Dissertations / Theses: 'Phase Field Fracture'

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Agrawal, Vaibhav. "Multiscale Phase-field Model for Phase Transformation and Fracture." Research Showcase @ CMU, 2016. http://repository.cmu.edu/dissertations/850.

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We address two problems in this thesis. First, a phase-field model for structural phase transformations in solids and second, a model for dynamic fracture. The existing approaches for both phase transformations and fracture can be grouped into two categories. Sharp-interface models, where interfaces are singular surfaces; and regularized-interface models, such as phase-field models, where interfaces are smeared out. The former are challenging for numerical solutions because the interfaces or crack needs to be explicitly tracked, but have the advantage that the kinetics of existing interfaces or cracks and the nucleation of new interfaces can be transparently and precisely prescribed. The diffused interface models such as phasefield models do not require explicit tracking of interfaces and makes them computationally attractive. However, the specification of kinetics and nucleation is both restrictive and extremely opaque in such models. This prevents straightforward calibration of phase-field models to experiment and/or molecular simulations, and breaks the multiscale hierarchy of passing information from atomic to continuum. Consequently, phase-field models cannot be confidently used in dynamic settings. We present a model which has all the advantages of existing phase-field models but also allows us to prescribe kinetics and nucleation criteria. We present a number of examples to characterize and demonstrate the features of the model. We also extend it to the case of multiple phases where preserving kinetics of each kind of interface is more complex. We use the phase transformation model with certain changes to model dynamic fracture. We achieve the advantage of prescribing nucleation and kinetics independent of each other. We demonstrate examples of anisotropic crack propagation and crack propagation on an interface in a composite material. We also report some limitations of phase-field models for fracture which have not been mentioned in the existing literature. These limitations include dependence of effective crack width and hence the effective surface energy on the crack speed, lack of a reasonable approximation for the mechanical response of cracked region and inability to model large deformations.

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Abdollahi, Amir. "Phase-field modeling of fracture in ferroelectric materials." Doctoral thesis, Universitat Politècnica de Catalunya, 2012. http://hdl.handle.net/10803/285833.

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The unique electro-mechanical coupling properties of ferroelectrics make them ideal materials for use in micro-devices as sensors, actuators and transducers. Nevertheless, because of the intrinsic brittleness of ferroelectrics, the optimal design of the electro-mechanical devices is strongly dependent on the understanding of the fracture behavior in these materials. Fracture processes in ferroelectrics are notoriously complex, mostly due to the interactions between the crack tip stress and electric fields and the localized switching phenomena in this zone (formation and evolution of domains of different crystallographic variants). Phase-field models are particularly interesting for such a complex problem, since a single partial differential equation governing the phase-field accomplishes at once (1) the tracking of the interfaces in a smeared way (cracks, domain walls) and (2) the modeling of the interfacial phenomena such as domain-wall energies or crack face boundary conditions. Such a model has no difficulty for instance in describing the nucleation of domains and cracks or the branching and merging of cracks. Furthermore, the variational nature of these models makes the coupling of multiple physics (electrical and mechanical fields in this case) very natural. The main contribution of this thesis is to propose a phase-field model for the coupled simulation of the microstructure formation and evolution, and the nucleation and propagation of cracks in single crystal ferroelectric materials. The model naturally couples two existing energetic phase-field approaches for brittle fracture and ferroelectric domain formation and evolution. The finite element implementation of the theory is described. Simulations show the interactions between the microstructure and the crack under mechanical and electro-mechanical loadings. Another objective of this thesis is to encode different crack face boundary conditions into the phase-field framework since these conditions strongly affect the fracture behavior of ferroelectrics. The smeared imposition of these conditions are discussed and the results are compared with that of sharp crack models to validate the proposed approaches. Simulations show the effects of different conditions, electro-mechanical loadings and media filling the crack gap on the crack propagation and the microstructure of the material. In a third step, the coupled model is modified by introducing a crack non-interpenetration condition in the variational approach to fracture accounting for the asymmetric behavior in tension and compression. The modified model makes it possible to explain anisotropic crack growth in ferroelectrics under Vickers indentation loading. This model is also employed for the fracture analysis of multilayer ferroelectric actuators, which shows the potential of the model for future application. The coupled phase-field model is also extended to polycrystals by introducing realistic polycrystalline microstructures in the model. Inter- and trans-granular crack propagation modes are observed in the simulations. Finally and for completeness, the phase-field theory is extended for the simulation of conducting cracks and some preliminary simulations are also performed in three dimensions. Salient features of the crack propagation phenomenon predicted by the simulations of this thesis are directly compared with experimental observations.
Los materiales ferroeléctricos poseen únicas propiedades electro-mecánicas y por eso se utilizan para los micro-dispositivos como sensores, actuadores y transductores. No obstante, debido a la fragilidad intrínseca de los ferroeléctricos, el diseño óptimo de los dispositivos electro-mecánicos es altamente dependiente de la comprensión del comportamiento de fractura en estos materiales. Los procesos de fractura en ferroeléctricos son notoriamente complejos, sobre todo debido a las interacciones entre campos de tensión y eléctricos y los fenómenos localizados en zona de fractura (formación y evolución de los dominios de las diferentes variantes cristalográficas). Los modelos de campo de fase son particularmente útiles para un problema tan complejo, ya que una sola ecuación diferencial parcial que gobierna el campo de fase lleva a cabo a la vez (1) el seguimiento de las interfaces de una manera suave (grietas, paredes de dominio) y (2) la modelización de los fenómenos interfaciales como las energías de la pared de dominio o las condiciones de las caras de grieta. Tal modelo no tiene ninguna dificultad, por ejemplo en la descripción de la nucleación de los dominios y las grietas o la ramificación y la fusión de las grietas. Además, la naturaleza variacional de estos modelos facilita el acoplamiento de múltiples físicas (campos eléctricos y mecánicos en este caso). La principal aportación de esta tesis es la propuesta de un modelo campo de fase para la simulación de la formación y evolución de la microestructura y la nucleación y propagación de grietas en materiales ferroeléctricos. El modelo aúna dos modelos de campo de fase para la fractura frágil y para la formación de dominios ferroeléctricos. La aplicación de elementos finitos a la teoría es descrita. Las simulaciones muestran las interacciones entre la microestructura y la fractura del bajo cargas mecánicas y electro-mecánicas. Otro de los objetivos de esta tesis es la codificación de diferentes condiciones de contorno de grieta porque estas condiciones afectan en gran medida el comportamiento de la fractura de ferroeléctricos. La imposición de estas condiciones se discuten y se comparan con los resultados de modelos clasicos para validar los modelos propuestos. Las simulaciones muestran los efectos de diferentes condiciones, cargas electro-mecánicas y medios que llena el hueco de la grieta en la propagación de las fisuras y la microestructura del material. En un tercer paso, el modelo se modifica mediante la introducción de una condición que representa el comportamiento asimétrico en tensión y compresión. El modelo modificado hace posible explicar el crecimiento de la grieta anisotrópica en ferroeléctricos. Este modelo también se utiliza para el análisis de la fractura de los actuadores ferroeléctricos, lo que demuestra el potencial del modelo para su futura aplicación. El modelo se extiende también a policristales mediante la introducción de microestructuras policristalinas realistas en el modelo. Modos de fractura inter y trans-granulares de propagación se observan en las simulaciones. Por último y para completar, la teoría del campo de fase se extiende para la simulación de las grietas conductivas y algunas simulaciones preliminares también se realizan en tres dimensiones. Principales características del fenómeno de la propagación de la grieta predicho por las simulaciones de esta tesis se comparan directamente con las observaciones experimentales.

