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In dem abgeschlossenen Vorhaben „Entwicklung von Rechenmodellen zur Lebensdauervorhersage von Motorbauteilen unter thermisch-mechanischer Ermüdungsbeanspruchung“ der Forschungsvereinigung Verbrennungskraftmaschinen e. V. (FVV) wurde am Fraunhofer Institut für Werkstoffmechanik IWM in Freiburg ein Materialmodell zur Lebensdauervorhersage thermomechanisch belasteter Komponenten entwickelt. Das Modell basiert auf einem viskoplastischen Verformungsmodell für Eisengusswerkstoffe und einem mechanismenbasierten Modell für Mikrorisswachstum zur Lebensdauervorhersage.
Für die Werkstoffe EN GJS700, EN GJV450 und EN GJL250 werden die Lebensdauern unter kombinierter thermomechanischer und hochfrequenter Belastung vorhergesagt. Hierzu wird ein mechanismenbasiertes Lebensdauermodell verwendet, das auf dem Wachstum von Mikrorissen beruht. Das Modell berücksichtigt das Wachstum von Rissen durch nieder- und überlagerte hochfrequente Belastungszyklen. Anhand von einachsigen Ermüdungsversuchen wurden die Parameter des Lebensdauermodells angepasst, sodass eine bestmögliche Lebensdauervorhersage erzielt wird. Dabei stimmen die vorhergesagten Lebensdauern gut mit den experimentell ermittelten Zyklenzahlen zum Versagen überein.
Bauteile in Dampfturbinen, stationäre Gasturbinen und Fluggasturbinen sind hohen Beanspruchungen ausgesetzt. Wenn die Turbinen gestartet werden, erwärmen sich die Bauteile im „heißen Bereich“ der Turbine auf über 1000 °C. Damit die Bauteile bei diesen Temperaturen nicht einfach dahinschmelzen, werden spezielle hochtemperaturfeste Legierungen verwendet, wie beispielsweise Nickelbasis-Superlegierungen. Die hohen Temperaturschwankungen die beim Starten und beim Abschalten der Turbine auftreten, machen aber auch diese Werkstoffe auf Dauer nicht mit. Beim Aufheizen dehnt sich das Material aus, beim Abkühlen zieht es sich wieder zusammen. Dieses Hin- und Her-Verformen führt dazu, dass der eingesetzte Werkstoff unter „Stress“ kommt und Spannungen im Werkstoff auftreten. Diese Spannungen können dazu führen, dass sich Risse im Material bilden, die unter der zyklischen Belastung (wiederholtes Starten und Abschalten) wachsen, bis das Bauteil kaputt ist. Der Fachmann spricht dabei von der thermo-mechanischen Ermüdung (Thermomechanical Fatigue, TMF) des Werkstoffs.
In this paper, the multiaxial formulation of a mechanism-based model for fatigue life prediction is presented whichcan be applied to low-cycle fatigue (LCF) and thermomechanical fatigue (TMF) problems in which high-cycle fa-tigue loadings are superimposed. The model assumes that crack growth is the lifetime limiting mechanism and thatthe crack advance in a loading cycleda/dNcorrelates with the cyclic crack-tip opening displacement ΔCTOD.The multiaxial formulation makes use of fracture mechanics solutions and thus, does not need additional modelparameters quantifying the effect of the multiaxiality. Furthermore, the model includes contributions of HCF on ΔCTODand assesses the effect of the direction of the HCF loadings with respect to LCF or TMF loadings inthe life prediction. The model is implemented into the finite-element program ABAQUS. It is applied to predictthe fatigue life of a thermomechanically loaded notched specimen that should represent the situation between theinlet and outlet bore holes of cylinder heads. A good correlation of the predicted and the measured fatigue lives isobtained.
Für langfaserverstärkte Thermoplaste (LFT) wird ein repräsentatives Volumenelement (RVE) für FEM-Simulationen generiert. Dies geschieht unter Berücksichtigung von mikrostrukturellen Kenngrößen wie Faserorientierungsverteilung, -volumengehalt und -längenverteilung, die für einen charakteristischen Werkstoffzustand experimentell ermittelt wurden. Mittels Mikrostruktursimulationen wird das Kriechverhalten von LFT untersucht. Das viskoelastische Verhalten der Matrix wird experimentell an Substanzproben aus Polypropylen ermittelt und in die RVE-Simulationen mit einem modifizierten Burgers-Modell implementiert. Schließlich werden die Rechnungen mit verschiedenen, fiktiven sowie experimentell ermittelten Faserlängenverteilungen mit Kriechversuchen am LFT verglichen. Es zeigt sich eine starke Abhängigkeit des Kriechverhaltens von der Faserlänge und eine hohe Prognosegüte der Simulationen, die die experimentell ermittelte Längenverteilung berücksichtigen.
