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High-performance fibre-reinforced polymer composites are important construction materials based not only on the specific properties of the reinforcing fibres and the flexible polymer Matrix but also on the compatible properties of the composite interphase. First, oxygen-free (a-CSi:H) and oxygen-binding (a-CSiO:H) plasma nanocoatings of different mechanical and tribological properties were deposited on planar silicon dioxide substrates that closely mimic E-glass. The nanoscratch test was used to characterize the nanocoating adhesion expressed in terms of critical normal load and work of adhesion. Next, the same nanocoatings were deposited on E-glass fibres, which were used as reinforcements in the polyester composite to affect its interphase properties. The shear properties of the polymer composite were characterized by macro- and micromechanical tests, namely a short beam shear test to determine the short-beam strength and a single fibre push-out test to determine the interfacial shear strength. The results of the polymer composites showed a strong correlation between the short-beam strength and the interfacial shear strength, proving that both tests are sensitive to changes in fibre-matrix adhesion due to different surface modifications of glass fibres (GF).
Finally, a strong correlation between the shear properties of the GF/polyester composite and the adhesion of the plasma nanocoating expressed through the work of adhesion was demonstrated.
Thus, increasing the work of adhesion of plasma nanocoatings from 0.8 to 1.5 mJ·m−2 increased the short-beam strength from 23.1 to 45.2 MPa. The results confirmed that the work of adhesion is a more suitable parameter in characterising the level of nanocoating adhesion in comparison with the critical normal load.
The onset of plasticity in a single crystal C60 fullerite was investigated by nanoindentation on the (111) crystallographic plane. The transition from elastic to plastic deformation in a contact was observed as pop-in events on loading curves. The respective resolved shear stresses were computed for the octahedral slip systems ⟨011¯¯¯⟩{111}, supposing that their activation resulted in the onset of plasticity. A finite element analysis was applied, which reproduced the elastic loading until the first pop-in, using a realistic geometry of the Berkovich indenter blunt tip. The obtained estimate of the C60 theoretical shear strength was about 1/11 of the shear modulus on {111} planes.
A potential repair alternative to restoring the mechanical properties of lightweight fiberreinforced polymer (FRP) structures is to locally patch these areas with scarf joints. The effects of such repair methods on the structural integrity, however, are still largely unknown. In this paper, the mechanical property restoration, failure mechanism, and influence of fiber orientation mismatch between parent and repair materials of 1:50 scarf joints are studied on monolithic glass fiber-reinforced polymer (GFRP) specimens under tensile load. Two different parent orientations of [-45/+45]2S and [0/90]2S are exemplarily examined, and control specimens are taken as a baseline for the tensile strength and stiffness property recovery assessment. Using a layer-wise stress analysis with finite element simulations conducted with ANSYS Composite PrepPost to support the experimental
investigation, the fiber orientation with respect to load direction is shown to affect the critical regions and thereby failure mechanism of the scarf joint specimens.
Atomistic deformation simulations in the nominally elastic regime are performed for a model binary glass with strain rates as low as 10 4 /s (corresponding to 0.01 shear strain per 1 μs). A strain rate dependent elastic softening due to a micro-plasticity is observed, which is mediated by thermally-activated localized structural transformations (LSEs). A closer inspection of the atomic-scale structure indicates the material response is distinctly different for two types of local atomic environments. A system spanning iscosahe- drally coordinated substructure responds purely elastically, whereas the remaining substructure admits both elastic and microplastic evolution. This leads to a heterogeneous internal stress distribution which, upon unloading, results in negative creep and complete residual-strain recovery. A detailed structural analysis in terms of local stress, atomic displacement, and SU(2) local bonding topology shows such mi- croscopic processes can result in large changes in local stress and are more likely to occur in geomet- rically frustrated regions characterized by higher free volume and softer elastic stiffness. The thermally- activated LSE activity also mediates structural relaxation, and in this way should be distinguished from stress-driven shear transformation activity which only rejuvenates glass structure. The frequency of LSE activity, and therefore the amount of micro-plasticity, is found to be related to the degree to which the glassy state is relaxed. These insights shed atomistic light onto the structural origins that may govern re- cent experimental observations of significant structural evolution in response to elastic loading protocols.
This study reports on the stress relaxation potential of stress-relieving heat treatments for laser powder bed fused 316L. The residual stress is monitored non-destructively using neutron diffraction before and after the heat treatment. Moreover, the evolution of the microstructure is analysed using scanning electron microscopy. The results show, that a strong relaxation of the residual stress is obtained when applying a heat treatment temperature at 900°C. However, the loss of the cellular substructure needs to be considered when applying this heat treatment strategy.
Superalloy inspired Al10Co25Cr8Fe15Ni36Ti6 compositionally complex alloy is known for its gamma-gamma' microstructure and the third Heusler phase. Variations of this alloy, gained by replacing 0.5 or 1 at. pct Al by the equivalent amount of Mo, W, Zr, Hf or B, can show more phases in addition to this three-phase morphology. When the homogenization temperature is chosen too high, a eutectic phase formation can take place at the grain boundaries, depending on the trace elements: Mo and W do not form eutectics while Hf, Zr and B do. In order to avoid the eutectic formation and the potential implied grain boundary weakening, the homogenization temperature must be chosen carefully by differential scanning calorimetry measurements. A too low homogenization temperature, however, could impede the misorientation alignment of the dendrites in the grain. The influence of grain boundary phases and incomplete dendrite re-orientation are compared and discussed.
Al2O3 has been widely used as a coating in industrial applications due to its excellent chemical and thermal resistance. Considering high temperatures and aggressive mediums exist in geothermal systems, Al2O3 can be a potential coating candidate to protect steels in geothermal applications. In this study, γ-Al2O3 was used as a coating on martensitic steels by applying AlOOH sol followed by a heat treatment at 600 °C. To evaluate the coating application process, one-, two-, and three-layer coatings were tested in the artificial North German Basin (NGB), containing 166 g/L Cl−, at 150 °C and 1 MPa for 168 h. To reveal the stability of the Al2O3 coating in NGB solution, three-layer coatings were used in exposure tests for 24, 168, 672, and 1296 h, followed by surface and cross-section characterization. SEM images show that the Al2O3 coating was stable up to 1296 h of exposure, where the outer layer mostly transformed into boehmite AlOOH with needle-like crystals dominating the surface. Closer analysis of cross-sections showed that the interface between each layer was affected in long-term exposure tests, which caused local delamination after 168 h of exposure. In separate experiments, electrochemical impedance spectroscopy (EIS) was performed at 150 °C to evaluate the changes of coatings within the first 24 h. Results showed that the most significant decrease in the impedance is within 6 h, which can be associated with the electrolyte penetration through the coating, followed by the formation of AlOOH. Here, results of both short-term EIS measurements (up to 24 h) and long-term exposure tests (up to 1296 h) are discussed.
