5.5 Materialmodellierung
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Organisationseinheit der BAM
- 5.2 Metallische Hochtemperaturwerkstoffe (79) (entfernen)
Eingeladener Vortrag
- nein (32)
Virtual-lab-based determination of a macroscopic yield function for additively manufactured parts
(2019)
This work aims for an yield function description of additively manufactured (AM) parts of S316L steel at the continuum-mechanical macro-scale by means of so-called virtual experiments using a crystal plasticity (CP) model at meso-scale. Additively manufactured parts require the consideration of the specific process-related microstructure, which prevents this material to be macroscopically treated as isotropic, because of crystallographic as well as topological textures.
EBSD/CT-Scans from in-house additively manufactured specimen extract the unique microstructural topology which is converted to a representative volume element (RVE) with grain structure and crystal orientations.
Crystal plasticity model parameters on this RVE are calibrated and validated by means of mechanical testing under different texture angles. From virtual experiments on this RVE, yield loci under various loading conditions are simulated. The scale bridging from meso- to macro-scale is realised by the identification of the simulated yield loci as a modified anisotropic Barlat-type yield model representation.
Single crystal superalloys usually contain pores of sizes 5-10 micro-m after casting and heat treatment. These pores can be reduced under compression by combined creep and diffusion in a subsequent treatment called Hot Isostatic Pressing (HIP). The paper presents a methodology to simulate pore shrinkage under HIP conditions in two dimensions (2D).
At the scale of the pores, which is also the scale of the sub-grains (<50 micro-m) the dislocation sources cannot be assumed to be homogeneously distributed. Thus, the applicability of classical crystal plasticity is questionable. In this case, the transport of dislocations under an applied stress from the location where they are nucleated must be explicitly modelled. This is done by solving the transport equations for the dislocation densities and the elasticity equations in 2D. The dislocations are assumed to be nucleated at Low Angle Boundaries. They glide or climb through the sub-grains with a stress dependent velocity.
The transport equations are solved by the Flux-Corrected Transport method, which belongs to the predictor-corrector class of algorithms. In the first step, an artificial diffusion is introduced, which suppresses spurious oscillations of the solution. In a second step, the solution is corrected in such a way that no additional extremes appear and that the extremes do not grow. The algorithm is validated by simulating the transport of simple distributions with a constant velocity field.
With the dislocation velocities and the computed dislocation densities, the inelastic shear rate at the slip system level is computed by integrating the Orowan equation. In the 2D-setting, three slip systems are considered. The contributions of these slip systems are summed up to obtain the total inelastic strain rate. Dislocation glide and climb and the coupling of climb with vacancies diffusion are considered.
The resolution of the equilibrium equations from the inelastic strains turned out to be prone to numerical instabilities. As an alternative, the stresses are directly computed from the distribution of geometrically necessary dislocations following the method presented in. The resulting boundary value problem is solved by the Least-Square Finite Element method.
Examples of simulations are presented for a representative region under creep tension and for a pore shrinking under external pressure.
A continuum damage model for concrete is developed with a focus on fatigue under compressive stresses. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from statictests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level. A multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
A continuum damage model for concrete is developed with a focus on fatigue under compressive stresses. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from statictests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level. A multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
Computational methods for lifetime prediction of metallic components under high-temperature fatigue
(2019)
The issue of service life prediction of hot metallic components subjected to cyclic loadings is addressed. Two classes of lifetime models are considered, namely, the incremental lifetime rules and the parametric models governed by the fracture mechanics concept. Examples of application to an austenitic cast iron are presented. In addition, computational techniques to accelerate the time integration of the incremental models throughout the fatigue loading history are discussed. They efficiently solve problems where a stabilized response of a component is not observed, for example due to the plastic strain which is no longer completely reversed and accumulates throughout the fatigue history. The performance of such an accelerated Integration technique is demonstrated for a finite element simulation of a viscoplastic solid under repeating loading–unloading cycles.
Virtual-lab-based determination of a macroscopic yield function for additively manufactured parts
(2019)
This work aims for a yield function description of additively manufactured parts of S316L steel at the continuum-mechanical macro-scale by means of so-called virtual experiments using a crystal plasticity (CP) model at meso-scale. Additively manufactured parts require the consideration of the specific process-related microstructure, which prevents this material to be macroscopically treated as isotropic, because of crystallographic as well as topological textures. From virtual experiments, yield loci under various loading conditions are simulated. The scale bridging from meso- to macro-scale is realised by the identification of the simulated yield loci as a modified anisotropic Barlat-type yield model representation.
