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High Temperature Fatigue Crack Growth in Nickel-Based Alloys Refurbished by Additive Manufacturing
(2024)
Hybrid additive manufacturing plays a crucial role in the restoration of gas turbine blades, where, e.g., the damaged blade tip is reconstructed by the additive manufacturing process on the existing blade made of a parent nickel-based alloy. However, inherent process-related defects in additively manufactured material, along with the interface created between the additively manufactured and the cast base material, impact the fatigue crack growth behavior in bi-material components. This study investigates the fatigue crack growth behavior in bi-material specimens of nickel-based alloys, specifically, additively manufactured STAL15 and cast alloy 247DS. The tests were conducted at 950 °C with stress ratios of 0.1 and −1. Metallographic and fractographic investigations were carried out to understand crack growth mechanisms. The results revealed significant retardation in crack growth at the interface. This study highlights the potential contributions of residual stresses and microstructural differences to the observed crack growth retardation phenomenon, along with the conclusion from an earlier study on the effect of yield strength mismatch on crack growth behavior at a perpendicular interface in bi-material specimens.
Low-Temperature High Stress (LTHS) creep plays a crucial role in Ni-base Superalloys, particularly affecting components like blades near the root. Below 850°C, the precipitate microstructure remains stable, characterized by periodically arranged ’ cubic precipitates surrounded by the -matrix. In these conditions, macroscopic traces of cubic slip have been observed in <111> oriented tensile specimens, whereas their microscopic origin has been a topic of debate. Furthermore, in LTHS conditions, Superlattice Intrinsic, Extrinsic Stacking Faults (SISF/SESF), or micro-twins are also frequently reported in crept specimens. Usually, these mechanisms are investigated separately, so that a unified picture and a detailed understanding of these mechanisms and their activation conditions have only recently emerged in the literature, despite the intensive investigations of the last decades.
The objective of this work is to develop a dislocation-based constitutive law that includes these recent developments. In particular, the pseudo-cubic slip mechanism is considered as resulting from the lack of hardening in <111> oriented tensile specimens and is represented by a novel estimate of the back-stresses based on the spectral decomposition of a tensorial representation of the back-stress. An additional novelty is that SISF- and SESF-related slip systems are accounted for as distinct slip systems with corresponding dislocation densities. The model has been implemented as a user-defined constitutive law for commercial Finite Element codes and identified as well as validated with data from the literature obtained with <001>, <011> and <111> oriented crystals tested in tension and compression creep.
The current lack of quantitative knowledge on processing-microstructure–property relationships is one of the major bottlenecks in today’s rapidly expanding field of additive manufacturing. This is centrally rooted in the nature of the processing, leading to complex microstructural features. Experimentally-guided modeling can offer reliable solutions for the safe application of additively manufactured materials. In this work, we combine a set of systematic experiments and modeling to address creep anisotropy and its correlation with microstructural characteristics in laser-based powder bed fusion (PBF-LB/M) additively manufactured Inconel-738LC (IN738LC). Three sample orientations (with the tensile axis parallel, perpendicular, and 45° tilted, relative to the building direction) are crept at 850 °C, accompanied by electron backscatter secondary diffraction (EBSD), scanning electron microscopy (SEM) and transmission electron microscopy (TEM) investigations. A crystal plasticity (CP) model for Ni-base superalloys, capable of modeling different types of slip systems, is developed and combined with various polycrystalline representative volume elements (RVEs) built on the experimental measurements. Besides our experiments, we verify our modeling framework on electron beam powder bed fusion (PBF-EB/M) additively manufactured Inconel-738LC. The results of our simulations show that while the crystallographic texture alone cannot explain the observed creep anisotropy, the superlattice extrinsic stacking faults (SESF) and related microtwinning slip systems play major roles as active deformation mechanisms. We confirm this using TEM investigations, revealing evidence of SESFs in crept specimens. We also show that the elongated grain morphology can result in higher creep rates, especially in the specimens with a tilted tensile axis.
Experimentally informed multiscale creep modelling of additive manufactured Ni-based superalloys
(2023)
Excellent creep resistance at elevated temperatures, i.e. T / T_m> 0.5, due to γ-γ’ microstructure is one of the main properties of nickel-based superalloys. Due to its great importance for industrial applications, a remarkable amount of research has been devoted to understanding the underlying deformation mechanism in a wide spectrum of temperature and loading conditions. Additive manufactured (AM) nickel-based superalloys while being governed by similar γ-γ’ microstructure, exhibit AM-process specific microstructural characteristics, such as columnar grains, strong crystallographic texture (typically <001> fiber texture parallel to build direction) and compositional inhomogeneity, which in turn leads to anisotropic creep response in both stationary and tertiary phases.
