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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).
Hot forging dies are subjected to high cyclic thermo-mechanical loads. In critical areas, the occurring stresses can exceed the material’s yield limit. Additionally, loading at high temperatures leads to thermal softening of the used martensitic materials. These effects can result in an early crack initiation and unexpected failure of the dies, usually described as thermo-mechanical fatigue (TMF). In previous works, a temperature-dependent cyclic plasticity model for the martensitic hot forging tool steel 1.2367 (X38CrMoV5-3) was developed and implemented in the finite element (FE)-software Abaqus. However, in the forging industry, application-specific software is usually used to ensure cost-efficient numerical process design. Therefore, a new implementation for the FE-software Simufact Forming 16.0 is presented in this work. The results are compared and validated with the original implementation by means of a numerical compression test and a cyclic simulation is calculated with Simufact Forming.
Pure orbital blowout fractures occur within the confines of the internal orbital wall. Restoration of orbital form and volume is paramount to prevent functional and esthetic impairment. The anatomical peculiarity of the orbit has encouraged surgeons to develop implants with customized features to restore its architecture. This has resulted in worldwide clinical demand for patient-specific implants (PSIs) designed to fit precisely in the patient’s unique anatomy. Material extrusion or Fused filament fabrication (FFF) three-dimensional (3D) printing technology has enabled the fabrication of implant-grade polymers such as Polyetheretherketone (PEEK), paving the way for a more sophisticated generation of biomaterials. This study evaluates the FFF 3D printed PEEK orbital mesh customized implants with a metric considering the relevant design, biomechanical, and morphological parameters. The performance of the implants is studied as a function of varying thicknesses and porous design constructs through a finite element (FE) based computational model and a decision matrix based statistical approach. The maximum stress values achieved in our results predict the high durability of the implants, and the maximum deformation values were under one-tenth of a millimeter (mm) domain in all the implant profile configurations. The circular patterned implant (0.9 mm) had the best performance score. The study demonstrates that compounding multi-design computational analysis with 3D printing can be beneficial for the optimal restoration of the orbital floor.
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.
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.
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.
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 work, time-independent and time-dependent plasticity models are presented that are well suited for the calculation of stresses and strains with the finite-element method to assess the low-cycle and thermomechanical fatigue life of engineering components. The focus are plasticity models that are available in finite-element programs nowadays as standard material models and describe isotropic and kinematic hardening, strain-rate dependency as well as static recovery of hardening. For the presented models, aspects relevant for the application of the models are addressed as the determination of the material properties and the numerical implementation. Nevertheless, the plasticity models are also embedded in the thermodynamic framework used for the derivation of thermodynamically consistent plasticity models. Only uniaxial formulations are used to achieve a good readability and preventing the use of tensors.
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.
In this paper, a temperature-dependent viscoplasticity model is presented that describes thermal and cyclic softening of the hot work steel X38CrMoV5-3 under thermomechanical fatigue loading. The model describes the softening state of the material by evolution equations, the material properties of which can be determined on the basis of a defined experimental program. A kinetic model is employed to capture the effect of coarsening carbides and a new isotropic cyclic softening model is developed that takes history effects during thermomechanical loadings into account. The temperature-dependent material properties of the viscoplasticity model are determined on the basis of experimental data measured in isothermal and thermomechanical fatigue tests for the material X38CrMoV5-3 in the temperature range between 20 and 650 ∘C. The comparison of the model and an existing model for isotropic softening shows an improved description of the softening behavior under thermomechanical fatigue loading. A good overall description of the experimental data is possible with the presented viscoplasticity model, so that it is suited for the assessment of operating loads of hot forging tools.
In this paper, the Bauschinger effect and latent hardening of single crystals are assessed in finite element calculations using a single crystal plasticity model with kinematic hardening. To this end, results of cyclic micro-bending experiments on single crystal Alloy 718 in different crystal orientations (single slip and multi slip) with respect to the loading direction are used to determine the slip system related material properties of the single crystal plasticity model. Two kinematic hardening laws are considered: a kinematic hardening law describing latent hardening and a kinematic hardening law without latent hardening. For the determination of material properties for both hardening laws, a gradient-based optimization method is used. The results show that the different strength levels observed for micro-bending tests on different crystal orientations can only be described with latent kinematic hardening well, whereas the pronounced Bauschinger effect is described well by both kinematic hardening laws. It is concluded that cyclic micro-bending experiments on single crystals using different crystal orientations give an appropriate data base for the determination of the slip system related material properties of the single crystal plasticity model with latent kinematic hardening.
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.
In this paper, the influence of the material hardening behavior on plasticity-induced fatigue crack closure is investigated for strain-controlled loading and fully plastic, large-scale yielding conditions by means of the finite element method. The strain amplitude and the strain ratio are varied for given Ramberg–Osgood material properties representing materials with different hardening behavior. The results show a pronounced influence of the hardening behavior on crack closure, while no significant effect is found from the considered strain amplitude and strain ratio. The effect of the hardening behavior on the crack opening stress cannot be described by existing crack opening stress equations.
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.
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.
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 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.
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.
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.