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A key limitation of the most constitutive models that reproduce a Degradation of quasi-brittle materials is that they generally do not address issues related to fatigue. One reason is the huge computational costs to resolve each load cycle on the structural level. The goal of this paper is the development of a temporal Integration scheme, which significantly increases the computational efficiency of the finite element method in comparison to conventional temporal integrations.
The essential constituent of the fatigue model is an implicit gradient-enhanced formulation of the damage rate. The evolution of the field variables is computed as amultiscale Fourier series in time.On a microchronological scale attributed to single cycles, the initial boundary value problem is approximated by linear BVPs with respect to the Fourier coefficients. Using the adaptive cycle jump concept, the obtained damage rates are transferred to a coarsermacrochronological scale associated with the duration of material deterioration. The performance of the developedmethod is hence improved due to an efficient numerical treatment of the microchronological problem in combination with the cycle jump technique on the macrochronological scale. Validation examples demonstrate the convergence of the obtained solutions to the reference simulations while significantly reducing the computational costs.
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
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.
The age hardening response of a high-purity Al–4Cu–1Li–0.25Mn alloy (wt. %) during isothermal aging without and with an applied external load was investigated. Plate shaped nanometer size T1 (Al2CuLi) and θ′ (Al2Cu) hardening phases were formed. The precipitates were analyzed with respect to the development of their structure, size, number density, volume fraction and associated transformation strains by conducting transmission electron microscopy (TEM) and scanning transmission electron microscopy (STEM) studies in combination with geometrical Phase analysis (GPA). Special attention was paid to the thickening of T1 phase. Two elementary types of single-layer T1 precipitate, one with a Li-rich (Type 1) and another with an Al-rich (Defect Type 1) central layer, were identified. The results show that the Defect Type 1 structure can act as a precursor for the Type 1 structure. The thickening of T1 precipitates occurs by alternative stacking of These two elementary structures. The thickening mechanism was analyzed based on the magnitude of strain associated with the precipitation transformation normal to its habit plane. Long-term aging and aging under load resulted in thicker and structurally defected T1 precipitates. Several types of defected precipitates were characterized and discussed. For θ′ precipitates, a ledge mechanism of
thickening was observed. Compared to the normal aging, an external load applied to the peak aged state leads to small variations in the average sizes and volume fractions of the precipitates.
Morphology and structure of TixOy nanoparticles generated by femtosecond laser ablation in water
(2018)
In this work femto-second pulsed laser ablation in liquid (PLAL) procedure for the generation of titanium oxide nanoparticles (NP) is reported with the purpose of understanding morphology and structure of the newly generated NPs. Ablation duration was varied for optimization of NP generation processes between 10 and 90 min. Surface morphology of NPs as well as their size and shape (distribution) were analysed by various complementary electron microscopy techniques, i.e. SEM, TSEM and TEM. The crystalline structure of titanium oxide particles was investigated byXRD(two instruments operated in different geometries) and HR-TEM. Concentration of generated titanium oxide NPs in liquid was analysed by ICP-MS. A mix of crystalline (mainly anatase), partly crystalline and amorphous spherical titanium oxide NPs can be reported having a mean size between 10 and 20 nm, which is rather independent of the laser ablation (LA) duration. A second component consisting of irregularly shaped, but crystalline titanium oxide nanostructures is co-generated in the LA water, with more pronounced occurrence at longer LA times. The provenance of this component is assigned to those spherical particles generated in suspension and passing through the converging laser beam, being hence subject to secondary irradiation effects, e. g. fragmentation.
The alloying system Co-Al-W-Ta is comprehensively investigated in the vicinity of the compositional point Co-9Al-10W-2Ta, at. pct. These investigations provided a large amount of quantitative information, which can be used for alloy development, namely, the compositional dependences of the The alloying system Co-Al-W-Ta is comprehensively investigated in the vicinity of the compositional point Co-9Al-10W-2Ta, at. pct. These investigations provided a large amount of quantitative information, which can be used for alloy development, namely, the compositional dependences of the γ‘-solvus, solidus, and liquidus temperatures; fraction of the extrinsic phases after casting; the compositional dependence of the γ/γ‘-lattice misfit; the element partitioning between γ- and γ‘-phases; and the two Phase compositional area γ/γ‘ in the Co-rich part of the Co-Al-W-Ta phase diagram at 900°C. It is shown that additions of Ta elevate the γ‘-solvus temperature and increase the γ/γ‘-lattice misfit, but adding more than about 3 at. pct Ta results in a large amount of undissolvable extrinsic phases. Additionally, two Co-Al-W-Ta alloys with lower content of W were developed and solidified as [001] single crystals for mechanical testing in a temperature range between 20 and 1200°C. These tests included measurement of the Young modulus, tensile tests with constant strain rate, and stress rupture tests. It was found that at temperatures up to about 750°C the ultimate tensile strength of Co-Al-Ta-W alloys can be at the same level or even higher than of Ni-based superalloys.
