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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.
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. The aim of this work is to present part of a fracture mechanics-based procedure under development which aims at replacing the tests on production-similar disks with lab tests on fracture mechanics specimens. The finite element simulation of the cracked disk considers the real thermal and mechanical loading conditions. In order to design a lab representative specimen, beside the crack driving force, expressed in terms of 𝐽-integral, also the constraint to plastic deformation e.g., stress triaxiality, at the crack-tip must be similar for the same crack in the specimen and in the disk. This has been achieved and as expected, both the highest 𝐽 -integral and constraint factor are calculated at the same location along the crack front for both disk and specimen. The results of the structural integrity assessment in the form of a Failure Assessment Diagram (FAD) show good agreement between designed specimen and disk both in terms of expected failure mode and value of the critical speed. In addition, probabilistic aspects are also considered in the calculations.
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.
Die Analyse der Lebensdauer von Bauteilen unter thermomechanischer Ermüdung (TMF) erfordert ein geeignetes Stoffgesetz, welches in der Lage ist, zyklische Plastizität die Abhängigkeit der Spannungsantwort nach der Dehnrate, Kriechen und Spannungsrelaxation temperaturabhängig zu beschreiben und ein Lebensdauermodell, welches in Abhängigkeit von der örtlich aufgelösten Spannungs- und Verformungsgeschichten eine Schätzung der Anzahl der Zyklen bis zum Anriss liefern kann.
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.
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.
Components in the Aerospace, Power and Automotive engineering sectors are frequently subjected to cyclic stresses induced by thermal fluctuations and mechanical loads. For the design of such components, reliable material property data are required which need to be acquired using well accepted and reproducible test procedures for thermo-mechanical fatigue (TMF) loading. There is limited availability of proven TMF data indicating there is need for further research and testing. The TMF behaviour of materials is often desired to be simulated in models which describe the cyclic stress-strain behaviour, the fatigue life and the cyclic crack growth behaviour. There is a continuous need for the development and amendment of such models. Models can be validated by using materials in industrial applications which are subjected to TMF loading.
The 3rd Workshop on Thermo-Mechanical Fatigue was held on 27–29 April 2016 at BAM, Berlin, Germany. The workshop was attended by 90 attendees coming from 17 countries in the world. 38 presentations including five poster presentations were held.
The following topics were covered by the workshop:
– TMF of materials coated with Thermal Barrier Coatings.
– Thermal Gradient Mechanical Fatigue.
– TMF crack growth.
– TMF + High Cycle Fatigue.
– TMF Modelling and Lifetime Prediction.
– TMF Properties of steels, cast iron, Al-, Mg- and Ni-alloys
– Advanced TMF Testing Techniques.
– Industrial Applications.
A panel discussion was held regarding the present state of TMF testing standards (ISO and ASTM) and their potential for improvement. The discussion and contributions were summarized and forwarded to the standard committees. The 3rd TMF-Workshop ensured the continuation of international exchange of knowledge providing a forum to present and discuss all recent developments in the field of thermo-mechanical fatigue.
The current special issue publishes eleven selected papers of the 3rd TMF-Workshop 2016. The papers were peer reviewed by a number of experts in the Thermo-Mechanical Fatigue sector. I hope you will enjoy reading papers of this special issue.
Die thermomechanische Ermüdung (TMF) von Bauteilen kann heutzutage mit der Finite-Elemente (FE) Methode simuliert werden. Dafür werden komplexe viskoplastische Stoffgesetze benötigt, welche in der Regel in kommerziellen FE Programme nicht zur Verfügung stehen. Im Vortrag wird gezeigt wie solche Stoffgesetze mit Hilfe von benutzerdefinierten Subroutinen in kommerzielle Finite-Elemente Programme implementiert werden können. Es wird auf die Vor- und Nachteile einer expliziten oder impliziten Integration der Entwicklungsgleichungen für die inneren Variablen hingewiesen. Schließlich wird ein Postprozessingstool beschrieben, mit dem die Überlagerung einer niederfrequenten (TMF) und einer hochfrequenten (HCF) Belastung im Bauteil analysiert werden können.
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.