We discuss a refined simulation approach which treats Kikuchi diffraction patterns in electron backscatter diffraction (EBSD) and transmission Kikuchi diffraction (TKD). The model considers the result of two combined mechanisms: (a) the dynamical diffraction of electrons emitted coherently from point sources in a crystal and (b) diffraction effects on incoherent diffuse intensity distributions. Using suitable parameter settings, the refined simulation model allows to reproduce various thickness- and energy-dependent features which are observed in experimental Kikuchi diffraction patterns. Excess-deficiency features are treated by the effect of gradients in the incoherent background intensity. Based on the analytical two-beam approximation to dynamical electron diffraction, a phenomenological model of excess-deficiency features is derived, which can be used for pattern matching applications. The model allows to approximate the effect of the incident beam geometry as a correction signal for template patterns which can be reprojected from pre-calculated reference data. As an application, we find that the accuracy of fitted projection centre coordinates in EBSD and TKDcan be affected by changes in the order of 10−3–10-2 if excess-deficiency features are not considered in the theoreticalmodel underlying a best-fit pattern matching approach. Correspondingly, the absolute accuracy of simulation-based EBSD strain determination can suffer frombiases of a similar order of magnitude if excess-deficiency effects are neglected in the simulation model.
The impact of the microstructure of Fe-16Cr-0.2C on high-temperature oxidation – sulphidation in SO2
(2021)
This study elucidates the impact of the microstructure of Fe-16Cr-0.2C on oxide layer formation at 650 ◦C in Ar-0.5 % SO2. A cold-rolled and two heat-treated states of the alloy were exposed for up to 1000 h. The samples were characterised in detail from microstructural and chemical perspectives using scanning electron microscopy (SEM), X-ray diffraction (XRD) and time-of-flight secondary ion mass spectrometry (ToF-SIMS). The microstructural modification of the alloy by heat-treatment was advantageous. It was found that Cr-carbides support chromia formation and reduce sulphidation when their area fraction is low and diameter is small.
Методом рентгеноструктурного анализа в интервале температур 18—1150 °С определены температурные зависимости периодов кристаллических решеток γ- и γ'-фаз, их размерно-го несоответствия (мисфит) и объемной доли γ'-фазы экспериментального монокристал-лического жаропрочного никелевого сплава. Определены диапазоны температур, в которых происходят интенсивные изменения структурно-фазовых характеристик исследованного сплава.
Signal optimization for transmission Kikuchi diffraction (TKD) measurements in the scanning electron microscope is investigated by a comparison of different sample holder designs. An optimized design is presented, which uses a metal shield to efficiently trap the electron beam after transmission through the sample. For comparison, a second holder configuration allows a significant number of the transmitted electrons to scatter back from the surface of the sample holder onto the diffraction camera screen. It is shown that the secondary interaction with the sample holder leads to a significant increase in the background level, as well as to additional noise in the final Kikuchi diffraction signal. The clean TKD signal of the optimized holder design with reduced background scattering makes it possible to use small signal changes in the range of 2% of the camera full dynamic range. As is shown by an analysis of the power spectrum, the signal-to-noise ratio in the processed Kikuchi diffraction patterns is improved by an order of magnitude. As a result, the optimized design allows an increase in pattern signal to noise ratio which may lead to increase in measurement speed and indexing reliability.
Kirkendall porosity that forms during interdiffusion in a diffusion couple of nickel-base superalloy CMSX-10 with pure nickel is investigated. The diffusion experiments are conducted at a temperature of 1250 °C, where the strengthening ƴ'-phase ist partially dissolved. The porosity is studied by X-ray sub-μ tomography with a spatial resolution of about 0.35³ μm³ at the European Synchrotron Radiation Facility (ESRF) in Grenoble, France. It is found that depending on the distance from the interface the Kirkendall pores take different shapes: octahedral, rounded pyramidal, drop shaped, dendritic, pear shaped, and joint shapes. Such a variety of pore morphologies indicates a complex multistage process of porosity nucleation and growth under vacancy supersaturation of different degrees. The experimental findings are interpreted on the basis of the results of diffusion modeling. It is shown that the kinetics of porosity growth is essentially influenced by the dissolution of the ƴ'-phase.
High-entropy alloys (HEAs) and compositionally complex alloys (CCAs) represent new classes of materials containing five or more alloying elements (concentration of each element ranging from 5 to 35 at. %). In the present study, HEAs are defined as single-phase solid solutions; CCAs contain at least two phases. The alloy concept of HEAs/CCAs is fundamentally different from most conventional alloys and promises interesting properties for industrial applications (e.g., to overcome the strength-ductility trade-off). To date, little attention has been paid to the weldability of HEAs/CCAs encompassing effects on the welding metallurgy. It remains open whether welding of HEAs/CCAs may lead to the formation of brittle intermetallics and promote elemental segregation at crystalline defects. The effect on the weld joint properties (strength, corrosion resistance) must be investigated. The weld metal and heat-affected zone in conventional alloys are characterized by non-equilibrium microstructural evolutions that most probably occur in HEAs/CCAs. The corresponding weldability has not yet been studied in detail in the literature, and the existing information is not documented in a comprehensive way. Therefore, this study summarizes the most important results on the welding of HEAs/CCAs and their weld joint properties, classified by HEA/CCA type (focused on CoCrFeMnNi and AlxCoCrCuyFeNi system) and welding process.
Thermal cycling of a Ni-excess NiTi alloy was conducted between 50 °C and liquid nitrogen temperature to induce martensitic transformations and to reverse them after. The starting point was an annealed and slowly cooled state, the end point a sample thermally cycled 1500 times. Positron annihilation lifetime spectra and Coincidence Doppler Broadening profiles were obtained in various states and at various tem- peratures. It was found that the initial state was low in defects with positron lifetimes close to that of bulk NiTi. Cycling lead to a continuous build-up of a defect structure up to 20 0 −50 0 cycles after which saturation was reached. Two types of defects created during cycling were identified, namely pure dislo- cations and vacancies attached to dislocations.
