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The heat-resistant cast iron EN-GJSA-XNiSiCr35-5-2 (Ni-Resist D-5S) was investigated for its fatigue crack growth behavior at room and high temperatures. Force-controlled tests were carried out at constant temperatures (20 °C, 500 °C, 700 °C) without and with hold time and different load ratios. The crack growth behavior was also characterized under TMF loading (Tmin = 400 °C, Tmax = 700 °C) by applying IP and OP conditions and different load ratios. Three different techniques were combined to monitor crack growth: potential drop, thermography, and compliance method. The effect of the different loading conditions on the fatigue crack growth behavior will be presented and discussed.
This is the stable version of the full-notch creep test ontology (OntoFNCT) that ontologically represents the full-notch creep test. OntoFNCT has been developed in accordance with the corresponding test standard ISO 16770:2019-09 Plastics - Determination of environmental stress cracking (ESC) of polyethylene - Full-notch creep test (FNCT).
The OntoFNCT provides conceptualizations that are supposed to be valid for the description of full-notch creep tests and associated data in accordance with the corresponding test standard. By using OntoFNCT for storing full-notch creep test data, all data will be well structured and based on a common vocabulary agreed on by an expert group (generation of FAIR data) which is meant to lead to enhanced data interoperability. This comprises several data categories such as primary data, secondary data and metadata. Data will be human and machine readable. The usage of OntoFNCT facilitates data retrieval and downstream usage. Due to a close connection to the mid-level PMD core ontology (PMDco), the interoperability of full-notch creep test data is enhanced and querying in combination with other aspects and data within the broad field of materials science and engineering (MSE) is facilitated.
The class structure of OntoFNCT forms a comprehensible and semantic layer for unified storage of data generated in a full-notch creep test including the possibility to record data from analysis and re-evaluation. Furthermore, extensive metadata allows to assess data quality and reliability. Following the open world assumption, object properties are deliberately low restrictive and sparse.
Extended X-ray absorption fine structure (EXAFS) conducted on an equiatomic MoNbTaW bcc medium-entropy alloy that was annealed at 2273 K reveals unexpectedly small 1st and 2nd shell element-specific lattice distortions. An experimental size-mismatch parameter, δexp, is determined to be ca. 50% lower than the corresponding calculated value. Around W, short-range order (SRO) preferring 4d elements in the 1st and 2nd shells persists. A Nb-W ordering is found, which is reminiscent of ordering emerging at lower temperatures in the B2(Mo,W;Ta,Nb)- and B32(Nb,W)-phases. With high-temperature ordering preferences in fcc also foreshadowing low-temperature phase, these findings suggest a general feature of high-temperature SRO.
Additive manufacturing (AM) offers significantly greater freedom of design compared to conventional manufacturing processes since the final parts are built layer by layer. This enables metal AM, also known as metal 3D printing, to be utilized for improving efficiency and functionality, for the production of parts with very complex geometries, and rapid prototyping. However, despite many technological advancements made in recent years, several challenges hinder the mass adoption of metal AM. One of these challenges is mechanical anisotropy which describes the dependency of material properties on the material orientation. Therefore, in this work, stainless steel 316L parts produced by laser-based powder bed fusion are used to isolate and understand the root cause of anisotropy in AM parts. Furthermore, an efficient and accurate multiscale numerical framework is presented for predicting the deformation behavior of actual AM parts on the macroscale undergoing large plastic deformations. Finally, a novel constitutive model for the plastic spin is formulated to capture the influence of the microstructure evolution on the material behavior on the macroscale.
A density-based phase field model is developed where the free energy functional is explicitly linked with molecular dynamics and is referred to as the Molecular Phase Field Method (MoPF). MoPF simulations involve expressing interatomic potentials in terms of density to form a density based free energy functional. Inputs to this functional are taken from atomistics such that the phase field density profile matches the corresponding density profile from atomistic simulations. We analyze our results by comparing the MoPF calculated excess interfacial energies with excess interfacial energies calculated using molecular dynamics associated with several nickel grain boundaries. Additionally, a comparison is made between our results and the interfacial energies of a \Sigma7 boundary across a variety of FCC systems simulated using density functional theory. The MoPF method is able to successfully predict grain boundary free energy trends between grain boundary and material types offering an atomistically informed mesoscale formulation for studying grain boundary physics.
Mean-field modeling and phase-field simulation of grain growth under directional driving forces
(2024)
Directional grain growth is a common phenomenon in the synthetic and natural evolution of various polycrystals. It occurs in the presence of an external driving force, such as a temperature gradient, along which grains show a preferred, yet competitive, growth. Novel additive manufacturing processes, with intense, localized energy deposition, are prominent examples of when directional grain growth can occur, beneath the melting pool. In this work, we derive a phenomenological mean-field model and perform 3D phase-field simulations to investigate the directional grain growth and its underlying physical mechanisms. The effect of the intensity of driving force is simulated and systematically analyzed at the evolving growth front as well as various cross-sections perpendicular to the direction of the driving force. We found that although the directional growth significantly deviates from normal grain growth, it is still governed by a power law relation <R> α tⁿ with an exponent n ~ 0.6–0.7. The exponent n exhibits a nontrivial dependence on the magnitude of the directional driving force, such that the lowest growth exponent is observed for intermediate driving forces. We elaborate that this can originate from the fact that the forces at grain boundary junctions evolve out of balance under the influence of the directional driving force. With increasing the driving forces, the growth exponent asymptotically approaches a value of n ≈ 0.63, imposed by the largest possible grain aspect ratio for given grain boundary energies. The current combined mean-field and phase-field framework pave the way for future exploration in broader contexts such as the evolution of complex additively manufactured microstructures.
