5 Werkstofftechnik
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Paper des Monats
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Single crystal superalloys usually contain pores of sizes 5-10 micro-m after casting and heat treatment. These pores can be reduced under compression by combined creep and diffusion in a subsequent treatment called Hot Isostatic Pressing (HIP). The paper presents a methodology to simulate pore shrinkage under HIP conditions in two dimensions (2D).
At the scale of the pores, which is also the scale of the sub-grains (<50 micro-m) the dislocation sources cannot be assumed to be homogeneously distributed. Thus, the applicability of classical crystal plasticity is questionable. In this case, the transport of dislocations under an applied stress from the location where they are nucleated must be explicitly modelled. This is done by solving the transport equations for the dislocation densities and the elasticity equations in 2D. The dislocations are assumed to be nucleated at Low Angle Boundaries. They glide or climb through the sub-grains with a stress dependent velocity.
The transport equations are solved by the Flux-Corrected Transport method, which belongs to the predictor-corrector class of algorithms. In the first step, an artificial diffusion is introduced, which suppresses spurious oscillations of the solution. In a second step, the solution is corrected in such a way that no additional extremes appear and that the extremes do not grow. The algorithm is validated by simulating the transport of simple distributions with a constant velocity field.
With the dislocation velocities and the computed dislocation densities, the inelastic shear rate at the slip system level is computed by integrating the Orowan equation. In the 2D-setting, three slip systems are considered. The contributions of these slip systems are summed up to obtain the total inelastic strain rate. Dislocation glide and climb and the coupling of climb with vacancies diffusion are considered.
The resolution of the equilibrium equations from the inelastic strains turned out to be prone to numerical instabilities. As an alternative, the stresses are directly computed from the distribution of geometrically necessary dislocations following the method presented in. The resulting boundary value problem is solved by the Least-Square Finite Element method.
Examples of simulations are presented for a representative region under creep tension and for a pore shrinking under external pressure.
Der Aufbau der Werkstoffe wird durch Merkmale wie Bindungsart, atomare Strukturen, Kristallstrukturen einschließlich ihrer Gitterbaufehler, Körner und Phasen bestimmt. Die Mikrostruktur (Gefüge) stellt den Verbund der Kristalle, Phasen und Gitterbaufehler auf mikroskopischer und nanoskopischer Skala dar. Die Grundlagen der Phasenumwandlungen werden behandelt und die Bedeutung von Diffusionsprozessen erläutert. Werkstoffe sind bedeutend für Kultur, Wirtschaft, Technik und Umwelt. Ihre Herstellung benötigt Ressourcen und Energie. Recycling ist eine Möglichkeit zur Erhöhung der Ressourcenproduktivität.
Fiber-reinforced-polymers (FRPs) are in current research focus in the lightweight construction industry, because of their extraordinary characteristics (stiffness and strength-to-density relation). The structure of polymer matrix and the interaction with reinforcement are crucial for optimization of the mechanical and thermal properties of FRPs. Due to the macromolecular chain structure, the mechanical properties of a polymer strongly vary with temperature: Below the glass transition, the chain segments of a polymer are “frozen”. Regarding fracture, the total changed energy during fracture if only dissipates for the generation of the new surfaces. However, in the region of the glass transition, the polymer chain segments start to get “unfrozen”, and the energy is not only required for generating new surfaces, but also for irreversibly deformation. This irreversible deformation is affected by the global temperature and the local temperature near the crack tip, which is affected by the local strain rate and crack propagation velocity.
Hence, in this research project, the irreversible deformation of neat and reinforced polymers will be controlled by changing the global temperature as well as the local temperature. With using different fracture experiments, the amount of energy required for creating new surfaces and for the irreversible deformation will be separated. In this presentation, I summarized of the first 15 months the whole project. In this period, the basic crack propagation theory for neat polymers is established and the special fracture experiment sample is prepared and tested at room temperature. In addition, the model of the specimen is first established.
Crack propagation in polymers: Separation of surface energy and irreversible deformation energy
(2019)
Fiber-reinforced-polymers (FRPs) are in current research focus in the lightweight construction industry, because of their extraordinary characteristics (stiffness and strength-to-density relation). The structure of polymer matrix and the interaction with reinforcement are crucial for optimization of the mechanical and thermal properties of FRPs. Due to the macromolecular chain structure, the mechanical properties of a polymer strongly vary with temperature: Below the glass transition, the chain segments of a polymer are “frozen”. Regarding fracture, the total changed energy during fracture if only dissipates for the generation of the new surfaces. However, in the region of the glass transition, the polymer chain segments start to get “unfrozen”, and the energy is not only required for generating new surfaces, but also for irreversibly deformation. This irreversible deformation is affected by the global temperature and the local temperature near the crack tip, which is affected by the local strain rate and crack propagation velocity.