Laser based powder bed fusion additive manufacturing offers the flexibility to incorporate standard and userdefined scan strategies in a layer or in between the layers for the customized fabrication of metallic components. In the present study, four different scan strategies and their impact on the development of microstructure, texture, and residual stresses in laser powder bed fusion additive manufacturing of a nickel-based superalloy Inconel 718 was investigated. Light microscopy, scanning electron microscopy combined with electron backscatter diffraction, and neutron diffraction were used as the characterization tools. Strong textures with epitaxially grown columnar grains were observed along the build direction for the two individual scan strategies. Patterns depicting the respective scan strategies were visible in the build plane, which dictated the microstructure development in the other planes. An alternating strategy combining the individual strategies in the successive layers and a 67◦ rotational strategy weakened the texture by forming finer microstructural features. Von Mises equivalent stress plots revealed lower stress values and gradients, which translates as lower distortions for the alternating and rotational strategies. Overall results confirmed the scope for manipulating the microstructure, texture, and residual stresses during laser powder bed fusion additive manufacturing by effectively controlling the scan strategies.
For more than half a century, spinodal decomposition has been a key phenomenon in considering the formation of secondary phases in alloys. The most prominent aspect of the spinodal phenomenon is the lack of an energy barrier on its transformation pathway, offering an alternative to the nucleation and growth mechanism. The classical description of spinodal decomposition often neglects the influence of defects, such as grain boundaries, on the transformation because the innate ability for like-atoms to cluster is assumed to lead the process. Nevertheless, in nanocrystalline alloys, with a high population of grain boundaries with diverse characters, the structurally heterogeneous landscape can greatly influence the chemical decomposition behavior. Combining atom-probe tomography, precession electron diffraction and density-based phase-field simulations, we address how grain boundaries contribute to the temporal evolution of chemical decomposition within the miscibility gap of a Pt-Au nanocrystalline system. We found that grain boundaries can actually have their own miscibility gaps profoundly altering the spinodal decomposition in nanocrystalline alloys. A complex realm of multiple interfacial states, ranging from competitive grain boundary segregation to barrier-free low-dimensional interfacial decomposition, occurs with a dependency upon the grain boundary character.
The phase-like behavior of grain boundaries (GBs), recently evidenced in several materials, is opening up new possibilities in the design of alloy microstructures. In this context, GB phase diagrams are contributing to a predictive description of GB segregation and (interfacial) phase changes. The influence of chemo-mechanical solute-GB interactions on the GB phase diagram remains elusive so far. This is particularly important for multi-component alloys where the elastic interactions among solute atoms, of various sizes and bonding energies, can prevail, governing a complex co-segregation phenomenon. Recently, we developed a density-based model for GB thermodynamics that intrinsically accounts for GB elasticity in pure elements. In this work, we incorporate the homogeneous and heterogeneous elastic energies associated with the solutes into the density-based framework. We derive the multi-component homogeneous elastic energy by generalizing the continuum misfitting sphere model and extend it for GBs. The density-based free energy functional directly uses bulk CALPHAD thermodynamic data. The model is applied to binary and ternary Al alloys. We reveal that the elastic energy can profoundly affect the GB solubility and segregation behavior, leading to Cu segregation in otherwise Cu-depleted Al GBs. Consequently, GB segregation transition, i.e., a jump in the GB segregation as a function of alloy composition, is revealed in Al-Cu and Al-Cu-Mg alloy systems with implications for subsequent GB precipitation in these alloys. CALPHAD-informed elasticity-incorporated GB phase diagrams enable addressing a broader range of GB phenomena in engineering multi-component alloys.
The elastic properties of the single-crystal nickel-base superalloy CMSX-4 used as a blade material in gas turbines were investigated by the sonic resonance method in the temperature interval between room temperature and 1300 °C. Elastic constants at such high temperatures are needed to model the mechanical behavior of blade material during manufacturing (hot isostatic pressing) as well as during technical accidents which may happen in service (overheating). High reliability of the results was achieved using specimens of different crystallographic orientations, exciting various vibration modes as well as precise measurement of the material density and thermal Expansion required for modeling the resonance frequencies by finite element method. Combining the results measured in this work and literature data the elastic constants of the gamma and gamma' phases were predicted.
This prediction was supported by measurement of the temperature dependence of the gamma'fraction.
All data obtained in this work are given in numerical or analytical forms and can be easily used for different scientific and engineering calculations.
Manufacturing defects, high residual stress (RS), and microstructures affect the structural integrity of laser powder bed fusion (LPBF) Ti-6Al-4V. In this study, the individual effect of these factors on fatigue performance at elevated temperature (300 °C) was evaluated. Material in as-built condition and subjected to post-processing, including two heat treatments and hot isostatic pressing, was investigated. It was found that in the absence of tensile RS, the fatigue life at elevated temperature is primary controlled by the defects; and densification has a much stronger effect than the considered heat treatments on the improvement of the mechanical performance.
The effectiveness of the mechanism of precipitation strengthening in metallic alloys depends on the shapes of the precipitates. Two different material systems are considered: tetragonal γ′′ precipitates in Ni-based alloys and tetragonal θ′ precipitates in Al-Cu-alloys. The shape formation and evolution of the tetragonally misfitting precipitates was investigated by means of experiments and phase-field simulations. We employed the method of invariant moments for the consistent shape quantification of precipitates obtained from the simulation as well as those obtained from the experiment. Two well-defined shape-quantities are proposed: (i) a generalized measure for the particles aspect ratio and (ii) the normalized λ2, as a measure for shape deviations from an ideal ellipse of the given aspect ratio. Considering the size dependence of the aspect ratio of γ′′ precipitates, we find good agreement between the simulation results and the experiment. Further, the precipitates’ in-plane shape is defined as the central 2D cut through the 3D particle in a plane normal to the tetragonal c-axes of the precipitate. The experimentally observed in-plane shapes of γ′′-precipitates can be quantitatively reproduced by the phase-field model.
