TY - JOUR A1 - Ruffini, A. A1 - Le Bouar, Y. A1 - Finel, A. A1 - Epishin, A. I. A1 - Fedelich, Bernard A1 - Feldmann, Titus A1 - Viguier, B. A1 - Poquillon, D. T1 - Dislocations interacting with a pore in an elastically anisotropic single crystal nickel-base superalloy during hot isostatic pressing N2 - The formation of pores in CMSX-4 nickel based superalloys is detrimental to the service life of the material. A way to avoid the problem is to treat the superalloys under Hot Isostatic Pressing (HIP), which enables a large volume fraction of pores to be annihilated. This paper aims to understand the contribution of plastic activity related to the gliding of dislocations on the pore annihilation. Simulations based on a phase-field model of dislocation are performed and make it possible to consider the strong anisotropy of the CMSX-4 under HIP conditions in conjunction to the strong elastic heterogeneity introduced by the pore. For pores with a radius of few micrometers, it is shown that edge parts of dislocation lines that present an extra half atomic plane oriented towards the pore are stacked above and under it in the direction which is perpendicular to their slip-planes, causing an increase of the number of dislocation along the four octahedral directions of the FCC single crystal which intersect the pore center. Results are streamlined within the isotropic elastic theory of dislocations. Effects of elastic anisotropy and dislocation reactions are also investigated in order to specify what would be the dislocation configuration around a pore in CMSX-4 under HIP conditions. Notably, the elastic anisotropy is shown to significantly modify the arrangement of dislocations close to the pore equator. Simulations also allow for the characterization of pore/dislocation interactions when dislocations are involved in Low Angle Boundaries as experimentally observed. KW - HIP KW - Superalloys KW - Dislocation KW - Pore KW - Phase-field PY - 2022 DO - https://doi.org/10.1016/j.commatsci.2021.111118 SN - 0927-0256 VL - 204 SP - 1 EP - 14 PB - Elsevier CY - Amsterdam AN - OPUS4-54220 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Ganesh, R. A1 - Gesell, Stephan A1 - Fedelich, Bernard A1 - Kuna, Meinhard A1 - Kiefer, B. T1 - Procrackplast: Eine Software zur Simulation des 3D-Risswachstums unter großen plastischen Deformationen T1 - Procrackplast: A software for simulating 3D crack growth under large plastic deformation N2 - The finite element software ProCrackPlast is developed for the automated simulation of fatigue crack growth in arbitrarily loaded three-dimensional components with large scale plastic deformations, in particular under cyclic thermomechanical (TMF) loading. ProCrackPlast is developed by extending the software Procrack, created at TU Freiberg for linear-elastic crack growth simulations. The pre-processing, FEM analysis, and the post-processing in ProCrackPlast are done by the commercial software ABAQUS. ProCrackPlast resorts to a crack growth procedure which adaptively updates the crack in finite increments based on the fracture-mechanical parameter, cyclic crack tip opening displacement ΔCTOD . Features of this software along with two application examples of fatigue crack growth in a typical cast steel, Ni-Resist, are presented in this paper to show its capability and performance. N2 - Es wird die Finite-Element-Software ProCrackPlast vorgestellt, die eine automatische Simulation der Ermüdungsrissausbreitung in beliebig belasteten dreidimensionalen Bauteilen mit größeren plastisch verformten Bereichen ermöglicht, insbesondere bei thermomechanischer Wechselbelastung (TMF). ProCrackPlast entstand durch Erweiterung des Programs ProCrack, das an der TU Freiberg für linear-elastische inkrementelle Rissfortschrittsanalysen entwickelt wurde. Das Pre-Processing, die FEM Analyse und das Post-Processing werden mit Hilfe der kommerziellen FE-Software ABAQUS durchgeführt. ProCrackPlast beruht auf einem Algorithmus, mit dem der Rissfortschritt adaptiv in endlichen Inkrementen unter Verwendung des bruchmechanischen Parameters der zyklischen Rissöffnungsverschiebung ΔCTOD gesteuert wird. Die Funktionseigenschaften dieser Software werden anhand von zwei Anwendungsbeispielen zum Ermüdungsrisswachstum für einen typischen Stahlguss, Ni-Resist, exemplarisch dargestellt, um die Möglichkeiten und Leistungsfähigkeit von ProCrackPlast zu demonstrieren. T2 - 54. Tagung des Arbeitskreises "Bruchmechanik und Bauteilsicherheit" CY - Online meeting DA - 22.02.2021 KW - Automated finite element analysis KW - Automatische Finite Element Simulation KW - Thermomechanical fatigue KW - Crack growth KW - Thermomechanische Ermüdung KW - Rissausbreitung PY - 2022 SP - 205 EP - 214 PB - Deutscher Verband für Materialforschung und -prüfung e.V. AN - OPUS4-54435 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - 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 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-542309 DO - https://doi.org/10.1002/adem.202101341 VL - 2022 PB - Wiley AN - OPUS4-54230 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - CONF A1 - Viguier, B. A1 - Epishin, A. A1 - Fedelich, Bernard T1 - Creep of single-crystals of nickel-base gamma-alloy