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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.

Cast aluminum alloys are frequently used as materials for cylinder head applications in internal combustion gasoline engines. These components must withstand severe cyclic mechanical and thermal loads throughout their lifetime. Reliable computational methods allow for accurate estimation of stresses, strains, and temperature fields and lead to more realistic Thermomechanical Fatigue (TMF) lifetime predictions. With accurate numerical methods, the components could be optimized via computer simulations and the number of required bench tests could be reduced significantly. These types of alloys are normally optimized for peak hardness from a quenched state that maximizes the strength of the material. However due to high temperature exposure, in service or under test conditions, the material would experience an over-ageing effect that leads to a significant reduction in the strength of the material. To numerically account for ageing effects, the Shercliff & Ashby ageing model is combined with a Chaboche-type viscoplasticity model available in the finite-element program ABAQUS by defining field variables. The constitutive model with ageing effects is correlated with uniaxial cyclic isothermal tests in the T6 state, the overaged state, as well as thermomechanical tests. On the other hand, the mechanism-based TMF damage model (DTMF) is calibrated for both T6 and over-aged state. Both the constitutive and the damage model are applied to a cylinder head component simulating several cycles on an engine dynamometer test. The effects of including ageing for both models are shown.

High temperature components in internal combustion engines and exhaust systems must withstand severe mechanical and thermal cyclic loads throughout their lifetime. The combination of thermal transients and mechanical load cycling results in a complex evolution of damage, leading to thermomechanical fatigue (TMF) of the material. Analytical tools are increasingly employed by designers and engineers for component durability assessment well before any hardware testing. The DTMF model for TMF life prediction, which assumes that micro-crack growth is the dominant damage mechanism, is capable of providing reliable predictions for a wide range of high-temperature components and materials in internal combustion engines. Thus far, the DTMF model has employed a local approach where surface stresses, strains, and temperatures are used to compute damage for estimating the number of cycles for a small initial defect or micro-crack to reach a critical length. In the presence of significant gradients of stresses, strains, and temperatures, the use of surface field values could lead to very conservative estimates of TMF life when compared with reported lives from hardware testing. As an approximation of gradient effects, a non-local approach of the DTMF model is applied. This approach considers through-thickness fields where the micro-crack growth law is integrated through the thickness considering these variable fields. With the help of software tools, this method is automated and applied to components with complex geometries and fields. It is shown, for the TMF life prediction of a turbocharger housing, that the gradient correction using the non-local approach leads to more realistic life predictions and can distinguish between surface cracks that may arrest or propagate through the thickness and lead to component failure.

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.

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.

In this paper, the temperature dependent cyclic mechanical properties of the martensitic hot work tool steel 1.2367 after tempering are investigated. To this end, hardness measurements as well as monotonic and cyclic tests at temperatures in the range from room temperature to 650 °C are performed on material tempered for different tempering times and temperatures. To describe the observed time and temperature dependent softening during tempering a kinetic model for the evolution of the mean size of secondary carbides based on Ostwald ripening is developed. Furthermore, mechanism-based as well as phenomenological relations for the cyclic mechanical properties of the Ramberg-Osgood model depending on carbide size and temperature are introduced. A good overall agreement of the measured and the calculated stress-strain hysteresis loops for different temperatures and heat treatments is obtained using the determined material properties of the kinetic and mechanical model.

In this paper the yield surface of a recently presented microstructure-based volume element of the gray cast iron material GJL-250 is assessed after different plastic loading histories. The evolution of the yield surface is investigated for different volumetric, deviatoric and uniaxial loadings. The micromechanical material properties of the metallic matrix and the graphite inclusions are validated by means experimental stress-strain hysteresis loops. The metallic matrix is modeled as elastic-plastic with a non-linear kinematic hardening law. The graphite inclusions are described by means of a volumetric strain state dependent Young’s modulus. The results show that the shape of the yield surface does not change significantly in comparison to the initial yield surface after pure deviatoric loadings. After volumetric loadings, the dependence of the material on the Lode angle is significantly reduced. Uniaxial tensile preloadings result in a deformed yield surface, whereby the magnitude of the deformation depends on the applied load. Uniaxial preloadings to compression do not change the shape of the initial yield surface.

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 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.

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.

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.

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.

A complete thermomechanical fatigue (TMF) life prediction methodology is developed for predicting the TMF life of cast iron cylinder heads for efficient heavy duty internal combustion engines. The methodology uses transient temperature fields as thermal loads for the non-linear structural finite-element analysis (FEA). To obtain reliable stress and strain histories in the FEA for cast iron materials, a time and temperature dependent plasticity model which accounts for viscous effects, non-linear kinematic hardening and tensioncompression asymmetry is required. For this purpose a unified elasto-viscoplastic Chaboche model coupled with damage is developed and implemented as a user material model (USERMAT) in the general purpose FEA program ANSYS. In addition, the mechanismbased DTMF model for TMF life prediction developed in Part I of the paper is extended to three-dimensional stress states under transient non-proportional loading conditions. The material properties of the plasticity model are determined for lamellar graphite cast iron GJL250 and vermicular graphite cast iron GJV450 from isothermal and non-isothermal uniaxial tests. The methodology is applied to obtain a TMF life prediction on two cast iron cylinder heads for heavy duty diesel engine applications made from both cast iron materials. It is shown that the life predictions using the developed methodology correlate very well with observed lives from two bench tests in terms of location as well as number of cycles to failure.

Warmumformwerkzeuge unterliegen während des Betriebes komplexen thermischen und mechanischen Beanspruchungen. In kritischen Bereichen können dadurch lokal Spannungen entstehen, die die Fließgrenze überschreiten. Bei der Serienproduktion führt dies zu zyklischen plastischen Verformungen und zur thermomechanischen Ermüdung, welche die Lebensdauer der Warmumformwerkzeuge maßgeblich bestimmen kann. Zur Bewertung der thermomechanischen Ermüdung der Warmumformwerkzeuge gibt es jedoch heute keine etablierten Konzepte, da dieser Aspekt erst durch die Notwendigkeit einer höheren Ressourcen- und Energieeffizienz und optimierter Produktionsprozesse (beispielsweise im Rahmen von Industrie 4.0) eine höhere Aufmerksamkeit erreicht. In dieser Arbeit wird zum einen die aktuell industriell angewandte Vorgehensweise zur Auslegung von Warmumformwerkzeugen hinsichtlich der Lebensdauer erläutert. Des Weiteren wird ein Überblick über existierende Plastizitätsmodelle und Lebensdauermodelle gegeben. Dabei wird zwischen rein phänomenologischen und mechanismenbasierten Modellen unterschieden. Aus der betriebenen Recherche wird ersichtlich, dass weiterer Forschungsbedarf auf diesem Gebiet notwendig ist.

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.