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Muixí, Ballonga Alba. "Locally adaptive phase-field models and transition to fracture." Doctoral thesis, Universitat Politècnica de Catalunya, 2020. http://hdl.handle.net/10803/669747.

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This thesis proposes a new computational model for the efficient simulation of crack propagation, through the combination of a phase-field model in small subdomains around crack tips and a discontinuous model in the rest of the domain. The combined model inherits the advantages of both approaches. The phase-field model determines crack propagation at crack tips, and the discontinuous model explicitly describes the crack elsewhere, enabling to use a coarser discretization and thus reducing the computational cost. In crack-tip subdomains, the discretization is refined to capture the phase-field solution, while in the discontinuous part, sharp cracks are incorporated into the coarse background discretization by the eXtended Finite Element Method (XFEM). As crack-tip subdomains move with crack growth, the discretization is automatically updated and phase-field bands are replaced by sharp cracks in the wake of cracks. The first step is the development of an adaptive refinement strategy for phase-field models. To this end, two alternatives are proposed. Both of them consider two types of elements, standard and refined, which are mapped into a fixed background mesh. In refined elements, the space of approximation is uniformly $h$-refined. Continuity between elements of different type is imposed in weak form to handle the non-conformal approximations in a natural way, without spreading of refinement nor having to deal with hanging nodes, leading to a very local refinement along cracks. The first adaptive strategy relies on a Hybridizable Discontinuous Galerkin (HDG) formulation of the problem, in which continuity between elements is imposed in weak form. The second one is based on a more efficient Continuous Galerkin (CG) formulation; a continuous FEM approximation is used in the standard and refined regions and, then, continuity on the interface between regions is imposed in weak form by Nitsche's method. The proposed strategies robustly refine the discretization as cracks propagate and can be easily incorporated into a working code for phase-field models. However, the computational cost can be further reduced by transitioning to the discontinuous in the combined model. In the wake of crack tips, the phase-field diffuse cracks are replaced by XFEM discontinuous cracks and elements are derefined. The combined model is studied within the adaptive CG formulation. Numerical experiments include branching and coalescence of cracks, and a fully 3D test.
En aquesta tesi es proposa un nou model computacional per a simular la propagació de fractures de manera eficient, a partir de la combinació d’un model de camp de fase en petits subdominis al voltant dels extrems de les fissures, i d’un model discontinu a la resta del domini. El model combinat manté els avantatges de tots dos tipus de model. El model continu determina la propagació de la fissura, i el model discontinu descriu explícitament la fissura en gairebé tot del domini, amb una discretització més grollera i el conseqüent estalvi en cost computacional. Als subdominis de camp de fase, la discretització es refina per tal d’aproximar bé la solució, mentre que a la part discontínua, les fissures s’incorporen a la discretització grollera a partir de l’eXtended Finite Element Method (XFEM). A mesura que les fissures es propaguen pel domini, la discretització s’actualitza automàticament i, lluny dels extrems, la representació suavitzada de les fissures a partir del camp de fase es reemplaça per una representació discontínua. El primer pas és definir una estratègia de refinament adaptatiu pels models continus de camp de fase. En aquesta tesi es proposen dues alternatives diferents. Totes dues consideren dos tipus d’elements, estàndards i refinats, que es mapen a la malla inicial. Als elements refinats, l’espai d’aproximació es refina uniformement. La continuïtat entre elements de tipus diferent s’imposa en forma feble per facilitar el tractament de les aproximacions no conformes, sense que s’escampi el refinament ni haver d’imposar restriccions als nodes de la interfície, donant lloc a un refinament molt localitzat. La primera estratègia adaptativa es basa en una formulació Hybridizable Discontinuous Galerkin (HDG) del problema, que imposa continuïtat entre elements en forma feble. La segona es basa en una formulació contínua més eficient; es fa servir una aproximació contínua del Mètode dels Elements Finits a les regions estàndards i refinades i, aleshores, a la interfície entre les dues regions s’imposa la continuïtat en forma feble amb el mètode de Nitsche. Les estratègies adaptatives refinen la discretització a mesura que les fissures es propaguen, i es poden afegir a un codi per a models de camp de fase de manera senzilla. No obstant, el cost computacional es pot reduir encara més fent servir el model combinat. Lluny dels extrems de les fissures, la representació suavitzada del camp de fase es substitueix per discontinuïtats en una discretització de XFEM, i els elements es desrefinen. El model combinat es formula a partir de l’estratègia adaptativa contínua. Els exemples numèrics inclouen bifurcació i coalescència de fissures, i un exemple en 3D.

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Ziaei-Rad, Vahid. "Phase field approach to fracture : massive parallelization and crack identification." Doctoral thesis, Universitat Politècnica de Catalunya, 2016. http://hdl.handle.net/10803/396154.