Despite the deep insights achieved recently on the correlation between process parameters and the resulting microstructure, the anisotropic creep behavior and corresponding deformation mechanism of these materials are insufficiently understood so far. One reason for this is the lack of capable material models that can link the microstructure to the mechanical behavior. To overcome this challenge, a multiscale microstructure-based approach has been applied by coupling crystal plasticity (CP) and polycrystal model which enables the inclusion of different deformation mechanisms and microstructural characteristics such as crystallographic texture and grain morphology. The method has been applied to experimental data for AM-manufactured INCONEL-738LC (IN738). The effect of different slip systems, texture, and morphology on creep anisotropy at 850°C has been investigated. Results suggest a strong correlation between superlattice extrinsic stacking fault (SESF) and microtwinning and observed creep anisotropy.
In nickelbasierten Superlegierungen, die für Gasturbinenschaufeln verwendet werden, sind bei hohen Betriebstemperaturen und -belastungen Kriechschäden, Ermüdung, Korrosion und Oxi-dation zu beobachten. Die betroffenen Turbinenschaufeln müssen ersetzt oder repariert werden, um Effizienzverluste und ein eventuelles Bauteilversagen zu vermeiden. In letzter Zeit wurden additive Fertigungs- und Lötverfahren für die Reparatur und das Fügen von Nickelbasiswerk-stoffen entwickelt, um die Einschränkungen der traditionellen Reparaturverfahren zu überwinden. Für eine auslegungsrelevante Bewertung des Risswachstumsverhaltens in den Fügezonen, die durch diese neuen Technologien erzeugt werden, sind Rissfortschrittsuntersuchungen erfor-derlich. Entsprechende Untersuchungen an gefügten Proben werden in diesem Beitrag vorge-stellt. Die Rissfortschrittsversuche werden an gefügten SEN-Proben (Single Edge Notch) bei einem Spannungsverhältnis von 0,1 und einer Temperatur von 950 °C durchgeführt. Das Riss-wachstum wird mit der DCPD-Methode (Direct Current Potential Drop) überwacht, und die ge-messenen Potenzialsignale werden anhand der optisch vermessenen Risslänge und einer Finite-Elemente-Analyse kalibriert. Der Spannungsintensitätsfaktor (SIF) für die gefügte SEN-Geometrie wird mit Hilfe von Finite-Elemente-Analysen berechnet. Auf diese Weise können Rissfortschrittskurven aus den experimentellen Daten abgeleitet werden.
Die Steigerung der Leistung und des thermodynamischen Wirkungsgrades von Verbrennungsmotoren führt zu erhöhten Anforderungen an die Festigkeit abgasführender Komponenten wie z. Bsp. Abgasturbolader. Als Folge erhöhter thermomechanischer Wechselbeanspruchungen (TMF) im Betrieb kommt es an den mechanisch und/oder thermisch höchst beanspruchten Stellen der Bauteile zur Bildung von Rissen, wodurch die Lebensdauer der Komponenten begrenzt wird. Derzeit werden bei Turboladern heißgehende Bauteile mit detektierten Rissen zumeist prophylaktisch ersetzt, da die weitere Ausbreitung der Risse während des Betriebs nicht vorhergesagt werden kann. Um diese aufwändige und un- ökonomische Praxis zu vermeiden, wurde im vorliegenden Forschungsvorhaben eine rechnerische Bewertungsmethode auf Basis der experimentellen und numerischen Bruchmechanik erarbeitet, mit deren Hilfe bereits in der Auslegungsphase oder während des Betriebs die (restliche) Lebensdauer der abgasführenden Komponenten vorhergesagt werden kann. Damit wird erstmalig die quantitative Vorhersage der Rissentwicklung bei TMF-Beanspruchungsbedingungen unter Berücksichtigung großer zyklischer viskoplastischer Verformungen ermöglicht.