Experimental and analytical investigation of the TMF-HCF lifetime behavior of two cast iron alloys
(2017)
The combined loading Thermomechanical Fatigue (TMF) with High Cycle Fatigue (HCF) has been experimentally investigated for two cast iron alloys. Both alloys contain globular graphite nodules but the first one has a ferritic structure while the second one has an austenitic crystal structure. In particular, the influences of the HCF frequency, of the HCF loading amplitude and of the location of the superposed HCF cycles have been investigated. It was observed that the HCF frequency has a limited impact on the fatigue life. On the other side, the HCF-strain amplitude has a highly non-linear influence on the fatigue life. The experimental results can be understood in terms of a fracture mechanics based damage mechanism: Cracks quickly initiate due to the TMF loading and the growth of the cracks up to a few mm controls the fatigue life. If HCF-loading cycles are superposed, cyclic crack propagation dramatically accelerates after a threshold has been reached. This threshold is regarded as controlling the fatigue life reduction. The previous ideas have been expressed in a model that can be very simply applied to estimate the fatigue life reduction ratio due to the superposed HCF cycles. It only contains two adjustable parameters and can be combined with any TMF life assessment model.
Modeling the lifetime reduction due to the superposition of TMF and HCF loadings in cast iron alloys
(2016)
The superposition of small amplitude, high frequency loading cycles (HCF) to slow, large amplitude loading cycles (TMF) can significantly reduce the fatigue life. In this work, the combined TMF+HCF loading has been experimentally investigated for a cast iron alloy. In particular, the influence of the HCF frequency of the HCF amplitude and of the location of the superposed HCF cycles has been assessed. It was observed that the HCF frequency has a limited impact on the TMF fatigue life. On the other side, the HCF-strain amplitude has a highly non-linear influence on the TMF fatigue life. A simple estimate for the fatigue life reduction due to the superposed HCF cycles has been derived from fracture mechanics considerations. It is assumed that the number of propagation cycles up to failure can be neglected after a threshold for the HCF loading has been reached. The model contains only two adjustable parameters and can be combined with any TMF life prediction model. The model predictions are compared with the test results for a large range of TMF+HCF loading conditions.
Experimental and analytical investigation of the TMF-HCF lifetime behavior of two cast iron alloys
(2016)
The superposition of small amplitude, high frequent loading cycles (HCF) to the slow, large amplitude, TMF loading cycles can significantly reduce the TMF life, i.e. the number of TMF blocks until failure. In this work, the combined TMF-HCF loading has been experimentally investigated for two cast iron alloys. Both alloys contain globular graphite nodules but the first one has a ferritic while the second one has an austenitic crystal structure. In particular, the influence of the HCF frequency, of the HCF loading amplitude and of the location of the superposed HCF cycles has been investigated. It was observed that the HCF frequency has a limited impact on the TMF fatigue life. In other words, the number of superposed HCF-cycles has only a slight influence on the TMF fatigue life, which contradicts the linear damage accumulation rule concept. On the other side, the HCF-strain amplitude has a highly non-linear influence on the TMF fatigue life.
The experimental results can be understood in terms of a fracture mechanics based damage mechanism [1]: Cracks readily initiate due to the TMF loading and the duration of the growth of the cracks up to a few mm controls the fatigue life. If HCF-loading cycles are superposed, cyclic crack propagation dramatically accelerates at some stage. This stage is related to the existence of a threshold for crack growth under pure HCF-conditions and largely controls the fatigue life of the combined loading.
The previous ideas have been expressed in a model that can be very simply applied to provide the fatigue life reduction factor due to the superposed HCF cycles. It only contains two additional adjustable parameters and can be combined with any TMF model.
Under cyclic thermomechanical loading, various effects such as strain accumulation, creep damage, ageing, fatigue etc. may occur in the material of a gas turbine blade. Depending on the loading conditions, all these effects contribute to reduce the lifetime of the component.
Subject of the present work is the development of a material model to describe the mechanical effects mentioned above and to subsequently predict lifetimes by using simulated stress strain data.
Starting point for deformation modeling is the well known viscoplastic model after Chaboche, which provides descriptions of isotropic and kinematic hardening, as well as dynamic and static recovery. The evolution equation for kinematic hardening model has been modified following the proposal of Ohno/Wang to better predict stress controlled cyclic strain accumulation, i.e. ratchetting. A damage variable has been included to represent tertiary creep according to the concept of Kachanov. Finally, the static recovery has been modified following Kindrachuk to account for strain induced ageing. The models parameters have been calibrated using isothermal test data only. The constitutive model has been validated by comparing experimental with predicted TMF stress-strain hystereses.