Simulation of the θ′ Precipitation Process with Interfacial Anisotropy Effects in Al-Cu Alloys
(2021)
The effects of anisotropic interfacial properties and heterogeneous elasticity on the growth and ripening of plate-like θ′-phase (Al2Cu) in Al-1.69 at.% Cu alloy are studied. Multi-phase-field simulations are conducted and discussed in comparison with aging experiments. The precipitate/matrix interface is considered to be anisotropic in terms of its energy and mobility. We find that the additional incorporation of an anisotropic interfacial mobility in conjunction with the elastic anisotropy result in substantially larger aspect ratios of the precipitates closer to the experimental observations. The anisotropy of the interfacial energy shows comparably small effect on the precipitate’s aspect ratio but changes the interface’s shape at the rim. The effect of the chemo-mechanical coupling, i.e., the composition dependence of the elastic constants, is studied as well. We show that the inverse ripening phenomenon, recently evidenced for δ’ precipitates in Al-Li alloys (Park et al. Sci. Rep. 2019, 9, 3981), does not establish for the θ′ precipitates. This is because of the anisotropic stress fields built around the θ′ precipitates, stemming from the precipitate’s shape and the interaction among different variants of the θ′ precipitate, that disturb the chemo-mechanical effects. These results show that the chemo-mechanical effects on the precipitation ripening strongly depend on the degree of sphericity and elastic isotropy of the precipitate and matrix phases.
Phase diagrams are the roadmaps for designing bulk phases. Similar to bulk, grain boundaries can possess various phases, but their phase diagrams remain largely unknown. Using a recently introduced density-based model, here we devise a strategy for computing multi-component grain boundary phase diagrams based on available bulk (CALPHAD) thermodynamic data. Fe-Mn-Cr, Fe-Mn-Ni, Fe-Mn-Co, Fe-Cr-Ni and Fe-Cr-Co alloy systems, as important ternary bases for several trending steels and high-entropy alloys, are studied. We found that despite its solute segregation enrichment, a grain boundary can have lower solubility limit than its corresponding bulk, promoting an interfacial chemical decomposition upon solute segregation. This is revealed here for the Fe-Mn-base alloy systems. The origins of this counter-intuitive feature are traced back to two effects, i.e., the magnetic ordering effect and the low cohesive energy of Mn solute element. Different aspects of interfacial phase stability and GB co-segregation in ternary alloys are investigated as well. We show that the concentration gradient energy contributions reduce segregation level but increase grain boundary solubility limit, stabilizing the GB against a chemical decomposition. Density-based grain boundary phase diagrams offer guidelines for systematic investigation of interfacial phase changes with applications to microstructure defects engineering.
The aluminum alloy 2618A is applied for engine components such as radial compressor wheels which operate for long time at elevated temperatures. This results in coarsening of the hardening precipitates and degradation in mechanical properties during the long-term operation, which is not taken into account in the current lifetime prediction models due to the lack of quantitative microstructural and mechanical data. To address this issue, a quantitative investigation on the evolution of precipitates during long-term aging at 190 °C for up to 25,000 h was conducted. Detailed transmission electron microscopy (TEM) was combined with Brinell hardness measurements and thorough differential scanning calorimetry (DSC) experiments. The results showthat GPB zones and S-phase Al2CuMg grow up to < 1,000 h during which the GPB zones dissolve and S-phase precipitates form. For longer aging times, only S-phase precipitates coarsen, which can be well described using the Lifshitz–Slyozov Wagner theory of ripening. A thorough understanding of the underlying microstructural processes is a prerequisite to enable the integration of aging behavior into the established lifetime models for components manufactured from alloy 2618A.
The determination of residual stresses becomes more complicated with increasing complexity of the structures investigated. Additive manufacturing techniques generally allow the production of ‘lattice structures’ without any additional manufacturing step. These lattice structures consist of thin struts and are thus susceptible to internal stress-induced distortion and even cracks. In most cases, internal stresses remain locked in the structures as residual stress.
The determination of the residual stress in lattice structures through nondestructive neutron diffraction is described in this work. It is shown how two difficulties can be overcome: (a) the correct alignment of the lattice structures within the neutron beam and (b) the correct determination of the residual stress field in a representative part of the structure. The magnitude and the direction of residual stress are discussed. The residual stress in the strut was found to be uniaxial and to follow the orientation of the strut, while the residual stress in the knots was more hydrostatic. Additionally, it is shown that strain measurements in at least seven independent directions are necessary for the estimation of the principal stress directions. The measurement directions should be chosen according to the sample geometry and an informed choice on the possible strain field. If the most prominent direction is not measured, the error in the calculated stress magnitude increases considerably.
For reliability and safety issues of injection wells, corrosion resistance of materials used needs to be determined. Herein, representative low-cost materials, including carbon steel X70/1.8977 and low alloyed steel 1.7225, were embedded in mortar to mimic the realistic casing-mortar interface. Two types of cement were investigated: (1) Dyckerhoff Variodur commercial Portland cement, representing a highly acidic resistant cement and (2) Wollastonite, which can react with CO2 and become stable under a CO2 stream due to the carbonation process. Exposure tests were performed under 10 MPa and at 333 K in artificial aquifer fluid for up to 20 weeks, revealing crevice corrosion and uniform corrosion instead of expected pitting corrosion. To clarify the role of cement, simulated pore water was made by dispersing cement powder in aquifer fluid and used as a solution to expose steels. Surface analysis, accompanied by element mapping on exposed specimens and their crosssections, was carried out to trace the chloride intrusion and corrosion process that followed.
Static immersion tests of potential injection pipe steels 42CrMo4, X20Cr13, X46Cr13, X35CrMo4, and X5CrNiCuNb16-4 at T = 60°C and ambient pressure, as well as p = 100 bar were performed for 700–8000 h in a CO2-saturated synthetic aquifer environment similar to CCS sites in the Northern German Basin (NGB). Corrosion rates at 100 bar are generally lower than at ambient pressure. The main corrosion products are FeCO3 and FeOOH with surface and local corrosion phenomena directly related to the alloy composition and microstructure. The appropriate heat treatment enhances corrosion resistance. The lifetime reduction of X46Cr13, X5CrNiCuNb16-4, and duplex stainless steel X2CrNiMoN22-5-3 in a CCS environment is demonstrated in the in situ corrosion fatigue CF experiments (axial push-pull and rotation bending load, 60°C , brine: Stuttgart Aquifer and NGB, flowing CO2: 30 L/h, +/- applied potential). Insulating the test setup is necessary to gain reliable data. S-N plots, micrographic-, phase-, fractographic-, and surface analysis prove that the life expectancy of X2CrNiMoN22-5-3 in the axial cyclic load to failure is clearly related to the surface finish, applied stress amplitude, and stress mode. The horizontal grain attack within corrosion pit cavities, multiple fatigue cracks, and preferable deterioration of austenitic phase mainly cause fatigue failure. The CF life range increases significantly when a protective potential is applied.
