behavior of single crystal superalloys. This in turn largely impedes the implementation of inelastic modeling in the industrial praxis.
The lecture summarizes the principal types of constitutive models for single crystal superalloys and reviews some recent advances in this area. In particular, it is shown how simulations at the microstructure scale level combined with conventional testing and microscopic analysis helped to improve our understanding of the mechanical behavior of single crystal superalloys. Directional coarsening, the importance of internal stresses, orientation dependency and the corresponding modeling issues are discussed. Also open questions are highlighted.

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.