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The phase field method has proven to be an important tool in computational fracture mechanics in that it does not require complicated crack tracking and is able to predict crack nucleation and branching. However, the computational cost of such a method is high due to a small regularization length parameter, which in turns restricts the maximum element size that can be used in a finite element mesh. In this work, we developed a massively parallel algorithm on the graphical processing unit (GPU) to alleviate this difficulty in the case of dynamic brittle fracture. In particular, we adopted the standard finite element method on an unstructured mesh combined with second order explicit integrators. As the explicit methods fit nicely with the GPU paradigm especially in terms of thread and memory hierarchy, we solve an elastodynamic problem when the phase field update is based on a gradient flow, so that a fully explicit implementation is feasible. To ensure stability, we designed a time adaptivity strategy to account for the decreasing critical time step during the evolution of the fields. We demonstrated the performance of the GPU-implemented phase field models by means of representative numerical examples, with which we studied the effect of the artificial viscosity, an artificial parameter to be input, and compared the crack path branching predictions from three popular phase field models. Moreover, we verified the method with convergence studies and performed a scalability study to demonstrate the desired linear scaling of the program in terms of the wall time per physical time as a function of the number of degrees of freedom. One of the main ideas of the phase field method is to employ a smeared representation of discrete cracks. However, in some applications it is still convenient to have the explicit crack path available, or even to develop a mechanism to introduce crack paths to partially replace a smeared crack propagation model. In this work, we presents a variational method to identify the crack path from phase field approaches to fracture. The method is proven to be successful not only for a simple curved crack but also for multiple and branched cracks. The algorithm employs the non-maximum suppression technique, a procedure borrowed from the image processing field, to detect a bounding area which covers the ridge of the phase field profile. After that, it is continued with the step to determine a cubic spline to represent the crack path and to improve it via a constrained optimization process. To demonstrate the performance of our method, we provide the results with three sets of representative examples. The developed algorithm can be combined with one on crack opening, for more elaborate interpretation of phase field simulations. This is the topic of the next part of the work. In this dissertation, we also provide a variational way to calculate the crack opening from phase field approaches to fracture. We also demonstrate the performance of our method with three sets of representative examples, and verify the results with a proper benchmark. Having the crack geometry available from a phase field approach can provide more elaborate interpretation of the phase field simulations. It may also offer a possibility of developing less expensive numerical schemes for a fluid-driven crack propagation of impermeable solids. This will be the topic of our future work.
El método de phase field ha demostrado ser una herramienta importante en la mecánica de fractura computacional el cual no requiere el seguimiento complicado de una fractura y es capaz de predecir la nucleación y la ramificación. Sin embargo, el coste computacional de un método de este tipo es alto debido a un pequeño parámetro de regularización de longitud, que a su vez limita el tamaño del elemento máximo que se puede utilizar en una malla de los elementos finitos. En esta disertación, hemos desarrollado un algoritmo paralelo de forma masiva en la unidad de procesamiento gráfico (GPU) para aliviar esta dificultad en el caso de rotura frágil dinámica. En particular, hemos adoptado el método de los elementos finitos en una malla no estructurada combinada con integradores explícitos de segundo orden. A medida que los métodos explícitos encajan adecuadamente con el paradigma de la GPU especialmente en términos de hilo y la jerarquía de memoria, se resuelve un problema de elastodinámica cuando la actualización de phase field se basa en un flujo de gradiente, de modo que una implementación totalmente explícita es factible. Para asegurar la estabilidad, se diseñó una estrategia adaptativa de tiempo para tener en cuenta la disminución del paso de tiempo crítico durante la evolución de los campos. Hemos demostrado el rendimiento de los modelos de phase field GPU-implementado por medio de ejemplos numéricos representativos, con los que se estudió el efecto de la viscosidad artificial, un parámetro artificial que sirva como