The locally varying tetragonality in martensite grains of a high-carbon steel (1.2 mass percent C) was resolved by electron backscatter diffraction (EBSD) with a spatial resolution in the order of 100 nm. Compared to spatially integrating X-ray diffraction, which yielded an average tetragonality fo c/a=1.05, the EBSD measurements in the scanning electron microscope allowed to image a local variation of the lattice papameter ration c/a in the range of 1.02 ≤ c/a ≤ 1.07. The local variation of tetragonality is confirmed by two different EBSD data analysis approaches based on the fitting of simulated to experimental EBSD patterns. The resulting EBSD-based tetragonality maps are pointing to a complex interaction of carbon concentration and local lattice distortions during the formation process of martensitic structures.
A new software is presented for the determination of crystal lattice parameters from the positions and widths of Kikuchi bands in a diffraction pattern. Starting with a single wide-angle Kikuchi pattern of arbitrary resolution and unknown phase, the traces of all visibly diffracting lattice planes are manually derived from four initial Kikuchi band traces via an intuitive graphical user interface. A single Kikuchi bandwidth is then used as reference to scale all reciprocal lattice point distances. Kikuchi band detection, via a filtered Funk transformation, and simultaneous display of the band intensity profile helps users to select band positions and widths. Bandwidths are calculated using the first derivative of the band profiles as excess-deficiency effects have minimal influence. From the reciprocal lattice, the metrics of possible Bravais lattice types are derived for all crystal systems. The measured lattice parameters achieve a precision of <1%, even for good quality Kikuchi diffraction patterns of 400 x 300 pixels. This band-edge detection approach has been validated on several hundred experimental diffraction patterns from phases of different symmetries and random orientations. It produces a systematic lattice parameter offset of up to ±4%, which appears to scale with the mean atomic number or the backscatter coefficient.
Due to its matrix/γ′ structure, the compositionally complex alloy (CCA) Al10Co25Cr8Fe15Ni36Ti6 has excellent properties that fulfill the requirements for a high-temperature material. This base alloy is alloyed with small amounts of high melting elements to a further improvement of its properties, which results in different shapes, fractions and sizes of the two phases γ′ and Heusler after various homogenization and annealing steps. By correlating this microstructure with time independent and dependent mechanical properties, conclusions can be drawn about the effects of the individual phases. The needle-shaped Heusler-phase leads to bad mechanical behavior if its phase fraction is too high. A fraction below 3 vol% is not critical in tensile tests, but it reduces the creep resistance compared to a purely two-phase matrix/γ′-alloy. Sharp-edged cubic γ′-particles and a coarse Heusler-phase without sharp edges in case of the base alloy with 0.5 at.% hafnium lead to the best tensile and creep properties in the high temperature range. At 750 °C, the Hf-containing alloy clearly outperforms two commercially used alloys in the targeted area of application when it comes to creep resistance.
Molten salt containing systems gain in importance for sustainable energy use and production. For research and development, interactions of molten salts with potential container materials are of major interest. This article introduces preparation procedures to display an intact metal and salt microstructure and their interface using light optical microscopy and scanning electron microscopy. The exemplary material combination is the ternary salt mixture NaCl-KCl-MgCl2 and the low alloyed steel 1.4901 (T92) with a maximum service temperature of 550 °C. These are potential elements/materials for use in latent heat thermal energy storages.
The underlying cause of mechanical anisotropy in additively manufactured (AM) parts is not yet fully understood and has been attributed to several different factors like microstructural defects, residual stresses, melt pool boundaries, crystallographic and morphological textures. To better understand the main contributing factor to the mechanical anisotropy of AM stainless steel 316L, bulk specimens were fabricated via laser powder bed fusion (LPBF). Tensile specimens were machined from these AM bulk materials for three different inclinations: 0◦, 45◦, and 90◦ relative to the build plate. Dynamic Young’s modulus measurements and tensile tests were used to determine the mechanical anisotropy. Some tensile specimens were also subjected to residual stress measurement via neutron diffraction, porosity determination with X-ray micro-computed tomography (μCT), and texture analysis with electron backscatter diffraction (EBSD). These investigations revealed that the specimens exhibited near full density and the detected defects were spherical. Furthermore, the residual stresses in the loading direction were between −74 ± 24 MPa and 137 ± 20 MPa, and the EBSD measurements showed a preferential ⟨110⟩ orientation parallel to the build direction. A crystal plasticity model was used to analyze the elastic anisotropy and the anisotropic yield behavior of the AM specimens, and it was able to capture and predict the experimental behavior accurately. Overall, it was shown that the mechanical anisotropy of the tested specimens was mainly influenced by the crystallographic texture.
Results of an extended TMF test program on grade P92 steel in the temperature range of 620 °C - 300 °C, comprising in-phase (IP) and out-of-phase (OP) tests, partly performed with symmetric dwells at Tmax/Tmin, are presented. In contrast to previous studies, the low-strain regime is also illuminated, which approaches flexible operation in a power plant with start/stop cycles. At all strain amplitudes, the material performance is characterized by continuous cyclic softening, which is retarded in tests at lower strains but reaches similar magnitudes in the course of testing. In the investigated temperature range, the phase angle does not affect fatigue life in continuous experiments, whereas the IP condition is more detrimental in tests with dwells. Fractographic analyses indicate creep-dominated and fatigue-dominated damage for IP and OP, respectively. Analyses of the (micro)hardness distribution in the tested specimens suggest an enhanced microstructural softening in tests with dwell times for the low- but not for the high-strain regime. To rationalize the obtained fatigue data, the fracture-mechanics-based D_TMF concept, which was developed for TMF life assessment of ductile alloys, was applied. It is found that the D_TMF parameter correlates well with the measured fatigue lives, suggesting that subcritical growth of cracks (with sizes from a few microns to a few millimeters) governs failure in the investigated range of strain amplitudes.
