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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. 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.
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.
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.
During their lifetime, polymer components subjected to mechanical loads and environmental influences show a loss of their mechanical properties required for their specific applications. In this respect, the craze-crack damage mechanism slow crack growth (SCG) is relevant for PE-HD components used in high-performance applications such as pipes and containers for the storage and transport of dangerous goods. SCG is considered to be the major failure mechanism in polyolefins and it typically occurs suddenly and unexpectedly. Due to the fields of application, SCG is a safety relevant issue. To test for the resistance of PE-HD pipe and container materials against SCG, the full-notch creep test (FNCT) is widely applied in Europe. In this study, SCG phenomena in PE-HD are investigated in detail based on an improved FNCT, especially including the consideration of the influence of environmental liquids effecting the damage mechanism. Using an enhanced fracture surface and a crack propagation analysis with imaging techniques such as light microscopy (LM), laser scanning microscopy (LSM), X-ray computed tomography (CT-scan) and scanning electron microscopy (SEM), detailed data concerning SCG are obtained.
The combined application of FNCT and such imaging techniques is explicitly advantageous and recommended to gain important information on damage occurring to PE-HD induced by mechanical stress and the influence of environmental liquids, which is essential within the Fourth Industry Revolution.
Carbon Capture Utilization and Storage (CCUS) is a promising technology to reach the target for reduction of CO2 emissions. Crucial points for a sustainable and future-proof CCUS system are reliability and cost efficiency of the whole process chain, including separation of CO2 from the source, compression of CO2, its subsequent transportation to the injection site and injection into geological formations, e.g. aquifers. Recent studies have shown that even at a very low concentration of impurities, condensation of sulfuric and nitric acids in dense phase CO2 are possible and observable. Thus, impact of impure CO2 stream toward corrosion susceptibility of materials to be used in CCUS system need to be considered. In this talk, basing on results achieved from two German long-term projects (COORAL and CLUSTER), the dominating impurities of the CO2 stream and corrosion mechanisms are addressed. Investigations cover the whole CCUS process chain and provide a material recommendation for certain parts.
Depending on the CO2 generating and the capture process as well as on consecutive purification steps applied, CO2 streams from different emitters may differ in their composition. When CO2 streams with different compositions are fed into a larger pipeline network, there are several aspects that must be considered: i) chemical reactions, such as acid formation, may occur within the joint CO2 stream; ii) there may be a variation of mass flow rate and CO2 stream composition within the pipeline network if the feed-in behavior of different CO2 sources changes with time. Potential impacts of changing CO2 stream compositions and mass flow rates in CCS cluster systems were investigated in the collaborative project "CLUSTER" (see also www.bgr.bund.de/CLUSTER). In this presentation, we focus on the experimental investigations of formation and condensation of strong acids and their impacts on the corrosion of pipeline steels. When SO2, NO2, O2 and H2O are present simultaneously in CO2 streams chemical cross-reactions may occur leading to the formation of strong acids such as sulfuric and nitric acid. To prevent this acid formation the concentration of at least one of these four impurities must be kept very low (e.g., Rütters et al., 2016). At temperatures below the acid dew point temperature, acids will condense, e.g., on pipeline steel surfaces. In turn, these acid condensates may trigger steel corrosion. To better understand the process of acid formation and condensation and its implications for steel corrosion, exposure tests were performed on pipeline steel X70 in dense CO2 with varying SO2, NO2 and O2 concentration under high pressure and at 278 K in an observable autoclave, in which water was added as droplets or as vapor. Further, electrochemical tests were carried out with X70 specimens immersed in 500 mL CO2-saturated synthetic condensate solution or in droplets of the same solution on the specimen’s surface. Depending on impurity concentrations in the CO2 streams, condensates consisting of different relative amounts of nitric and sulfuric acid were formed. In condensates containing both nitric and sulfuric acid, corrosion rates were higher than the sum of those of the individual acids. In addition, corrosion products and forms depended on the condensate composition. Investigations of water droplets on steel surfaces in impurity-containing dense-phase CO2 revealed the diffusion of SO2 and NO2, followed by cross-reactions forming corresponding acids. An increase in droplet size (from 1 to 5 µl) lead to higher corrosion rates. However, in comparison to measurements in bulk solution, corrosion reactions in droplets resulted in thick, high-resistance corrosion products and observed droplet corrosion rates were significantly lower. In addition, the possibility of acid droplet formation and growth in impure liquid CO2 is influenced by the wetting behavior of the acid droplet on the steel surface. Thus, the contact angle between a water droplet and the surface steel specimens in a CO2 atmosphere was investigated in a high pressure view cell following the sessile drop method. The contact angle wasand found to be larger at higher CO2 pressures (studied from 5 to 20 MPa) and at higher temperatures (e.g. 278 K to 333 K). Further, measured contact angles were larger on rough than on smooth metal surfaces. In addition, acid formation reduced the contact angle, i.e. lead to better wetting, thereby stimulating condensation that was followed by a corrosion process. These detailed insights on the complex interplay of acid formation, condensation, wetting behavior and corrosion allow a better assessment of material suitability for pipeline transportation of impure CO2 streams
CO2 quality specifications are not only a matter of CO2 purity (i.e. CO2 content).
The “rest” also matters, in particular contents of reactive impurities affecting material corrosion (and rock alteration).
Also chemical reactions in CO2 stream needs to be considered, in particular when combining CO2 streams of different compositions.
The durability of concrete structures and its performance over the lifetime is strongly influenced by many interacting phenomena such as e.g. mechanical degradation due to fatigue loading, loss of prestress, degradation due to chemical reactions or creep and shrinkage. Failure due to cyclic loading is generally not instantaneous, but characterized by a steady damage accumulation.
Many constitutive models for concrete are currently available, which are applicable for specific loading regimes, different time scales and different resolution scales. A key limitation is that the models often 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.
The objective of this paper is the presentation of numerical methods for the simulation of concrete under fatigue loading using a temporal multiscale method.
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. 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 time integration schemes.
This contribution provides current findings regarding materials susceptibility for carbon capture, utilization and storage (CCUS) applications. Basing on results gathered in 2 German long-term projects (COORAL and CLUSTER) suitable materials are introduced as well as dominating impurities of the CO2-stream and corrosion mechanisms. Investigations cover the whole CCUS process chain and provide material recommendations for certain parts.