entrada, y se compara las predicciones de la trayectoria ramificada de la grieta a partir de tres modelos de phase field populares. Por otra parte, se verificó el método de convergencia con los estudios y se realizó un estudio para demostrar la escala lineal deseada del programa en términos del tiempo de reloj de pared por el tiempo físico en función del número de grados de libertad. Una de las ideas principales del método de phase field es emplear una representación distribuida de una grieta discreta. Sin embargo, en algunas aplicaciones todavía es conveniente tener la ruta de grieta explícita disponible, o incluso desarrollar un mecanismo para introducir caminos de crack con el objetivo de sustituir en parte un modelo de fisura distribuida de propagación. En esta disertación, se presenta un método variacional para identificar la ruta de grietas en los enfoques de phase field en problemas de fractura. El método ha demostrado ser un éxito no sólo por una simple grieta curvada, sino también por múltiples grietas y ramificadas. El algoritmo emplea la técnica de supresión no máxima, un procedimiento tomado del campo de procesamiento de imágenes, para detectar un área de delimitación que cubre la cresta del perfil de phase field. A continuación, se continúa con la etapa de determinar un spline cúbico para representar la trayectoria de la grieta y mejorarlo a través de un proceso de optimización restringida. Para demostrar la eficacia de nuestro método, proporcionamos los resultados con tres conjuntos de ejemplos representativos. El algoritmo desarrollado se puede combinar con uno en apertura crack, para la interpretación más elaborada de simulaciones de phase field. Este es el tema de la siguiente parte de la tesis. En esta tesis, también ofrecemos una forma variacional para calcular la apertura de grietas de los enfoques de phase field a la fractura. También demostramos el rendimiento de nuestro método con tres conjuntos de ejemplos representativos, y verificar los resultados con un valor de referencia apropiado. Tener la geometría grieta disponible a partir de un enfoque de phase field puede proporcionar una interpretación más elaborada de las simulaciones de phase field. También puede ofrecer una posibilidad de desarrollar esquemas numéricos con menos costes para una propagación de la grieta de accionamiento hidráulico de sólidos impermeables. Este será el tema de nuestro futuro trabajo.

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Omatuku, Emmanuel Ngongo. "Phase field modeling of dynamic brittle fracture at finite strains." Master's thesis, Faculty of Engineering and the Built Environment, 2019. http://hdl.handle.net/11427/30172.

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Fracture is the total or partial separation of an initially intact body through the propagation of one or several cracks. Computational methods for fracture mechanics are becoming increasingly important in dealing with the nucleation and propagation of these cracks. One method is the phase field approach, which approximates sharp crack discontinuities with a continuous scalar field, the so-called phase field. The latter represents the smooth transition between the intact and broken material phases. The evolution of the phase field due to external loads describes the fracture process. An original length scale is used to govern the diffusive approximation of sharp cracks. This method further employs a degradation function to account for the loss of the material stiffness during fracture by linking the phase field to the body’s bulk energy. To prevent the development of unrealistic crack patterns and interpenetration of crack faces under compression, this study uses the anisotropic split of the bulk energy, as proposed by Amor et al. [5], to model the different fracture behavior in tension, shear and compression. This research is part of a larger project aimed at the modeling of Antarctic sea ice dynamics. One aspect of this project is the modeling of the gradual break-up of the consolidated ice during spring. As a first step, this study reviews a phase field model used for dynamic brittle fracture at finite strains. Subsequently, this model is implemented into the in-house finite element software SESKA to solve the benchmark tension and shear tests on a single-edge notched block. The implementation adopts the so-called monolithic scheme, which computes the displacement and phase field solutions simultaneously, with a Newmark time integration scheme. The results of the solved problems demonstrate the capabilities of the implemented dynamic phase field model to capture the nucleation and propagation of cracks. They further confirm that the choice of length-scale and mesh size influences the solutions. In this regard, a small value of the length-scale converges to the sharp crack topology and yields a larger stress value. On the other hand, a large length-scale parameter combined with a too coarse mesh size can yield unrealistic results.