Lifetime aspects including fatigue failure of concrete structures were traditionally only of minor importance. Because of the growing interest in maxing out the capacities of concrete, its fatigue failure under compression has become an issue. A variety of interacting phenomena such as e.g. loss of prestress, degradation due to chemical reactions or creep and shrinkage influence the fatigue resistance. Failure due to cyclic loads is generally not instantaneous, but characterized by a steady damage accumulation. Therefore, a reliable numerical model to predict the performance of concrete over its lifetime is required, which accurately captures order effects and full three-dimensional stress states.
Many constitutive models for concrete are currently available, which are applicable for specific loading regimes, different time scales and different resolution scales.
However, a key limitation of those models is that they generally do not address issues related to fatigue on a structural level. Very few models can be found in the literature that reproduce deterioration of concrete under repeated loading-unloading cycles. This is due to the computational effort necessary to explicitly resolve every cycle which exceeds the currently available computational resources. The limitation can only be overcome by the application of multiscale methods in time.
The objective of the paper is the development of numerical methods for the simulation of concrete under fatigue loading using temporal multiscale methods.
First, a continuum damage model for concrete is developed with a focus on fatigue under compressive stresses [1]. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from static tests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level.
Second, a multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach [2]. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
Finally, the developed methods will be validated and compared to experimental data.
[1] Vitaliy Kindrachuk, Marc Thiele, Jörg F. Unger. Constitutive modeling of creep-fatigue interaction for normal strength concrete under compression, International Journal of Fatigue, 78:81-94, 2015
[2] Vitaliy Kindrachuk, Jörg F. Unger. A Fourier transformation-based temporal integration scheme for viscoplastic solids subjected to fatigue deterioration, International Journal of Fatigue, 100:215-228, 2017
Lifetime aspects including fatigue failure of concrete structures were traditionally only of minor importance. Because of the growing interest in maxing out the capacities of concrete, its fatigue failure under compression has become an issue. A variety of interacting phenomena such as e.g. loss of prestress, degradation due to chemical reactions or creep and shrinkage influence the fatigue resistance. Failure due to cyclic loads is generally not instantaneous, but characterized by a steady damage accumulation. Therefore, a reliable numerical model to predict the performance of concrete over its lifetime is required, which accurately captures order effects and full three-dimensional stress states.
Many constitutive models for concrete are currently available, which are applicable for specific loading regimes, different time scales and different resolution scales.
However, a key limitation of those models is that they generally do not address issues related to fatigue on a structural level. Very few models can be found in the literature that reproduce deterioration of concrete under repeated loading-unloading cycles. This is due to the computational effort necessary to explicitly resolve every cycle which exceeds the currently available computational resources. The limitation can only be overcome by the application of multiscale methods in time.
The objective of the paper is the development of numerical methods for the simulation of concrete under fatigue loading using temporal multiscale methods.
First, a continuum damage model for concrete is developed with a focus on fatigue under compressive stresses. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from static tests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level.
Second, a multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
Finally, the developed methods will be validated and compared to experimental data.
Due to their excellent creep resistance and good oxidation resistance, 9–12% Cr ferritic–martensitic stainless steels are widely used as high temperature construction materials in power plants. However, the mutual combination of different loadings (e.g., creep and fatigue), due to a “flexible” operation of power plants, may seriously reduce the lifetimes of the respective components. In the present study, low cycle fatigue (LCF) and relaxation fatigue (RF) tests performed on grade P92 helped to understand the behavior of ferritic–martensitic steels under a combined loading. The softening and lifetime behavior strongly depend on the temperature and total strain range. Especially at small strain amplitudes, the lifetime is seriously reduced when adding a hold time which indicates the importance of considering technically relevant small strains.
Modelling of environmentally assisted material degradation in the crack phase-field framework
(2019)
The simulation of crack propagation was conducted with a diffusive crack model in a variational framework. Moreover, the physically sound introduction of mass transport and coupling mechanisms due to environmentally assisted effects could be realised in this framework. The objective consists of the application of the phase-field Approach towards the simulation of environmentally assisted material degradation with the advantage of a non-required predefined crack path and a mesh-independent non-local formulation that facilitates the damage evolution with respect to material softening. The sharp crack is regularised by the introduction of a phase-field order parameter leading to a diffusive crack formulation.
Besides the equations originating from the linear momentum balance an additional evolution equation for the crack phase-field is introduced. Furthermore, mass transport is simulated by a Diffusion equation. The description delivered by the variational phase-field framework is able to simulate crack propagation according to published numerical test cases.
Additionally, the calculation of stress intensity factors is possible as well as crack resistance curves that describe stable crack propagation.
