5 Werkstofftechnik
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Temperature-induced, stress-induced martensitic phase transitions and martensite reorientation process in Ni rich (50.9 at.%) NiTi pseudoelastic NiTi wires with ultra-fine grained (UFG) microstructure were studied by electrical resistance measurements. Measurements of the electrical resistance as a function of temperature at different constant mechanical loads accompanied by complementary experiments with variable loads at constant temperature were performed. Results show that the transformation mechanisms in UFG microstructures exhibit a higher level of complexity when compared with those characterizing the behavior of other microstructures (e.g., recrystallized or larger grains size). It was found that a threshold stress level below 150 MPa delimits the transition from a homogeneous (low stress) to localized but reversible Lüders type transformation (high stress) when the transformations are induced under constant applied stress and that reorientation processes require stresses of 100 MPa in the present UFG wires. Even though the strain evolutions do not always show two distinct yielding events during cooling or heating, electrical resistance measurements proved that a two-step transformation involving R-phase and B19' martensite was always present in the extended range of temperatures and stresses investigated here.
Die Mikrostruktur von ausscheidungsgehärteten Aluminiumlegierungen ist von herausragender Bedeutung für ihre Festigkeit, da nur Werkstoffe mit gezielt eingestellter Mikrostruktur für Radialverdichterräder ausreichende Festigkeiten erreichen. Diese optimierte Mikrostruktur ändert sich jedoch während des Betriebs, denn die Bauteile werden bei Temperaturen eingesetzt, die nahe der Aushärtetemperatur liegen oder sogar darüber hinausgehen und folglich ist mit Alterung der Mikrostruktur und damit einhergehender Degradation der Eigenschaften zu rechnen. Diese Effekte konnten bisher in der Lebensdauervorhersage nicht berücksichtigt werden, da ihre diesbezüglichen Auswirkungen lediglich qualitativ bekannt waren. In diesem Forschungsvorhaben wurde daher für die Legierung EN AW-2618A einerseits eine sorgfältige und umfassende Charakterisierung der Gefügeentwicklung für anwendungsrelevante Temperaturen und Zeiten bis zu 25.000 h vorgenommen und andererseits eine solide Datenbasis bezüglich der mechanischen Eigenschaften (Zugfestigkeit, Kriechwiderstand, LCF-, TMF-Verhalten) und ihren Änderungen geschaffen. Darauf aufbauend wurde ein Verfahren entwickelt, um die Genauigkeit der Lebensdauerbewertung für Abgasturbolader (ATL)-Verdichterräder aus EN AW-2618A zu verbessern. Ein zeit- und temperaturabhängiges Verformungsmodell nach Chaboche, welches die wesentlichen Phänomene der Hochtemperaturverformung und der Wechselplastizität beschreibt, wurde erweitert und berücksichtigt nun die Werkstoffalterung, indem die Festigkeit nicht nur als Funktion der Temperatur, sondern auch des Alterungszustands (d. h. des mittleren Radius der Ausscheidungen) dargestellt wird. Für die Erweiterung des Modells zur Bewertung der Ermüdungslebensdauer unter Rainflow-klassierten Betriebslastkollektiven wurde analog verfahren. Die berechnete Lebensdauer der im Verlauf des Vorhabens durchgeführten LCF- und TMF-Versuche stimmt gut mit den experimentellen Ergebnissen überein.
In diesem Forschungsvorhaben wurde ein Verfahren entwickelt, um die Genauigkeit der Lebensdauerbewertung für Abgasturbolader (ATL)-Verdichterräder aus der ausscheidungs-härtbaren Aluminiumlegierung EN AW-2618A zu verbessern. Dies umfasst insbesondere die Berücksichtigung der Werkstoffalterung, mit der beim Einsatz dieser Bauteile unter entsprechender Betriebsbeanspruchung (Temperatur, Zeit, Spannung) gerechnet werden muss. Zunächst wurde eine solide experimentelle Datenbasis für den untersuchten Werkstoff geschaffen. Dies umfasste sowohl eine mechanische als auch eine mikrostrukturelle Charakterisierung des Ausgangszustands (T61) sowie von ausgelagerten Zuständen bis zu 25.000 h bei betriebsrelevanten Temperaturen (160 °C, 180 °C, 190 °C). Bei den Untersuchungen zur Mikrostruktur wurde der Fokus auf die Entwicklung der Radien der stäbchen-förmigen aushärtenden Phase gelegt, die während der Alterung vergröbern. Der Zusammenhang zwischen Auslagerungstemperatur, -zeit und ggfs. mechanischer Belastung wurde erstmals in diesem Umfang quantifiziert und entsprechende Gesetzmäßigkeiten zur Beschreibung der Vergröberung ermittelt. Vergleichend dazu wurde der Einfluss der Alterung auf die Härte, die Festigkeit, das Kriechverhalten und die Ermüdungslebensdauer (LCF, TMF) bestimmt, so dass eine Korrelation zur Mikrostruktur vorliegt.