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Schlueter, Alexander [Verfasser], and Charlotte [Akademischer Betreuer] Kuhn. "Phase Field Modeling of Dynamic Brittle Fracture / Alexander Schlueter ; Betreuer: Charlotte Kuhn." Kaiserslautern : Technische Universität Kaiserslautern, 2018. http://d-nb.info/116213397X/34.

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Deogekar, Sai Sharad. "A Computational Study of Dynamic Brittle Fracture Using the Phase-Field Method." University of Cincinnati / OhioLINK, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1439455086.

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Tanne, Erwan. "Variational phase-field models from brittle to ductile fracture : nucleation and propagation." Thesis, Université Paris-Saclay (ComUE), 2017. http://www.theses.fr/2017SACLX088/document.

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Les simulations numériques des fissures fragiles par les modèles d’endommagement à gradient deviennent main- tenant très répandues. Les résultats théoriques et numériques montrent que dans le cadre de l’existence d’une pre-fissure la propagation suit le critère de Griffith. Alors que pour le problème à une dimension la nucléation de la fissure se fait à la contrainte critique, cette dernière propriété dimensionne le paramètre de longueur interne.Dans ce travail, on s’attarde sur le phénomène de nucléation de fissures pour les géométries communément rencontrées et qui ne présentent pas de solutions analytiques. On montre que pour une entaille en U- et V- l’initiation de la fissure varie continument entre la solution prédite par la contrainte critique et celle par la ténacité du matériau. Une série de vérifications et de validations sur diffèrent matériaux est réalisée pour les deux géométries considérées. On s’intéresse ensuite à un défaut elliptique dans un domaine infini ou très élancé pour illustrer la capacité du modèle à prendre en compte les effets d’échelles des matériaux et des structures.Dans un deuxième temps, ce modèle est étendu à la fracturation hydraulique. Une première phase de vérification du modèle est effectuée en stimulant une pré-fissure seule par l’injection d’une quantité donnée de fluide. Ensuite on étudie la simulation d’un réseau parallèle de fissures. Les résultats obtenus montrent qu’il a qu’une seule fissure qui se propage et que ce type de configuration minimise mieux l’énergie la propagation d’un réseau de fractures. Le dernier exemple se concentre sur la stabilité des fissures dans le cadre d’une expérience d’éclatement à pression imposée pour l’industrie pétrolière. Cette expérience d’éclatement de la roche est réalisée en laboratoire afin de simuler les conditions de confinement retrouvées lors des forages.La dernière partie de ce travail se concentre sur la rupture ductile en couplant le modèle à champ de phase avec les modèles de plasticité parfaite. Grâce à l’approche variationnelle du problème on décrit l’implantation numérique retenue pour le calcul parallèle. Les simulations réalisées montrent que pour une géométrie légèrement entaillée la phénoménologie des fissures ductiles comme par exemple la nucléation et la propagation sont en concordances avec ceux reportées dans la littérature
Phase-field models, sometimes referred to as gradient damage, are widely used methods for the numerical simulation of crack propagation in brittle materials. Theoretical results and numerical evidences show that they can predict the propagation of a pre-existing crack according to Griffith’s criterion. For a one- dimensional problem, it has been shown that they can predict nucleation upon a critical stress, provided that the regularization parameter is identified with the material’s internal characteristic length.In this work, we draw on numerical simulations to study crack nucleation in commonly encountered geometries for which closed-form solutions are not available. We use U- and V-notches to show that the nucleation load varies smoothly from the one predicted by a strength criterion to the one of a toughness criterion when the strength of the stress concentration or singularity varies. We present validation and verification of numerical simulations for both types of geometries. We consider the problem of an elliptic cavity in an infinite or elongated domain to show that variational phase field models properly account for structural and material size effects.In a second movement, this model is extended to hydraulic fracturing. We present a validation of the model by simulating a single fracture in a large domain subject to a control amount of fluid. Then we study an infinite network of pressurized parallel cracks. Results show that the stimulation of a single fracture is the best energy minimizer compared to multi-fracking case. The last example focuses on fracturing stability regimes using linear elastic fracture mechanics for pressure driven fractures in an experimental geometry used in petroleum industry which replicates a situation encountered downhole with a borehole called burst experiment.The last part of this work focuses on ductile fracture by coupling phase-field models with perfect plasticity. Based on the variational structure of the problem we give a numerical implementation of the coupled model for parallel computing. Simulation results of a mild notch specimens are in agreement with the phenomenology of ductile fracture such that nucleation and propagation commonly reported in the literature

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Parrinello, Antonino. "A rate-pressure-dependent thermodynamically-consistent phase field model for the description of failure patterns in dynamic brittle fracture." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:c6590f4f-f4e2-40e3-ada1-49ba35c2a594.