Lifetime prediction is done with the TMF lifetime model proposed by Riedel. The model assumes that fatigue life is controlled by the propagation of short cracks. Besides pure fatigue, it takes the local creep deformations at the crack tip into account. The model is applied to a broad variety of isothermal and non isothermal tests over temperatures up to 950°C and different loading conditions. The evaluation shows that throughout satisfying results can be achieved using a limited number of model parameters for the whole test data base.
In diesem Forschungsvorhaben erfolgte eine Überprüfung der Übertragbarkeit der Werkstoff- und Rechenmodelle für die Lebensdauervorhersage von ATL-Heißteilen unter TMF-Beanspruchung auf eine andere Werkstoffklasse, d. h. auf eine austenitische Gusseisenlegierung mit Kugelgraphit. Dafür wurde die Legierung EN-GJSA-XNiSiCr35-5-2 (Ni-Resist D-5S) ausgewählt. Zunächst wurde für diesen Werkstoff eine experimentelle Datenbasis geschaffen, da diese vor Beginn des Vorhabens nicht ausreichend war. Dazu wurden Zug-, Kriech-, LCF- und TMF-Versuche durchgeführt, die der Kalibrierung der Modelle dienten. Unter TMF-Belastung zeigte der untersuchte Werkstoff ein stark abweichendes Verhalten von den im vorangegangenen Vorhaben untersuchten ferritischen SiMo-Legierungen: Der Werkstoff Ni-Resist zeigte insgesamt eine vergleichbare Festigkeit unter OP- und IP-Bedingungen, während die ferritischen Legierungen unter IP-Beanspruchung eine deutlich höhere Festigkeit aufweisen. Mit zunehmenden Temperaturen und Haltezeiten unter Zugspannungen wurden dagegen beim Werkstoff Ni-Resist Hinweise auf Kriechschädigung gefunden, die schädigungsrelevant sind. Auch dies ist ein deutlicher Unterschied zu den SiMo-Legierungen. Das Spannungs-Verformungs-Verhalten in den LCF- und TMF-Versuchen wird durch das Modell auch für den neuen Werkstoff überwiegend gut beschrieben. Das Gleiche gilt für die Lebensdauervorhersage, die mit Ausnahme der Prüftemperatur 900 °C innerhalb eines Fak-tors zwei liegt. Eine Verifikation des Modells erfolgte mit Hilfe eines Bauteilversuchs an einem Abgassammler, der abwechselnd mit heißem und kaltem Gas durchströmt wurde. Ziel der Bauteilsimulation war insbesondere die Vorhersage der Rissbildungsorte. Eine Vorhersage der exakten Lebensdauer wurde nicht erwartet, da das Bauteil mit einer Gusshaut behaftet war, während die für die Kalibrierung des Lebensdauermodells verwendeten Versuche an bearbeiteten, glatten Proben ohne Gusshaut durchgeführt wurden. Die überwiegende Anzahl der experimentell ermittelten Rissorte wurden vorhergesagt. Schließlich war ein wesentliches Ziel des Vorhabens, den Einfluss von HCF-Schwingungen auf die TMF-Lebensdauer vertieft experimentell zu untersuchen und das bereits bestehende Lebensdauermodell auf HCF-Überlagerung zu erweitern. Dazu wurde zunächst die Daten-basis aus dem Vorgängervorhaben am Bespiel von SiMo 4.05 deutlich ausgebaut, um die verschiedenen Einflussparameter zu erfassen. Es wurde ein Ansatz entwickelt, in dem die Lebensdauerminderung durch die überlagerten HCF-Schwingungen abgebildet wird. Dabei wird davon ausgegangen, dass ab einer bestimmten Risstiefe die Überlagerung der HCF-Schwingungen die Rissausbreitung stark beschleunigt. Der Zeitpunkt, wann diese Beschleunigung eintritt, wird als maßgeblich für die Lebensdauerminderung angesehen. Mit diesem Ansatz lassen sich die Lebensdauern für beide Werkstoffe in guter Übereinstimmung mit dem Experiment vorhersagen.