Die Ergebnisse der Kriechversuche wurden zur Kalibrierung eines modifizierten Sinus-hyperbolicus-Kriechmodells verwendet. Ein zeit- und temperaturabhängiges Verformungsmodell nach Chaboche, welches die wesentlichen Phänomene der Hochtemperaturverformung und der Wechselplastizität beschreibt, wurde erweitert und berücksichtigt nun die Werkstoffalterung, indem die Festigkeit nicht nur als Funktion der Temperatur, sondern auch des Alterungszustands (d. h. des mittleren Radius der Ausscheidungen) dargestellt wird. Für die Erweiterung des Modells zur Bewertung der Ermüdungslebensdauer wurde analog verfahren. Die berechnete Lebensdauer der im Verlauf des Vorhabens durchgeführten LCF- und TMF-Versuche stimmt gut mit den experimentellen Ergebnissen überein. Lediglich ein LCF-Versuch mit einer Haltezeit von 900 s im Zug weicht deutlich vom Mittelwert ab und zeigt die Grenzen des zeitunabhängigen Schädigungsmodells auf. Versuche mit kürzeren Haltezeiten bis zu 60 s liegen im Streuband, ebenso die verschiedenen Alterungszustände. Eine Schädigungsakkumulation unter Berücksichtigung der fortschreitenden Alterung über der Lebensdauer wurde entwickelt und implementiert. Neben der Berücksichtigung der Alterung in der Verformungs- und Lebensdaueranalyse besteht auch die Möglichkeit, komplexe Belastungszyklen in einem Postprozessing zu bewerten, indem Rainflow-Klassierungen typischer komplexer Belastungszyklen vorgenommen werden.
Die Methodik und die Modelle wurden in die Finite-Elemente-Programme Abaqus und Ansys implementiert und stehen für die rechnerische Bewertung von Bauteilen zur Verfügung.
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.
A study was made on the effect of creep loading on the precipitate radii evolution of the aluminum alloy 2618A.
The overageing process of the alloy was investigated under load at a temperature of 190 °C with stresses between 79 and 181 MPa and compared to stress free isothermal ageing. The precipitates responsible for strength were characterized using dark-field transmission electron microscopy (DFTEM). This allows the experimental Determination of radii distributions of the rod-shaped Al2CuMg precipitates and the evaluation regarding their mean precipitate radius. It was found that the mean precipitate radius enables the comparison of the different microstructural conditions of crept and uncrept samples. The mean precipitate radii of the samples experiencing creep are significantly higher than those of undeformed samples. It was shown that the acquired radii distributions are viable to determine averaged particle radii for comparison of the aged samples. A ripening process including pipe diffusion along dislocations describes the data on coarsening very well for the creep samples.
Les aubes de turbines à gaz utilisées en particulier pour les turboréacteurs de l’aéronautique sont élaborées par fonderie en superalliage monocristallin à base de nickel. Le procédé de fonderie, ainsi que les traitements thermique d’homogénéisation réalisés à très haute température, induisent la présence de pores au sein des pièces qui affectent les propriétés mécaniques et la durée de vie des aubes. Afin de réduire cette porosité les motoristes effectuent un traitement de compression isostatique à chaud (CIC) au cours duquel la porosité diminue par fermeture des pores. Afin de mieux comprendre les mécanismes impliqués au cours du traitement de CIC, nous avons lancé un programme de recherche dans le cadre du projet ERA-Net MICROPORE. La modélisation par champ de phase des mécanismes en jeu est présentée au cours de ce colloque. Nous présentons dans cette affiche un des volets de la caractérisation expérimentale du projet.
Des échantillons de superalliage CMSX4 sont observés après traitement de mise en solution et CIC sous 103 MPa à 1288°C pour différentes durées. Les pores présents sont caractérisés par microscopie électronique à balayage (MEB) afin de suivre l’évolution du taux de porosité au cours du traitement. Une caractérisation plus détaillée de pores partiellement refermés est menée par MEB et grâce à la diffraction des électrons rétrodiffusés (EBSD). Une vision tridimensionnelle de ces défauts est obtenue par des coupes métallographiques effectuées par découpe ionique (FIB).
Le projet ERA – Net MICROPORE est financé en Allemagne par la DFG (projects EP 136/1-1 and FE933/2-1) et en France par l’ANR (projects ANR15-MERA-000-03 and ANR15-MERA-0003-04).
A key limitation of the most constitutive models that reproduce a Degradation of quasi-brittle materials is that they generally do not address issues related to fatigue. One reason is the huge computational costs to resolve each load cycle on the structural level. The goal of this paper is the development of a temporal Integration scheme, which significantly increases the computational efficiency of the finite element method in comparison to conventional temporal integrations.
