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Interrupted LCF-tests at 850 deg C for Inconel 738LC have been carried out and the specimens have been intensively examined by REM to quantify the evolution of fatigue damage. Surface crack nucleation at oxidatized grain boundaries and coalescence of neighboring flaws occurred during the whole experiment. An anomalous fast single crack growth is observed just after nucleation, followed by a relative stagnation of the propagation in absence of coalescence. A statistical model is proposed that describes these pheonmena. It leads to an integro-differential equation for the crack density f(c,n) after n cycles, similar to the Bolzmann equation which describes the collision of molecules in a dilute gas.
A stochastic model for fatigue short crack growth is presented. It takes into account the interaction between the crack-tip plastic zone and grain boundaries. The process is Markovian. It is completely described by the crack length and the size of the plastic zone. The integro-differential equation giving the evolution of the transition probability distribution is derived.
A constitutive model for the mechanical behavior at high temperatures of superalloys with a high volume fraction of the ? ? phase is derived from an analysis of the main deformation mechanisms. The model assumes periodically distributed cubic ? ? particles and an homogeneous slip distribution perpendicular to the slip planes inside the matrix channels and the particles. It accounts for octahedral and cubic slip in the ? channels, recovery by climb of loops around the precipitates until complete annihilation, shear of both matrix and precipitates by complete matrix dislocations and partial slip reversal during unloading. The back-stresses of the constitutive law are identified with the long-range internal stresses in the microstructure which are explicitly calculated by Fourier series for a simplified distribution of the plastic strains in the microstructure. In particular the three types of channels are distinguished. The internal variables of the model are the plastic strains produced by each mechanism, the number of mobile loops in the ? channels and the scalar dislocation density in the ?/? ? interfaces for each slip system.
Das zyklische mechanische Verhalten der einkristallinen Superlegierungen und deine Modellierung
(2002)
Modeling the reinforcement of alloys by hard precipitates: The example of Nibase of superalloy
(2002)
On the Connection between Continuum Crystal Plasticity and the Mechanics of Discrete Dislocations
(2003)
Experimentshow that the strength of Ni-base superalloystrongly depends on the actual morphology of the microstructure. This makes a multiphase micro-mechanical modelling indispensable for a reliable safety analysis. Unfortunately, the classical crystal plasticity theory leads to erroneous predictions, when applied to the scale of the microstructure. This paper suggests that this failure is related to a breakdown of the meaning of plastic strain at the scale of the size of dislocation loops. We propose a global modelling of the compound that overcomes the deficiencies of local crystal plasticity at this description level.
The calculation of the glide force on a dislocation in finite elasticity requires a suitable description of the variation of the deformation due to dislocation motion. This is achieved in this paper by extending the linear Somigliana-type dislocation model to finite strains. The core is modeled by a strip of finite width where the displacement jump continuously decreases with the distance to the dislocation tip. In the case of finite transformations, this distance can be defined in the deformed or in the undeformed state. By defining it in the undeformed natural state of the crystal, we show that the work dissipated by friction in the core region only depends on the dislocation motion. Using the principle of virtual work, the equation of the dislocation motion and several alternative expressions for the glide force are derived. The obtained force may be interpreted as a generalization of Eshelby's configurational forces for a noncoherent singular surface. In the linear case, the glide force of Peach and Koehler as well as the well-known expression of the self-force due to De Wit and Koehler are retrieved.
Für viskoplastische Stoffgesetze wird das prinzipielle Verfahren der Identifikation von Materialmodell-Parametern für das Spannungs-Verformungs- und Versagens-Verhalten metallischer Werkstoffe am Beispiel von Hochtemperatur-Ermüdung aufgezeigt. Dies betrifft zum Einen die Verwendung geeigneter und auch möglichst weniger Experimente zur Hervorbringung der zu beschreibenden Phänomene des Werkstoffverhaltens und deren gezielte Auswertung sowie zum Anderen die physikalisch kontrollierte Führung einer numerischen Optimierung zur Ermittlung vertrauenswürdiger Materialparameterwerte. Diese Vorgehensweise wurde erfolgreich auf Warmarbeitsstähle sowie poly- und einkristalline Superlegierungen angewendet.