Zentrales Ergebnis des Vorhabens ist eine automatisierte Berechnungsprozedur auf der Basis spezieller Finite-Elemente-Techniken (FEM), womit sowohl der Pfad als auch die Größe eines Risses als Funktion der Anzahl der Lastwechsel in Bauteilen unter TMF-Bedingungen berechnet werden kann. Als geeigneter Beanspruchungsparameter zur Bewertung des Rissfortschritts unter TMF wurde die zyklische Rissöffnungsverschiebung ΔCTOD verwendet. Das Werkstoffverhalten des betrachteten austenitischen Gusseisens Ni-Resist D-5S wurde mit einem validierten viskoplastischen, temperaturabhängigen Materialmodell modelliert, das zur Berücksichtigung große Verzerrungen und Rotationen am Riss erweitert wurde. Für die genaue Berechnung des ΔCTOD bei TMF wurden effiziente FEM-Techniken erarbeitet. Zur Simulation der Rissausbreitung wurde ein automatischer FEM-Algorithmus mit inkrementeller adaptiver Neuvernetzung entwickelt, bei dem die Verformungen und inelastischen Zustandsvariablen jeweils vom alten auf das neue Netz übertragen werden. Dieser Algorithmus wurde im Software-Paket ProCrackPlast implementiert, das in Verbindung mit dem kommerziellen FEM-Code Abaqus zur Lösung dreidimensionaler Rissprobleme zur Verfügung steht. Ziel der umfangreichen experimentellen Arbeiten war es, an isothermen LCF und anisothermen TMF-Versuchen mit gekerbten Flachzugproben (SENT) das Risswachstum im Temperaturbereich von 20 °C bis 700 °C zu ermitteln. Mit Hilfe begleitender 2D FEM Simulationen wurden anhand dieser Datenbasis die Rissfortschrittskurven des Werkstoffs unter Anwendung des ΔCTOD-Konzepts bestimmt und in geeigneter, parametrisierter Form den Nutzern zur Verfügung gestellt. Die Versuche an SENT-Proben wurden mit der entwickelten Software ProCrackPlast als 3D Modell simuliert. Der Vergleich der 2D und 3D Simulationen ergab einen systematischen Unterschied im CTOD und CTOD, der mit Hilfe eines Übertragungsfaktors korrigiert wurde. Der Vergleich der 3D Berechnungen mit den Experimenten zeigte eine zufriedenstellende Übereinstimmung der er- reichten Risslänge mit der Zahl der Lastzyklen im gesamten Temperaturbereich, wobei die numerische Prognose meist auf der konservativen / sicheren Seite lag. Die Übertragbarkeit der Ergebnisse der 2D Parameteridentifikation auf 3D Risskonfigurationen mit Mixed-Mode Beanspruchung ist mit zusätzlichen Versagenshypothesen verbunden, die aufgrund fehlender Versuchsdaten im Vorhaben nicht endgültig geklärt werden konnten. Zur Validierung des Gesamtkonzeptes wurden LCF-Proben mit einem bauteil- typischen Oberflächenriss experimentell und numerisch untersucht. In der Simulation konnte die komplexe Form und Größe der Rissentwicklung zufriedenstellend (richtig) vorhergesagt werden. Die Leis- tungsfähigkeit der erarbeiteten rechnerische Bewertungsmethode wurde an weiteren TMF-Beispielen vorgestellt und diskutiert. Die Software ProCrackPlast und die viskoplastische Materialroutine wurden dem Anwenderkreis des Vorhabens zusammen mit einem Nutzer-Handbuch und Verifikationsbeispielen zur Verfügung gestellt.
Das Ziel des Forschungsvorhabens ist erreicht worden.
Crack propagation under low cycle fatigue and thermomechanical fatigue is characterized by high plastic and creep strains that extend over large regions around the crack, so that concepts of linear-elastic fracture mechanics cannot be applied. In these cases, the cyclic crack tip opening displacement 𝛥CTOD is a promising loading parameter to quantify crack growth. In this work, suitable definitions and Finite Element techniques are investigated and compared for an accurate calculation of 𝛥CTOD under cyclic mechanical and/or thermal loading. A viscoplastic temperature dependent material model of Chaboche-type is used along with large strain settings, specified for the austenitic cast iron Ni-resist. Extensive two-dimensional analyses of Single Edge Notch Tension specimens revealed that collapsed special crack tip elements are superior compared with commonly used regular quadrilateral 8-node elements. At the same level of accuracy of 𝛥CTOD, they require an about ten times coarser mesh and show less sensitivity
w.r.t. element size for both stationary and propagating cracks. In order to simulate fatigue crack growth, an efficient, fully automated FE-technique is developed for an incremental crack propagation by successive remeshing, whereby the deformations and internal state variables are mapped from the old mesh onto the new one. Recommendations are made regarding important numerical control parameters like optimal size of crack tip elements, length of crack growth increment in relation to plastic zone size and 𝛥CTOD value.