Schnelle Lastwechsel führen v.a. in dickwandigen Kraftwerksbauteilen zu starken thermischen und mechanischen Beanspruchungen, da sich hohe Temperaturgradienten über der Wand des Bauteils einstellen. Es ergeben sich komplexe Lastkollektive aus zeitlich veränderlichen Spannungen/Dehnungen und Temperaturen, die formal einer Kombination aus Kriechbeanspruchung, Kriechermüdung und thermomechanischer Ermüdung (TMF) entsprechen.
In diesem Forschungsvorhaben erfolgte eine Überprüfung der Übertragbarkeit der Werkstoff- und Rechenmodelle für die Lebensdauervorhersage von ATL-Heißteilen unter TMF-Beanspruchung auf eine andere Werkstoffklasse als im Vorgängervorhaben, d.h. auf das austenitische Gusseisen EN-GJSA-XNiSiCr35-5-2 (Ni-Resist D-5S). Zunächst wurde dafür eine experimentelle Datenbasis geschaffen, da diese vor Beginn des Vorhabens nicht ausreichend war. Dazu wurden Zug-, Kriech-, LCF- und TMF-Versuche durchgeführt, die der Kalibrierung der Modelle dienten. Das Spannungs-Verformungs-Verhalten und die Lebensdauer in den LCF- und TMF-Versuchen werden durch das Modell auch für den neuen Werkstoff überwiegend gut beschrieben. LCF-Versuche mit Haltezeit bei 900 °C sowie IP-TMFVersuche mit einer Obertemperatur von 900 °C werden weniger gut vorhergesagt, da sich der Schädigungsmechanismus ändert. Eine Verifikation des Modells erfolgte mit Hilfe eines Bauteilversuchs an einem Abgassammler. Die überwiegende Anzahl der experimentell ermittelten Rissorte wurden von dem Modell vorhergesagt.
Ein wesentliches Ziel des Vorhabens war, den Einfluss von HCF-Schwingungen auf die TMF-Lebensdauer vertieft experimentell zu untersuchen und das bereits bestehende Lebensdauermodell auf HCF-Überlagerung zu erweitern. Es wurde ein bruchmechanisch motivierter Ansatz entwickelt, in dem die Lebensdauerminderung durch die im TMF-Zyklus überlagerten HCF-Schwingungen abgebildet wird. Mit diesem Ansatz lassen sich die Lebensdauern sowohl für den Werkstoff SiMo 4.05 als auch für den Ni-Resist in guter Übereinstimmung mit dem Experiment Vorhersagen.
Das Ziel des Forschungsvorhabens ist erreicht worden.
Data about the creep behaviour 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 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 HlPed at temperatures between y'-solvus and solidus where superalloy has no strengthening y'-phase and therefore is very soft. For example, the Company Howmet Castings HIPs the superalloy CMSX-4 at the temperature 1288aC, which corresponds to a homologous temperature of about 0.97=1561 K/1612 K (solidus temperature). Therefore knowledge about the creep behaviour of CMSX-4 at this temperature and understanding of the creep mechanisms are necessary to model the kinetics of pore closure during HIP as well as to plan the Parameters of the HIP process.
The stress States of components under Service conditions differ in general from the loading conditions that are routinely applied during material testing. When data that results, e.g., from uniaxial testing should be used for lifetime assessment, a good understanding of the failure behaviour in dependence of the stress state is necessary. For polycrystalline materials under high temperature loading, the development of creep damage is one important factor that limits a component’s lifetime. For cases where creep damage is related to the nucleation and growth of grain boundary cavities, the local normal stress acting on a grain boundary has been found to have a strong influence on the damage development. Hence, creep damage is usually localized along planes that lie perpendicular to the maximum principal tensile stress.
The elastic anisotropy caused by the texture in the Nb3Sn filaments of PIT and RRP wires has been calculated by averaging the estimates of Voigt and Reuss, using published Nb3Sn single crystal elastic constants and the Nb3Sn grain orientation distribution determined in both wire types by Electron Backscatter Diffraction. At ambient temperature the calculated Nb3Sn E-moduli in axial direction in the PIT and the RRP wire are 130 GPa and 140 GPa, respectively. The calculated E-moduli are compared with tensile test results obtained for the corresponding wires and extracted filament bundles.