The dataset provided in this repository comprises data obtained from a series of full-notch creep tests (FNCT) performed on selected high-density polyethylene (PE-HD) materials (for further details, see section 1 Materials in this document) in accordance with the corresponding standard ISO 16770.
The FNCT is one of the mechanical testing procedures used to characterize polymer materials with respect to their environmental stress cracking (ESC) behavior. It is widely applied for PE-HD materials, that are predominantly used for pipe and container applications. It is based on the determination of the time to failure for a test specimen under constant mechanical load in a well-defined and temperature controlled liquid environment. The test device used here also allows for continuous monitoring of applied force, specimen elongation and temperature.
A giant Zn segregation transition is revealed using CALPHAD-integrated density-based modeling of segregation into Fe grain boundaries (GBs). The results show that above a threshold of only a few atomic percent Zn in the alloy, a substantial amount of up to 60 at.% Zn can segregate to the GB. We found that the amount of segregation abruptly increases with decreasing temperature, while the Zn content in the alloy required for triggering the segregation transition decreases. Direct evidence of the Zn segregation transition is obtained using high-resolution scanning transmission electron microscopy. Base on the model, we trace the origin of the segregation transition back to the low cohesive energy of Zn and a miscibility gap in Fe-Zn GB, arising from the magnetic ordering effect, which is confirmed by ab-initio calculations. We also show that the massive Zn segregation resulting from the segregation transition greatly assists with liquid wetting and reduces the work of separation along the GB. The current predictions suggest that control over Zn segregation, by both alloy design and optimizing the galvanization and welding processes, may offer preventive strategies against liquid metal embrittlement.
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 fracturemechanics-based DTMF concept, which was developed for TMF life assessment of ductile alloys, was applied. It is found that the DTMF 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.
Inconel 718 (IN718) is a traditional age-hardenable nickel-based alloy that has been increasingly processed by additive manufacturing (AM) in recent years. In the as-solidified condition, IN718 exhibits chemical segregation and the undesired Laves phase, requiring a solution annealing (SA) prior to aging. The material produced by AM does not respond to the established thermal routines in the same way as conventionally produced IN718, and there is still no consensus on which routine yields optimal results. This work aims to provide a fundamental understanding of the heat treatment (HT) response by continuously monitoring the microstructural evolution during SA via time-resolved synchrotron x-ray diffraction, complemented by ex-situ scanning electron microscopy (SEM). The samples were produced by laser powder bed fusion to a geometry of 10x20x90 mm³, from which Ø1x5 mm³ cylindric specimens were extracted. Two different scanning strategies – incremental 67° rotations, Rot, and alternating 0°/67° tracks, Alt – were used, leading to two different as-built conditions. 1-hour SAs were carried out in the beamline ID22 of the ESRF at 50 KeV. Two SA temperatures, SA1 = 1020 °C, and SA2 = 1080 °C were tested for each scanning strategy. Data were processed using the software PDIndexer. In the as-built state, all samples showed typical subgrain columnar cell structures with predominant Nb/Mo segregation and Laves phase at the cell walls, as seen by SEM. The Alt scan induced higher intensity on the Laves peaks than the Rot scan, suggesting a greater content of Laves. Chemical homogenization in the SA was largely achieved during the heating ramp (Fig. 1). SA2 eliminated the Laves peaks just before reaching 1080 °C, and mitigated differences between Rot and Alt samples. On the other hand, SA1 induced the precipitation of the generally detrimental δ phase, also observed by SEM. Furthermore, the Rot scan showed higher δ peak intensities than the Alt scan, indicating a higher content of δ in the latter. No signs of recrystallization were observed in any of the investigated SAs.
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.
Recent advances in Deep Learning (DL) have significantly impacted the field of materials modelling. DL tools have been recently considered as promising tools to address the complex relationships among processing, microstructure and property of materials. The thermal stability of polycrystalline materials is a highly interesting and complex problem that could be addressed using DL techniques. The Multi-Phase-Field (MPF) method has emerged as a powerful tool for addressing grain growth phenomena from multiple perspectives. Unlike sharp-interface based methods, the MPF approach bypasses the need for detailed information on individual grains. In this work, we use DL to address issues related to MPF simulations of grain growth including numerical efficiency, computing speed, and resource consumption. This presents specific challenges for high-performance computing (HPC) due to the large datasets and complex computations required by both MPF and DL methods. We study various 3D microstructure settings with the goal of accelerating the simulation process while exploring different physical effects. In particular, the impact of grain boundary and triple junction energies on grain growth are to be investigated. The results will be presented in terms of the evolving size and shape distribution of the grains.