The essential constituent of the fatigue model is an implicit gradient-enhanced formulation of the damage rate. The evolution of the field variables is computed as amultiscale Fourier series in time.On a microchronological scale attributed to single cycles, the initial boundary value problem is approximated by linear BVPs with respect to the Fourier coefficients. Using the adaptive cycle jump concept, the obtained damage rates are transferred to a coarsermacrochronological scale associated with the duration of material deterioration. The performance of the developedmethod is hence improved due to an efficient numerical treatment of the microchronological problem in combination with the cycle jump technique on the macrochronological scale. Validation examples demonstrate the convergence of the obtained solutions to the reference simulations while significantly reducing the computational costs.
It is widely accepted that the magnetic state of a ferromagnetic material may be irreversibly altered by mechanical loading due to magnetoelastic effects. A novel standardized nondestructive testing (NDT) technique uses weak magnetic stray fields, which are assumed to arise from inhomogeneous deformation, for structural health monitoring (i.e., for detection and assessment of damage). However, the mechanical and microstructural complexity of damage has hitherto only been insufficiently considered. The aim of this study is to discuss the phenomenon of inhomogeneous “self-magnetization” of a polycrystalline ferromagnetic material under inhomogeneous deformation experimentally and with stronger material-mechanical focus. To this end, notched specimens were elastically and plastically deformed. Surface magnetic states were measured by a three-axis giant magnetoresistant (GMR) sensor and were compared with strain field (digital image correlation) and optical topography measurements. It is demonstrated that the stray fields do not solely form due to magnetoelastic effects. Instead, inhomogeneous plastic deformation causes topography, which is one of the main origins for the magnetic stray field formation. Additionally, if not considered, topography may falsify the magnetic signals due to variable lift-off values. The correlation of magnetic vector components with mechanical tensors, particularly for multiaxial stress/strain states and inhomogeneous elastic-plastic deformations remains an issue.
This study examines the relationship between the magnetic mesostructure with the microstructure of low carbon steel tungsten inert gas welds. Optical microscopy revealed variation in the microstructure of the parent material, in the heat affected and fusion zones, correlating with distinctive changes in the local magnetic stray fields measured with high spatial resolution giant magneto resistance sensors. In the vicinity of the heat affected zone high residual stresses were found using neutron diffraction.
Notably, the gradients of von Mises stress and triaxial magnetic stray field modulus follow the same tendency transverse to the weld. In contrast, micro-X-ray fluorescence characterization indicated that local changes in element composition had no independent effect on magnetic stray fields.
In Germany spent nuclear fuel (SNF) and high level radioactive waste (HLW) are stored in interim storage containers with double lid systems. Those lids are equipped with metal seals (e.g. Helicoflex®) that ensure the safe enclosure of the inventory. Being licensed for up to 40 years of interim storage the evaluation of the long-term behavior of the seals is necessary, taking into account storage conditions, decay heat and possible mechanical loads.
In Germany spent nuclear fuel and high level radioactive waste is stored in interim storage containers with double lid systems. Those lids are equipped with metal seals (e.g. Helicoflex®) that ensure the safe enclosure of the inventory. The used metal seals consist of three components as can be seen in the cross-sectional view in Figure 1. The innermost part is a helical spring that is surrounded by an inner jacket made of stainless steel. The outer jacket that is made of a softer material which in case of assembly in the aforementioned storage containers is silver or aluminum (i.e. Al 99.5). During application the seal is compressed and due to the restoring force of the helical spring, the outer jacket is plastically deformed and adapts to the sealing surface. Hence, leakage paths are closed and the sealing function is generated. In Germany the above-mentioned containers are licensed for up to 40 years of interim storage, which in case extended storage becomes necessary before a final repository is available will have to be extended to even longer periods. Therefore, the evaluation of the long-term behavior of the seals is necessary, taking into account storage conditions, decay heat and possible mechanical loads as well.
At Bundesanstalt für Materialforschung und –prüfung (BAM) long-term investigations are being conducted in which seals are assembled in test flanges and aged at temperatures ranging from room temperature to 150°C for accelerated aging. The aged seals are tested semi-annually (after the first 6 months in which the seals are tested more frequently) regarding the sealing performance, the remaining seal force, and the useable resilience upon decompression. Results of these investigations have been published over the past years (e.g. Grelle, Wolff, Probst, Jaunich, & Völzke, 2017; Völzke, Wolff, Probst, Nagelschmidt, & Schulz, 2014). It was found that the seal force and the useable resilience decrease with time and temperature, which is in agreement with the result of other studies (Sassoulas et al., 2006; Wataru et al., 2016) as well. Geometry change of the outer jacket has been identified as the main reason for this seal behavior. At the prevailing operating temperatures and stresses the aluminum is subjected to creep deformation leading to a thinning of the outer jacket. Since the seal groove depth remains unchanged the helical spring expands, which in turn leads to a decrease of the generated spring and seal force.
