5 Werkstofftechnik
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Artificial bone replacement by individual customized three-dimensional resorbable bioactive glass has not yet been widely established in the clinical use. This is mainly due to the antagonism of sintering ability and suitable bioactivity. Competitive crystallization often prevents the generation of dense sintered bodies, especially for additive manufactured 3D structures. Previous studies of the fluoride-containing glass F3 have shown its potential to combine both sintering ability and suitable bioactivity. Furthermore, the occurring sintering blockade by surface crystallization of Na2CaSi2O6 was tunable by glass particle size.
In this study the glasses F3, F3-Cu with 1 mol% CuO added at the expense of CaO and the well-known 13-93 were chosen to determine the influence of surface crystallization on 3D printed sinter bodies. For this purpose, grain size fractions in range of smaller 32 µm to 315 µm in fraction size of 6-20 µm were sieved from jaw crushed glass frit as well as glass cubes were cut from casted blocks for all glasses. Sintering behavior of both pressed and printed powder compacts was observed via heating microscopy. Crystallization was determined by DTA and crystallization progress was monitored on fractured sinter bodies and polished cubes via electron and laser scanning microscopy as well as with diffractometry.
Depending on grain size the formation of crystalline support framework along former grain boundaries shows the capability to stabilize fully densified sinter bodies before softening. Beside of this, the generation of complex hierarchic porosity was possible as well.
The Layerwise Slurry Deposition is a technology for the deposition of highly packed powder layers. A powder bed is achieved by depositing and drying layers of a ceramic suspension by means of a doctor blade. This deposition technique was combined with the binder jetting technology to develop a novel Additive Manufacturing technology, named LSD-print. The LSD-print was applied to a porcelain ceramic. It is shown that it was possible to produce parts with high definition, good surface finish and at the same time having physical and mechanical properties close to those of traditionally processed porcelain, e.g. by slip casting.
This technology shows high future potential for being integrated alongside traditional production of porce-lain, as it is easily scalable to large areas while maintaining a good definition. Both the Layerwise Slurry Deposition method and the binder jetting technologies are readily scalable to areas as large as > 1 m2.
A shape evolution approach based on the thermally activated self-organization of 3D printed parts into minimal surface area structures is presented. With this strategy, the present communication opposes currently established additive manufacturing strategies aiming to stipulate each individual volumetric element (voxel) of a part. Instead, a 3D structure is roughly defined in a 3D printing process, with all its advantages, and an externally triggered self-organization allows the formation of structural elements with a definition greatly exceeding the volumetric resolution of the printing process. For enabling the self-organization of printed objects by viscous flow of material, functionally graded structures are printed as rigid frame and melting filler. This approach uniquely combines the freedom in design, provided by 3D printing, with the mathematical formulation of minimal surface structures and the knowledge of the physical potentials governing self-organization, to overcome the paradigm which strictly orrelates the geometrical definition of 3D printed parts to the volumetric resolution of the printing process. Moreover, a transient liquid phase allows local programming of functionalities, such as the alignment of functional particles, by means of electric or magnetic fields.
Dislocations are the carriers of plastic deformation. As such, their characterization offers important information on the properties they affect. In this contribution, a new tool is presented, which is incorporated in Amira ZIB Edition and allows for three-dimensional (3D) imaging and quantification of dislocations substructures from thick regions an electron-transparent specimen. In the tool, the dislocation segments are traced on diffraction contrast images that are obtained in the transmission electron microscope (TEM). The uncertainties related to the experimental setup and to the proposed method are discussed on the base of a tilt series.
The presentation gives an overview of two slurry-based additive manufacturing (AM) technologies specifically developed for advanced ceramic materials.
The “Layerwise Slurry Deposition” (LSD-print) is a modification of Binder Jetting making use of a ceramic slurry instead of a dry powder as a feedstock. In this process, a slurry is deposited layer-by-layer by means of a doctor blade and dried to achieve a highly packed powder layer, which is then printed by jetting a binder. The LSD-print technology combines the high-speed printing of binder jetting with the possibility of producing a variety of high-quality ceramics with properties comparable to those achieved by traditional processing.
The Laser Induced Slip casting (LIS) technology follows a novel working principle by locally drying and selectively consolidating layer-by-layer a ceramic green body in a vat of slurry, using a laser as energy source. LIS combines elements of Vat Photopolymerization with the use of water-based feedstocks containing a minimal amount of organic additives. The resulting technology can be directly integrated into a traditional ceramic process chain by manufacturing green bodies that are sintered without the need of a dedicated debinding.
Both technologies offer high flexibility in the ceramic feedstock used, especially concerning material and particle size. Advantages and disadvantages are briefly described to outline the specific features of LSD-print and LIS depending on the targeted application.
Lifetime aspects including fatigue failure of concrete structures were traditionally only of minor importance. Because of the growing interest in maxing out the capacities of concrete, its fatigue failure under compression has become an issue. A variety of interacting phenomena such as e.g. loss of prestress, degradation due to chemical reactions or creep and shrinkage influence the fatigue resistance. Failure due to cyclic loads is generally not instantaneous, but characterized by a steady damage accumulation. Therefore, a reliable numerical model to predict the performance of concrete over its lifetime is required, which accurately captures order effects and full three-dimensional stress states.
Many constitutive models for concrete are currently available, which are applicable for specific loading regimes, different time scales and different resolution scales.
However, a key limitation of those models is that they generally do not address issues related to fatigue on a structural level. Very few models can be found in the literature that reproduce deterioration of concrete under repeated loading-unloading cycles. This is due to the computational effort necessary to explicitly resolve every cycle which exceeds the currently available computational resources. The limitation can only be overcome by the application of multiscale methods in time.
The objective of the paper is the development of numerical methods for the simulation of concrete under fatigue loading using temporal multiscale methods.
First, a continuum damage model for concrete is developed with a focus on fatigue under compressive stresses [1]. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from static tests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level.
Second, a multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach [2]. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
Finally, the developed methods will be validated and compared to experimental data.
[1] Vitaliy Kindrachuk, Marc Thiele, Jörg F. Unger. Constitutive modeling of creep-fatigue interaction for normal strength concrete under compression, International Journal of Fatigue, 78:81-94, 2015
[2] Vitaliy Kindrachuk, Jörg F. Unger. A Fourier transformation-based temporal integration scheme for viscoplastic solids subjected to fatigue deterioration, International Journal of Fatigue, 100:215-228, 2017
Lifetime aspects including fatigue failure of concrete structures were traditionally only of minor importance. Because of the growing interest in maxing out the capacities of concrete, its fatigue failure under compression has become an issue. A variety of interacting phenomena such as e.g. loss of prestress, degradation due to chemical reactions or creep and shrinkage influence the fatigue resistance. Failure due to cyclic loads is generally not instantaneous, but characterized by a steady damage accumulation. Therefore, a reliable numerical model to predict the performance of concrete over its lifetime is required, which accurately captures order effects and full three-dimensional stress states.
Many constitutive models for concrete are currently available, which are applicable for specific loading regimes, different time scales and different resolution scales.
However, a key limitation of those models is that they generally do not address issues related to fatigue on a structural level. Very few models can be found in the literature that reproduce deterioration of concrete under repeated loading-unloading cycles. This is due to the computational effort necessary to explicitly resolve every cycle which exceeds the currently available computational resources. The limitation can only be overcome by the application of multiscale methods in time.
The objective of the paper is the development of numerical methods for the simulation of concrete under fatigue loading using temporal multiscale methods.
First, a continuum damage model for concrete is developed with a focus on fatigue under compressive stresses. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from static tests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level.
Second, a multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
Finally, the developed methods will be validated and compared to experimental data.
A continuum damage model for concrete is developed with a focus on fatigue under compressive stresses. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from statictests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level. A multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
A continuum damage model for concrete is developed with a focus on fatigue under compressive stresses. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from statictests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level. A multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
Due to combined cyclic mechanical and thermal loading during operation, the material of exhaust gas conducting components of combustion engines is exposed to thermomechanical fatigue (TMF). This leads to formation and growth of cracks, especially at the most highly stressed points of these components. In order to better predict the service life of cracked components before failure, it is necessary to identify a crack propagation law for the material used. Isothermal crack propagation tests have been carried out at several temperatures with a typical cast iron to identify such a law. The crack length is measured by the potential drop method. The compliance method, fractography and thermographic camera measurements have been used to validate and calibrate the potential drop measurements. Each of the isothermal tests has been simulated using a specially developed FEM-algorithm based on remeshing and remapping. This algorithm has been implemented in python and ABAQUS. Thereby, the crack tip region is modeled by collapsed Quad8 elements. From the individual simulations, the cyclic crack tip opening displacement (ΔCTOD) is extracted and regarded as a potential fracture mechanics parameter which controls the crack growth rate. By combining the data from the experiments and the simulations, the crack propagation law has been identified. Finally, anisothermal crack propagation tests have been performed for validation of the crack growth law.
The multi-phase approach has proven to widen the application properties of high entropy alloys. After a decade of testing different alloys in the Al-Co-Cr-Cu-Fe-Ni-Ti family the Al10Co25Cr8Fe15Ni36Ti6 was found to be a solid base for more fine-tuned microstructural optimization. Following the example of superalloys, the Al10Co25Cr8Fe15Ni36Ti6 alloy aims for a γ/γ' microstructures in order to guarantee a good microstructural stability at high temperatures. The shape and volume fraction of the γ' particles is known to influence the mechanical properties of superalloys, and they do so in the high entropy family as well [1]. Shape, misfit and creep properties of several modified versions of the Al10Co25Cr8Fe15Ni36Ti6 alloy are compared and discussed in this talk.
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.
Systematic microstructure design requires reliable thermodynamic descriptions of each and all microstructure elements. While such descriptions are well established for most bulk phases, thermodynamic assessment of microstructure defects is challenging because of their individualistic nature. In this paper, a model is devised for assessing grain boundary thermodynamics based on available bulk thermodynamic data. We propose a continuous relative atomic density field and its spatial gradients to describe the grain boundary region with reference to the homogeneous bulk and derive the grain boundary Gibbs free energy functional. The grain boundary segregation isotherm and phase diagram are computed for a regular binary solid solution, and qualitatively benchmarked for the Pt–Au system. The relationships between the grain boundary's atomic density, excess free volume, and misorientation angle are discussed. Combining the current density-based model with available bulk thermodynamic databases enables constructing databases, phase diagrams, and segregation isotherms for grain boundaries, opening possibilities for studying and designing heterogeneous microstructures.
Additive manufacturing (AM) offers significantly greater freedom of design compared to conventional manufacturing processes since the final parts are built layer by layer. This enables metal AM, also known as metal 3D printing, to be utilized for improving efficiency and functionality, for the production of parts with very complex geometries, and rapid prototyping. However, despite many technological advancements made in recent years, several challenges hinder the mass adoption of metal AM. One of these challenges is mechanical anisotropy which describes the dependency of material properties on the material orientation. Therefore, in this work, stainless steel 316L parts produced by laser-based powder bed fusion are used to isolate and understand the root cause of anisotropy in AM parts. Furthermore, an efficient and accurate multiscale numerical framework is presented for predicting the deformation behavior of actual AM parts on the macroscale undergoing large plastic deformations. Finally, a novel constitutive model for the plastic spin is formulated to capture the influence of the microstructure evolution on the material behavior on the macroscale.
The search for strong and tough oxide glasses is important for making safer, more environmentally friendly, thinner glass products. However, this task remains generally difficult due to the material’s inherent brittleness. In search for tougher glasses, fracture toughness (KIC) prediction models are helpful tools to screen for promising candidates.
In this work, a novel model to predict KIC via the fracture surface energy, γ, is presented. Our approach uses readily available crystallographic structure data of the glass’s isochemical crystal and tabled diatomic chemical bond energies, D0. The method assumes that γ of a glass equals the fracture surface energy of the most likely cleavage plane of the crystal. Calculated values were not only in excellent agreement with those calculated with a former well-working model, but also demonstrates a remarkable equivalence between crystal cleavage planes and glass fracture surfaces.
Finally, the effectiveness of fracture toughness enhancement by chemical substitution is discussed based on our results and alternative toughening strategies will be suggested.
The system Na2O.B2O3-SiO2 (NBS) is the basis of many industrial glass applications and therefore one of the most studied systems at all. Glass formation is possible over a wide compositional range, but the system also contains ranges of pronounced phase separation and crystallization tendency. Despite its importance, experimental data are limited to few compositional areas. The general understanding and modelling of glass formation, phase separation, and crystallization in this system would therefore be easier if small step melt series could be studied. The efficient melting of such glass series is now possible with the new robotic glass melting system at the Federal Institute for Materials Research and Testing (BAM, Division Glasses). Using three exemplary joins within this NBS system, the small step changes of glass transition temperature (Tg), crystallization behavior as well as glass density (Roh) was studied. Additionally, experimental Tg and Roh data were compared with their modeled counterparts using SciGlass and a newly developed DFT model, respectively.
Additive manufacturing of alkali-activated materials currently attracts a lot of attention, because of the possibility to produce customized high-performance elements for a range of applications, potentially being more resource-efficient than conventionally produced parts. Here, we describe a new additive manufacturing process for alkali-activated materials that is based on selective laser-heating of lithium aluminate/microsilica slurries. The new process-material combination allows to manufacture elements with complex geometries at high building rates and high accuracy. The process is versatile and transferrable to structures of sizes differing by orders of magnitude. The mechanical strength of the obtained materials was in the range of values reported for conventional metakaolin-based geopolymers, and superior to what has been hitherto reported for alkali-activated materials produced by additive manufacturing. This mechanical performance was obtained despite the fact that the degree of reaction of the lithium aluminate and the microsilica was low, suggesting that significant reactions took place only at the surface of the microsilica particles.
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.