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The investigation of failure in brittle materials, subjected to dynamic transient loading conditions, represents one of the ongoing challenges in the mechanics community. Progresses on this front are required to support the design of engineering components which are employed in applications involving extreme operational regimes. To this purpose, this thesis is devoted to the development of a framework which provides the capabilities to model how crack patterns form and evolve in brittle materials and how they affect the quantitative description of failure. The proposed model is developed within the context of diffusive interfaces which are at the basis of a new class of theories named phase field models. In this work, a set of additional features is proposed to expand their domain of applicability to the modelling of (i) rate and (ii) pressure dependent effects. The path towards the achievement of the first goal has been traced on the desire to account for micro-inertia effects associated with high rates of loading. Pressure dependency has been addressed by postulating a mode-of-failure transition law whose scaling depends upon the local material triaxiality. The governing equations have been derived within a thermodynamically-consistent framework supplemented by the employment of a micro-forces balance approach. The numerical implementation has been carried out within an updated lagrangian finite element scheme with explicit time integration. A series of benchmarks will be provided to appraise the model capabilities in predicting rate-pressure-dependent crack initiation and propagation. Results will be compared against experimental evidences which closely resemble the boundary value problems examined in this work. Concurrently, the design and optimization of a complimentary, improved, experimental characterization platform, based on the split Hopkinson pressure bar, will be presented as a mean for further validation and calibration.

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Kuhn, Charlotte [Verfasser], and Ralf [Akademischer Betreuer] Müller. "Numerical and Analytical Investigation of a Phase Field Model for Fracture / Charlotte Kuhn. Betreuer: Ralf Müller." Kaiserslautern : Technische Universität Kaiserslautern, 2013. http://d-nb.info/1035405563/34.

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Bhowmick, Sauradeep. "Advanced Smoothed Finite Element Modeling for Fracture Mechanics Analyses." University of Cincinnati / OhioLINK, 2021. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1623240613376967.

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Cajuhi, Tuanny Verfasser], Lorenzis Laura [Akademischer Betreuer] De, and Pietro [Akademischer Betreuer] [Lura. "Fracture in porous media : phase-field modeling, simulation and experimental validation / Tuanny Cajuhi ; Laura De Lorenzis, Pietro Lura." Braunschweig : Technische Universität Braunschweig, 2019. http://d-nb.info/1180601521/34.

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Sridhar, Ashish [Verfasser], and Marc-André [Akademischer Betreuer] Keip. "Phase-field modeling of microstructure and fracture evolution in magneto-electro-mechanics / Ashish Sridhar ; Betreuer: Marc-André Keip." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2020. http://d-nb.info/1232727903/34.

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Nigro, Claudio F. "Phase field modeling of flaw-induced hydride precipitation kinetics in metals." Licentiate thesis, Malmö högskola, Institutionen för materialvetenskap och tillämpad matematik (MTM), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:mau:diva-7787.

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Hydrogen embrittlement can manifest itself as hydride formation in structures when in contact with hydrogen-rich environments, e.g. in space and nuclear power applications. To supplant experimentation, modeling of such phenomena is beneficial to make life prediction reduce cost and increase the understanding. In the present work, two different approaches based on phase field theory are employed to study the precipitation kinetics of a second phase in a metal, with a special focus on the application of hydride formation in hexagonal close-packed metals. For both presented models, a single component of the non-conserved order parameter is utilized to represent the microstructural evolution. Throughout the modelling the total free energy of the system is minimized through the time-dependent Ginzburg-Landau equation, which includes a sixth order Landau potential in the first model, whereas one of fourth order is used for the second model. The first model implicitly incorporates the stress field emanating from a sharp crack through the usage of linear elastic fracture mechanics and the governing equation is solved numerically for both isotropic and anisotropic bodies by usage of the finite volume method. The second model is applied to plate and notched cantilever geometries, and it includes an anisotropic expansion of the hydrides that is caused by the hydride precipitation. For this approach, the mechanical and phase transformation aspects are coupled and solved simultaneously for an isotropic material using the finite element method. Depending on the Landau potential coefficients and the crack-induced hydrostatic stress, for the first model the second-phase is found to form in a confined region around the crack tip or in the whole material depending on the material properties. From the pilot results obtained with the second model, it is shown that the applied stress and considered anisotropic swelling induces hydride formation in preferential directions and it is localized in high stress concentration areas. The results successfully demonstrate the ability of both approaches to model second-phase formation kinetics that is triggered by flaw-induced stresses and their capability to reproduce experimentally observed hydride characteristics such as precipitation location, shape and direction.

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Aldakheel, Fadi [Verfasser], and Christian [Akademischer Betreuer] Miehe. "Mechanics of nonlocal dissipative solids : gradient plasticity and phase field modeling of ductile fracture / Fadi Aldakheel ; Betreuer: Christian Miehe." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2016. http://d-nb.info/1118370228/34.

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Schwaab, Marie-Émeline. "Growth of interacting cracks : numerical approach to "En-passant" fracture." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSE1276/document.