Density-based phase-field (DPF) methods have emerged as a technique for simulating grain boundary thermodynamics and kinetics. Compared to the classical phase-field, DPF gives a more physical description of the grain boundary structure and chemistry, bridging CALPHAD databases and atomistic simulations, with broad applications to grain boundary and segregation engineering. Notwithstanding their notable progress, further advancements are still warranted in DPF methods. Chief among these are the requirements to resolve its performance constraints associated with solving fourth-order partial differential equations (PDEs) and to enable the DPF methods for simulating moving grain boundaries. Presented in this work is a means by which the aforementioned problems are addressed by expressing the density field of a DPF simulation in terms of a traditional order parameter field. A generic DPF free energy functional is derived and used to carry out a series of equilibrium and dynamic simulations of grain boundaries in order to generate trends such as grain boundary width vs. gradient energy coefficient, grain boundary velocity vs. applied driving force, and spherical grain radius vs. time. These trends are compared with analytical solutions and the behavior of physical grain boundaries in order to ascertain the validity of the coupled DPF model. All tested quantities were found to agree with established theories of grain boundary behavior. In addition, the resulting simulations allow for DPF simulations to be carried out by existing phase-field solvers.
Liquid-metal embrittlement (LME) of galvanized (Zn-coated) advanced high-strength steels is a long-known problem in materials science. Here we reveal the initial microstructural processes underneath the Zn-coating that lead to LME-microcrack initiation in the steel substrate. We track the microstructural evolution during the first tens of milliseconds and find pronounced signatures of Fe-Zn intermetallic precipitation in both ferrite grain boundaries and at internal ferrite-oxide phase boundaries. In concert with novel CALPHAD-integrated density-based thermodynamic modelling, we demonstrate that Zn-rich intermetallic phase-nucleation can occur at markedly low processing temperatures due to a segregation transition. We show that a small Znenrichment caused by Zn bulk-diffusion during the initial temperature rise in a joining process is sufficient to induce the segregation transition and subsequent nucleation of Fe-Zn intermetallic grain-boundary phases, which the experiments link to crack initiation sites. These findings direct focus onto LME-controlling microstructural and thermodynamic phenomena at temperatures below the ductility trough and the austenite formation temperature.
Grain boundary (GB) chemical and structural variations can significantly influence materials performance. The former is generally ascribed to the structural gradient between the grain and GB. While GB segregation may be accompanied by chemical and structural variations, clear insights about the GB’s thermodynamic phase behaviour upon coupling between its chemistry and structure is lacking. Using the CALPHAD integrated density-based phase field model, we study the co-evolution of GB’s structure and segregation in Fe-Mn alloys. We found that the GB segregation transition is amplified if its structure can respond to chemical variation. Additionally, the coupling between GB structural and segregation evolution was found to enable co-existence of the spinodally formed low- and high-Mn phases within the GB. In the light of atomistic simulations, we expand on investigating the correlation between the parameters that characterise the GB density map with GB properties.
Several recent studies have revealed that the phase decomposition in medium- and high-entropy alloys is triggered by solute segregation at grain boundaries. The chemically complex nature of these alloys already clues that such segregation in materials should be something more than the interaction between solutes and grain boundary, but also affected by the solute-solute interactions during the segregation. In fact, experiments indicate the significance of such solute-solute interaction. Yet, the mechanisms of co-segregation in multi-component alloys are rather challenging to explore and rarely studied quantitatively. Recently, a CALPHAD-integrated density-based phase-field model has been proposed for studying grain boundary phenomena. Several applications of this model have shown its expansive capacity for investigating grain boundary segregation and phase behavior. In this talk, the applications of this model to studying co-segregation phenomena and grain boundary phase diagrams in multi-component alloys are presented ––the term ‘co-segregation’ here refers to co-evolution and any mutual interplay among the solutes and grain boundary during the segregation. In particular, the iron-based ternary and quaternary alloys are discussed. I show how a grain boundary may have its own miscibility gap and how this immiscibility can influence the co-segregation behavior. As an alternative to grain boundary phase diagrams, rather suited for binary and ternary alloys, a new concept of co-segregation maps for screening and segregation design in multi-component alloys is presented. Applying the co-segregation maps, the nonlinear Mn and Cr co-segregation in Fe-Co-Mn-Cr is discussed.
The essence of dynamic failure is closely linked to the formation of adiabatic shear bands (ASB), which result from the localization of shear strain under high deformation speeds accompanied by a rapid temperature increase. Understanding this phenomenon is crucial in view of safety issues when impacts of fast rotating machine components (i.e. aircraft turbine blades) may occur. Our contribution addresses both the experimental evidence and characterization of ASBs due to high-speed impact tests at the Split HOPKINSON pressure bar (SHPB) setup and the finite element analysis to determine the parameters of the underlying constitutive model, which is closely related to JOHNSON-COOK (JC) material model.