Although the main reason for the change of seal parameters over time and temperature is known, a detailed characterization of the seal behavior and a reliable prediction of the parameter development for aging times that exceed the experimental time frame have not been possible, yet.
For deeper understanding of the aging processes, an Investigation program, which is covered in this contribution, is conducted at Bundesanstalt für Materialforschung und –prüfung (BAM) that focusses on the behavior of the aluminum jacket and its influence on the long-term sealing performance. The program investigates properties of material samples as well as the behavior of the seal as a component.
Original sheet material of the same aluminum that is used for manufacturing of the seals is investigated in compression creep tests. For this, a DMA (dynamic mechanical analysis) machine is employed (here used for static tests) that allows for a measurement of the specimens deformation under forces of up to 500 N. The advantage of this method is that the original material can be tested in the same shape as used for the seals which is 0.5 mm thick sheet material. For investigation of tensile creep standard specimens are used, that were machined from surrogate material of the same composition and annealing condition.
Furthermore, aluminum seals that are cut into smaller segments are assembled in flanges and placed in heating chambers at temperatures ranging from 23°C to 150°C. After different periods of time from 3 days to 300 days the segments are taken out of the flanges and are investigated, thus giving information on different states of aging. Measurements of the development of the seal contact width and the aluminum jacket thickness are done with an optical microscope. Further investigations on the segments will include metallography and hardness measurements.
From the detailed material and component behavior including the results of the long-term seal force and useable resilience investigations a better understanding of the overall seal behavior can be gained. The aim is to contribute to the development of material models and analytical approaches for the prediction of the sealing behavior in dependence of time and temperature.
The influence of heat treatment and creep loading on the microstructure of an Al-Cu-Li alloy was investigated. Especially the formation of different precipitates (T1 and Theta') were characterized and the microstructural changes under different ageing conditions (with and without external strain) were investigated to determine the effect od stress on the ageing process.
The influence of heat treatment and creep loading on the microstructure of an Al-Cu-Li alloy was investigated. Especially the formation of different precipitates (T1 and Theta') were characterized and the microstructural changes under different ageing conditions (with and without external strain) were investigated to determine the effect od stress on the ageing process.
Shear testing can contribute to a better understanding of the plastic deformation of Ni-base superalloy single crystals. In the present study, shear testing is discussed with special emphasis placed on its strengths and weaknesses. Key mechanical and microstructural results which were obtained for the high-temperature (T ≈ 1000 °C) and low-stress (τ ≈ 200 MPa) creep regime are briefly reviewed. New 3D stereo STEM images of dislocation substructures which form during shear creep deformation in this regime are presented. It is then shown which new aspects need to be considered when performing double shear creep testing at lower temperatures (T < 800 °C) and higher stresses (τ > 600 MPa). In this creep regime, the macroscopic crystallographic [11−2](111) shear system deforms significantly faster than the [01−1](111) system. This represents direct mechanical evidence for a new planar fault nucleation scenario, which was recently suggested (Wu et al. in Acta Mater 144:642–655, 2018). The double shear creep specimen geometry inspired a micro-mechanical in-situ shear test specimen. Moreover, the in-situ SEM shear specimen can be FIB micro-machined from prior dendritic and interdendritic regions. Dendritic regions, which have a lower γ′ volume fraction, show a lower critical resolved shear stress.
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.
Giant magneto-resistive (GMR) sensor based metal magnetic memory (MMM) technique is proposed for mapping of deformation-induced self-magnetic leakage fields (SMLFs) in carbon steel. The specimens were subjected to different amounts of tensile deformation and the deformation-induced SMLFs were measured using a GMR sensor after unloading the specimens. 3D-nonlinear finite element modeling was performed to predict stress–strain state in a steel specimen under tensile load. The experimentally obtained SMLF images were correlated with the finite element model predicted stress–strain states. Studies reveal that the MMM technique can detect the plastic deformation with signal-to-noise ratio better than 20 dB. The technique enables the mapping of plastic deformation in carbon steels for the evaluation of the severity of deformation. The study also reveals that deformation-induced SMLF is influenced by the presence of initial surface residual stress, introduced by shot peening. The intensity of SMLF signal is found to increase with increase in tensile load and decrease with shot peening.
A numerical pre-study has shown that cracks in a flat sample featuring a drilled hole can be classified into one of three crack shape classes based on the combined evaluation of various types of test data.
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.