Crack growth tests have been performed at 950 °C with Single Edge Notch specimens of the Ni-based single crystal superalloy PWA1483. In particular, several orientations and frequencies have been investigated, thus allowing the assessment of the influence of these parameters on the crack growth rate. In addition, oxidation experiments have been carried out to characterize the kinetics of the outer oxide scale growth at the same temperature.
On the other side, crack growth has been simulated with the Finite Element program ABAQUS in real test conditions by the node release technique. The nodes are released according to the measured crack growth rate.
The simulation results are compared with the test results on the basis of the computed Crack Tip Opening Displacement (CTOD). For this purpose, the crack is propagated until a stabilized value of the CTOD is obtained. This is usually the case when the crack has crossed the initial plastic zone. The procedure provides an evaluation of the effects of cycle frequency, crystal orientation, plasticity and oxide induced crack closure.
The oxidation behaviour of single crystal PWA 1483 at 950 °C was investigated by means of XRD, SEM and EDS. The parabolic oxidation behaviour, as defined by mass gain and the respective oxide layer thicknesses, is characterized by a parabolic rate constant of about 4 × 10-6 mg²/(cm4 × s) and the formation of a multi-layered oxide scale. An outer scale contains a Ti-bearing thin film composed of TiO2 and NiTiO3 but mostly Cr in Cr2O3 and (Ni/Co)Cr2O4 besides NiTaO4. This outer scale is connected to a discontinuous layer of Al2O3 and an area of γ?'-depletion within the base material.
Constitutive modelling of creep degradation due to rafting in single crystal Ni-base superalloys
(2008)
It is shown experimentally that, during annealing and creep under low applied stresses, matrix dislocation loops frequently cross-glide. The periodic length of the zigzag dislocations deposited in the interfaces is equal to that of the γ/γ'-microstructure. Initially, the zigzag dislocations move in the (001) interface by a combination of glide and climb but then they stop near the γ'-edges and align along (100). Reactions of such dislocations lead to the formation of square interfacial networks consisting of (100) oriented edge dislocations. The complex dislocation movement is explained by the inhomogeneity of the misfit stresses between γ- and γ'-lattices. The tensile components of the stress tensor drive the dislocations through the channel, whereas the shear components near the γ'-edges cause the zigzag movement and the (100) alignment. The total effect is the most efficient relaxation of the misfit stresses. The results are relevant, especially for single-crystal superalloys of the newest generations, which have an increased γ/γ'-misfit due to the high level of refractory elements.
A new experimental technique (repeated load annealing of flat wedge shaped specimens) was proposed for characterization of microstructural degradation under creep conditions. This technique was applied to investigate the microstructural degradation of the nickel-base superalloy CMSX-4 in a wide range of temperatures and stress levels. The results obtained allowed to describe analytically the kinetics of rafting, which is important to predict the reduction of fatigue lifetime and yield stress.
Constitutive modelling of creep degradation due to rafting in single-crystalline Ni-base superalloys
(2009)
A constitutive model for the mechanical behaviour of single-crystalline superalloys at high temperatures has been developed. The model relies on the slip system theory and is able to predict rafting and its influence on plastic flow. The kinetics of rafting are assumed to be driven by the reduction of the internal stresses represented by the macroscopic back-stress. The rafting effect is incorporated in the model through the dependence of the Orowan stress on the channel width. The model has been validated for the alloy CMSX-4 at 950 °C. The rafting part of the model has been calibrated by measurements of the channel widths after several levels of creep strains and for several loads.
Simulation of fatigue crack growth by crack tip plastic blunting using cohesive zone elements
(2010)
The propagation of a fatigue crack in 2D specimens by crack tip plastic blunting is simulated by using a Finite Element implementation of the strip-yield model. At each cycle, the crack growth is assumed to result from the variation of the Crack Tip Opening Displacement (ΔCTOD). The implementation is based on cohesive elements with an elastic perfectly plastic behavior, which allows to simulate, the crack closure phenomena due to the plastic wake behind the crack tip. A mesh sensitivity analysis provides the minimum number of elements requested in the crack tip plastic zone for a given accuracy. Then, the advance scheme based on crack tip blunting is described. Finally, the variation of the opening load with respect to the load ratio R, and to the maximum load is investigated and compared with analytical results.