The current competitive situation on electricity markets forces power plants into cyclic operation regimes with frequent load shifts and starts/shutdowns. In the present work, the cyclic mechanical behavior of ferritic-martensitic 9-12 % Cr steels under isothermal and thermomechanical loading was investigated for the example of grade P92 material. A continuous softening was observed under all loading conditions. The introduction of hold periods to the applied cycles reduced material lifetime, with most prominent effects at technologically relevant small strain levels. The microstructural characterization reveals a coarsening of the original “martensitic” lath-type microstructure to a structure with polygonal subgrains and reduced dislocation density. The microstructural data forms the input for a physically-based modelling approach.
9-12% Cr ferritic-martensitic stainless steels are widely used as high temperature construction materials in power plants due to their excellent creep and oxidation resistance. The growing share of renewable energy sources in power generation forces many of these plants into more flexible operation with frequent load shifts or shutdowns. These cyclic operation profiles constitute a major lifetime issue.
The present contribution reports on current findings obtained in a multidisciplinary project which combines cyclic mechanical and cyclic oxidation testing with detailed microstructural analyses. Mechanical analyses are carried out on P92 and P91 steel grades to give an overview of softening phenomena and lifetimes obtained in isothermal cyclic loading (low cycle fatigue, LCF), non-isothermal cyclic loading (thermo-mechanical fatigue, TMF), and service-like combinations of creep and fatigue periods (creep-fatigue interaction).
Oxidation testing focuses on the grades P92 and VM12 with the intention of clarifying the impact of frequent passes through intermediate temperature levels on the kinetics of steam-side oxidation and the characteristics of the evolving oxide scales. An attempt is made to evaluate their composition, strength, integrity and adhesion after up to 250 temperature cycles. Flat coupons as well as curved tube sections are tested to assess the mutual influence of geometry on oxide scale integrity.
Complementary microstructural investigations by scanning and transmission electron microscopy plus EBSD are used for phase identification and substrate/oxide interface characterisation. The evolutions of grain size and dislocation density under different test conditions are quantified.
9-12% Cr ferritic-martensitic stainless steels are widely used as high temperature construction materials in power plants due to their excellent creep and oxidation resistance. The growing share of renewable energy sources in power generation forces many of these plants into more flexible operation with frequent load shifts or shutdowns. These cyclic operation profiles constitute a major lifetime issue. The present contribution reports on current findings obtained in a multidisciplinary project which combines cyclic mechanical and cyclic oxidation testing of different 9-12% Cr grades with detailed microstructural analyses.
Mechanical analyses are carried out on P92 and P91 steel grades to give an overview of softening phenomena and lifetimes obtained in isothermal cyclic loading (low cycle fatigue, LCF), non-isothermal cyclic loading (thermo-mechanical fatigue, TMF), and service-like combinations of creep and fatigue periods.
Complementary microstructural investigations by scanning and transmission electron microscopy plus EBSD are used for phase identification, substrate/oxide interface characterization and quantification of the microstructure evolution under cyclic conditions.
The employment of renewable energy resources, which are naturally intermittent, for electricity generation has altered the working conditions of conventional power plants from continuous (baseload) to cyclic or flexible operation. For a long time, 9-12% Cr ferritic-martensitic stainless steels have been widely used in power plants due to their favorable characteristics such as high creep strength at high temperatures and oxidation and corrosion resistance. The components of power plants are subjected to long term cyclic loadings including fatigue and creep-fatigue at high temperatures. As ferritic-martensitic steels are known to exhibit cyclic softening when subjected to such loading scenarios, it is crucial to study the material response in such conditions. Since it is impossible to test the material behavior exactly as the operation conditions of power plants, due to technical difficulties and cost issues, it is necessary to develop physically-based material models that can predict the material behavior in more realistic situations.
In recent years, many material models have been proposed to describe the behavior of 9-12% Cr ferritic-martensitic stainless steels, which follow phenomenological or physically-based approaches. Phenomenological models provide a stress-strain relation based on empirical observations although they usually lack physical background. To alleviate this drawback and to allow for more flexibility and wider ranges of strain-rate and temperature, physically-based models are suggested. In this approach, microstructural evolution, dislocation movement and/or kinetics of plastic deformation processes are included. The physically-based models allow for a better extrapolation from the experiment results to other operation conditions and their material constants can be interpreted physically. Compared to the former approach, the material behavior can be described more accurately and flexibly and the number of material constants is less in general. In the presented work, the existing micromechanical models developed for P92 steel are compared and extended to allow for new dislocation-based strengthening/cyclic mechanisms. Their performance is assessed in the light of mechanical test data from creep-fatigue and thermo-mechanical fatigue experiments and detailed characterizations of the microstructure evolution in the fatigued material.
Es konnte anhand einer numerischen Voruntersuchung gezeigt werden, dass anhand der kombinierten Auswertung der im Versuch verwendeten Sensorik eine Einteilung der unter Ermüdung in Bohrlochproben auftretenden Rissformen in verschiedene Hauptkategorien (Eckriss, Oberflächenriss, Durchgangsriss) möglich ist.