Werkstoffe im Hochtemperatureinsatz verändern mit der Zeit ihre Mikrostruktur. Mit diesem Alterungsprozess einher geht eine Veränderung der mechanischen Eigenschaften ebenso wie eine Veränderung des Schädigungsverhaltens. Im Rahmen des FVV Vorhabens „Alterung und Lebensdauer“ haben das Fraunhofer IWM in Freiburg und die BAM in Berlin die weit verbreitete warmfeste Aluminiumlegierung EN AW-2618A in verschiedenen Alterungszuständen experimentell charakterisiert und darauf aufbauend Modelle für die Lebensdauerbewertung mit der Finite-Elemente- Methode implementiert.
Materials subjected to high-temperature service conditions will change their microstructure with time. Associated with this aging process is a change of mechanical properties as well as a change of damage mechanisms. Within the scope of the FVV project Aging and Lifetime, Fraunhofer IWM in Freiburg and BAM in Berlin (both Germany) experimentally characterized the widespread high-temperature aluminum alloy EN AW-2618A in different overaging states. Based on the experimental findings, models for numerical lifetime assessment with the finite-element method were implemented.
Virtual-lab-based determination of a macroscopic yield function for additively manufactured parts
(2018)
This work presents a method for the yield function determination of additively manufactured parts of S316L steel. A crystal plasticity model is calibrated with test results and used afterwards to perform so-called virtual experiments, that account for the specific process-related microstructure including crystallographic and morphological textures. These simulations are undertaken on a representative volume element (RVE), that is generated from EBSD/CT-Scans on in-house additively manufactured specimen, considering grain structure and crystal orientations. The results of the virtual experiments are used to determine an anisotropic Barlat yield function, that can be used in a macroscopical continuum-sense afterwards. This scale-bridging approach enables the calculation of large-scale parts, that would be numerically too expensive to be simulated by a crystal plasticity model.
Die warmfeste austenitische Gusseisenlegierung EN-GJSA-XNiSiCr35-5-2 (häufig auch als Ni-Resist D-5S bezeichnet) wurde hinsichtlich ihres mechanischen Verhaltens bei hoher Temperatur charakterisiert. Dazu wurden (isotherme) niederzyklische (LCF-) und (nicht-isotherme) thermomechanische Ermüdungsversuche (TMF) zwischen Raumtemperatur und 900 °C durchgeführt. Diese Ergebnisse dienten (zusammen mit weiteren Versuchsdaten) der Kalibrierung werkstoffmechanischer Modelle. Bei den höchsten Prüftemperaturen wurde Schädigung in Form von Kriechen beobachtet und metallographisch dokumentiert.
A constitutive model for the mechanical behaviour of single crystal Ni-base superalloys under high temperature conditions has been developed in the framework of a Cooretec project in cooperation with Siemens AG, MTU Aero Engines AG and University Bayreuth. In addition to the conventional material properties e.g. elastic constants, the model requires the parameters of the initial microstructure as an input. Thus, the γ’-precipitate size and the channel width of the γ-matrix were obtained from SEM micrographs. The model uses the slip system theory and describes the movement, multiplication and annihilation of dislocations in the channels. Furthermore, the cutting of precipitates is another mechanism contributing to the plastic flow. The evolution of the morphology due to rafting and its effects on the deformation have been implemented according to. The kinematic hardening is introduced as a stress tensor to realistically represent the strain hardening of arbitrary oriented single crystals.
The mechanical behaviour of single crystal specimens has been experimentally investigated in tension tests at different strain rates and in creep tests under various loads. The constitutive model has been calibrated based on the experimental data for temperatures of 950°C and 850°C and the [001] and [111] crystallographic orientations.
Finally, a micromechanical model was created to simulate the creep response of additive manufactured polycrystalline structures. An EBSD image is taken to obtain the grain geometry and their respective orientation. The grain boundaries are discretised using cohesive elements, whereas the single crystal model was applied to each grain in the representative volume. The polycrystal model is generated using Dream3D, NetGen and other software previously developed at the BAM.
The methods of computational damage mechanics are well-established for the description of degradation of materials under monotone loading. An extension to structural damage induced by cyclic loading is however significantly limited. This is due to enormous computational costs required to resolve each load cycle by conventional temporal incremental integration schemes while a typical fatigue loading history comprises between thousands and millions of cycles. Despite the permanent increase of computational resources and algorithmic performance, a successful approach is rather based on the development of novel multiscale in time integration schemes.
A Fourier transformation-based temporal integration (FTTI) is represented, which takes advantage of temporal scale separation incorporated into the cycle jump method. The response fields are approximated by a Fourier series whose coefficients undergo the evolution on a long-time scale. This is correlated with the evolution of the history variables, including damage, by means of the adaptive cycle jump method of various orders. The necessary extrapolation rates are obtained from the underlying solution of a short-time scale problem, which results from the oscillatory boundary condition and fulfills the global equilibrium of the Fourier coefficients. In this way, a remarkable speedup is achieved because the number of cycles to be fully integrated dramatically decreases.