Hence, in this research project, the irreversible deformation of neat and reinforced polymers will be controlled by changing the global temperature as well as the local temperature. With using different fracture experiments, the amount of energy required for creating new surfaces and for the irreversible deformation will be separated. This poster is the summary of the first part of the whole project. In the first part, the basic crack propagation theory for neat polymers is established and the special fracture experiment sample is prepared and tested at room temperature. In addition, the fracture experiment at room temperature is validated numerically.
Fiber-reinforced-polymers (FRPs) are in current research focus in the lightweight construction industry, because of their extraordinary characteristics (stiffness and strength-to-density relation). The structure of polymer matrix and the interaction with reinforcement are crucial for optimization of the mechanical and thermal properties of FRPs. Due to the macromolecular chain structure, the mechanical properties of a polymer strongly vary with temperature: Below the glass transition, the chain segments of a polymer are “frozen”. Regarding fracture, the total changed energy during fracture if only dissipates for the generation of the new surfaces. However, in the region of the glass transition, the polymer chain segments start to get “unfrozen”, and the energy is not only required for generating new surfaces, but also for irreversibly deformation. This irreversible deformation is affected by the global temperature and the local temperature near the crack tip, which is affected by the local strain rate and crack propagation velocity.
Hence, in this research project, the irreversible deformation of neat and reinforced polymers will be controlled by changing the global temperature as well as the local temperature. With using different fracture experiments, the amount of energy required for creating new surfaces and for the irreversible deformation will be separated. The fracture tests include the conventional tensile test, the macroscopic peel test and the single fiber peel – off test.
Modern wind turbine rotor blades consist of sandwich shell segments made from glass fiber reinforced polymers. During manufacturing, defects can arise which could lead to failure of the whole component under dynamic mechanical and thermal loads. Hence during operation defects can arise which, if detected, can be repaired locally and in-situ by applying repair patches instead of taking the whole rotor blade down and repair it remotely. This method is much more time and cost effective, since the shut-down time of the energy converter is limited to a minimum. These repair patches can, however, also lead to new defects if not applied optimally. Therefore, it is necessary to control the quality of the repair patches to ensure the best possible restoration of structural integrity of the component. As a rotor blade is an object with a large aspect ratio, X-ray laminography is predestined to provide 3D information of the objective volume. To enhance the amount of information gained from laminographic reconstruction, we use in this study a photon counting and energy discriminating X-ray detector and apply a material decomposition algorithm to the data. By inherently separating the incident spectra within the detection process into two distinct energy bins, the basis material decomposition can provide material resolved images. Choosing glass and epoxy resin as basis materials and numerically solving the inverse dual-energy equation system, the reconstructed laminographic datasets contain highly valuable information about the distribution of the basis materials within the structure. Furthermore, cross- artifacts arising from the limited angle of the projection data can be reduced by this method which allows to investigate structures that were hidden underneath the artefacts.
Modern wind turbine rotor blades consist of sandwich shell segments made from glass fiber reinforced polymers. During manufacturing, defects can arise which could lead to failure of the whole component under dynamic mechanical and thermal loads. Hence during operation defects can arise which, if detected, can be repaired locally and in-situ by applying repair patches instead of taking the whole rotor blade down and repair it remotely. This method is much more time and cost effective, since the shut-down time of the energy converter is limited to a minimum. These repair patches can, however, also lead to new defects if not applied optimally. Therefore, it is necessary to control the quality of the repair patches to ensure the best possible restoration of structural integrity of the component. As a rotor blade is an object with a large aspect ratio, X-ray laminography is predestined to provide 3D information of the objective volume. To enhance the amount of information gained from laminographic reconstruction, we use in this study a photon counting and energy discriminating X-ray detector and apply a material decomposition algorithm to the data. By inherently separating the incident spectra within the detection process into two distinct energy bins, the basis material decomposition can provide material resolved images. Choosing glass and epoxy resin as basis materials and numerically solving the inverse dual-energy equation system, the reconstructed laminographic datasets contain highly valuable information about the distribution of the basis materials within the structure. Furthermore, cross- artifacts arising from the limited angle of the projection data can be reduced by this method which allows to investigate structures that were hidden underneath the artefacts.