Pore annihilation was investigated in the single-crystal nickel-base superalloy CMSX-4. HIP tests at 1288 °C/103 MPa were interrupted at different times, then the specimens were investigated by TEM, metallography and density measurements. The kinetics of pore annihilation was determined. The pore closure mechanism was identified as plastic deformation on the octahedral slip systems. A model describing the kinetics of pore closure has been developed on the base of crystal plasticity and large strain theory. Mechanical tests with the superalloy CMSX-4 and the Ru-containing superalloy VGM4 showed, that HIP significantly increases the fatigue life at low temperatures but has no effect on creep strength.
A micromechanical model of creep induced grain boundary damage is proposed, which allows for the simulation of creep damage in a polycrystal with the finite element method. Grain boundary cavitation and sliding are considered via a micromechanically motivated cohesive zone model, while the grains creep following the slip system theory. The model has been calibrated with creep test data from pure Cu single crystals and a coarse-grained polycrystalline Cu-Sb alloy. The test data includes porosity measurements and estimates of grain boundary sliding. Finally, the model has been applied to Voronoi models of polycrystalline structures. In particular the influence of grain boundary sliding on the overall creep rate is demonstrated.
Under cyclic thermomechanical loading conditions, various effects such as strain accumulation, creep damage, ageing, fatigue etc. may occur in the material of a gas turbine blade. Depending on the loading conditions, all these effects contribute to reduce the lifetime of the component. Subject of the present work is the development of a lifetime model able to discriminate between the different damage mechanisms, as well as the development of a material model to describe the mentioned effects and thus providing the input data for lifetime prediction.
Material modelling and lifetime prediction of Ni-base gas turbine blades under TMF conditions
(2014)
Under cyclic thermomechanical loading conditions, various damage mechanisms such as strain accumulation, creep cavitation, ageing, fatigue surface cracking etc. may take place in the material of a gas turbine blade. Depending on the loading conditions, all these effects can contribute to reduce the lifetime of the component. Subject of the present work is the development of a material model to describe the mechanical effects mentioned above, as well as the development of a lifetime model able to discriminate the different damage mechanisms.
Pore annihilation during hot isostatic pressing (HIP) was investigated in the single-crystal nickel-base superalloy CMSX-4 experimentally by interrupted HIP tests at 1288 °C/103 MPa. The kinetics of pore annihilation was determined by density measurement and quantitative metallography. Transmission electron microscopy of a HIPed specimen showed that the pores shrink via dislocation movement on octahedral glide planes. Theoretically pore closure under HIP condition was modelled by the finite element method using crystal plasticity and large strain theories. The modelling gives a similar kinetics of pore annihilation as observed experimentally, however somewhat higher annihilation rate.
Micromechanical investigations and modelling of a copper-antimony-alloy under creep conditions
(2014)
In many practical applications, creep damage is the limiting factor of a components lifetime. A micromechanical model of creep induced grain boundary damage is proposed, which allows for the simulation of creep damage in a polycrystal within the framework of finite element analysis. The model considers grain boundary cavitation and sliding according to a micromechanically motivated cohesive zone model while creep deformation of the grains is described following the slip system theory. The model can be applied to idealised polycrystalline structures, such as a Voronoi tessellation or, like demonstrated here, to real grain structures of miniature creep specimens. Creep tests with pure Cu single crystals and with a coarse-grained polycrystalline Cu-1 wt.% Sb alloy at 823 K have been performed and used to calibrate the polycrystal model. The grain structure of the polycrystalline CuSb specimens has been revealed by the EBSD method. Extensive grain boundary sliding and cavitation has been observed in the crept specimens. Grain boundary sliding has been found to promote wedge-type damage at grain boundary triple junctions and to contribute significantly to the total creep strain. Furthermore, the assumed stress sensitivity of the models grain boundary cavity nucleation rate strongly influences the development of wedge-type damage.