The key idea behind the FTTI method is that the global in space equilibrium problem is linear since it is decoupled from the evolution equations. The latter are solved in the quadrature points under response fields prescribed throughout the whole load cycle. Consequently, integration of a single load cycle is much more efficient than the conventional single scale integration where the global equilibrium iteration and the local iteration of the evolution equations are coupled. This results in an additional speedup of the FTTI method.
The performance of the FTTI technique is demonstrated for two different constitutive behaviors: a viscoplastic model with a damage variable governed by the local equivalent viscoplastic strain; a quasi-brittle response where the damage variable is driven by a non-local equivalent strain. The latter is implicitly introduced as proposed by Peerlings. Both, the explicit and implicit extrapolation schemes are validated. The FTTI solutions agree very well with the reference cycle-by -cycle solutions, while significantly reducing the computational costs. The adaptive determination of the jump length can properly recognize the particular responses throughout the fatigue loading history (stationary fatigue, acceleration of fatigue damage when approaching failure) as well as stress redistribution phenomena.
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.
Es wird eine neu entwickelte Methode zur Thermographiebasierten Rissmessung vorgestellt. Darüber hinaus wird eine numerische Vorarbeit präsentiert, die zeigt, dass anhand der gemeisamen Auswertung der Versuchsdaten aus unterschiedlicher Sensorik die Möglichkeit besteht, die unter Ermüdungsbelastung in Bohrlochproben auftretenden Risse in Geometriekategorien zu unterteilen.
The employment of renewable energy resources, which are naturally intermittent, for electricity generation has altered the working conditions of conventional power plants from continuous (baseload) to cyclic or flexible operation. For a long time, 9-12% Cr ferritic-martensitic stainless steels have been widely used in power plants due to their favorable characteristics such as high creep strength at high temperatures and oxidation and corrosion resistance. The components of power plants are subjected to long term cyclic loadings including fatigue and creep-fatigue at high temperatures. As ferritic-martensitic steels are known to exhibit cyclic softening when subjected to such loading scenarios, it is crucial to study the material response in such conditions. Since it is impossible to test the material behavior exactly as the operation conditions of power plants, due to technical difficulties and cost issues, it is necessary to develop physically-based material models that can predict the material behavior in more realistic situations.
In recent years, many material models have been proposed to describe the behavior of 9-12% Cr ferritic-martensitic stainless steels, which follow phenomenological or physically-based approaches. Phenomenological models provide a stress-strain relation based on empirical observations although they usually lack physical background. To alleviate this drawback and to allow for more flexibility and wider ranges of strain-rate and temperature, physically-based models are suggested. In this approach, microstructural evolution, dislocation movement and/or kinetics of plastic deformation processes are included. The physically-based models allow for a better extrapolation from the experiment results to other operation conditions and their material constants can be interpreted physically. Compared to the former approach, the material behavior can be described more accurately and flexibly and the number of material constants is less in general. In the presented work, the existing micromechanical models developed for P92 steel are compared and extended to allow for new dislocation-based strengthening/cyclic mechanisms. Their performance is assessed in the light of mechanical test data from creep-fatigue and thermo-mechanical fatigue experiments and detailed characterizations of the microstructure evolution in the fatigued material.
9-12% Cr ferritic-martensitic stainless steels are widely used as high temperature construction materials in power plants due to their excellent creep and oxidation resistance. The growing share of renewable energy sources in power generation forces many of these plants into more flexible operation with frequent load shifts or shutdowns. These cyclic operation profiles constitute a major lifetime issue.
The present contribution reports on current findings obtained in a multidisciplinary project which combines cyclic mechanical and cyclic oxidation testing with detailed microstructural analyses. Mechanical analyses are carried out on P92 and P91 steel grades to give an overview of softening phenomena and lifetimes obtained in isothermal cyclic loading (low cycle fatigue, LCF), non-isothermal cyclic loading (thermo-mechanical fatigue, TMF), and service-like combinations of creep and fatigue periods (creep-fatigue interaction).
Oxidation testing focuses on the grades P92 and VM12 with the intention of clarifying the impact of frequent passes through intermediate temperature levels on the kinetics of steam-side oxidation and the characteristics of the evolving oxide scales. An attempt is made to evaluate their composition, strength, integrity and adhesion after up to 250 temperature cycles. Flat coupons as well as curved tube sections are tested to assess the mutual influence of geometry on oxide scale integrity.
Complementary microstructural investigations by scanning and transmission electron microscopy plus EBSD are used for phase identification and substrate/oxide interface characterisation. The evolutions of grain size and dislocation density under different test conditions are quantified.