Undetected and undesired microstructural variations in components produced by laser powder bed fusion are a major challenge, especially for safety-critical components. In this study, an in-depth analysis of the microstructural features of 316L specimens produced by laser powder bed fusion at different levels of volumetric energy density and different levels of inter layer time is reported. The study has been conducted on specimens with an application relevant build height
(>100 mm). Furthermore, the evolution of the intrinsic preheating temperature during the build-up of specimens was monitored using a thermographic in-situ monitoring set-up. By applying recently determined emissivity values of 316L powder layers, real temperatures could be quantified. Heat accumulation led to preheating temperatures of up to about 600 °C. Significant differences in the preheating temperatures were discussed with respect to the individual process parameter combinations, including the build height. A strong effect of the inter layer time on the heat accumulation was observed. A shorter inter layer time resulted in an increase of the preheating temperature by more than a factor of 2 in the upper part of the specimens compared to longer inter layer times. This, in turn, resulted in heterogeneity of the microstructure and differences in material properties within individual specimens. The resulting differences in the microstructure were analyzed using electron back scatter diffraction and scanning electron microscopy. Results from chemical analysis as well as electron back scatter diffraction measurements indicated stable conditions in terms of chemical alloy composition and austenite phase content for the used set of parameter combinations. However, an increase of the average grain size by more than a factor of 2.5 could be revealed within individual specimens. Additionally, differences in feature size of the solidification cellular substructure were examined and a trend of increasing cell sizes was observed. This trend was attributed to differences in solidification rate and thermal gradients induced by differences in scanning velocity and preheating temperature. A change of the thermal history due to intrinsic preheating could be identified as the main cause of this heterogeneity. It was induced by critical combinations of the energy input and differences in heat transfer conditions by variations of the inter layer time. The microstructural variations were directly correlated to differences in hardness.
The longitudinal and transverse strength of three unidirectional thermoplastic prepreg systems: carbon fiber/polypropylene (CF/PP), polyamide 6 (CF/PA6), and polyphenylene sulfide (CF/PPS) are studied and analytical formulas are proposed for the estimation of matrix and fiber/matrix interface properties from composites properties. Since the matrices are semi-crystalline thermoplastics, the influence of cooling rate on the strength is statistically evaluated. While the 0° tensile strength is found to be independent of the cooling rate, the 90° tensile strength is strongly influenced by the matrix type and cooling rate. The matrix modulus increases as the cooling rate is decreased; the degree of crystallinity also increases. The matrix residual stress, interfacial shear strength, and mode II interlaminar fracture toughness are also found to depend on the cooling rate, with the trends different for different matrices.
To explore the impact of ambient and structural water on static fatigue, the initiation and growth of 3279 Vickers induced median radial cracks were automatically recorded and analyzed. We find that humidity is more efficient in initiating cracks and promoting their growth than water, which is dissolved in the glass structure. In particular for slow crack growth (< 3x10-6 m s-1), tests in dry nitrogen showed a considerable decrease in the crack growth exponent with increasing water content of the glasses. On the other hand, if tests were performed in humid air, the crack growth exponent was independent of the water content of the hydrous glasses, while stress intensity decreased slightly. These observations indicate that water promotes the processes at the crack-tip regardless of its origin. However, ambient water is more efficient.
This manuscript is based on an oral contribution to the TMS 2020 annual meeting and is dedicated to Prof. Peter Liaw, who for decades has shown great interest in serrated plastic flow.
Here we will focus on the case of bulk metallic glasses, and begin with briefly summarizing some aspects of serrated and non-serrated inhomogeneous flow—a phenomenon that has perplexed materials scientists for decades. Four directions of research are identified that emerged out of the desire to fundamentally understand the intermittent inhomogeneous flow response. These research directions gear away from the phenomenological stress–strain behavior but put the underlying shear defect into focus. Unsolved problems and future research topics are discussed.
Subjecting metallic glasses repeatedly to liquid nitrogen temperature has become a popular method to homogeneously rejuvenate the material. Here we reveal the atomic-scale structural dynamics using in- situ x-ray photon correlation spectroscopy (XPCS) during and after cryogenic cycling of a Zr-based metallic glass in two structural states (plate and ribbon). Heterogeneous structural dynamics is observed at 300 K that changes to monotonic aging at 78 K. It is found that cryogenic cycling homogenizes the relaxation time distribution. This effect is much more pronounced in the ribbon, which is the only structural state that rejuvenates upon cycling. We furthermore reveal how fast atomic-scale dynamics is correlated with longtime structural relaxation times irrespective of the structural state, and that the ribbon exhibits unexpected additional fast atomic-scale relaxation in comparison to the plate material. A structural picture emerges that points towards heterogeneities in the fictive temperature as a requirement for cryogenic energy storage.
The influence of the atomization technique on the suitability of granules for dry pressing is the focus of the presented investigations. Therefore, destabilized alumina, zirconia, and zirconia toughened alumina (ZTA) slurries were spray dried and the obtained granules were used to fabricate green and finally sintered bodies for evaluation.
Granules made in a laboratory spray dryer with a two-fluid nozzle served as a reference. An ultrasonic atomizer was integrated into the same spray dryer and the influence on the granule properties was evaluated. Untapped bulk density, granule size distribution, and flowability are among the evaluated granule-related properties as well as the granule yield which is used as an indicator of the process efficiency.
Yield and flowability as most important granule properties are clearly improved when atomization is realized with ultrasound. The investigated sinter body properties include porosity, sinter body density, and biaxial strength and are as well positively affected by switching the atomization technique to ultrasound. Therefore, the Approach to improve the compressibility of granules by ultrasonic atomization, which leads to an improved microstructure, density, and strength of sintered bodies, has proven to be successful for single-component ceramics (alumina and zirconia) as well as for the multicomponent ceramic ZTA.
To understand the influence of water and alkalis on aluminosilicate glasses, three polymerized glasses with varying ratios of Na/K were synthesized [(22. 5-x)Na2O-xK2O-22.5 Al2O3-55 SiO2 with x = 0, 7.5, and 11.25]. Subsequently, these glasses were hydrated (up to 8 wt% H2O) in an internally heated gas pressure vessel. The density of hydrous glasses linearly decreased with water content above 1 wt%, consistent with the partial molar volume of H2O of 12 cm3/mol. Near-infrared spectroscopy revealed that hydroxyl groups are the dominant species at water content of <4 wt%, and molecular water becomes dominating at water content of >5 wt%. The fraction of OH is particularly high in the pure Na-bearing glass compared to the mixed alkali glasses. 27Al magic angle spinning-NMR spectroscopy shows that aluminum is exclusively fourfold coordinated with some variations in the local geometry. It appears that the local structure around Al becomes more ordered with increasing K/Na ratio. The incorporation of H2O reinforces this effect. The differential thermal analysis of hydrous glasses shows a significant mass loss in the range of glass transition already during the first upscan, implying the high mobility of water in the glasses. This observation can be explained by the open structure of the aluminosilicate network and by the low dissociation enthalpy of H2O in the glasses (≈ 8 kJ/mol). The effect of the dissolved H2O on the glass transition temperature is less pronounced than for other aluminosilicate glasses, probably because of the large fraction of Al in the glasses.