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La rupture macroscopique d’un matériau intervient généralement lorsque des micro-défauts coalescent, plutôt que par la propagation catastrophique d’une seule fissure. Il est donc souhaitable d’étudier des configurations de rupture où de multiples fissures interagissent. Les paires de fissures en-passant (EP), où deux fissures parallèles croissent l’une vers l’autre, sont particulièrement intéressantes d’un point de vue applicatif. Cette configuration de rupture se retrouve aussi bien dans des situations naturelles (os, dorsales océaniques,…) qu’industrielles (génie civil, pièces métalliques,…). Malgré la diversité de tailles et de matériaux dans lesquels ces fissures existent, leurs trajectoires ont une forme typique en crochet quasi-universelle dont l’origine, résultant de l’interaction fissure-fissure répulsive puis attractive, est mal comprise. En particulier, le comportement répulsif initial semble mettre à mal la mécanique élastique linéaire de la rupture (MELR). Dans cette thèse, nous avons d’abord étudié les fissures EP dans le cadre de la MELR. L’étude de l’angle initial de déviation et la simulation de trajectoires a montré contre toute attente que la MELR permet de reproduire qualitativement la forme en crochet. Prédire précisément certaines caractéristiques, comme l’intensité de la phase répulsive, nécessite plus de finesse au niveau de la représentation du comportement matériau. Nous avons ensuite utilisé un modèle par champ de phase pour enrichir le modèle matériau. Les nouvelles trajectoires simulées étant fortement influencées par la longueur caractéristique du champ de phase, il est possible d’obtenir un modèle plus juste quantitativement. Une perspective intéressante reste de relier cette longueur à la microstructure du matériau
Macroscopic failure of a material happens generally through the coalescence of micro-defects rather than the catastrophic propagation of a single crack. It is therefore advisable to study fracture problems in which many cracks interact. The case of en-passant crack pairs (EP-cracks), two parallel and offset cracks approaching each other by propagating through their inner tips, presents a marked interest as these cracks can be found in various natural (bones, oceanic rifts,..) or industrial (civil engineering,…) situations. Despite the large variety of scales and materials in which these cracks are observed, their trajectories present a remarkably self-similar hook-shape. This shape result from the crack-crack interaction, first repulsive before becoming attractive, and its origin is poorly understood. In particular, the initial repulsive behaviour seems to question the validity of linear elastic fracture mechanics (LEFM). In this thesis, we first studied EP-cracks in the LEFM framework. The study of the initial kink angle and the simulation of crack paths showed against all expectations that LEFM is able to reproduce qualitatively the hook-shaped paths. Precise predictions of specific characteristics, such as the magnitude of repulsion, requires a more refined model of the material behaviour. We then used a phase-field model to augment the material representation. As they are strongly influenced by the characteristic length scale of the phase-field, the new simulated trajectories indicate that it is possible to develop a more quantitatively correct model. An attractive prospect is to link this characteristic length to the material microstructure

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Li, Tianyi. "Gradient-damage modeling of dynamic brittle fracture : variational principles and numerical simulations." Thesis, Université Paris-Saclay (ComUE), 2016. http://www.theses.fr/2016SACLX042/document.

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Une bonne tenue mécanique des structures du génie civil en béton armé sous chargements dynamiques sévères est primordiale pour la sécurité et nécessite une évaluation précise de leur comportement en présence de propagation dynamique de fissures. Dans ce travail, on se focalise sur la modélisation constitutive du béton assimilé à un matériau élastique-fragile endommageable. La localisation des déformations sera régie par un modèle d'endommagement à gradient où un champ scalaire réalise une description régularisée des phénomènes de rupture dynamique. La contribution de cette étude est à la fois théorique et numérique. On propose une formulation variationnelle des modèles d'endommagement à gradient en dynamique. Une définition rigoureuse de plusieurs taux de restitution d'énergie dans le modèle d'endommagement est donnée et on démontre que la propagation dynamique de fissures est régie par un critère de Griffith généralisé. On décrit ensuite une implémentation numérique efficace basée sur une discrétisation par éléments finis standards en espace et la méthode de Newmark en temps dans un cadre de calcul parallèle. Les résultats de simulation de plusieurs problèmes modèles sont discutés d'un point de vue numérique et physique. Les lois constitutives d'endommagement et les formulations d'asymétrie en traction et compression sont comparées par rapport à leur aptitude à modéliser la rupture fragile. Les propriétés spécifiques du modèle d'endommagement à gradient en dynamique sont analysées pour différentes phases de l'évolution de fissures : nucléation, initiation, propagation, arrêt, branchement et bifurcation. Des comparaisons avec les résultats expérimentaux sont aussi réalisées afin de valider le modèle et proposer des axes d'amélioration
In civil engineering, mechanical integrity of the reinforced concrete structures under severe transient dynamic loading conditions is of paramount importance for safety and calls for an accurate assessment of structural behaviors in presence of dynamic crack propagation. In this work, we focus on the constitutive modeling of concrete regarded as an elastic-damage brittle material. The strain localization evolution is governed by a gradient-damage approach where a scalar field achieves a smeared description of dynamic fracture phenomena. The contribution of the present work is both theoretical and numerical. We propose a variationally consistent formulation of dynamic gradient damage models. A formal definition of several energy release rate concepts in the gradient damage model is given and we show that the dynamic crack tip equation of motion is governed by a generalized Griffith criterion. We then give an efficient numerical implementation of the model based on a standard finite-element spatial discretization and the Newmark time-stepping methods in a parallel computing framework. Simulation results of several problems are discussed both from a computational and physical point of view. Different damage constitutive laws and tension-compression asymmetry formulations are compared with respect to their aptitude to approximate brittle fracture. Specific properties of the dynamic gradient damage model are investigated for different phases of the crack evolution: nucleation, initiation, propagation, arrest, kinking and branching. Comparisons with experimental results are also performed in order to validate the model and indicate its further improvement