The shape of X-ray reflections from the cuboidal γ/γ'-microstructure was investigated. The measurements were performed on the 4th generation single-crystal nickel-base superalloy TMS138. It is shown that reflections from non-cubic crystallographic planes split not only in d-scale due to the different spacing of the γ- and γ'-lattices but also in the pole figure due to the tilting of γ-lattice planes. This tilting results from the elastic distortion of the γ-lattice caused by the γ/γ'-misfit. The results obtained are discussed under the methodical aspect of misfit measurement.
Multiscale modelling of diffusion controlled grain boundary cavitation during creep of metals
(2010)
Creep damage of single-crystal nickel base superalloys: mechanisms and effect on low cycle fatigue
(2010)
The main mechanisms of creep damage of single-crystal nickel-base superalloys are the loss of the interface coherency, coarsening of the γ / γ'-microstructure, precipitation of topologically closed packed phases and growth of porosity. This degradation deteriorates the mechanical properties such as yield stress, creep lifetime and especially low-cycle fatigue life, which can be reduced nearly by a factor of 10. The degradation kinetics during creep was characterised quantitatively on the superalloy CMSX-4. A new non-destructive testing technique was applied to cover a wide test parameter range with few specimens in a relatively short time: repeated load annealing of wedge shaped specimens.
The present work focuses on the cubic slip phenomenon in single crystal superalloys with a high fraction of γ' precipitates at high temperature.
The macroscopically apparent cubic slip mechanism is known to significantly reduce the tensile and creep strength of <1 1 1> oriented specimens. However, recent results obtained by 3D dislocation dynamics (Vattré et al., 2009) suggest a new interpretation of the so-called pseudo-cubic slip related to the nature of the dislocation network formation at the interfaces. These results are taken into account in a micromechanical model to improve the estimation of the strain hardening anisotropy. In accordance with the discrete simulations, it is shown that a key role is played by the combination of the activated octahedral slip systems as a function of the crystal orientation. In the <1 1 1> case, the contribution of the activated systems to kinematical hardening compensate, whereas strain hardening remains high for the <0 0 1> case. The experimental dependence of plastic flow on the orientation is also explained at the dislocation-scale mechanisms.
Results are presented for the alloy CMSX-4 in several orientations.
A crystallographic constitutive model is developed, which accounts for both rate-sensitive and rate-insensitive flow. Single-crystal plasticity and viscoplasticity are the limiting cases of the model, so that it properly reflects the material response over a wide temperature range. A non-linear dynamic recovery is included to properly describe ratchetting. We provide a robust integration scheme based on generalization of the return-mapping algorithm and of the procedure for active set search.
The implicit integration and consistent tangent are implemented through the UMAT subroutine in the ABAQUS finite element program. The capability of the model to account for both high and low strain rates is demonstrated in numerical examples. Finally, the stability of integration scheme and quadratic convergence of the global NewtonRaphson equilibrium iterations are demonstrated on the example of a notched bar under tension.
Experimental Characterization and Modelling of Thermo Mechanical Fatigue of Cast Iron Turbochargers
(2011)
Experimental characterization and mechanical modelling of creep induced rafting in superalloys
(2011)
Simulations of cavitation processes on a grain boundary under creep conditions have been carried out, taking into account nucleation, growth, coalescence and sintering of multiple cavities. Cavity growth rates have been calculated through a resolution procedure based on the use of holomorphic complex functions. Three dimensionless parameters have been identified that are responsible for the cavitation development. Parameter studies have been carried out in order to characterise the mechanisms that are responsible for the cavitation development. These studies have been used to develop a physically motivated, simplified model in order to describe the cavitation development of the simulations in terms of global state variables. The simplified model is able to reproduce the cavitation development for all considered combinations of the dimensionless parameters and allows the description of the thickening behaviour of a cavitating grain boundary.