Aero-engine turbine disks are safety-relevant components which are operated under high thermal and mechanical stress conditions. The actual part qualification and certification procedures make use of spin-tests conducted on production-similar disks. While these tests provide, on the one hand, a reliable definition of the critical conditions for real components, on the other hand they represent a relevant cost item for engine manufacturers. The aim of this work is to present two alternative burst speed assessment methods under development based on the Failure Assessment Diagram (FAD) and a global stability criterion, respectively. In the scope of the fracture mechanics assessment, the failure modes hoop-burst and rim-peeling are investigated with semicircular surface cracks modelled at the critical regions on the turbine disk. The comparison of the predicted critical rotational speed shows good agreement between the assessment methods.
Turbine blades often contain cylindric holes used to generate an air film that protects the blade alloy from the hot gases. These cooling holes of diameter around one mm are drilled by laser through the thickness of the blades. Unfortunately, the resulting stress concentration and the drilling-induced damage are known to favor crack initiation from the holes. It is thus necessary to assess the impact of these cooling holes on the structural integrity of the blades. Since cracks initiate very readily, the fatigue life of the components is mainly controlled by the propagation of the cracks in the stress gradient induced by the holes.
For this purpose, displacement controlled high-temperature LCF (Low-Cycle-Fatigue) tests were performed with center hole specimens of a coarse-grained Nickel base Superalloy. The tests were stopped after a defined load drop. In addition, crack propagation tests with Double Edge Notch specimens were performed. Moreover, specimens with different hole surface finishes were investigated, which showed a detrimental effect of the hole surface roughness. In parallel, an evaluation of the LCF tests based on a fracture mechanics-based model (Madia et al., Eng. Fract. Mech., 2018) has been applied. Thereby, the specimen life is controlled by the crack propagation time until failure. Crack growth is controlled by a modified NASGRO equation accounting for large-scale yielding and a progressive build-up of crack closure. The initial crack size has been derived from the measurements of defects around the borehole. A reasonable agreement between predicted and measured lifetimes is observed if one keeps in mind the large uncertainty regarding the effective shape of the cracks.
The scatter of fatigue crack growth data can become significant for coarse grained materials. By using a probabilistic description of crack propagation as the foundation of a lifetime prediction model, lifetime scatter of laboratory specimens can be reproduced. However, the lifetime of real components is subjected to additional scattering factors such as surface condition or uncertainty regarding direction and shape of emerging cracks. These factors need to be addressed in order to exploit the advantages of probabilistic description, i.e. the reduction of unnecessary conservatisms.
High temperature LCF (Low-Cycle-Fatigue) tests were performed with center hole specimens of a coarse-grained Nickel base Superalloy. In addition, crack propagation tests with Double Edge Notch specimens were performed. A procedure to detect the shape of the starting crack that combines the potential drop method and induction thermography was developed. The geometry and the number of notches were varied. Moreover, specimen with different hole surface finishes were investigated, which showed a detrimental effect of the roughness of the hole surface.
The results have been compared to predictions of a probabilistic tool for the estimation of lcf lifetime that has been calibrated beforehand on laboratory specimens with and without notches. In parallel, a fracture mechanics-based lifetime model was developed, which includes the initial crack size as a critical parameter. Thereby, the influence of the large grain size (>1mm), and the shape of the starting crack at the notch were considered.
Acknowledgements
The investigations are conducted as part of the joint research program COOREFLEX-Turbo in the frame of AG Turbo. The work is supported by Siemens AG and the Bundesministerium für Wirtschaft und Technologie (BMWi) as per resolution of the German Federal Parliament under grant number 03ET7071E.
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.
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.
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.
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.
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.
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.
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
The cyclic crack tip opening displacement ΔCTOD is a promising loading Parameter to quantify the crack propagation under thermomechanical fatigue (TMF). In this work, suitable techniques are investigated and compared for an accurate calculation of ΔCTOD under TMF loading using a viscoplastic temperature dependent material model.