at high temperatures N2 - 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. T2 - 15th International Conference on Creep and Fracture of Engineering Materials and Structures CY - Online meeting DA - 14.06.2021 KW - Nickel-base superalloys KW - Creep KW - Single-Crystal PY - 2021 AN - OPUS4-53935 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 DO - 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 - Kindrachuk, Vitaliy A1 - Klunker, Andre T1 - Phase field modeling of Hertzian cone cracks under spherica indentation N2 - A phase field model of brittle fracture has been developed to simulate the Hertzian crack induced by penetration of a rigid sphere to an isotropic linear-elastic half-space. The fracture formation is regarded as a diffusive field variable, which is zero for the intact material and unity if there is a crack. Crack growth is assumed to be driven by a strain invariant. The numerical implementation is performed with the finite element method and an implicit time integration scheme. The mechanical equilibrium and the phase field equations are solved in a staggered manner, sequentially updating the displacement field and the phase field variable. Numerical examples demonstrate the capability of the model to reproduce the nucleation and growth of the Hertzian cone crack. KW - Hertzian cracks KW - Phase field model KW - Contact mechanics PY - 2021 DO - https://doi.org/10.1007/s11223-021-00251-9 VL - 52 IS - 6 SP - 967 EP - 974 AN - OPUS4-52276 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 orientation and elastic properties N2 - The elastic constants are the most basic mechanical properties of a material and are needed for any structural analysis of a component. For example, they have a major influence on the eigenfrequencies of vibrating parts. Single crystals of Ni-base superalloys are strongly anisotropic, which means that the observed properties are orientation dependent. Tensor algebra is then required to mathematically formulate the elastic properties and their relations to the crystal orientation. Hence, this chapter first summarizes some basic definitions and calculation rules for Rotation matrices, including the definition of the Euler angles, which are most commonly used to define the relative orientations of the crystal and the component. Parts of this chapter closely follow the lines of the excellent exposition of the topic by Olschewski. KW - Nickel-base superalloys KW - Elasticity PY - 2022 SN - 978-0-12-819357-0 SP - 41 EP - 67 PB - Elsevier Inc. AN - OPUS4-53435 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 - JOUR A1 - Epishin, A. A1 - Camin, B. A1 - Hansen, L. A1 - Heuser, M. A1 - Lopez-Galilea, I. A1 - Ruttert, B. A1 - Theisen, W. A1 - Fedelich, Bernard T1 - Refinement and Experimental Validation of a Vacancy Model of Pore Annihilation in Single-Crystal Nickel-Base Superalloys during Hot Isostatic Pressing N2 - Initially, as-cast and homogenized single crystals of nickel-base superalloy CMSX-4 are subjected to hot isostatic pressing at 1288 °C. Two series of experiments are conducted: under the same pressure of 103 MPa but with different durations, between 0.5 and 6 h, and under different pressures, between 15 and 150 MPa, but for the same time of 0.5 h. The porosity annihilation is investigated metallographically and by high-resolution synchrotron X-ray tomography. The obtained experimental results are compared with the predictions of the vacancy model proposed recently in the group. Herein, the model is further refined by coupling with X-ray tomography. The model describes the evolution of the pore arrays enclosed in the 3D synchrotron tomograms during hot isostatic pressing and properly predicts the time and stress dependences of the pore annihilation kinetics. The validated model and the obtained experimental results are used for selecting the optimal technological parameters such as applied pressure and processing time KW - Superalloys KW - HIP KW - Single-Crystal KW - Diffusion PY - 2021 UR - https://nbn-resolving.org/urn:nbn:de:kobv:b43-526859 DO - https://doi.org/10.1002/adem.202100211 VL - 23 IS - 7 SP - 211 AN - OPUS4-52685 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER - TY - JOUR A1 - Epishin, A. A1 - Bokstein, B. A1 - Svetlov, I. A1 - Fedelich, Bernard A1 - Feldmann, Titus A1 - Le Bouar, Y. A1 - Ruffini, A. A1 - Finel, A. A1 - Viguier, B. A1 - Poquillon, D. T1 - A vacancy model for pore annihilation during hot isostatic pressing of single-crystal nickel-base superalloys N2 - An improved diffusion model is proposed for pore annihilation during HIP of single-crystal nickel-base superalloys. The model assumes the pore dissolution by emission of vacancies and their sink to the low angle boundaries. Calculation, considering distribution of the pore sizes, predicts the kinetics of pore annihilation similar to the experimental one. KW - Single crystal superalloys KW - Hot isostatic pressing (HIP) KW - Porosity KW - Diffusion KW - Vacancies PY - 2018 DO - https://doi.org/10.1134/S2075113318010100 SN - 2075-1133 VL - 9 IS - 1 SP - 57 EP - 65 PB - Pleiades Publishing, Ltd. AN - OPUS4-43990 LA - eng AD - Bundesanstalt fuer Materialforschung und -pruefung (BAM), Berlin, Germany ER -