To increase efficiency, modern steam plants are pushing their operational regime from super-critical (600 °C/300 bar) to ultra-super-critical (740/760 °C/350 bar) stretching existing turbine materials to their limits. The focus is on new generation functional materials and technologies which complement the inherent properties of existing materials.
Current work proposes a novel High Power Impulse Magnetron Sputtering (HIPIMS) Deposition technology, for the first time, for deposition of a ceramic based CrN/NbN coating with a nanoscale multilayer structure (bi-layer thickness Δ = 1.9 nm) with superior adhesion (LC2 = 80 N) to protect low Chromium P92 steel widely used in steam power plants. Thermodynamic calculations predict the equilibrium phases and aggressive gaseous compounds generated by the interaction of steam with the coating. CrN/NbN coated P92 steel samples oxidised at 600 °C in a high pressure (50 bar) 100% steam atmosphere for up to 1000 h reveal the coating's superior oxidation resistance and protective mechanisms, especially against the detrimental effect of Hydrogen. High temperature (650 °C) Tensile Strength, Low Cycle Fatigue and Creep tests confirm that, unlike other state-of-the-art PVD technologies, HIPIMS is not detrimental to the mechanical properties of the substrate material. Water droplet erosion tests confirm no measurable weight loss after 2.4 X 10⁶ impacts.
Comprehensive insights into the early stages of corrosion mechanisms provide fundamental knowledge to further understand and model long time material behaviour. The present work studies the early stages of combined oxidation and sulphidation of ferritic model alloys for time scales up to 250 h at 650 °C to observe the influence of chromium during the corrosion under SO2. Model alloys were used to focus on the reaction of the intended elements: Fe, Cr, S, and O. Pure iron simultaneously forms magnetite and iron sulphide in an early stage of corrosion, covered by a pure oxide layer after 100 h. Iron with 13 wt% Cr shows hematite and mixed Fe-Cr-oxides first, before sulphides nucleate in the inner corrosion zone. With increasing ageing time a magnetite layer is observed below the hematite layer. Quantitative phase fractions of all corrosion products observed were determined from cross section images. Characterization of the Fe13Cr corrosion scale by FIB revealed a highly porous structure in the inner corrosion zone where Cr-rich (Fe, Cr)-sulphides are present, and caused the scale to spall easily.
Thin Sol-Gel Alumina Coating as Protection of a 9% Cr Steel Against Flue Gas Corrosion at 650 °C
(2018)
Samples of sol-gel alumina coated and uncoated P92 steel were exposed to flue gas at 650 °C for 300 h. As result of this treatment a 50 µm thick bi-layered oxide scale had formed on the surface of the uncoated sample. Below the scale a 40 µm thick inner oxidation zone was detected. In contrast, the porous, micron thick alumina coating enabled the formation of a chromium oxide scale with a thickness of some nanometers at the interface between steel substrate and coating. In this case high temperature corrosion of the steel was prevented so far.
Due to the increasing global demand for pure silver, native wire silver aggregates in very high purities are gaining more industrial attention. Up to the present, no substantial metallurgical Investigation of natural wire silver exists in the accessible literature. To convey urgently needed cross-disciplinary fundamental knowledge for geoscientists and metallurgical engineers, twenty natural wire silver specimens from eight different ore deposits have been investigated in detail for the first time by EBSD (Electron Back Scattering Diffraction), supported by light microscopy and micro-probe analyses. The improved understanding of the natural silver wire microstructure provides additional Information regarding the growth of natural silver aggregates in comparison to undesired artificial growth on electronic devices. Clear evidence is provided that natural silver curls and hairs exhibit a polycrystalline face-centered cubic microstructure associated with significant twinning. Although the investigated natural wire silver samples have relatively high purity (Ag > 99.7 wt.-%), they contain a variety of trace elements such as, S, Cu, Mn, Ni, Zn, Co and Bi, As and Sb. Additionally, Vickers micro-hardness measurements are provided for the first time which revealed that natural silver wires and curls are softer than it might be expected from conversion of the general Mohs hardness of 2.7.