Die Metal Magnetic Memory (MMM) Methode ist ein standardisiertes, zerstörungsfreies Prüfverfahren, das für die Detektion von lokal geschädigten Materialbereichen in ferromagnetischen Bauteilen oder Proben verwendet wird. Es basiert auf der Annahme lokaler magnetoelastischer Wechselwirkungen an Spannungskonzentrationsstellen, die schwache magnetische Streufelder an den geschädigten Prüfkörperoberflächen hervorrufen. Die MMM-Methode überträgt dabei die für einachsige und elastische Verformungen entwickelten magnetoelastischen Modellvorstellungen ohne weitere Anpassungen in den Schädigungskontext, der jedoch mehrachsige Beanspruchungen und elastisch-plastische Deformationsprozesse erwarten lässt. Das Ziel der Arbeit ist es daher, die gängigen MMM-Hypothesen zur Signalentstehung fach- und skalenübergreifend und unter stärkerer Berücksichtigung mechanischer und mikrostruktureller Aspekte zu überprüfen.
Zu diesem Zweck wurden zum einen gekerbte Flachzugproben aus einem unlegierten Baustahl inhomogen elastisch-plastisch verformt und die entstehenden magnetischen Streufelder an deren Oberflächen mit einem Drei-Achsen-GMR-Magnetometer detektiert. Die so ermittelten Magnetfeld-verteilungen wurden für unterschiedliche Verformungszustände ortsaufgelöst und richtungsabhängig mit gemessenen Dehnungsverteilungen (digitale Bildkorrelation) und mit simulierten Lastspannungs-verteilungen korreliert. Die eingeschnürten Probenbereiche wurden zusätzlich topographisch mittels Streifenlichtprojektion und Weißlichtinterferenzmikroskopie vermessen, um den Magnetisierungs-prozess ebenfalls vor dem Hintergrund geometrischer Effekte diskutieren zu können.
Um systematische, verformungsinduzierte Veränderungen der magnetischen Mikrostruktur (magnetischer Domänen) im polykristallinen, quasi-isotropen Material nachzuweisen, wurde zum anderen ein in dieser Arbeit entwickelter statistischer Ansatz der Domänenanalyse angewandt. Hierfür wurde das Material zunächst durch Härteeindrücke mehrachsig elastisch-plastisch verformt, und die verformten Probenbereiche wurden anschließend mit Hilfe der Bitterstreifentechnik hauptsächlich bei niedriger Vergrößerung lichtmikroskopisch untersucht. Die beobachteten makroskopischen Domänen-kontraste wurden über ein analytisches, kontaktmechanisches (ECM-) Modell und über Makro-Eigen-spannungsmessungen (energiedispersive Synchrotron-Beugungsuntersuchungen) charakteristischen Verformungszonen unter den Härteeindrücken zugeordnet.
Die Ergebnisse dieser Untersuchungen belegen, dass die Entstehung der Streufelder – entgegen bisheriger Annahmen – nicht allein auf mechanische Spannungs- und Verformungsgradienten im Material zurückzuführen, sondern auch topographisch bedingt ist. Die Vernachlässigung überlagerter geometrischer Effekte kann zu sicherheitsrelevanten Fehlinterpretationen der magnetischen Signale führen. Einachsige magnetoelastische Modellvorstellungen sollten zudem nicht ohne Anpassungen auf komplexe Beanspruchungen übertragen werden, da u. a. sowohl mechanische Größen (wie Spannungen oder Dehnungen) als auch mikrostrukturelle Parameter (wie z. B. Versetzungsdichten) bei komplexen Belastungen als ortsabhängige Variablen behandelt werden müssen. Die in dieser Arbeit beobachteten Domänenkontraste lassen sich zweifelsfrei charakteristischen Verformungszonen zuordnen, mikro-strukturell jedoch nicht allein mit anzunehmenden Gradienten der Versetzungsdichte erklären. Statt-dessen entstehen beispielsweise lokale Verformungstexturen, die zusätzliche magnetische Anisotropien bewirken könnten. Da bisher weder die makroskopischen noch die mikrostrukturellen Ursachen der Streufeldentstehung hinreichend verstanden sind, scheint die MMM-Methode für die quantitative Bewertung des Schädigungszustands derzeit ungeeignet.
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.