Numerical simulation of fatigue crack growth in a single crystal superalloy at high temperature
(2013)
Rafting during high temperature deformation in a single crystal superalloy: experiments and modeling
(2012)
Rafting during high temperature deformation in a single crystal superalloy: Experiments and modeling
(2012)
Experimental characterization and mechanical modeling of creep induced rafting in superalloys
(2012)
A constitutive model has been developed for the high temperature mechanical behavior of single crystal superalloys, including rafting and its consequences. The flow stress depends on the γ channel width via the Orowan stress. An evolution equation for channel widening during high temperature straining has been derived and calibrated with measurements. Therein, rafting is assumed to be driven by the relaxation of internal stresses. The model is able to represent the mechanical softening at high stresses consecutive to rafting. The model has been applied to simulate rafting during uniaxial creep in several crystal orientations, in notched specimens as well as in cyclically loaded specimens.
An extension of the constitutive viscoplastic model of Meric and Cailletaud is presented. The new model
accounts for coupling of plasticity and viscoplasticity to describe the rate dependence at low and moderate
temperatures. The model contains two boundaries: an elastic one and a viscoplastic one. Between the
boundaries, the only contribution to yielding is the rate dependent viscoplastic mechanism. Once the viscoplastic
boundary is reached, an additional rate independent flow mechanism becomes active. However, the extended
model is not able to predict properly both creep and long-term relaxation tests simultaneously. Therefore, a
deformation-induced softening is assumed, which is supposed to mainly affect static recovery.
The model has been calibrated with the mechanical tests on a single crystal nickel-basis superalloy. The uniaxial
tests have been carried out in the temperature interval 600°C – 1100°C in [001], [011] and [111] specimens.
The predicted creep, relaxation and non-isothermal cyclic tests exhibit reasonable agreement with the
experimental observations.
Simulations of cavitation processes on a grain boundary under creep conditions have been carried out, taking into account nucleation, growth, coalescence and sintering of multiple cavities. Cavity growth rates have been calculated through a resolution procedure based on the use of holomorphic complex functions. Three dimensionless parameters have been identified that are responsible for the cavitation development. Parameter studies have been carried out in order to characterise the mechanisms that are responsible for the cavitation development. These studies have been used to develop a physically motivated, simplified model in order to describe the cavitation development of the simulations in terms of global state variables. The simplified model is able to reproduce the cavitation development for all considered combinations of the dimensionless parameters and allows the description of the thickening behaviour of a cavitating grain boundary.
The present work focuses on the cubic slip phenomenon in single crystal superalloys with a high fraction of γ' precipitates at high temperature.
The macroscopically apparent cubic slip mechanism is known to significantly reduce the tensile and creep strength of <1 1 1> oriented specimens. However, recent results obtained by 3D dislocation dynamics (Vattré et al., 2009) suggest a new interpretation of the so-called pseudo-cubic slip related to the nature of the dislocation network formation at the interfaces. These results are taken into account in a micromechanical model to improve the estimation of the strain hardening anisotropy. In accordance with the discrete simulations, it is shown that a key role is played by the combination of the activated octahedral slip systems as a function of the crystal orientation. In the <1 1 1> case, the contribution of the activated systems to kinematical hardening compensate, whereas strain hardening remains high for the <0 0 1> case. The experimental dependence of plastic flow on the orientation is also explained at the dislocation-scale mechanisms.
Results are presented for the alloy CMSX-4 in several orientations.
A crystallographic constitutive model is developed, which accounts for both rate-sensitive and rate-insensitive flow. Single-crystal plasticity and viscoplasticity are the limiting cases of the model, so that it properly reflects the material response over a wide temperature range. A non-linear dynamic recovery is included to properly describe ratchetting. We provide a robust integration scheme based on generalization of the return-mapping algorithm and of the procedure for active set search.
The implicit integration and consistent tangent are implemented through the UMAT subroutine in the ABAQUS finite element program. The capability of the model to account for both high and low strain rates is demonstrated in numerical examples. Finally, the stability of integration scheme and quadratic convergence of the global NewtonRaphson equilibrium iterations are demonstrated on the example of a notched bar under tension.
Creep damage of single-crystal nickel base superalloys: mechanisms and effect on low cycle fatigue
(2010)
The main mechanisms of creep damage of single-crystal nickel-base superalloys are the loss of the interface coherency, coarsening of the γ / γ'-microstructure, precipitation of topologically closed packed phases and growth of porosity. This degradation deteriorates the mechanical properties such as yield stress, creep lifetime and especially low-cycle fatigue life, which can be reduced nearly by a factor of 10. The degradation kinetics during creep was characterised quantitatively on the superalloy CMSX-4. A new non-destructive testing technique was applied to cover a wide test parameter range with few specimens in a relatively short time: repeated load annealing of wedge shaped specimens.