An extension of the constitutive viscoplastic model of Meric and Cailletaud is presented. The new model
accounts for coupling of plasticity and viscoplasticity to describe the rate dependence at low and moderate
temperatures. The model contains two boundaries: an elastic one and a viscoplastic one. Between the
boundaries, the only contribution to yielding is the rate dependent viscoplastic mechanism. Once the viscoplastic
boundary is reached, an additional rate independent flow mechanism becomes active. However, the extended
model is not able to predict properly both creep and long-term relaxation tests simultaneously. Therefore, a
deformation-induced softening is assumed, which is supposed to mainly affect static recovery.
The model has been calibrated with the mechanical tests on a single crystal nickel-basis superalloy. The uniaxial
tests have been carried out in the temperature interval 600°C – 1100°C in [001], [011] and [111] specimens.
The predicted creep, relaxation and non-isothermal cyclic tests exhibit reasonable agreement with the
experimental observations.
Rafting during high temperature deformation in a single crystal superalloy: experiments and modeling
(2012)
Rafting during high temperature deformation in a single crystal superalloy: Experiments and modeling
(2012)
Experimental characterization and mechanical modeling of creep induced rafting in superalloys
(2012)
A constitutive model has been developed for the high temperature mechanical behavior of single crystal superalloys, including rafting and its consequences. The flow stress depends on the γ channel width via the Orowan stress. An evolution equation for channel widening during high temperature straining has been derived and calibrated with measurements. Therein, rafting is assumed to be driven by the relaxation of internal stresses. The model is able to represent the mechanical softening at high stresses consecutive to rafting. The model has been applied to simulate rafting during uniaxial creep in several crystal orientations, in notched specimens as well as in cyclically loaded specimens.
Numerical simulation of fatigue crack growth in a single crystal superalloy at high temperature
(2013)
Pore annihilation during hot isostatic pressing (HIP) was investigated in the single-crystal nickel-base superalloy CMSX-4 experimentally by interrupted HIP tests at 1288 °C/103 MPa. The kinetics of pore annihilation was determined by density measurement and quantitative metallography. Transmission electron microscopy of a HIPed specimen showed that the pores shrink via dislocation movement on octahedral glide planes. Theoretically pore closure under HIP condition was modelled by the finite element method using crystal plasticity and large strain theories. The modelling gives a similar kinetics of pore annihilation as observed experimentally, however somewhat higher annihilation rate.
Micromechanical investigations and modelling of a copper-antimony-alloy under creep conditions
(2014)
In many practical applications, creep damage is the limiting factor of a components lifetime. A micromechanical model of creep induced grain boundary damage is proposed, which allows for the simulation of creep damage in a polycrystal within the framework of finite element analysis. The model considers grain boundary cavitation and sliding according to a micromechanically motivated cohesive zone model while creep deformation of the grains is described following the slip system theory. The model can be applied to idealised polycrystalline structures, such as a Voronoi tessellation or, like demonstrated here, to real grain structures of miniature creep specimens. Creep tests with pure Cu single crystals and with a coarse-grained polycrystalline Cu-1 wt.% Sb alloy at 823 K have been performed and used to calibrate the polycrystal model. The grain structure of the polycrystalline CuSb specimens has been revealed by the EBSD method. Extensive grain boundary sliding and cavitation has been observed in the crept specimens. Grain boundary sliding has been found to promote wedge-type damage at grain boundary triple junctions and to contribute significantly to the total creep strain. Furthermore, the assumed stress sensitivity of the models grain boundary cavity nucleation rate strongly influences the development of wedge-type damage.
A micromechanical model of creep induced grain boundary damage is proposed, which allows for the simulation of creep damage in a polycrystal with the finite element method. Grain boundary cavitation and sliding are considered via a micromechanically motivated cohesive zone model, while the grains creep following the slip system theory. The model has been calibrated with creep test data from pure Cu single crystals and a coarse-grained polycrystalline Cu-Sb alloy. The test data includes porosity measurements and estimates of grain boundary sliding. Finally, the model has been applied to Voronoi models of polycrystalline structures. In particular the influence of grain boundary sliding on the overall creep rate is demonstrated.