In this paper, an unconditionally stable algorithm for the numerical integration and finite-element implementation of a class of pressure dependent plasticity models with nonlinear isotropic and kinematic hardening is presented. Existing algorithms are improved in the sense that the number of equations to be solved iteratively is significantly reduced. This is achieved by exploitation of the structure of Armstrong-Frederik-type kinematic hardening laws. The consistent material tangent is derived analytically and compared to the numerically computed tangent in order to validate the implementation. The performance of the new algorithm is compared to an existing one that does not consider the possibility of reducing the number of unknowns to be iterated. The algorithm is used to implement a time and temperature dependent cast iron plasticity model, which is based on the pressure dependent Gurson model, in the finite-element program ABAQUS. The implementation is applied to compute stresses and strains in a large-scale finite-element model of a three cylinder engine block. This computation proofs the applicability of the algorithm in industrial practice that is of interest in applied sciences.
In this paper the fatigue life of three cast iron materials, namely EN-GJS-700, EN-GJV-450 and EN-GJL-250, is predicted for combined thermomechanical fatigue and high cycle fatigue loading. To this end, a mechanism-based model is used, which is based on microcrack growth. The model considers crack growth due to low frequency loading (thermomechanical and low cycle fatigue) and due to high cycle fatigue. To determine the model parameters for the cast iron materials, fatigue tests are performed under combined loading and crack growth is measured at room temperature using the replica technique. Superimposed high cycle fatigue leads to an accelerated crack growth as soon as a critical crack length and thus the threshold stress intensity factor is exceeded. The model takes this effect into account and predicts the fatigue lives of all cast iron materials investigated under combined loadings very well.
This paper reports on the evolution of cracks in the cylinder heads of a large V8 Diesel engine during cyclic engine tests. The observations are compared with the predictions of a lifetime model for combined thermo-mechanical (TMF) and high cycle fatigue (HCF) loading, which is based on a fracture mechanics analysis of microcrack growth in viscoplastic solids and assumes that the crack advance per cycle is proportional to the cyclic crack tip opening displacement. Since the material of the cylinder heads, the cast iron EN-GJV450, exhibits the typical features of cast iron, namely pressure dependence of the yield stress, dilatancy and tension-compression asymmetry, the Gurson model is applied and combined with the viscoplastic Chaboche model. This constitutive model together with the lifetime model is implemented into a finite element code as a user defined material routine. Published model parameters for the considered cast iron are used to carry out the simulation of the engine test. This simulation comprises a CFD analysis to determine the heat transfer coefficients, a thermal analysis of the load cycle and the mechanical analysis. The thermal analysis reproduces the temperatures at various measuring points sufficiently accurately. Finally, the mechanical analysis predicts the location and orientation of the cracks in the valve bridges correctly in all cases. However, the lifetime predictions are rather conservative compared to the tests (by a factor of 1 to 5 in lifetime). This is discussed and explained by the fact that the cracks were detected in the tests only when they had already spread over a substantial fraction of the valve bridge width. To describe this situation a long-crack analysis would be necessary, which is not yet included in the applied lifetime model.
HiSiMo cast irons are frequently used as material for high temperature components in engines as e.g. exhaust manifolds and turbo chargers. These components must withstand severe cyclic mechanical and thermal loads throughout their service life. The combination of thermal transients with mechanical load cycles results in a complex evolution of damage, leading to thermomechanical fatigue (TMF) of the material and, after a certain number of loading cycles, to failure of the component. In this paper (Part I), the low-cycle fatigue (LCF) and TMF properties of HiSiMo are investigated in uniaxial tests and the damage mechanisms are addressed. On the basis of the experimental results a fatigue life model is developed which is based on elastic, plastic and creep fracture mechanics results of short cracks, so that time and temperature dependent effects on damage are taken into account. The model can be used to estimate the fatigue life of components by means of finite-element calculations (Part II of the paper).