Experimental characterization and mechanical modelling of creep induced rafting in superalloys
(2011)
Experimental Characterization and Modelling of Thermo Mechanical Fatigue of Cast Iron Turbochargers
(2011)
Simulation of fatigue crack growth by crack tip plastic blunting using cohesive zone elements
(2010)
The propagation of a fatigue crack in 2D specimens by crack tip plastic blunting is simulated by using a Finite Element implementation of the strip-yield model. At each cycle, the crack growth is assumed to result from the variation of the Crack Tip Opening Displacement (ΔCTOD). The implementation is based on cohesive elements with an elastic perfectly plastic behavior, which allows to simulate, the crack closure phenomena due to the plastic wake behind the crack tip. A mesh sensitivity analysis provides the minimum number of elements requested in the crack tip plastic zone for a given accuracy. Then, the advance scheme based on crack tip blunting is described. Finally, the variation of the opening load with respect to the load ratio R, and to the maximum load is investigated and compared with analytical results.
Multiscale modelling of diffusion controlled grain boundary cavitation during creep of metals
(2010)
The shape of X-ray reflections from the cuboidal γ/γ'-microstructure was investigated. The measurements were performed on the 4th generation single-crystal nickel-base superalloy TMS138. It is shown that reflections from non-cubic crystallographic planes split not only in d-scale due to the different spacing of the γ- and γ'-lattices but also in the pole figure due to the tilting of γ-lattice planes. This tilting results from the elastic distortion of the γ-lattice caused by the γ/γ'-misfit. The results obtained are discussed under the methodical aspect of misfit measurement.
It is shown experimentally that, during annealing and creep under low applied stresses, matrix dislocation loops frequently cross-glide. The periodic length of the zigzag dislocations deposited in the interfaces is equal to that of the γ/γ'-microstructure. Initially, the zigzag dislocations move in the (001) interface by a combination of glide and climb but then they stop near the γ'-edges and align along (100). Reactions of such dislocations lead to the formation of square interfacial networks consisting of (100) oriented edge dislocations. The complex dislocation movement is explained by the inhomogeneity of the misfit stresses between γ- and γ'-lattices. The tensile components of the stress tensor drive the dislocations through the channel, whereas the shear components near the γ'-edges cause the zigzag movement and the (100) alignment. The total effect is the most efficient relaxation of the misfit stresses. The results are relevant, especially for single-crystal superalloys of the newest generations, which have an increased γ/γ'-misfit due to the high level of refractory elements.
A new experimental technique (repeated load annealing of flat wedge shaped specimens) was proposed for characterization of microstructural degradation under creep conditions. This technique was applied to investigate the microstructural degradation of the nickel-base superalloy CMSX-4 in a wide range of temperatures and stress levels. The results obtained allowed to describe analytically the kinetics of rafting, which is important to predict the reduction of fatigue lifetime and yield stress.
Constitutive modelling of creep degradation due to rafting in single-crystalline Ni-base superalloys
(2009)
A constitutive model for the mechanical behaviour of single-crystalline superalloys at high temperatures has been developed. The model relies on the slip system theory and is able to predict rafting and its influence on plastic flow. The kinetics of rafting are assumed to be driven by the reduction of the internal stresses represented by the macroscopic back-stress. The rafting effect is incorporated in the model through the dependence of the Orowan stress on the channel width. The model has been validated for the alloy CMSX-4 at 950 °C. The rafting part of the model has been calibrated by measurements of the channel widths after several levels of creep strains and for several loads.
The oxidation behaviour of single crystal PWA 1483 at 950 °C was investigated by means of XRD, SEM and EDS. The parabolic oxidation behaviour, as defined by mass gain and the respective oxide layer thicknesses, is characterized by a parabolic rate constant of about 4 × 10-6 mg²/(cm4 × s) and the formation of a multi-layered oxide scale. An outer scale contains a Ti-bearing thin film composed of TiO2 and NiTiO3 but mostly Cr in Cr2O3 and (Ni/Co)Cr2O4 besides NiTaO4. This outer scale is connected to a discontinuous layer of Al2O3 and an area of γ?'-depletion within the base material.