Due to the different thermal expansion of the constituent materials, cyclic thermal loading of FRP induces alternating stresses in the material at two scales: at the micro scale (level of fibre–matrix-interaction) and at the macro scale (level of the multidirectional laminate). Especially the micro scale effect is not comprehensively investigated yet. Additionally, computational investigations mostly neglect this effect due to the homogenous modelling of the composite material. As this effect is assumed to significantly contribute to the fatigue of FRP at thermal loads, the present paper suggests an experimental and numerical multiscale approach including Experiments at the different involved material scales to separately observe the effects acting at these scales. The approach also includes numerical modelling for each scale to complement the knowledge gained from the Experiments and to create a basis for the consideration of the micro effect even in macroscopic fatigue models treating homogeneous modelled composites. The main focus of the contribution is to bring the overall Approach up for discussion, rather than to present the multiscale modelling details.
In the past few years, a new phase, Ba0.5Sr0.5Zn2Si2O7 with negative thermal expansion has been described in the literature. Some excess of SiO2 is necessary to produce glasses from which the Ba0.5Sr0.5Zn2Si2O7 phase can be crystallized.
Unfortunately, in such glasses usually surface crystallization occurs; however, the addition of nucleating agents such as trace quantities of platinum or relatively high quantities of ZrO2 is necessary to achieve bulk nucleation. These additional components also affect the crystal growth velocity, which furthermore is different for crystal growth from the surface and in the bulk. In this paper, three different chemical compositions containing different ZrO2 concentrations, where one composition additionally contains 100 ppm platinum, are studied with respect to their crystallization behaviour. Although the compositions do not differ much, the crystallization behaviour and also the Crystal growth velocities are surprisingly different.
Stable crack growth was measured for nominal dry and water-bearing (6 wt%) soda-lime silicate glasses in double cantilever beam geometry and combined with DMA studies on the effects of dissolved water on internal friction and glass transition, respectively. In vacuum, a decreased slope of logarithmic crack growth velocity versus stress intensity factor is evident for the hydrous glass in line with an increase of b-relaxation intensity indicating more energy Dissipation during fracture. Further, inert crack growth in hydrous glass is found to be divided into sections of different slope, which indicates different water related crack propagation mechanism. In ambient air, a largely extended region II is observed for the hydrous glass, which indicates that crack growth is more sensitive to ambient water.
In the present study, a simple approach was used to investigate the effect of UV-exposure on two high density Polyethylene materials (PE-HD), commonly used for storage tanks, on fuel sorption behavior and colonization by microorganisms. The aim was to investigate whether the sorption behavior of the fuels (diesel/biodiesel) and the colonization by microorganisms, frequently occurring in the fuel, is affected and may lead to undesirable or safety-relevant material changes. We showed that the UV-irradiation leads to significant changes of the sorption behavior due to chemi-crystallization and crosslinking. The fuel Sorption is affected by the UV-induced formation of polar carbonyl and hydroxyl groups predominantly occurring at the surface. With respect to microbial colonization behavior for Bacillus subtilis and Pseudomonas aeruginosa, isolated from a contaminated diesel sample, differences of the initial adhesion could be shown depending on the initial type of polyethylene as well as on the degree of UV-induced degradation.
Future lunar exploration can benefit greatly from In-Situ Resource Utilization. Accordingly, the in-Situ Resource Utilization approach highlights the need for detailed analysis of lunar regolith. In this study, JSC-2A Simulant was studied regarding its sintering and melting behaviour using Differential Thermal Analysis under ambient and inert conditions. The minerals at the crystalline peaks were determined using X-Ray Diffraction analysis.
Moreover, melting droplet shape and wetting behaviour of pressed regolith samples of different particle size distributions were studied by Hot Stage Microscopy technique. Hot Stage Microscopy experiments were performed at different heating rates under ambient conditions. Bloating effects within the solidified samples were then qualitatively examined by X-ray tomography. Lastly, the optimization of processing strategies for the Additive Manufacturing of lunar regolith is discussed.
The wet processing of regolith simulant for clay in situ resource utilization (ISRU) on Mars is presented. The two raw materials from the Mars global simulant family, one without clay (MGS-1) and one with clay - sodium montmorillonite smectite - (MGS-1C) were milled and mixed to produce a simulant with small particle size and reduced clay content (MGS-1C/8). All three simulants and the pure clay raw material were extensively characterized using XRF, synchrotron XRD, gas adsorption and gas pycnometry methods. In a straightforward processing approach, MGS-1C/8 was mixed with water and different dispersant approaches were investigated, all of which gave stable slurries. Particle size distribution, rheology, ion concentration, pH and electrical conductivity of these slurries were characterized. The slurry systems can easily be adapted to fit all typical ceramic shaping routes and here parts of varying complexity from slip casting, throwing on a potter's wheel and additive manufacturing, including material extrusion (robocasting) and binder jetting (powder bed 3D printing) were produced.
The unique properties of the sodium montmorillonite clay, which is readily accessible in conjunction with magnesium sulfate on the Martian surface, acted as a natural nanosized binder and produced high strength green bodies (unfired ceramic body) with compressive strength from 3.3 to 7.5 MPa. The most elaborate additive manufacturing technique layerwise slurry deposition (LSD) produced water-resistant green bodies with a compressive strength of 30.8 ± 2.5 MPa by employing a polymeric binder, which is similar or higher than the strength of standard concrete. The unfired green bodies show sufficient strength to be used for remote Habitat building on Mars using additive manufacturing without humans being present.
The impact fracture behavior of two common high-density polyethylene grades for container applications were intensively studied by the instrumented Charpy impact test after well-defined exposure to UV-irradiation. Individual stages of the impact event, such as crack initiation and crack propagation energy as well as maximum impact load, were investigated from the recorded load–deflection curves. UV-induced material property changes were further investigated by infrared spectroscopy, differential scanning calorimetry, and dynamic-mechanical analysis as well as density measurements. Based on the results of the Charpy impact test, three indicators were identified to describe the extend of photooxidation on high-density polyethylene: (a) a reduced Charpy impact strength—at least to half of its initial value for a distinctly brittle impact fracture, (b) a marked decrease in the crack propagation contribution to the impact strength, and (c) an increase of the brittle features of the fracture surface.