It turned out that collapsed special crack tip elements give the best results. An efficient FEM-technique is developed to simulate the incremental crack growth by successive remeshing, whereby the deformations and internal state variables are mapped from the old mesh onto the new one. The developed techniques are demonstrated and discussed for two-dimensional examples like TMF-specimens. Recommendations are made regarding important numerical control parameters like optimal size of crack tip elements, length of crack growth increment in relation to plastic zone size and ΔCTOD value.
Results of an extended TMF test program on grade P92 steel in the temperature range of 620 °C - 300 °C, comprising in-phase (IP) and out-of-phase (OP) tests, partly performed with symmetric dwells at Tmax/Tmin, are presented. In contrast to previous studies, the low-strain regime is also illuminated, which approaches flexible operation in a power plant with start/stop cycles. At all strain amplitudes, the material performance is characterized by continuous cyclic softening, which is retarded in tests at lower strains but reaches similar magnitudes in the course of testing. In the investigated temperature range, the phase angle does not affect fatigue life in continuous experiments, whereas the IP condition is more detrimental in tests with dwells. Fractographic analyses indicate creep-dominated and fatigue-dominated damage for IP and OP, respectively. Analyses of the (micro)hardness distribution in the tested specimens suggest an enhanced microstructural softening in tests with dwell times for the low- but not for the high-strain regime. To rationalize the obtained fatigue data, the fracture-mechanics-based D_TMF concept, which was developed for TMF life assessment of ductile alloys, was applied. It is found that the D_TMF parameter correlates well with the measured fatigue lives, suggesting that subcritical growth of cracks (with sizes from a few microns to a few millimeters) governs failure in the investigated range of strain amplitudes.
The elastic properties of the single-crystal nickel-base superalloy CMSX-4 used as a blade material in gas turbines were investigated by the sonic resonance method in the temperature interval between room temperature and 1300 °C. Elastic constants at such high temperatures are needed to model the mechanical behavior of blade material during manufacturing (hot isostatic pressing) as well as during technical accidents which may happen in service (overheating). High reliability of the results was achieved using specimens of different crystallographic orientations, exciting various vibration modes as well as precise measurement of the material density and thermal Expansion required for modeling the resonance frequencies by finite element method. Combining the results measured in this work and literature data the elastic constants of the gamma and gamma' phases were predicted.
This prediction was supported by measurement of the temperature dependence of the gamma'fraction.
All data obtained in this work are given in numerical or analytical forms and can be easily used for different scientific and engineering calculations.
Mit Hilfe des HIP-Verfahrens („Hot Isostatic Pressing“) werden Poren in der einkristallinen Nickel-Basis Superlegierung CMSX-4 kontinuierlich geschrumpft und dadurch die nach der Erstarrung und der Wärmebehandlung vorhandene Porosität stark reduziert. In diesem Beitrag werden experimentelle und numerische Untersuchungen zu den Mechanismen der Porenschrumpfung zusammengefasst. Es zeigt sich, dass das Verformungsverhalten während Kriechversuchen bei der HIP-Temperatur durch Versetzungsgleitung auf oktaedrischen Ebenen dominiert wird.
Dagegen zeigen Messungen der Porositätsabnahme und Simulationen des Porenschließens, dass die Kinetik der Porenschrumpfung durch das Phänomen der Leerstellendiffusion zwischen Poren und Kleinwinkelkorngrenzen („Low Angle Boundary“, LAB) bestimmt wird. Im Gegensatz führt die klassische Kristallviskoplastizität zu einer systematischen Überschätzung dieser Kinetik. Der scheinbare Widerspruch lässt sich auflösen, wenn man bedenkt, dass auf der Skala der Poren Versetzungsquellen nicht gleichmäßig verteilt sind, wie in der konventionellen Kristallplastizität implizit angenommen wird. Stattdessen wird in einem weiterführenden Modell davon ausgegangen, das Kleinwinkelkorngrenzen (LABs) als Versetzungsquellen fungieren, während die Scherspannungen sehr stark in der Nähe der Poren lokalisiert sind, was die Emission von Versetzungen deutlich reduziert.