HiSiMo cast irons are frequently used as material for high temperature components in engines as e.g. exhaust manifolds and turbo chargers. These components must withstand severe cyclic mechanical and thermal loads throughout their life cycle. The combination of thermal transients with mechanical load cycles results in a complex evolution of damage, leading to thermomechanical fatigue (TMF) of the material and, after a certain number of loading cycles, to failure of the component. In Part I of the paper, a fracture mechanics model for TMF life prediction was developed based on results of uniaxial tests. In this paper (Part II), the model is formulated for three-dimensional stress states, so that it can be applied in a post-processing step of a finite-element analysis. To obtain reliable stresses and (time dependent plastic) strains in the finite-element calculation, a time and temperature dependent plasticity model is applied which takes non-linear kinematic hardening into account. The material properties of the model are identified from the results of the uniaxial test. The plasticity model and the TMF life model are applied to assess the lifetime of an exhaust manifold.
In this paper, the initial multiaxial yield behavior of three different gray cast iron materials with lamellar shaped graphite inclusions is numerically investigated by means of the finite-element method. Therefore, volume elements including the real microstructure of the materials are loaded bi- and triaxially beyond macroscopic yield. The shape of the obtained yield surfaces are compared to the surfaces of four continuum models which, amongst others, are proposed in literature to describe the inelastic behavior of gray cast iron with lamellar shaped graphite inclusions. It is found that the presented continuum models and the macroscopic yield surfaces obtained with microstructure-based finite-element models deviate. Furthermore, the initial inelastic flow direction is computed at the onset of macroscopic yielding. The analysis show that the inelastic flow is normal to the yield surface.
In this paper fatigue crack closure under in-phase and out-of-phase thermomechanical fatigue (TMF) loading is studied using a temperature dependent strip yield model. It is shown that fatigue crack closure is strongly influenced by the phase relation between mechanical loading and temperature, if the temperature difference goes along with a temperature dependence of the yield stress. In order to demonstrate the effect of the temperature dependent yield stress, the influence of in-phase and out-of-phase TMF loading is studied for a polycrystalline nickel-base superalloy. By using a mechanism based lifetime model, implications for fatigue lives are demonstrated.
In this paper, the correlation of the cyclic J-integral, ΔJ, and the cyclic crack-tip opening displacement, ΔCTOD, is studied in the presence of crack closure to assess the question if ΔJ describes the crack-tip opening displacement in this case. To this end, a method is developed to evaluate ΔJ numerically within finite-element calculations. The method is validated for an elastic–plastic material that exhibits Masing behavior. Different strain ranges and strain ratios are considered under fully plastic cyclic conditions including crack closure. It is shown that the cyclic J-integral is the parameter to determine the cyclic crack-tip opening displacement even in cases where crack closure is present.
This paper focuses on the microstructure-dependent inelastic behavior of lamellar gray cast iron. It comprises the reconstruction of three dimensional volume elements by use of the serial sectioning method for the materials GJL-150, GJL-250 and GJL-350. The obtained volume elements are prepared for the numerical analyses by means of finite-element method. In the finite-element analysis, the metallic matrix is modeled with an elastic–plastic deformation law. The graphite inclusions are modeled nonlinear elastic with a decreasing value of Young’s modulus for increasing tensile loading. Thus, the typical tension–compression asymmetry of this material class can be described. The stress–strain curves obtained with the microstructure-based finite-element models agree well with experimental curves of tension and compression tests. Besides the analysis of the whole volume element, the scatter of the stress–strain response in smaller statistical volume elements is investigated. Furthermore, numerical studies are performed to reduce computational costs.
A new yield function for lamellar gray cast iron materials is proposed. The new model is able to describe the results of recently performed microstructure-based finite-element computations that resolve the three dimensional yield surface of three different gray cast irons. The yield function requires only the yield stress in tension and compression of the respective material as model parameters. Furthermore, the algorithmic formulation of the new model is assessed for numerical robustness and efficiency.
A crack opening stress equation for in-phase and out-of-phase thermomechanical fatigue loading
(2016)
In this paper, a crack opening stress equation for in-phase and out-of-phase thermomechanical fatigue (TMF) loading is proposed. The equation is derived from systematic calculations of the crack opening stress with a temperature dependent strip yield model for both plane stress and plane strain, different load ratios and different ratios of the temperature dependent yield stress in compression and tension. Using a load ratio scaled by the ratio of the yield stress in compression and tension, the equation accounts for the effect of the temperature dependent yield stress and the constraint on the crack opening stress. Based on the scaling relation established in this paper, Newman's crack opening stress equation for isothermal loading is enabled to predict the crack opening stress under TMF loading.