9-12% Cr ferritic-martensitic stainless steels are widely used as high temperature construction materials in power plants due to their excellent creep and oxidation resistance. The growing share of renewable energy sources in power generation forces many of these plants into more flexible operation with frequent load shifts or shutdowns. These cyclic operation profiles constitute a major lifetime issue. The present contribution reports on current findings obtained in a multidisciplinary project which combines cyclic mechanical and cyclic oxidation testing of different 9-12% Cr grades with detailed microstructural analyses.
Mechanical analyses are carried out on P92 and P91 steel grades to give an overview of softening phenomena and lifetimes obtained in isothermal cyclic loading (low cycle fatigue, LCF), non-isothermal cyclic loading (thermo-mechanical fatigue, TMF), and service-like combinations of creep and fatigue periods.
Complementary microstructural investigations by scanning and transmission electron microscopy plus EBSD are used for phase identification, substrate/oxide interface characterization and quantification of the microstructure evolution under cyclic conditions.
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.
The age hardening response of a high-purity Al–4Cu–1Li–0.25Mn alloy (wt. %) during isothermal aging without and with an applied external load was investigated. Plate shaped nanometer size T1 (Al2CuLi) and θ′ (Al2Cu) hardening phases were formed. The precipitates were analyzed with respect to the development of their structure, size, number density, volume fraction and associated transformation strains by conducting transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM) studies in combination with geometrical Phase analysis (GPA). Special attention was paid to the thickening of T1 phase. Two elementary types of single-layer T1 precipitate, one with a Li-rich (Type 1) and another with an Al-rich (Defect Type 1) central layer, were identified. The results show that the Defect Type 1 structure can act as a precursor for the Type 1 structure. The thickening of T1 precipitates occurs by alternative stacking of These two elementary structures. The thickening mechanism was analyzed based on the magnitude of strain associated with the precipitation transformation normal to its habit plane. Long-term aging and aging under load resulted in thicker and structurally defected T1 precipitates. Several types of defected precipitates were characterized and discussed. For θ′ precipitates, a ledge mechanism of
thickening was observed. Compared to the normal aging, an external load applied to the peak aged state leads to small variations in the average sizes and volume fractions of the precipitates.
Lifetime aspects including fatigue failure of concrete structures were traditionally only of minor importance. Because of the growing interest in maxing out the capacities of concrete, its fatigue failure under compression has become an issue. A variety of interacting phenomena such as e.g. loss of prestress, degradation due to chemical reactions or creep and shrinkage influence the fatigue resistance. Failure due to cyclic loads is generally not instantaneous, but characterized by a steady damage accumulation. Therefore, a reliable numerical model to predict the performance of concrete over its lifetime is required, which accurately captures order effects and full three-dimensional stress states.
Many constitutive models for concrete are currently available, which are applicable for specific loading regimes, different time scales and different resolution scales.
However, a key limitation of those models is that they generally do not address issues related to fatigue on a structural level. Very few models can be found in the literature that reproduce deterioration of concrete under repeated loading-unloading cycles. This is due to the computational effort necessary to explicitly resolve every cycle which exceeds the currently available computational resources. The limitation can only be overcome by the application of multiscale methods in time.
The objective of the paper is the development of numerical methods for the simulation of concrete under fatigue loading using temporal multiscale methods.
First, a continuum damage model for concrete is developed with a focus on fatigue under compressive stresses [1]. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from static tests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level.
Second, a multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach [2]. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
Finally, the developed methods will be validated and compared to experimental data.
[1] Vitaliy Kindrachuk, Marc Thiele, Jörg F. Unger. Constitutive modeling of creep-fatigue interaction for normal strength concrete under compression, International Journal of Fatigue, 78:81-94, 2015
[2] Vitaliy Kindrachuk, Jörg F. Unger. A Fourier transformation-based temporal integration scheme for viscoplastic solids subjected to fatigue deterioration, International Journal of Fatigue, 100:215-228, 2017
Lifetime aspects including fatigue failure of concrete structures were traditionally only of minor importance. Because of the growing interest in maxing out the capacities of concrete, its fatigue failure under compression has become an issue. A variety of interacting phenomena such as e.g. loss of prestress, degradation due to chemical reactions or creep and shrinkage influence the fatigue resistance. Failure due to cyclic loads is generally not instantaneous, but characterized by a steady damage accumulation. Therefore, a reliable numerical model to predict the performance of concrete over its lifetime is required, which accurately captures order effects and full three-dimensional stress states.
Many constitutive models for concrete are currently available, which are applicable for specific loading regimes, different time scales and different resolution scales.
However, a key limitation of those models is that they generally do not address issues related to fatigue on a structural level. Very few models can be found in the literature that reproduce deterioration of concrete under repeated loading-unloading cycles. This is due to the computational effort necessary to explicitly resolve every cycle which exceeds the currently available computational resources. The limitation can only be overcome by the application of multiscale methods in time.