This chapter first gives an introduction to the concepts of SSA and volume-specific surface area (VSSA) and an outline of the BET method. It continues with a discussion of the relationship between particle size, shape, and the VSSA, followed by an overview of instrumentation, experimental methods, and standards. Finally, sections on the use of the VSSA as a tool to identify nanomaterials and non-nanomaterials and its role in a regulatory context provide some insight on the importance of VSSA in the current Regulation of nanomaterials.
Bioactive glass ceramics have excellent biocompatibility and osteoconductivity; and can form direct chemical bonds with human bones; thus, these ceramic are considered as “Smart” materials. In this study, we develop a new type of bioactive glass ceramic (AP40mod) as a scaffold containing Endothelial progenitor cells (EPCs) and Mesenchymal stem cells (BMSCs) to repair critical-sized bone defects in rabbit mandibles. For in vitro experiments:
AP40mod was prepared by Dgital light processing (DLP) system and the optimal ratio of EPCs/BMSCs was screened by analyzing cell proliferation and ALP activity, as well as the influence of genes related to osteogenesis and angiogenesis by direct inoculation into scaffolds. The scaffold showed suitable mechanical properties, with a Bending strength 52.7 MPa and a good biological activity. Additionally, when EPCs/BMSCs ratio were combined at a ratio of 2:1 with AP40mod, the ALP activity, osteogenesis and angiogenesis were significantly increased. For in vivo experiments: application of AP40mod/EPCs/BMSCs (after 7 days of in vitro spin culture) to repair and reconstruct critical-sized mandible defect in rabbit showed that all scaffolds were successfully accurately implanted into the defect area. As revealed by macroscopically and CT at the end of 9 months, defects in the AP40mod/EPCs/BMSCs group were nearly completely covered by normal bone and the degradation rate was 29.9% compared to 20.1% in the AP40mod group by the 3D reconstruction. As revealed by HE and Masson staining analyses, newly formed blood vessels, bone marrow and collagen maturity were significantly increased in the AP40mod/EPCs/BMSCs group compared to those in the AP40mod group. We directly inoculated cells on the novel material to screen for the best inoculation ratio. It is concluded that the AP40mod combination of EPCs/BMSCs is a promising approach for repairing and reconstructing large load bearing bone defect.
Accelerator magnets that can reach magnetic fields well beyond the Nb-Ti performance limits are presently being built and developed, using Nb3Sn superconductors. This technology requires reaction heat treatment (RHT) of the magnet coils, during which Nb3Sn is formed from its ductile precursor materials (a “wind and react” approach). The Nb3Sn microstructure and microchemistry are strongly influenced by the conductor fabrication route, and by the Phase changes during RHT. By combining in situ differential scanning calorimetry, high Energy synchrotron x-ray diffraction, and micro-tomography experiments, we have acquired a unique data set that describes in great detail the phase and microstructure changes that take place during the processing of restacked rod process (RRP), powder-in-tube (PIT), and internal tin (IT) Nb3Sn wires. At temperatures below 450 ° the phase evolutions in the three wire types are similar, with respectively solid state interdiffusion of Cu and Sn, Cu6Sn5 formation, and Cu6Sn5 peritectic transformation. Distinct differences in phase evolutions in the wires are found when temperatures exceed 450 °C. The volume changes of the conductor during RHT are a difficulty in the production of Nb3Sn accelerator magnets. We compare the wire diameter changes measured in situ by dilatometry with the phase and void volume evolution of the three types of Nb3Sn wire. Unlike the Nb3Sn wire length changes, the wire diameter evolution is characteristic for each Nb3Sn wire type. The strongest volume increase, of about 5%, is observed in the RRP wire, where the main diameter increase occurs above 600 °C upon Nb3Sn formation.
Transformers couple two sections of a circuit by electromagnetic induction. They are widely used to either transform alternating voltage levels or to transmit power or signals across galvanic isolation. Both of these functions are essential for the operation of sensors and controllers. Covering all aspects from idea to circuit performance and from design to manufacture, this paper presents the first comprehensive description of the making of miniaturized, rugged, up-to-100W transformers for embedding into multilayer circuit boards. For circular coils, the well-manageable Ampere-Laplace law is shown to yield reliable designs, predicting correctly the performance of manufactured hardware. This enables fast design without lengthy finite element modelling. In the low-power linear regime, basic relations describe how the device’s characteristics evolve from the material properties and device structure. While scattering Parameters are useful for the analysis of isolated transformers with their intrinsic parasitics, the interaction with the components of the final circuit and the aspects of power and efficiency are addressed by chain matrixes.
While these design rules are similar for multilayer boards of different material (like epoxy, Teflon, ceramics), the manufacturing of ceramic board transformers is considered here in detail. Low-temperature-cofired ceramic (LTCC) boards being sintered at 900 °C are particularly suited for harsh environments with chemical or thermal stress as frequently found at sensor positions. The transformer performance usually benefits from or even requires an integrated ceramic core of higher permeability, a ferrite, to shape the magnetic flux. Methods to sinter ferrites inside a dielectric ceramic multilayerandto measure their performance are therefore described in detail.Asthe sintering behaviour of dielectricandmagnetic ceramics differs considerably, their simultaneous sintering is challenging.However, the sintering temperatures of the usefulMnZnand NiZnCu ferrites can be lowered to that of the dielectric material with only moderate loss of permeability by glass additives. Furthermore, thermal mismatch between materials causes catastrophic failure or at least stress and loss of magnetic performance during cooling to room temperature after sintering. This is avoidable by either adjusting the thermal expansion coefficient of the ferrite or by enclosing the ferrite between stressreleasing separation layers.We present the state of the art in materials development according to the first approach as well as fully functional devices made with the second technique.
Other applications not directly addressed but well related to this work are characterized by low load resistance in relation to the coil resistance of the transformer. Efficient power transmission then requires that technological solutions are applied to achieve the lowest possible resistive loss inside the coils by an enlarged conductor cross-section.
As this is particularly challenging for LTCC boards, a technique is discussed to fabricate conductor traces with a thickness larger than their width.