Pore annihilation was investigated in the single-crystal nickel-base superalloy CMSX-4. HIP tests at 1288 °C/103 MPa were interrupted at different times, then the specimens were investigated by TEM, metallography and density measurements. The kinetics of pore annihilation was determined. The pore closure mechanism was identified as plastic deformation on the octahedral slip systems. A model describing the kinetics of pore closure has been developed on the base of crystal plasticity and large strain theory. Mechanical tests with the superalloy CMSX-4 and the Ru-containing superalloy VGM4 showed, that HIP significantly increases the fatigue life at low temperatures but has no effect on creep strength.
Material modelling and lifetime prediction of Ni-base gas turbine blades under TMF conditions
(2014)
Under cyclic thermomechanical loading conditions, various damage mechanisms such as strain accumulation, creep cavitation, ageing, fatigue surface cracking etc. may take place in the material of a gas turbine blade. Depending on the loading conditions, all these effects can contribute to reduce the lifetime of the component. Subject of the present work is the development of a material model to describe the mechanical effects mentioned above, as well as the development of a lifetime model able to discriminate the different damage mechanisms.
Under cyclic thermomechanical loading conditions, various effects such as strain accumulation, creep damage, ageing, fatigue etc. may occur in the material of a gas turbine blade. Depending on the loading conditions, all these effects contribute to reduce the lifetime of the component. Subject of the present work is the development of a lifetime model able to discriminate between the different damage mechanisms, as well as the development of a material model to describe the mentioned effects and thus providing the input data for lifetime prediction.
The stress States of components under Service conditions differ in general from the loading conditions that are routinely applied during material testing. When data that results, e.g., from uniaxial testing should be used for lifetime assessment, a good understanding of the failure behaviour in dependence of the stress state is necessary. For polycrystalline materials under high temperature loading, the development of creep damage is one important factor that limits a component’s lifetime. For cases where creep damage is related to the nucleation and growth of grain boundary cavities, the local normal stress acting on a grain boundary has been found to have a strong influence on the damage development. Hence, creep damage is usually localized along planes that lie perpendicular to the maximum principal tensile stress.
Schnelle Lastwechsel führen v.a. in dickwandigen Kraftwerksbauteilen zu starken thermischen und mechanischen Beanspruchungen, da sich hohe Temperaturgradienten über der Wand des Bauteils einstellen. Es ergeben sich komplexe Lastkollektive aus zeitlich veränderlichen Spannungen/Dehnungen und Temperaturen, die formal einer Kombination aus Kriechbeanspruchung, Kriechermüdung und thermomechanischer Ermüdung (TMF) entsprechen.
The elastic anisotropy caused by the texture in the Nb3Sn filaments of PIT and RRP wires has been calculated by averaging the estimates of Voigt and Reuss, using published Nb3Sn single crystal elastic constants and the Nb3Sn grain orientation distribution determined in both wire types by Electron Backscatter Diffraction. At ambient temperature the calculated Nb3Sn E-moduli in axial direction in the PIT and the RRP wire are 130 GPa and 140 GPa, respectively. The calculated E-moduli are compared with tensile test results obtained for the corresponding wires and extracted filament bundles.
Data about the creep behaviour of metals and their alloys at temperatures close to the melting point are very limited. The reason is that most engineering alloys are used at temperatures below 0.6-0.8 of their melting point, so, Investigation of creep at higher temperatures has no practical relevance. For some special applications however it is important, in our case hot isostatic pressing (HIP) of single-crystal turbine blades cast from nickel-base superalloys. In order to remove porosity the blades are HlPed at temperatures between y'-solvus and solidus where superalloy has no strengthening y'-phase and therefore is very soft. For example, the Company Howmet Castings HIPs the superalloy CMSX-4 at the temperature 1288aC, which corresponds to a homologous temperature of about 0.97=1561 K/1612 K (solidus temperature). Therefore knowledge about the creep behaviour of CMSX-4 at this temperature and understanding of the creep mechanisms are necessary to model the kinetics of pore closure during HIP as well as to plan the Parameters of the HIP process.