Interdiffusion in the Face-Centered Cubic Phase of the Co-Al-W-Ta System Between 1090 and 1240 °C
(2018)
Interdiffusion of Al, W, Ta and Co in a Co-base alloy at temperatures between 1090 and 1240 °C has been investigated. The interdiffusion coefficients were found to be close to those reported for these elements in Ni-base alloys. Combining the diffusion simulation software DICTRA with the Ni-base diffusion databases TCNi5 and MobNi3, the interdiffusion profiles of Co, Al W, and Ta were modeled for Co9Al8W2Ta/Co diffusion couples annealed at different temperatures and for different times. The results show that interdiffusion in the Co-Al-W-Ta alloys can be modeled reasonably well using the available commercial databases for thermodynamics and kinetics of Ni-base systems.
Technically relevant P92 steel (9% Cr) was coated with a micron-thick porous alumina layer prepared by sol-gel technique and treated with flue gas (60 CO2-30 H2O-2 O2-1 SO2-7 N2 (mole fraction in %)) at 650 ° to mimic an oxyfuelcombustion process. Local defects in the coating were marked using focused ion beam (FIB) technique and were inspected after exposition to hot flue gas atmosphere at 300, 800, and 1300 h, respectively. Local defects like agglomerated alumina sol particles tend to spall off from the coating uncovering the underlying dense chromia scale. Re-coating was found to restore the protection ability from oxidation when repeatedly treated with hot flue gas. Cracks and voids did not promote the local oxidation due to the formation of crystalline Mn/S/O species within and on top of the coating. The protective character of the steel-coating system is a result of (i) the fast formation of a dense chromia scale at the surface of sol-gel alumina-coated P92 steel bars in combination with (ii) the porous alumina coating acting as diffusion barrier, but also as diffusion partner in addition with (iii) fast Mn outward diffusion capturing the S species from flue gas.
Metal sulfide grain boundary precipitates of a ferrous model alloy with 13 wt.% chromium formed at 650°C under a gas atmosphere containing 0.5% SO2 and 99.5% Ar were investigated after ageing for 3 h, 6 h, and 12 h. The precipitates formed along grain boundaries were identified as Cr5S6 using energy-dispersive x-ray spectroscopy in transmission electron microscopy and electron backscatter diffraction analysis. Serial focused ion beam slicing was conducted followed by three-dimensional reconstruction to determine the number, size, and penetration depth of the precipitates evolved at the different time steps. There was a linear increase in the number of precipitates with time, while their average size increased only for the initial aging time but became constant after 6 h. Based on these results, a model for grain boundary sulfidation of ferritic alloys is discussed.
Pipe steels suitable for carbon capture and storage technology (CCS) require resistance against the corrosive environment of a potential CCS-site, e.g. heat, pressure, salinity of the aquifer, CO2-partial pressure. Samples of different mild and high alloyed stainless injection-pipe steels partially heat treated: 42CrMo4, X20Cr13, X46Cr13, X35CrMo4 as well as X5CrNiCuNb16-4 were kept at T=60 °C and ambient pressure as well as p=100 bar for 700 h - 8000 h in a CO2-saturated synthetic aquifer environment similar to possible geological on-shore CCS-sites in the northern German Basin. Main corrosion products are FeCO3 and FeOOH. Corrosion rates obtained at 100 bar are generally much lower than those measured at ambient pressure. Highest surface corrosion rates are 0.8 mm/year for 42CrMo4 and lowest 0.01 mm/year for X5CrNiCuNb16-4 in the vapour phase at ambient pressure. At 100 bar the highest corrosion rates are 0.01 mm/year for 42CrMo4, X20Cr13 (liquid phase), X46Cr13 and less than 0.01 mm/year for X35CrMo4 and X5CrNiCuNb16-4 after 8000 h of exposure with no regard to atmosphere. Martensitic microstructure offers good corrosion resistance.
This study examines the relationship between the magnetic mesostructure with the microstructure of low carbon steel tungsten inert gas welds. Optical microscopy revealed variation in the microstructure of the parent material, in the heat affected and fusion zones, correlating with distinctive changes in the local magnetic stray fields measured with high spatial resolution giant magneto resistance sensors. In the vicinity of the heat affected zone high residual stresses were found using neutron diffraction.
Notably, the gradients of von Mises stress and triaxial magnetic stray field modulus follow the same tendency transverse to the weld. In contrast, micro-X-ray fluorescence characterization indicated that local changes in element composition had no independent effect on magnetic stray fields.
