5 Werkstofftechnik
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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.
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.
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.
Abstract While classically used to visualise the magnetic microstructure of functional materials (e.g., for magnetic applications), in this study, the Bitter technique was applied for the first time to visualise macroscopic deformation gradients in a polycrystalline low-carbon steel. Spherical indentation was chosen to produce a multiaxial elastic–plastic deformation state. After removing the residual imprint, the Bitter technique was applied, and macroscopic contrast differences were captured in optical microscopy. To verify this novel characterisation technique, characteristic “hemispherical” deformation zones evolving during indentation were identified using an analytical model from the field of contact mechanics. In addition, near-surface residual stresses were determined experimentally using synchrotron radiation diffraction. It is established that the magnetic domain distribution contrast provides deformation-related information: regions of different domain wall densities correspond to different “hemispherical” deformation zones (i.e., to hydrostatic core, plastic zone and elastic zone, respectively). Moreover, the transitions between these three zones correlate with characteristic features of the residual stress profiles (sign changes in the radial and local extrema in the hoop stress). These results indicate the potential of magnetic domain distribution imaging: visualising macroscopic deformation gradients in fine-grained ferromagnetic material with a significantly improved spatial resolution as compared to integral, mean value-based measurement methods.
The sound numerical prediction of welding-induced thermal stresses, residual stresses, and distortions strongly depends on the accurate description of a welded material’s thermomechanical deformation behaviour. In this work, we provide experimental data on the viscoplastic deformation behaviour of a grade-s960ql steel up to a temperature of 1000 ◦C. In addition, a multi-phase viscoplastic material model is proposed, which accounts for the experimentally observed isothermal deformation behaviour of grade-s960ql steel base and austenitised material, as well as for athermal contributions that originate from solid-state phase transformations. The multi-phase viscoplastic and a classic rateindependent isotropic hardening material model were applied in the numerical simulations of both-ends-fixed bar Satoh tests and a single-pass gas metal arc weld. The influence of material modelling choices on the agreement between numerical simulation and experimental results is discussed, and recommendations for further work are given.
With the introduction of a mass transport mechanism the entire problem is subjected to a time frame that dictates the time-dependent action of soluted species on mechanical properties. A numerical framework within the phase-field approach is presented with an embrittlement-based coupling mechanism. The underlying functionals are expressed in terms of the displacement, mass concentration and crack phase-field. Within the phase-field approach the modelling of sharp crack discontinuities is replaced by a diffusive crack model facilitating crack initiation and complex crack topologies without the requirement of a predefined crack path. The isotropic hardening of the elasto-plastic deformation model and the local fracture criterion are affected by the species concentration. This allows for embrittlement and leads to an accelerated crack propagation. An extended mass transport equation for hydrogen embrittlement, accounting for mechanical stresses and deformations, is implemented. For stabilisation purposes a staggered scheme is applied to solve the system of partial differential equations by a multi-field finite-element method. A thermodynamically consistent coupling relation that accommodates the required mechanisms is presented.