Experimental investigations were performed on notched shear specimens made of the fine -grained structural steel S690QL and the displacements in the regions affected by shear localization were measured with subset-based local Digital Image Correlation (DIC). The displacement fields, obtained in the SHPB tests, were considered as an objective to validate and to identify the constitutive parameters with. The JC model could reasonably reproduce the displacement distribution. In order to overcome the issues with mesh dependency we provide a nonlocal extension based on the implicit gradient model approach.
The embrittlement of metallic alloys by liquid metals leads to catastrophic material failure and severely impacts their structural integrity. The weakening of grain boundaries by the ingress of liquid metal and preceding segregation in the solid are thought to promote early fracture. However, the potential of balancing between the segregation of cohesion-enhancing interstitial solutes and embrittling elements inducing grain boundary decohesion is not understood. Here, we unveil the mechanisms of how boron segregation mitigates the detrimental effects of the prime embrittler, zinc, in a Σ5 [0 0 1] tilt grain boundary in α −Fe (4 at.% Al). Zinc forms nanoscale segregation patterns inducing structurally and compositionally complex grain boundary states. Ab-initio simulations reveal that boron hinders zinc segregation and compensates for the zinc induced loss in grain boundary cohesion. Our work sheds new light on how interstitial solutes intimately modify grain boundaries, thereby opening pathways to use them as dopants for preventing disastrous material failure.
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.
This contribution contains the raw data used to compare experimental results with thermodynamic calculations using the CALPHAD method, which is related to the research article “The AlMo0.5NbTa0.5TiZr refractory high entropy superalloy: experimental findings and comparison with calculations using the CALPHAD method” [1] , and therefore this article can be used as a basis for interpreting the data contained therein. The AlMo0.5NbTa0.5TiZr refractory superalloy was characterized in the cast and annealed condition (1400 °C for 24 h) in order to measure grain size and to identify and measure the size and area fraction of the phases present. The raw data of this article include X-ray diffraction (XRD) measurements, microstructural characterization by scanning and transmission electron microscopy (SEM and TEM), and elemental analysis by energy dispersive X-ray spectroscopy (EDX). XRD includes the determination of phases and the lattice parameters (A2, B2, and hexagonal structure). Microstructural analysis by scanning and transmission electron microscopy includes (1) identification of composition, size, and volume fraction of the present phases and (2) determination of grain size. Based on these experimental data, it is possible to identify similarities and discrepancies with the data calculated using the CALPHAD method for the alloy under study in Ref. [1] , which provides the basis for better and more efficient development of reliable databases.
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.
This contribution contains the raw data used to compare experimental results with thermodynamic calculations using the CALPHAD method, which is related to the research article “The AlMo0.5NbTa0.5TiZr refractory high entropy superalloy: experimental findings and comparison with calculations using the CALPHAD method” [1] , and therefore this article can be used as a basis for interpreting the data contained therein. The AlMo0.5NbTa0.5TiZr refractory superalloy was characterized in the cast and annealed condition (1400 °C for 24 h) in order to measure grain size and to identify and measure the size and area fraction of the phases present. The raw data of this article include X-ray diffraction (XRD) measurements, microstructural characterization by scanning and transmission electron microscopy (SEM and TEM), and elemental analysis by energy dispersive X-ray spectroscopy (EDX). XRD includes the determination of phases and the lattice parameters (A2, B2, and hexagonal structure). Microstructural analysis by scanning and transmission electron microscopy includes (1) identification of composition, size, and volume fraction of the present phases and (2) determination of grain size. Based on these experimental data, it is possible to identify similarities and discrepancies with the data calculated using the CALPHAD method for the alloy under study in Ref. [1] , which provides the basis for better and more efficient development of reliable databases.
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.
A main source of current challenges in materials science and engineering is the ever-increasing complexity in materials chemistry and processing resulting in complex microstructures, making the assessment of process-microstructure-property-performance relations difficult, even unmanageable. Here the computational materials science is facing the same situation. In this talk, I share a viewpoint that the complexities in chemistry, processing and microstructures can be circumscribed by integrating existing knowledges of bulk thermodynamics and kinetics to the unknown thermodynamics and kinetics of microstructure elements. To this end, I discuss several successful examples on grain boundary segregation engineering how this scientific advance can be conducted. A roadmap is proposed, beginning to form on generalizing the concept of phase diagrams.