Mit Hilfe des HIP-Verfahrens („Hot Isostatic Pressing“) werden Poren in der einkristallinen Nickel-Basis Superlegierung CMSX-4 kontinuierlich geschrumpft und dadurch die nach der Erstarrung und der Wärmebehandlung vorhandene Porosität stark reduziert. In diesem Beitrag werden experimentelle und numerische Untersuchungen zu den Mechanismen der Porenschrumpfung zusammengefasst. Es zeigt sich, dass das Verformungsverhalten während Kriechversuchen bei der HIP-Temperatur durch Versetzungsgleitung auf oktaedrischen Ebenen dominiert wird.
Dagegen zeigen Messungen der Porositätsabnahme und Simulationen des Porenschließens, dass die Kinetik der Porenschrumpfung durch das Phänomen der Leerstellendiffusion zwischen Poren und Kleinwinkelkorngrenzen („Low Angle Boundary“, LAB) bestimmt wird. Im Gegensatz führt die klassische Kristallviskoplastizität zu einer systematischen Überschätzung dieser Kinetik. Der scheinbare Widerspruch lässt sich auflösen, wenn man bedenkt, dass auf der Skala der Poren Versetzungsquellen nicht gleichmäßig verteilt sind, wie in der konventionellen Kristallplastizität implizit angenommen wird. Stattdessen wird in einem weiterführenden Modell davon ausgegangen, das Kleinwinkelkorngrenzen (LABs) als Versetzungsquellen fungieren, während die Scherspannungen sehr stark in der Nähe der Poren lokalisiert sind, was die Emission von Versetzungen deutlich reduziert.
The current competitive situation on electricity markets forces conventional power plants into cyclic operation regimes with frequent load shifts and starts/shutdowns. In the present work, the cyclic mechanical behavior of ferritic-martensitic 9-12 % Cr steels under isothermal and thermomechanical loading was investigated for the example of grade P92 material. A continuous softening was observed under all loading conditions. The introduction of hold periods to the applied cycles reduced material lifetime, with most prominent effects at technologically relevant small strain levels. The microstructural characterization reveals a coarsening of the original “martensitic” lath-type microstructure to a structure with polygonal subgrains and reduced dislocation density. The microstructural data forms the input for a physically-based modelling approach.
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.
Computational methods for lifetime prediction of metallic components under high-temperature fatigue
(2019)
The issue of service life prediction of hot metallic components subjected to cyclic loadings is addressed. Two classes of lifetime models are considered, namely, the incremental lifetime rules and the parametric models governed by the fracture mechanics concept. Examples of application to an austenitic cast iron are presented. In addition, computational techniques to accelerate the time integration of the incremental models throughout the fatigue loading history are discussed. They efficiently solve problems where a stabilized response of a component is not observed, for example due to the plastic strain which is no longer completely reversed and accumulates throughout the fatigue history. The performance of such an accelerated Integration technique is demonstrated for a finite element simulation of a viscoplastic solid under repeating loading–unloading cycles.
Due to their excellent creep resistance and good oxidation resistance, 9–12% Cr ferritic–martensitic stainless steels are widely used as high temperature construction materials in power plants. However, the mutual combination of different loadings (e.g., creep and fatigue), due to a “flexible” operation of power plants, may seriously reduce the lifetimes of the respective components. In the present study, low cycle fatigue (LCF) and relaxation fatigue (RF) tests performed on grade P92 helped to understand the behavior of ferritic–martensitic steels under a combined loading. The softening and lifetime behavior strongly depend on the temperature and total strain range. Especially at small strain amplitudes, the lifetime is seriously reduced when adding a hold time which indicates the importance of considering technically relevant small strains.
The current competitive situation on electricity markets forces power plants into cyclic operation regimes with frequent load shifts and starts/shutdowns. In the present work, the cyclic mechanical behavior of ferritic-martensitic 9-12 % Cr steels under isothermal and thermomechanical loading was investigated for the example of grade P92 material. A continuous softening was observed under all loading conditions. The introduction of hold periods to the applied cycles reduced material lifetime, with most prominent effects at technologically relevant small strain levels. The microstructural characterization reveals a coarsening of the original “martensitic” lath-type microstructure to a structure with polygonal subgrains and reduced dislocation density. The microstructural data forms the input for a physically-based modelling approach.
Es konnte anhand einer numerischen Voruntersuchung gezeigt werden, dass anhand der kombinierten Auswertung der im Versuch verwendeten Sensorik eine Einteilung der unter Ermüdung in Bohrlochproben auftretenden Rissformen in verschiedene Hauptkategorien (Eckriss, Oberflächenriss, Durchgangsriss) möglich ist.
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.
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.