Shear testing can contribute to a better understanding of the plastic deformation of Ni-base superalloy single crystals. In the present study, shear testing is discussed with special emphasis placed on its strengths and weaknesses. Key mechanical and microstructural results which were obtained for the high-temperature (T ≈ 1000 °C) and low-stress (τ ≈ 200 MPa) creep regime are briefly reviewed. New 3D stereo STEM images of dislocation substructures which form during shear creep deformation in this regime are presented. It is then shown which new aspects need to be considered when performing double shear creep testing at lower temperatures (T < 800 °C) and higher stresses (τ > 600 MPa). In this creep regime, the macroscopic crystallographic [11−2](111) shear system deforms significantly faster than the [01−1](111) system. This represents direct mechanical evidence for a new planar fault nucleation scenario, which was recently suggested (Wu et al. in Acta Mater 144:642–655, 2018). The double shear creep specimen geometry inspired a micro-mechanical in-situ shear test specimen. Moreover, the in-situ SEM shear specimen can be FIB micro-machined from prior dendritic and interdendritic regions. Dendritic regions, which have a lower γ′ volume fraction, show a lower critical resolved shear stress.
We describe a lattice-based crystallographic approximation for the analysis of distorted crystal structures via Electron Backscatter Diffraction (EBSD) in the scanning electron microscope. EBSD patterns are closely linked to local lattice parameter ratios via Kikuchi bands that indicate geometrical lattice plane projections. Based on the transformation properties of points and lines in the real projective plane, we can obtain continuous estimations of the local lattice distortion based on projectively transformed Kikuchi diffraction simulations for a reference structure. By quantitative image matching to a projective transformation model of the lattice distortion in the full solid angle of possible scattering directions, we enforce a crystallographically consistent approximation in the fitting procedure of distorted simulations to the experimentally observed diffraction patterns. As an application example, we map the locally varying tetragonality in martensite grains of steel.
Subsurface characterization of high-strength high-interstitial austenitic steels after impact wear
(2018)
The microstructure of the subsurface after impact wear of three high-strength high interstitial austenitic steels has been analysed using transmission electron microscopy (TEM) in alloys with C and N as interstitial elements. In all cases, a nanocrystalline region followed by a transition zone and a cold-worked area are present. Additionally, microhardness and nano-scratching tests were conducted to study the wear-related properties of the impact subsurface and the base material. The results of the microstructural analysis reveal that the following mechanisms are involved during impact wear: abrasion (ploughing), microcrack formation associated with contact fatigue, entrapment and adhesion of SiO2 particles. The analysis of the wear-related properties indicates that the subsurface acts as a self-protective layer that prevents the deterioration of the substrate.
Insights into early damage mechanisms during high-temperature gas corrosion provide important aspects for the prediction of the long-term stability of hightemperature materials exposed to a hot and corrosive environment. The current work presents a real time study concerning the combined oxidation and sulfidation of ferritic model alloys in a hot SO2 containing atmosphere using energy dispersive X-ray diffraction. The applied high temperature reactor allows the transmittance of high energetic X-rays in order to collect X-ray diffraction pattern of the sample surface in situ during the reaction with the reactive environment. The results revealed that the first phases crystallizing on iron with 2 wt% chromium and with 9 wt% chromium are oxides. The aging experiments at T = 650° C with 0.5% SO2 and 99.5% Ar were followed in situ and caused an external mixed oxide-sulfide layer on top of iron with 2 wt% chromium. On the higher alloyed material the external scale consists of iron oxides and the inner scale of mixed (Fe,Cr)-oxides and chromium-sulfides. The oxide content continuously increases parallel to an increase of the sulfide amount. Thus, the initially formed (Fe,Cr)-oxides do not have a protective character and support the transport of sulfur through the growing oxide scale.
A great amount of material properties is strongly influenced by dislocations, the carriers of plastic deformation. It is therefore paramount to have appropriate tools to quantify dislocation substructures with regard to their features, e.g., dislocation density, Burgers vectors or line direction. While the transmission electron microscope (TEM) has been the most widely-used equipment implemented to investigate dislocations, it usually is limited to the two-dimensional (2D) observation of three-dimensional (3D) structures. We reconstruct, visualize and quantify 3D dislocation substructure models from only two TEM images (stereo pairs) and assess the results. The reconstruction is based on the manual interactive tracing of filiform objects on both images of the stereo pair. The reconstruction and quantification method are demonstrated on dark field (DF) scanning (S)TEM micrographs of dislocation substructures imaged under diffraction contrast conditions. For this purpose, thick regions (> 300 nm) of TEM foils are analyzed, which are extracted from a Ni-base superalloy single crystal after high temperature creep deformation. It is shown how the method allows 3D quantification from stereo pairs in a wide range of tilt conditions, achieving line length and orientation uncertainties of 3% and 7°, respectively. Parameters that affect the quality of such reconstructions are discussed.