Along with the desire for developing novel multi-principal element alloys, also known as high-entropy alloys, the concern about their safe application is also increasingly growing. This relates to the alloys’ phase stability, in particular, the control required over unexpected phase decompositions resulting from solute segregation at grain boundaries. Yet, the mechanisms of co-segregation and grain boundary phase decomposition in multi-component alloys are rather challenging to explore. In fact, quantitative investigation of grain boundary behaviors is mostly conducted for binary and a few ternary alloys. In this work, we apply the recently introduced CALPHAD-integrated density-based formalism [RSC Advances 10 (2020) 26728-26741] for considering co-segregation phenomena in alloys with an arbitrary number of components —the term ‘co-segregation’ here refers to co-evolution and any mutual interplay among the solute atoms during their interaction with a grain boundary. Quaternary Fe-Co-Mn-Cr alloy system is studied. We present two major advances beyond previous results: First, a co-segregation-induced multi-component grain boundary spinodal decomposition is quantitatively simulated for the first time. We found that in addition to its low cohesive energy and asymmetrical mixing enthalpy due to magnetic ordering, Mn plays a leading role in triggering interfacial phase decomposition by having a relatively large, concentration-dependent atomic mobility. Second, as an alternative to grain boundary phase diagrams proposed for binary and ternary alloys, we introduce the concept of co-segregation maps for grain boundary segregation screening and design in multi-component alloys. Applying the co-segregation maps, the nonlinear Mn and Cr co-segregation are discussed. Depicted on the alloying composition and phase space, the co-segregation maps enable the required insights to guide a safer, more controlled design of high-entropy alloys.
Grain boundaries (GBs)’s role in determining the functional and mechanical properties of polycrystalline materials is inscribed in both their structure and chemistry. Upon solute segregation, the structure and composition of a GB can change concurrently. We study the co-evolution of GB’s structure and segregation by enhancing the density-based phase-field model to account for the in-plane structural variations in the GB. Significant mutual coupling is revealed between the GB’s chemical and structural states during Mn segregation in Fe-Mn alloys. We found that the structural degrees of freedom in a GB (the ability of the GB structure to respond to the chemical variation) amplifies Mn segregation transition, even when the GB structure stays unchanged. When the GB structure is not uniform, that is the usual case, the coupling between GB structure and segregation evolution also enables the spinodally formed low- and high-Mn phases (upon segregation transition) to co-exist within the GB region. These findings explain the stabilizing mechanism of pronounced interfacial segregation fluctuations, experimentally evidenced in Fe-Mn GBs, and give new insights on the structural sensitivity of GBs’ segregation phenomena and the mutual chemo-structural interplay.
Mit der Digitalisierung von Materialien und Prozessen ist ein Paradigmenwechsel in der Materialentwicklung, -gestaltung und -optimierung verbunden, welcher gleichermaßen vielseitige Möglichkeiten eröffnet und eine große Herausforderung darstellt. Insbesondere sind bei den Digitalisierungsbestrebungen die Qualitätssicherung von Prozessen und Ausgabedaten sowie die Interoperabilität zwischen Anwendungen nach FAIR-Prinzipien (Findability, Accessibility, Interoperability, Reusability) sicherzustellen. Dies umfasst die Speicherung, Verarbeitung und Abfrage von Daten in möglichst standardisierter Form, wobei entsprechend auch Normungs- und Standardisierungsgremien beteiligt werden müssen. Um der Herausforderung gerecht zu werden, Materialdaten für alle Beteiligten konsistent zu kontextualisieren, müssen alle notwendigen Informationen zum Zustand des Materials inklusive produktions- und anwendungsbedingter Veränderungen über eine einheitliche, maschinenlesbare Beschreibung verfügbar gemacht werden. Hierfür sollen Ontologien genutzt werden, da sie maschinenverständliche und -interpretierbare Wissensrepräsentationen durch semantische Konzeptualisierungen ermöglichen, die für das Datenmanagement und die Digitalisierung im Bereich der Materialwissenschaften benötigt werden.
Dieses hochaktuelle Thema der Integration und Wiederverwendung von Wissen und Daten aus Herstellung, Bearbeitung und Charakterisierung von Materialien wird in den Projekten Innovationsplattform MaterialDigital (PMD, materialdigital.de) und Materials-open-Lab (Mat-o-Lab, matolab.org) adressiert. Diese beiden unter der Beteiligung der Bundeanstalt für Materialforschung und -prüfung (BAM) durchgeführten Projekte wurden auf der 39. Vortrags- und Diskussionstagung „Werkstoffprüfung“ (2021) grundlegend vorgestellt. In dieser Präsentation sollen die Weiterentwicklungen hinsichtlich der Speicherung von Zugversuchsdaten gemäß einer normenkonformen ontologischen Repräsentation vorgestellt werden. Das umfasst den Weg von der Entwicklung einer Ontologie nach Norm, der Konvertierung von Daten aus Standardtests in das interoperable RDF-Format bis hin zur Verknüpfung von Ontologie und Daten. Letztendlich können die entsprechenden Daten in einem Triple Store abgelegt und abgefragt werden.
Die übliche Standardisierung von mechanischen Prüfverfahren im Bereich der Materialwissenschaft und Werkstofftechnik dient als solide Grundlage für die Ontologieentwicklung. Daher wurde der Zugversuch von Metallen bei Raumtemperatur nach DIN EN ISO Norm 6892-1:2019-11 als einer der ersten Anwendungsfälle in den genannten Projekten ausgewählt. Die Betrachtung und Beschreibung des Zugversuchs beinhaltet sowohl dessen ontologische Darstellung als auch eine exemplarische Datengenerierung. Die semantische Verbindung von Ontologie und Daten führt zu Interoperabilität und einer verbesserten Abfragefähigkeit.