The objective of the paper is the development of numerical methods for the simulation of concrete under fatigue loading using temporal multiscale methods.
First, a continuum damage model for concrete is developed with a focus on fatigue under compressive stresses. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from static tests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level.
Second, a multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
Finally, the developed methods will be validated and compared to experimental data.
Performing mechanical tests at high temperatures is a nontrivial issue: Compared to room temperature testing, additional phenomena like time-dependent Deformation processes and oxidation effects raise the complexity of the material’s response, while more sophisticated test setups and additional control parameters increase the number of potential sources of error. To a large extent, these complications can be overcome by carefully following all recommendations given in the respective high temperature testing standards, but more comprehensive background information helps to identify points of specific importance in particular test campaigns. In this chapter, an overview is given on general high temperature testing issues like the appropriate choice of experimental equipment and key aspects of temperature measurement. In subsequent sections, the major static and dynamic high temperature test methods are reviewed and their Special features, as compared to testing at room temperature, are highlighted based on example data sets. Influences of specimen size and environmental effects are shortly outlined in a concluding section. In the whole chapter, a focus is set on testing of “classical” metallic high temperature materials, but many considerations are equally valid for testing of intermetallics, composites, and high temperature ceramics.
The knowledge of the temperature-induced changes of the superconductor volume and of the thermomechanical behavior of the different coil and tooling materials is required for predicting the coil geometry and the stress distribution in the coil after the Nb3Sn reaction heat treatment. In this paper, we have measured the Young’s and shear moduli of the HL-LHC 11 T Nb3Sn dipole magnet coil and reaction tool constituents during in situ heat cycles with the dynamic resonance method. The thermal expansion behaviors of the coil components and of a free standing Nb3Sn wire were compared based on dilation experiments.
A continuum damage model for concrete is developed with a focus on fatigue under compressive stresses. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from statictests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level. A multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
A continuum damage model for concrete is developed with a focus on fatigue under compressive stresses. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from statictests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level. A multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
Die warmfeste austenitische Gusseisenlegierung EN-GJSA-XNiSiCr35-5-2 (häufig auch als Ni-Resist D-5S bezeichnet) wurde hinsichtlich ihres mechanischen Verhal-tens bei hoher Temperatur charakterisiert. Dazu wurden (isotherme) niederzyklische (LCF-) und (nicht-isotherme) thermomechanische Ermüdungsversuche (TMF) zwischen Raumtemperatur und 900 °C durchgeführt. Diese Ergebnisse dienten (zu-sammen mit weiteren Versuchsdaten) der Kalibrierung werkstoffmechanischer Modelle. Bei den höchsten Prüftemperaturen wurde Schädigung in Form von Kriechen beobachtet und metallographisch dokumentiert.
Abstract While classically used to visualise the magnetic microstructure of functional materials (e.g., for magnetic applications), in this study, the Bitter technique was applied for the first time to visualise macroscopic deformation gradients in a polycrystalline low-carbon steel. Spherical indentation was chosen to produce a multiaxial elastic–plastic deformation state. After removing the residual imprint, the Bitter technique was applied, and macroscopic contrast differences were captured in optical microscopy. To verify this novel characterisation technique, characteristic “hemispherical” deformation zones evolving during indentation were identified using an analytical model from the field of contact mechanics. In addition, near-surface residual stresses were determined experimentally using synchrotron radiation diffraction. It is established that the magnetic domain distribution contrast provides deformation-related information: regions of different domain wall densities correspond to different “hemispherical” deformation zones (i.e., to hydrostatic core, plastic zone and elastic zone, respectively). Moreover, the transitions between these three zones correlate with characteristic features of the residual stress profiles (sign changes in the radial and local extrema in the hoop stress). These results indicate the potential of magnetic domain distribution imaging: visualising macroscopic deformation gradients in fine-grained ferromagnetic material with a significantly improved spatial resolution as compared to integral, mean value-based measurement methods.
Virtual-lab-based determination of a macroscopic yield function for additively manufactured parts
(2018)
This work presents a method for the yield function determination of additively manufactured parts of S316L steel. A crystal plasticity model is calibrated with test results and used afterwards to perform so-called virtual experiments, that account for the specific process-related microstructure including crystallographic and morphological textures. These simulations are undertaken on a representative volume element (RVE), that is generated from EBSD/CT-Scans on in-house additively manufactured specimen, considering grain structure and crystal orientations. The results of the virtual experiments are used to determine an anisotropic Barlat yield function, that can be used in a macroscopical continuum-sense afterwards. This scale-bridging approach enables the calculation of large-scale parts, that would be numerically too expensive to be simulated by a crystal plasticity model.