Components of rocket engines as actively cooled combustion chambers must withstand high pressure as well as severe and complex thermal transients. While the thermal transients result in temperature gradients and, thus, in constraint thermal strains, the pressure load induces mean stresses. To assess the mechanical behaviour of such components during design via finite-element calculations, constitutive models are necessary that describe the time- and temperature-dependent plasticity of the material appropriately.
Advanced models account for viscoplastic deformations including isotropic and kinematic hardening, recovery and ratcheting. However, the models contain a relatively large number of temperature-dependent material properties that must be determined on the basis of data of material tests. The determination of the properties is a non-trivial task because it is not clear which loading history must be applied in the tests for a certain material to obtain stable and robust (i.e. objective) material properties. Consequently, the determined properties are depending on the underlying loading history in the tests as well as on the experience and valuation of the person that determined the properties. This results in uncertainties during the assessment of the components that must be faced with conservative designs leading to negative consequences in terms of mass and costs.
It is the aim of this work funded by the European Space Agency ESA to derive a procedure to determine stable and robust material properties of an advanced viscoplastic constitutive model for aerospace materials. To this end, a special loading history is applied in isothermal material tests conducted with copper at different temperatures in the temperature range from 300 to 700 K. To determine the material properties and to assess stability and robustness methods for numerical optimization as well as analytical and statistical methods are used. The determined material properties are validated on the basis of results of thermomechanical material tests also conducted in the temperature range from 300 to 700 K.
The following contribution deals with the growth of cracks in low-cycle fatigue (LCF) and thermomechanical fatigue (TMF) tested specimens of Inconel 718 measured by using the replica method. The specimens are loaded with different strain rates. The material shows a significantly higher crack growth rate if the strain rate is decreased. Electron backscatter diffraction (EBSD) is adopted to identify the failure mechanism and the misorientation relationship of failed grain boundaries in secondary cracks. The analyzed cracks propagated mainly transgranular but also intergranular failure can be observed in some areas. It is found that grain boundaries with coincidence site lattice (CSL) boundary structure are generally less susceptible for intergranular failure than grain boundaries with random misorientation. For modeling the experimentally identified crack behavior an existing model for fatigue crack growth based on the mechanism of time dependent elastic–plastic crack tip blunting is enhanced to describe environmental effects based on the mechanism of oxygen diffusion at the crack tip. For the diffusion process the temperature dependent parabolic diffusion law is assumed. As a result, the time dependent cyclic crack tip opening displacement (DCTOD) is used as representative value to describe both mechanisms. Thus, most
of the included model parameters characterize the deformation behavior of the material and can be determined by independent material tests. With the determined material properties, the proposed model describes the experimentally measured crack growth curves very well. The model is validated based on predictions of the number of cycles to failure of LCF as well as in-phase and out-of-phase TMF tests in the temperature range between room temperature and 650 °C.
Cast iron materials are used as materials for cylinder heads for heavy duty internal combustion engines. These components must withstand severe cyclic mechanical and thermal loads throughout their service life. While high-cycle fatigue (HCF) is dominant for the material in the water jacket region, the combination of thermal transients with mechanical load cycles results in thermomechanical fatigue (TMF) of the material in the fire deck region, even including superimposed TMF and HCF loads. Increasing the efficiency of the engines directly leads to increasing combustion pressure and temperature and, thus, lower safety margins for the currently used cast iron materials or alternatively the need for superior cast iron materials. In this paper (Part I), the TMF properties of the lamellar graphite cast iron GJL250 and the vermicular graphite cast iron GJV450 are characterized in uniaxial tests and a mechanism-based model for TMF life prediction is developed for both materials. The model can be used to estimate the fatigue life of components by means of finite-element calculations (Part II of the paper) and supports engineers in finding the appropriate material and design. Furthermore, the effect of the elastic, plastic and creep properties of the materials on the fatigue life can be evaluated with the model. However, for a material selection also the thermophysical properties, controlling to a high level the thermal stresses in the component, must be considered. Hence, the need for integral concepts for material characterization and selection from a multitude of existing and soon-to-be developed cast iron materials is discussed.