Engineering grain boundaries demands a quantitative description of both their segregation and specific phase behavior. Recently I have proposed a density-based model for grain boundary thermodynamics that enables CALPHAD integrated derivation of grain boundary phase diagrams, broadly applied now in studying various alloys. Combining this model with experimental investigations, in this talk, new aspects of interfacial segregation and phase transformation revealed in polycrystalline alloys are discussed. The effect of elastic interaction on grain boundary phase behavior is incorporated. We consider Al alloys and novel high-entropy alloys and discuss a general strategy for grain boundary engineering.
Following the new paradigm of materials development, design and optimization, the digitalization of materials and processes is the main goal which imposes a huge challenge. In this respect, the quality assurance of processes and output data as well as the interoperability between applications following FAIR (findability, accessibility, interoperability, reusability) principles are to be ensured. This includes storage, processing and querying of data in a preferably standardized form, also addressing the incorporation of standardization bodies. To meet the challenge to contextualize material data in a way that is consistent with all stakeholders, all necessary information on the condition of the material including production and application-related changes have to be made available via a uniform, machine-readable description. For this purpose, ontologies are to be used since they allow for machine-understandable knowledge representations and semantic conceptualizations that are needed for data management and the digitalization in the field of materials science.
With respect to this currently ever-growing topic of integration and reuse of data and knowledge from synthesis, production and characterization of materials, this presentation shows the efforts taken within the project Platform MaterialDigital (PMD, materialdigital.de) to store tensile test data in accordance with a standard-compliant ontological representation. The includes the path from developing an ontology in accordance with the respective standard, converting ordinary and arbitrarily selected data gained from standard tests into the interoperable RDF format, up to connecting the ontology and data, respectively. Finally, such data can be queried from a triple store.
In the field of material science and engineering (MSE), most mechanical test methods are standardized which serves as a valid basis for ontology development. Therefore, the well-known tensile test of metals at room temperature (DIN EN ISO standard 6892-1:2019-11) was selected to be considered as one of the first use cases in PMD. This consideration within the PMD features both, the ontological representation of such a tensile test in accordance with the standard as well as exemplary data generation. The semantic connection of the ontology and data leads to interoperability and an enhanced ability of querying.
Entwicklung der Mikrostruktur der mechanischen Eigenschaften und der Eigenspannungen in L-PBF 316L
(2022)
Die additive Fertigung (AM) metallischer Werkstoffe mittels Laser Powder Bed Fusion (L-PBF) ermöglicht einzigartige hierarchische Mikrostrukturen, die zu Verbesserungen bestimmter mechanischer Eigenschaften gegenüber konventionell hergestellten Varianten derselben Legierung führen können. Allerdings ist das L-PBF-Verfahren häufig durch das Vorhandensein hoher Eigenspannungen gekennzeichnet, die es zu verstehen und zu mindern gilt. Daher ist das Verständnis der Mikrostrukturen, der Eigenspannungen und der daraus resultierenden mechanischen Eigenschaften entscheidend für eine breite Akzeptanz bei sicherheitskritischen Anwendungen. Die BAM hat ein multidisziplinäres Forschungsprogramm gestartet, um diese Aspekte bei LPBF 316L zu untersuchen. Der vorliegende Beitrag stellt einige der wichtigsten Ergebnisse vor: der Einfluss von Prozessparametern auf die Mikrostruktur, der Einfluss von Mikrostruktur und Textur auf die Festigkeit, Kriechverhalten und Schädigung und die Stabilität von Eigenspannungen und Mikrostruktur unter Wärmebehandlungsbedingungen.
Monte-Carlo-Analysis of Minimum Burst Requirements for Composite Cylinders for Hydrogen Service
(2021)
For achieving Net Zero-aims hydrogen is an indispensable component, probably the main component. For the usage of hydrogen, a wide acceptance is necessary, which requires trust in hydrogen based on absence of major incidents resulting from a high safety level. Burst tests stand for a type of testing that is used in every test standard and regulation as one of the key issues for ensuring safety in use. The central role of burst and proof test is grown to historical reasons for steam engines and steel vessels but - with respect for composite pressure vessels (CPVs) - not due an extraordinary depth of outcomes. Its importance results from the relatively simple test process with relatively low costs and gets its importance by running of the different test variations in parallel. In relevant test und production standards (as e. g. ECE R134) the burst test is used in at least 4 different meanings. There is the burst test on a) new CPVs and some others b) for determining the residual strength subsequent to various simulations of ageing effects. Both are performed during the approval process on a pre-series. Then there is c) the batch testing during the CPVs production and finally d) the 100% proof testing, which means to stop the burst test at a certain pressure level. These different aspects of burst tests are analysed and compared with respect to its importance for the resulting safety of the populations of CPVs in service based on experienced test results and Monte-Carlo simulations. As main criterial for this the expected failure rate in a probabilistic meaning is used. This finally ends up with recommendations for relevant RC&S especially with respect to GTR 13.