In diesem Forschungsvorhaben erfolgte eine Überprüfung der Übertragbarkeit der Werkstoff- und Rechenmodelle für die Lebensdauervorhersage von ATL-Heißteilen unter TMF-Beanspruchung auf eine andere Werkstoffklasse als im Vorgängervorhaben, d.h. auf das austenitische Gusseisen EN-GJSA-XNiSiCr35-5-2 (Ni-Resist D-5S). Zunächst wurde dafür eine experimentelle Datenbasis geschaffen, da diese vor Beginn des Vorhabens nicht ausreichend war. Dazu wurden Zug-, Kriech-, LCF- und TMF-Versuche durchgeführt, die der Kalibrierung der Modelle dienten. Das Spannungs-Verformungs-Verhalten und die Lebensdauer in den LCF- und TMF-Versuchen werden durch das Modell auch für den neuen Werkstoff überwiegend gut beschrieben. LCF-Versuche mit Haltezeit bei 900 °C sowie IP-TMFVersuche mit einer Obertemperatur von 900 °C werden weniger gut vorhergesagt, da sich der Schädigungsmechanismus ändert. Eine Verifikation des Modells erfolgte mit Hilfe eines Bauteilversuchs an einem Abgassammler. Die überwiegende Anzahl der experimentell ermittelten Rissorte wurden von dem Modell vorhergesagt.
Ein wesentliches Ziel des Vorhabens war, den Einfluss von HCF-Schwingungen auf die TMF-Lebensdauer vertieft experimentell zu untersuchen und das bereits bestehende Lebensdauermodell auf HCF-Überlagerung zu erweitern. Es wurde ein bruchmechanisch motivierter Ansatz entwickelt, in dem die Lebensdauerminderung durch die im TMF-Zyklus überlagerten HCF-Schwingungen abgebildet wird. Mit diesem Ansatz lassen sich die Lebensdauern sowohl für den Werkstoff SiMo 4.05 als auch für den Ni-Resist in guter Übereinstimmung mit dem Experiment Vorhersagen.
Das Ziel des Forschungsvorhabens ist erreicht worden.
In diesem Forschungsvorhaben erfolgte eine Überprüfung der Übertragbarkeit der Werkstoff- und Rechenmodelle für die Lebensdauervorhersage von ATL-Heißteilen unter TMF-Beanspruchung auf eine andere Werkstoffklasse, d. h. auf eine austenitische Gusseisenlegierung mit Kugelgraphit. Dafür wurde die Legierung EN-GJSA-XNiSiCr35-5-2 (Ni-Resist D-5S) ausgewählt. Zunächst wurde für diesen Werkstoff eine experimentelle Datenbasis geschaffen, da diese vor Beginn des Vorhabens nicht ausreichend war. Dazu wurden Zug-, Kriech-, LCF- und TMF-Versuche durchgeführt, die der Kalibrierung der Modelle dienten. Unter TMF-Belastung zeigte der untersuchte Werkstoff ein stark abweichendes Verhalten von den im vorangegangenen Vorhaben untersuchten ferritischen SiMo-Legierungen: Der Werkstoff Ni-Resist zeigte insgesamt eine vergleichbare Festigkeit unter OP- und IP-Bedingungen, während die ferritischen Legierungen unter IP-Beanspruchung eine deutlich höhere Festigkeit aufweisen. Mit zunehmenden Temperaturen und Haltezeiten unter Zugspannungen wurden dagegen beim Werkstoff Ni-Resist Hinweise auf Kriechschädigung gefunden, die schädigungsrelevant sind. Auch dies ist ein deutlicher Unterschied zu den SiMo-Legierungen. Das Spannungs-Verformungs-Verhalten in den LCF- und TMF-Versuchen wird durch das Modell auch für den neuen Werkstoff überwiegend gut beschrieben. Das Gleiche gilt für die Lebensdauervorhersage, die mit Ausnahme der Prüftemperatur 900 °C innerhalb eines Fak-tors zwei liegt. Eine Verifikation des Modells erfolgte mit Hilfe eines Bauteilversuchs an einem Abgassammler, der abwechselnd mit heißem und kaltem Gas durchströmt wurde. Ziel der Bauteilsimulation war insbesondere die Vorhersage der Rissbildungsorte. Eine Vorhersage der exakten Lebensdauer wurde nicht erwartet, da das Bauteil mit einer Gusshaut behaftet war, während die für die Kalibrierung des Lebensdauermodells verwendeten Versuche an bearbeiteten, glatten Proben ohne Gusshaut durchgeführt wurden. Die überwiegende Anzahl der experimentell ermittelten Rissorte wurden vorhergesagt. Schließlich war ein wesentliches Ziel des Vorhabens, den Einfluss von HCF-Schwingungen auf die TMF-Lebensdauer vertieft experimentell zu untersuchen und das bereits bestehende Lebensdauermodell auf HCF-Überlagerung zu erweitern. Dazu wurde zunächst die Daten-basis aus dem Vorgängervorhaben am Bespiel von SiMo 4.05 deutlich ausgebaut, um die verschiedenen Einflussparameter zu erfassen. Es wurde ein Ansatz entwickelt, in dem die Lebensdauerminderung durch die überlagerten HCF-Schwingungen abgebildet wird. Dabei wird davon ausgegangen, dass ab einer bestimmten Risstiefe die Überlagerung der HCF-Schwingungen die Rissausbreitung stark beschleunigt. Der Zeitpunkt, wann diese Beschleunigung eintritt, wird als maßgeblich für die Lebensdauerminderung angesehen. Mit diesem Ansatz lassen sich die Lebensdauern für beide Werkstoffe in guter Übereinstimmung mit dem Experiment vorhersagen.
Modeling the lifetime reduction due to the superposition of TMF and HCF loadings in cast iron alloys
(2016)
The superposition of small amplitude, high frequency loading cycles (HCF) to slow, large amplitude loading cycles (TMF) can significantly reduce the fatigue life. In this work, the combined TMF+HCF loading has been experimentally investigated for a cast iron alloy. In particular, the influence of the HCF frequency of the HCF amplitude and of the location of the superposed HCF cycles has been assessed. It was observed that the HCF frequency has a limited impact on the TMF fatigue life. On the other side, the HCF-strain amplitude has a highly non-linear influence on the TMF fatigue life. A simple estimate for the fatigue life reduction due to the superposed HCF cycles has been derived from fracture mechanics considerations. It is assumed that the number of propagation cycles up to failure can be neglected after a threshold for the HCF loading has been reached. The model contains only two adjustable parameters and can be combined with any TMF life prediction model. The model predictions are compared with the test results for a large range of TMF+HCF loading conditions.
Under cyclic thermomechanical loading, various effects such as strain accumulation, creep damage, ageing, fatigue etc. may occur in the material of a gas turbine blade. Depending on the loading conditions, all these effects contribute to reduce the lifetime of the component.
Subject of the present work is the development of a material model to describe the mechanical effects mentioned above and to subsequently predict lifetimes by using simulated stress strain data.
Starting point for deformation modeling is the well known viscoplastic model after Chaboche, which provides descriptions of isotropic and kinematic hardening, as well as dynamic and static recovery. The evolution equation for kinematic hardening model has been modified following the proposal of Ohno/Wang to better predict stress controlled cyclic strain accumulation, i.e. ratchetting. A damage variable has been included to represent tertiary creep according to the concept of Kachanov. Finally, the static recovery has been modified following Kindrachuk to account for strain induced ageing. The models parameters have been calibrated using isothermal test data only. The constitutive model has been validated by comparing experimental with predicted TMF stress-strain hystereses.
Lifetime prediction is done with the TMF lifetime model proposed by Riedel. The model assumes that fatigue life is controlled by the propagation of short cracks. Besides pure fatigue, it takes the local creep deformations at the crack tip into account. The model is applied to a broad variety of isothermal and non isothermal tests over temperatures up to 950°C and different loading conditions. The evaluation shows that throughout satisfying results can be achieved using a limited number of model parameters for the whole test data base.