TY - JOUR A1 - Feldmann, Titus A1 - Fedelich, Bernard A1 - Epishin, A. T1 - Simulation of Hot Isostatic Pressing in a Single-Crystal Ni Base Superalloy with the Theory of Continuously Distributed Dislocations Combined with Vacancy Diffusion N2 - 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. KW - Nickel-base superalloys KW - HIP KW - Dislocation KW - Creep KW - Model PY - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:b43-542309 VL - 2022 PB - Wiley AN - OPUS4-54230 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CHAP A1 - Fedelich, Bernard ED - Cailletaud, G. ED - Cormier, J. ED - Eggeler, G. ED - Maurel, V. ED - Nazé, L. T1 - Crystal plasticity models: dislocation based N2 - 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. KW - Nickel-base superalloys KW - Creep KW - Plasticity PY - 2022 SN - 978-0-12-819357-0 SP - 401 EP - 427 PB - Elsevier Inc. ET - 1 AN - OPUS4-53436 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Fedelich, Bernard A1 - Feldmann, Titus A1 - Charmi, Amir A1 - Epishin, A. T1 - Simulation of pore shrinkage with crystal plasticity and dislocation transport N2 - 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. T2 - International Conference on Material Modelling, ICMM 6 CY - Lund, Sweden DA - 26.06.2019 KW - Superalloy KW - Pores KW - Creep KW - Dislocations PY - 2019 AN - OPUS4-48488 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Fedelich, Bernard A1 - Epishin, A. A1 - Nolze, Gert A1 - Schriever, Sina A1 - Feldmann, Titus A1 - Ijaz, M. A1 - Viguier, B. A1 - Poquillon, D. A1 - Le Bouar, Y. A1 - Ruffini, A. A1 - Finel, A. T1 - Creep of single-crystals of nickel-base superalloys at ultra-high homologous temperature N2 - 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. T2 - EuroSuperalloys 2018 CY - Oxford, UK DA - 09.09.2018 KW - Nickel-base superalloys KW - Single-crystals KW - Creep PY - 2018 AN - OPUS4-45989 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Epishin, A. I. A1 - Fedelich, Bernard A1 - Viguier, B. A1 - Schriever, Sina A1 - Svetlov, I. L. A1 - Petrushin, N. V. A1 - Saillard, R. A1 - Proietti, A. A1 - Poquillon, D. A1 - Chyrkin, A. T1 - Creep of single-crystals of nickel-base γ-alloy at temperatures between 1150 °C and 1288 °C N2 - 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. KW - Nickel alloys KW - Single-crystals KW - Creep KW - Electron microscopy KW - Deformation mechanisms PY - 2021 U6 - https://doi.org/10.1016/j.msea.2021.141880 SN - 0921-5093 VL - 825 SP - 1 EP - 13 PB - Elsevier CY - Amsterdam AN - OPUS4-53132 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Epishin, A. A1 - Fedelich, Bernard A1 - Nolze, Gert A1 - Schriever, Sina A1 - Feldmann, Titus A1 - Farzik Ijaz, M. A1 - Viguier, B. A1 - Poquillon, D. A1 - Le Bouar, Y. A1 - Ruffini, A. A1 - Finel, A. T1 - Creep of single crystals of nickel-based superalloys at ultra-high homologous temperature N2 - 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. T2 - 3rd European Conference on Superalloys (‘Eurosuperalloys 2018’) CY - Oxford, UK DA - 9.9.2018 KW - Single-crystal KW - Superalloy KW - Creep KW - Isostatic hot pressing (HIP) PY - 2018 U6 - https://doi.org/10.1007/s11661-018-4729-6 SN - 1073-5623 SN - 1543-1940 VL - 49A IS - 9 SP - 3973 EP - 3987 PB - Springer Sciences & Business Media CY - New York, NY AN - OPUS4-45660 LA - deu AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -