5 Werkstofftechnik
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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.
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.
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 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.
The methods of computational damage mechanics are well-established for the description of degradation of materials under monotone loading. An extension to structural damage induced by cyclic loading is however significantly limited. This is due to enormous computational costs required to resolve each load cycle by conventional temporal incremental integration schemes while a typical fatigue loading history comprises between thousands and millions of cycles. Despite the permanent increase of computational resources and algorithmic performance, a successful approach is rather based on the development of novel multiscale in time integration schemes.
A Fourier transformation-based temporal integration (FTTI) is represented, which takes advantage of temporal scale separation incorporated into the cycle jump method. The response fields are approximated by a Fourier series whose coefficients undergo the evolution on a long-time scale. This is correlated with the evolution of the history variables, including damage, by means of the adaptive cycle jump method of various orders. The necessary extrapolation rates are obtained from the underlying solution of a short-time scale problem, which results from the oscillatory boundary condition and fulfills the global equilibrium of the Fourier coefficients. In this way, a remarkable speedup is achieved because the number of cycles to be fully integrated dramatically decreases.
The key idea behind the FTTI method is that the global in space equilibrium problem is linear since it is decoupled from the evolution equations. The latter are solved in the quadrature points under response fields prescribed throughout the whole load cycle. Consequently, integration of a single load cycle is much more efficient than the conventional single scale integration where the global equilibrium iteration and the local iteration of the evolution equations are coupled. This results in an additional speedup of the FTTI method.
The performance of the FTTI technique is demonstrated for two different constitutive behaviors: a viscoplastic model with a damage variable governed by the local equivalent viscoplastic strain; a quasi-brittle response where the damage variable is driven by a non-local equivalent strain. The latter is implicitly introduced as proposed by Peerlings. Both, the explicit and implicit extrapolation schemes are validated. The FTTI solutions agree very well with the reference cycle-by -cycle solutions, while significantly reducing the computational costs. The adaptive determination of the jump length can properly recognize the particular responses throughout the fatigue loading history (stationary fatigue, acceleration of fatigue damage when approaching failure) as well as stress redistribution phenomena.
A constitutive model for the mechanical behaviour of single crystal Ni-base superalloys under high temperature conditions has been developed in the framework of a Cooretec project in cooperation with Siemens AG, MTU Aero Engines AG and University Bayreuth. In addition to the conventional material properties e.g. elastic constants, the model requires the parameters of the initial microstructure as an input. Thus, the γ’-precipitate size and the channel width of the γ-matrix were obtained from SEM micrographs. The model uses the slip system theory and describes the movement, multiplication and annihilation of dislocations in the channels. Furthermore, the cutting of precipitates is another mechanism contributing to the plastic flow. The evolution of the morphology due to rafting and its effects on the deformation have been implemented according to. The kinematic hardening is introduced as a stress tensor to realistically represent the strain hardening of arbitrary oriented single crystals.
The mechanical behaviour of single crystal specimens has been experimentally investigated in tension tests at different strain rates and in creep tests under various loads. The constitutive model has been calibrated based on the experimental data for temperatures of 950°C and 850°C and the [001] and [111] crystallographic orientations.
Finally, a micromechanical model was created to simulate the creep response of additive manufactured polycrystalline structures. An EBSD image is taken to obtain the grain geometry and their respective orientation. The grain boundaries are discretised using cohesive elements, whereas the single crystal model was applied to each grain in the representative volume. The polycrystal model is generated using Dream3D, NetGen and other software previously developed at the BAM.
With the introduction of a mass transport mechanism the entire problem is subjected to a time frame that dictates the time-dependent action of soluted species on mechanical properties. A numerical framework within the phase-field approach is presented with an embrittlement-based coupling mechanism. The underlying functionals are expressed in terms of the displacement, mass concentration and crack phase-field. Within the phase-field approach the modelling of sharp crack discontinuities is replaced by a diffusive crack model facilitating crack initiation and complex crack topologies without the requirement of a predefined crack path. The isotropic hardening of the elasto-plastic deformation model and the local fracture criterion are affected by the species concentration. This allows for embrittlement and leads to an accelerated crack propagation. An extended mass transport equation for hydrogen embrittlement, accounting for mechanical stresses and deformations, is implemented. For stabilisation purposes a staggered scheme is applied to solve the system of partial differential equations by a multi-field finite-element method. A thermodynamically consistent coupling relation that accommodates the required mechanisms is presented.
An improved diffusion model is proposed for pore annihilation during HIP of single-crystal nickel-base superalloys. The model assumes the pore dissolution by emission of vacancies and their sink to the low angle boundaries. Calculation, considering distribution of the pore sizes, predicts the kinetics of pore annihilation similar to the experimental one.
The possibility to produce dense monolithic ceramic parts with additive manufacturing is at the moment restricted to small parts with low wall thickness. Up to now, the additive manufacturing of voluminous ceramic parts is realized by powder bed based processes which, however, generate parts with residual porosity. Via infiltration these parts can be processed to dense parts like for example SiC but this is not possible for all ceramics like for example Si3N4. There is a lack of methods for the additive manufacturing of dense voluminous parts for most ceramics.
We have developed a new additive manufacturing technology, the Laser Induced Slip casting (LIS), based on the layerwise deposition of slurries and their local drying by laser radiation. Laser Induced Slip casting generates ceramic green bodies which can be sintered to dense ceramic components like traditional formed ceramic powder compacts. We will introduce the LIS technology, green bodies and sintered parts will be shown and their microstructure and mechanical properties will be discussed.
Most additive manufacturing processes which produce dense ceramics are nowadays limited in size because of inevitable post-processing steps like for example binder removal in stereolithography. The additive manufacturing of voluminous ceramic parts is realized by powder bed based processes which, however, generate parts with residual porosity. Via infiltration these parts can be processed to dense parts like for example SiC but this is not possible for all ceramics like for example Si3N4. There is a lack of methods for the additive manufacturing of dense voluminous parts for most ceramics.
We have developed a new additive manufacturing technology, the Laser Induced Slip casting (LIS), based on the layerwise deposition of slurries and their local drying by laser radiation. Laser Induced Slip casting generates ceramic green bodies which can be sintered to dense ceramic components like traditional formed ceramic powder compacts. We will introduce the LIS technology, green bodies and sintered parts will be shown and their microstructure and mechanical properties will be discussed.
Most additive manufacturing processes which produce dense ceramics are nowadays limited in size because of inevitable post-processing steps like for example binder removal in stereolithography. The additive manufacturing of voluminous ceramic parts is realized by powder bed based processes which, however, generate parts with residual porosity. Via infiltration these parts can be processed to dense parts like for example SiC but this is not possible for all ceramics like for example Si3N4. There is a lack of methods for the additive manufacturing of dense voluminous parts for most ceramics.
We have developed a new additive manufacturing technology, the Laser Induced Slip casting (LIS), based on the layerwise deposition of slurries and their local drying by laser radiation. Laser Induced Slip casting generates ceramic green bodies which can be sintered to dense ceramic components like traditional formed ceramic powder compacts. We will introduce the LIS technology, green bodies and sintered parts will be shown and their microstructure and mechanical properties will be discussed.
For the additive manufacturing of large components typically powder-based methods are used. A powder is deposited layer by layer by means of a recoater, then, the component structure is printed into each individual layer. We introduce here the new method of local laser drying, which is a suspension-based method specially developed for the manufacturing of large voluminous ceramic parts. The structure information is directly written into the freshly deposited layer of suspension by laser drying. Initially, the technology was developed for ceramic suspensions, however, first experiments with geopolymers reveal a high potential for this class of materials. Metakaolin, fly ash and lithium aluminate-based one-part geopolymers were used in first experiments. The local annealing of the geopolymer slurry results in a drying and crosslinking reaction and, thus, in a local consolidation of the material. First parts made are introduced and their properties are discussed.
The EC’s recommendation for a definition of nanomaterial (2011/696/EU) should allow the identification of a particulate nanomaterial based on the number-based metric criterion according to which at least 50% of the constituent particles have the smallest dimension between 1 and 100 nm. However, it has been recently demonstrated that the implementation of this definition for regulatory purposes is conditioned by the large deviations between the results obtained by different sizing methods or due to practical reasons such as high costs and time-consuming (SEM, TEM).
Within the European project NanoDefine (www.nanodefine.eu) a two-tier approach has been developed, whereby firstly a screening method is applied for the rough classification as a nano-/non-nanomaterial, and for borderline cases a confirmatory method (imaging methods or field flow fractionation) must be considered.
One of the measurement methods well suited to particulate powder is the determination of volume-specific surface area (VSSA) by means of gas adsorption as well as skeletal density. The value of 60 m2/cm3 corresponding to spherical, monodisperse particles with a diameter of 100 nm constitutes the threshold for decisioning if the material is a nano- or non-nanomaterial. The correct identification of a nanomaterial by VSSA method is accepted by the EU recommendation.
However, the application of the VSSA method is associated also by some limitations. The threshold of 60 m2/cm3 is dependent on the particle shape, so that it changes considerably with the number of nano-dimensions of the particles. For particles containing micro-pores or having a microporous coating false positive results will be produced. Furthermore, broad particle size distributions make necessary to adjust the threshold. Based on examples of commercially available ceramic powders, the applicability of the VSSA approach will be tested (in relation with SEM and TEM measurements) in order to expand the actual knowledge and to improve this good available and agglomeration tolerant method.
The EU recommendation for a definition of nanomaterial (2011/696/EU) should allow the identification of a particulate nanomaterial based on the number-based metric criterion according to which at least 50% of the constituent particles have the smallest dimension between 1 and 100 nm. Within the European Project NanoDefine (www.nanodefine.eu) a two-tier approach has been developed, whereby firstly a screening method is applied for the rough classification as a nanomaterial or non-nanomaterial, and for borderline cases a confirmatory method (imaging methods or field flow fractionation) must be considered.
One of the measurement methods well suited to particulate powder is the determination of volume-specific surface area (VSSA) by means of gas adsorption as well as skeletal density. The value of 60 m2/cm3 corresponding to spherical, monodisperse particles with a diameter of 100 nm constitutes the threshold for decisioning if the material is a nanomaterial or non-nanomaterial. The correct identification of a nanomaterial by VSSA method (positive test) is accepted by the EU recommendation.
However, the application of the VSSA method is associated also by some limitations. The threshold of 60 m2/cm3 is dependent on the particle shape. For particles containing micro-pores or having a microporous coating, false positive results will be produced.
Furthermore, broad particle size distributions – as typically for ceramic materials – as well as multi-modal size distributions make necessary to adjust the threshold.
Based on examples of commercially available ceramic powders, the applicability of the VSSA approach will be tested (in relation with SEM and TEM measurements) in order to expand the actual knowledge and
improve the method.
Common air-coupled transducers for non-destructive testing consist of a piezocomposite material and several matching layers. Better acoustical matching to air is achieved by transducers based on charged cellular polypropylene (PP). This material has about hundred times lower acoustic impedance than any piezocomposite, having about the same piezoelectric coefficient. The piezoelectric properties of cellular PP are caused by the polarization of air cells. Alternatively, a ferroelectret receiver can be understood as a capacitive microphone with internal polarization creating permanent internal voltage. The sensitivity of the receiver can be increased by applying additional bias voltage. We present an ultrasonic receiver based on cellular PP including a high-voltage module providing bias voltage up to 2 kV. The application of bias voltage increased the signal by 12 to 15 dB with only 1 dB increase of the noise.
This receiver was combined with a cellular PP transmitter in through transmission to inspect several test specimens consisting of glass-fiber-reinforced polymer face sheets and a porous closed-cell PVC core. These test specimens were inspected before and after load. Fatigue cracks in the porous PVC core and some fatigue damage in the face sheets were detected. These test specimens were originally developed to emulate a rotor blade segment of a wind power plant. Similar composite materials are used in lightweight aircrafts for the general aviation. The other inspected test specimen was a composite consisted of glass-fiber-reinforced polymer face sheets and a wooden core. The structure of the wooden core could be detected only with cellular PP transducers, while commercial air-coupled transducers lacked the necessary sensitivity. Measured on a 4-mm thick carbon-fiber-reinforced polymer plate, cellular PP transducers with additional bias voltage achieved a 32 dB higher signal-to-noise ratio than commercial air-coupled transducers.