Es wird eine neu entwickelte Methode zur Thermographiebasierten Rissmessung vorgestellt. Darüber hinaus wird eine numerische Vorarbeit präsentiert, die zeigt, dass anhand der gemeisamen Auswertung der Versuchsdaten aus unterschiedlicher Sensorik die Möglichkeit besteht, die unter Ermüdungsbelastung in Bohrlochproben auftretenden Risse in Geometriekategorien zu unterteilen.
The methods of computational damage mechanics are well-established for the description of degradation of materials under monotone loading. An extension to structural damage induced by cyclic loading is however significantly limited. This is due to enormous computational costs required to resolve each load cycle by conventional temporal incremental integration schemes while a typical fatigue loading history comprises between thousands and millions of cycles. Despite the permanent increase of computational resources and algorithmic performance, a successful approach is rather based on the development of novel multiscale in time integration schemes.
A Fourier transformation-based temporal integration (FTTI) is represented, which takes advantage of temporal scale separation incorporated into the cycle jump method. The response fields are approximated by a Fourier series whose coefficients undergo the evolution on a long-time scale. This is correlated with the evolution of the history variables, including damage, by means of the adaptive cycle jump method of various orders. The necessary extrapolation rates are obtained from the underlying solution of a short-time scale problem, which results from the oscillatory boundary condition and fulfills the global equilibrium of the Fourier coefficients. In this way, a remarkable speedup is achieved because the number of cycles to be fully integrated dramatically decreases.
The key idea behind the FTTI method is that the global in space equilibrium problem is linear since it is decoupled from the evolution equations. The latter are solved in the quadrature points under response fields prescribed throughout the whole load cycle. Consequently, integration of a single load cycle is much more efficient than the conventional single scale integration where the global equilibrium iteration and the local iteration of the evolution equations are coupled. This results in an additional speedup of the FTTI method.
The performance of the FTTI technique is demonstrated for two different constitutive behaviors: a viscoplastic model with a damage variable governed by the local equivalent viscoplastic strain; a quasi-brittle response where the damage variable is driven by a non-local equivalent strain. The latter is implicitly introduced as proposed by Peerlings. Both, the explicit and implicit extrapolation schemes are validated. The FTTI solutions agree very well with the reference cycle-by -cycle solutions, while significantly reducing the computational costs. The adaptive determination of the jump length can properly recognize the particular responses throughout the fatigue loading history (stationary fatigue, acceleration of fatigue damage when approaching failure) as well as stress redistribution phenomena.
A constitutive model for the mechanical behaviour of single crystal Ni-base superalloys under high temperature conditions has been developed in the framework of a Cooretec project in cooperation with Siemens AG, MTU Aero Engines AG and University Bayreuth. In addition to the conventional material properties e.g. elastic constants, the model requires the parameters of the initial microstructure as an input. Thus, the γ’-precipitate size and the channel width of the γ-matrix were obtained from SEM micrographs. The model uses the slip system theory and describes the movement, multiplication and annihilation of dislocations in the channels. Furthermore, the cutting of precipitates is another mechanism contributing to the plastic flow. The evolution of the morphology due to rafting and its effects on the deformation have been implemented according to. The kinematic hardening is introduced as a stress tensor to realistically represent the strain hardening of arbitrary oriented single crystals.
The mechanical behaviour of single crystal specimens has been experimentally investigated in tension tests at different strain rates and in creep tests under various loads. The constitutive model has been calibrated based on the experimental data for temperatures of 950°C and 850°C and the [001] and [111] crystallographic orientations.
Finally, a micromechanical model was created to simulate the creep response of additive manufactured polycrystalline structures. An EBSD image is taken to obtain the grain geometry and their respective orientation. The grain boundaries are discretised using cohesive elements, whereas the single crystal model was applied to each grain in the representative volume. The polycrystal model is generated using Dream3D, NetGen and other software previously developed at the BAM.
Virtual-lab-based determination of a macroscopic yield function for additively manufactured parts
(2018)
This work presents a method for the yield function determination of additively manufactured parts of S316L steel. A crystal plasticity model is calibrated with test results and used afterwards to perform so-called virtual experiments, that account for the specific process-related microstructure including crystallographic and morphological textures. These simulations are undertaken on a representative volume element (RVE), that is generated from EBSD/CT-Scans on in-house additively manufactured specimen, considering grain structure and crystal orientations. The results of the virtual experiments are used to determine an anisotropic Barlat yield function, that can be used in a macroscopical continuum-sense afterwards. This scale-bridging approach enables the calculation of large-scale parts, that would be numerically too expensive to be simulated by a crystal plasticity model.