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 large surface-to-volume ratio of nanoparticles is understood to be the source of many interesting phenomena. The melting temperature of nanoparticles is shown to dramatically reduce compared to bulk material. Yet, at temperatures below this reduced melting point, a liquid-like atomic arrangement on the surface of nanoparticles is still anticipated to influence its properties. To understand such surface effects, here, we study the coalescence of Au nanoparticles of various sizes using molecular dynamics simulations. Analysis of the potential energy and Lindemann index distribution across the nanoparticles reveals that high-energy, high-mobility surface atoms can enable the coalescence of nanoparticles at temperatures much lower than their corresponding melting point. The smaller the nanoparticles, the larger the difference between their melting and coalescence temperatures. For small enough particles and/or elevated enough temperatures, we found that the coalescence leads to a melting transition of the two nominally solid nanoparticles, here discussed in relation to the heat released due to the surface reduction upon the coalescence and the size dependence of latent heat. Such discontinuous melting transitions can lead to abrupt changes in the properties of nanoparticles, important for their applications at intermediate temperatures.
Detailed microstructural characterization of the AlMo0.5NbTa0.5TiZr refractory high entropy superalloy in the as-cast state is reported for first time and compared with the state annealed at 1400 oC for 24 h. The former shows a dendritic structure, with a mixture of A2/B2 phases < 20 nm in both the dendritic and interdendritic regions. A mostly amorphous phase, rich in Al and Zr, is found within the interdendritic region. The annealed state reproduced the combination of A2/B2/Al-Zr-rich phases reported previously. Calculations from two relevant ThermoCalc databases were compared with the experimental results. Equilibrium calculations were compared with results for the annealed alloy, whereas solidification paths calculated using Scheil-Gulliver model were used for comparison with the as-cast alloy. A previously hypothesized spinodal decomposition during cooling as the mechanism responsible for the patterned A2/B2 microstructure is confirmed via the CALPHAD calculations, pointing to its use as an efficient design tool for such alloys. Finally, the comparison between the experimental and computational findings allowed better understanding the solidification path and equilibrium stability of this alloy, giving a base to make better decisions on the field of new refractory superalloy design.
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.
Grain boundaries (GBs) are planar lattice defects that govern the properties of many types of polycrystalline materials. Hence, their structures have been investigated in great detail. However, much less is known about their chemical features, owing to the experimental difficulties to probe these features at the atomic length scale inside bulk material specimens. Atom probe tomography (APT) is a tool capable of accomplishing this task, with an ability to quantify chemical characteristics at near-atomic scale. Using APT data sets, we present here a machine-learning-based approach for the automated quantification of chemical features of GBs. We trained a convolutional neural network (CNN) using twenty thousand synthesized images of grain interiors, GBs, or triple junctions. Such a trained CNN automatically detects the locations of GBs from APT data. Those GBs are then subjected to compositional mapping and analysis, including revealing their in-plane chemical decoration patterns. We applied this approach to experimentally obtained APT data sets pertaining to three case studies, namely, Ni-P, Pt-Au, and Al-Zn-Mg-Cu alloys. In the first case, we extracted GB specific segregation features as a function of misorientation and coincidence site lattice character. Secondly, we revealed interfacial excesses and in-plane chemical features that could not have been found by standard compositional analyses. Lastly, we tracked the temporal evolution of chemical decoration from early-stage solute GB segregation in the dilute limit to interfacial phase separation, characterized by the evolution of complex composition patterns. This machine-learning-based approach provides quantitative, unbiased, and automated access to GB chemical analyses, serving as an enabling tool for new discoveries related to interface thermodynamics, kinetics, and the associated chemistry-structure-property relations.
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.
Laser powder bed fusion (LPBF) is an additive manufacturing process for materials which inherently tends to yield various degrees of metastable hierarchical microstructures, defects and high residual stresses in the as-built condition depending on the process parameters. The understanding of the evolution of these typical features during heat treatment and subsequent thermal and mechanical ageing is crucial for the wider acceptance for safety critical structures. A multi-disciplinary research project at BAM studying the development of the microstructure, defects, residual stresses typical of LPBF 316L and their evolution during thermal and mechanical ageing has led to insights into the stability of these inherent features. This presentation aims to give a broad overview of the project with a few specific cases of investigation. Firstly, the formation of residual stresses, the nature of the initial microstructure, the tensile properties and a modelling approach to understand the anisotropy will be presented. This will be followed by examples of studies of their evolution during heat treatment, long term thermal exposure, and room temperature and high temperature mechanical testing compared to a baseline of conventional wrought variant of the same alloy.
Porosity in single-crystal nickel-base superalloys is removed by hot isostatic pressing (HIP) at temperatures above gamma’-solvus where the material is very soft and ductile. For example, single-crystal nickel-base superalloy CMSX-4 is HIPed at temperature 1288 °C, which is slightly higher than the gamma’-solvus temperature of this alloy equal to about 1280 °C. It is assumed that pore shrinking during HIP is mostly due to dislocation creep. Such a modelling of HIP of CMSX-4 was started in our group on the base of results of creep tests of [001] single-crystals at 1288 °C [1]. However, it was found later [2] that the alloy CMSX-4 shows very strong creep anisotropy at 1288 °C. Therefore, for calibration of the creep law, creep tests of different orientations under different stress levels are required at the HIP temperature. This was the main task of present work. Single-crystals of CMSX-4 of axial orientations [001], [011], [123] and [111] were cast by VIAM Moscow and tested by BAM Berlin under creep conditions at 1288 °C and stress levels between 4 MPa and 16 MPa. At all stress levels, the creep rate increases by an order of magnitude when changing the orientation from [001] to [111] with [011] and [123] orientations in between. Such a character of creep anisotropy corresponds to the orientation dependence of the Schmid factor for octahedral glide.
The crystal viscoplasticity model developed in [1] was improved to better represent the time induced softening observed during creep. The creep tests for different stresses and orientations as well as pore closure were simulated. The results of pore closure simulation are compared with measurements of porosity decrease during Hiping.
The Gibbs free energy of a grain boundary is a complex thermodynamic function of temperature, pressure, and composition. These complexities add to the intrinsic crystallographic and chemical constraints imposed by the adjacent bulk phase. Recently we have proposed a density-based model for assessing grain boundary thermodynamics that enables a CALPHAD-informed description of the grain boundary. As such, the Gibbs free energy of the grain boundary is directly linked with available CALPHAD thermodynamic data. In this talk, new aspects of interfacial segregation and phase transformation are revealed by benchmarking the current model for various experimental cases, including several steels, high-entropy alloys and aluminum alloys. The effects of elastic interactions on the grain boundary segregation and the application of the model to a nanocrystalline Pt-Au alloy, with numerous grain boundaries of various characters, will be discussed.
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.
The elastic energy of mixing for multi-component solid solutions is derived by generalizing Eshelby's sphere-in-hole model. By surveying the dependence of the elastic energy on the chemical composition and lattice misfit, we derive a lattice strain coefficient λ*. Studying several high-entropy alloys and superalloys, we propose that most solid solution multi-component alloys are stable when λ*<0.16, generalizing the Hume-Rothery atomic-size rule for binary alloys. We also reveal that the polydispersity index δ, frequently used for describing strain in multi-component alloys, directly represents the elastic energy e with e=qδ², q being an elastic constant. Furthermore, the effects of (i) the number and (ii) the atomic-size distribution of constituting elements on the phase stability of high-entropy alloys were quantified. The present derivations and discussions open for richer considerations of elastic effects in high-entropy alloys, offering immediate support for quantitative assessments of their thermodynamic properties and studying related strengthening mechanisms.
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.
The phase-like behavior of grain boundaries (GBs), recently evidenced in several materials, is opening up new possibilities in the design of alloy microstructures. In this context, GB phase diagrams are contributing to a predictive description of GB segregation and (interfacial) phase changes. The influence of chemo-mechanical solute-GB interactions on the GB phase diagram remains elusive so far. This is particularly important for multi-component alloys where the elastic interactions among solute atoms, of various sizes and bonding energies, can prevail, governing a complex co-segregation phenomenon. Recently, we developed a density-based model for GB thermodynamics that intrinsically accounts for GB elasticity in pure elements. In this work, we incorporate the homogeneous and heterogeneous elastic energies associated with the solutes into the density-based framework. We derive the multi-component homogeneous elastic energy by generalizing the continuum misfitting sphere model and extend it for GBs. The density-based free energy functional directly uses bulk CALPHAD thermodynamic data. The model is applied to binary and ternary Al alloys. We reveal that the elastic energy can profoundly affect the GB solubility and segregation behavior, leading to Cu segregation in otherwise Cu-depleted Al GBs. Consequently, GB segregation transition, i.e., a jump in the GB segregation as a function of alloy composition, is revealed in Al-Cu and Al-Cu-Mg alloy systems with implications for subsequent GB precipitation in these alloys. CALPHAD-informed elasticity-incorporated GB phase diagrams enable addressing a broader range of GB phenomena in engineering multi-component alloys.
For more than half a century, spinodal decomposition has been a key phenomenon in considering the formation of secondary phases in alloys. The most prominent aspect of the spinodal phenomenon is the lack of an energy barrier on its transformation pathway, offering an alternative to the nucleation and growth mechanism. The classical description of spinodal decomposition often neglects the influence of defects, such as grain boundaries, on the transformation because the innate ability for like-atoms to cluster is assumed to lead the process. Nevertheless, in nanocrystalline alloys, with a high population of grain boundaries with diverse characters, the structurally heterogeneous landscape can greatly influence the chemical decomposition behavior. Combining atom-probe tomography, precession electron diffraction and density-based phase-field simulations, we address how grain boundaries contribute to the temporal evolution of chemical decomposition within the miscibility gap of a Pt-Au nanocrystalline system. We found that grain boundaries can actually have their own miscibility gaps profoundly altering the spinodal decomposition in nanocrystalline alloys. A complex realm of multiple interfacial states, ranging from competitive grain boundary segregation to barrier-free low-dimensional interfacial decomposition, occurs with a dependency upon the grain boundary character.
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.