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Schänzel, Lisa-Marie [Verfasser], and Christian [Akademischer Betreuer] Miehe. "Phase field modeling of fracture in rubbery and glassy polymers at finite thermo-viscoelastic deformations / Lisa-Marie Schänzel. Betreuer: Christian Miehe." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2015. http://d-nb.info/1069107409/34.

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Wu, Chi. "Time-dependent Topology Optimisation for Implantable Devices." Thesis, The University of Sydney, 2022. https://hdl.handle.net/2123/29237.

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Implantable load-bearing devices signify a class of major biomechanical devices that replace damaged organs/tissue to restore desired functionalities. So far, implant designs often follow trial-and-error or experience-based protocols rather than patient-specific designs. In addition, in-vivo studies have demonstrated that implant design can substantially determine long-term treatment outcomes and longevity. Therefore, rather than empirical guidelines, efficient and elegant design approaches are urgently required to consider both initial conditions and time-dependent behaviours to promise an optimal outcome over time. One of the critical issues associated with implant devices is fracture failure due to low tensile strength and low fracture toughness at initial conditions or over time. Thus, topology optimisation for implantable devices considering path/time-dependent fracture failure was explored in this thesis. Then, a level-set based topology optimisation approach was developed to maximise fracture resistance of composite biomaterials. Load-bearing implants can change local biomechanical conditions, notably affecting long-term treatment outcomes. Considering this time-dependent nature, the thesis proposed a time-dependent topology optimisation framework for design of bone fixation plates and tissue scaffolds by incorporating bone adaptation and regeneration. Accurately predicting bone growth and remodelling results rely on the inverse-identification of tissue ingrowth/remodelling-related parameters from in-vivo data. To tackle this issue, the thesis investigated a novel machine learning-based multiscale model to predict bone growth in scaffolds efficiently. The inversely identified remodelling-related parameters were then used for a machine learning-based design of patient-specific scaffolds by incorporating ceramic additive manufacturing.

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Wu, Yi. "Topology optimization in structural dynamics : vibrations, fracture resistance and uncertainties." Thesis, Paris Est, 2022. http://www.theses.fr/2022PESC2007.

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L'objectif de cette thèse est de développer des méthodes d'optimisation topologiques basées sur la densité pour plusieurs problèmes difficiles de structure en dynamique. Premièrement, nous proposons une stratégie de normalisation en élasto-dynamique en vue d'obtenir une distribution optimale de matériau dans la structure qui réduit la réponse aux excitations dynamiques en fréquence et améliore la stabilité numérique dans la méthode BESO (bi-directional evolutionary structural optimisation). Ensuite, pour décrire les incertitudes de paramètres pouvant intervenir dans des problèmes réalistes en ingénierie, un modèle d'incertitudes à intervalle hybride est développé pour prendre en compte les incertitudes dans le problème d'optimisation en dynamique. Une méthode de perturbation est développée pour une optimisation topologique robuste vis-à-vis des incertitudes et permettant des gains de temps de calculs importants. De plus, nous introduisons un modèle d'incertitude de champ d'intervalle dans ce cadre. L'approche est appliquée à l'optimisation topologique des structures mono-matériaux, composites et multi-échelles. Enfin, nous développons un cadre d'optimisation topologique pour la résistance des structures à la fissuration quasi-fragile dans un cadre dynamique, par combinaison avec la méthode de champs de phase. Ce cadre est étendu à la conception de structures résistantes à des impacts. Contrairement aux approches basées sur les contraintes, la totalité de la propagation des fissures est prise en compte dans le processus d'optimisation
The objective of this thesis is to develop density based-topology optimization methods for several challenging dynamic structural problems. First, we propose a normalization strategy for elastodynamics to obtain optimized material distributions of the structures that reduces frequency response and improves the numerical stabilities of the bi-directional evolutionary structural optimization (BESO). Then, to take into account uncertainties in practical engineering problems, a hybrid interval uncertainty model is employed to efficiently model uncertainties in dynamic structural optimization. A perturbation method is developed to implement an uncertainty-insensitive robust dynamic topology optimization in a form that greatly reduces the computational costs. In addition, we introduce a model of interval field uncertainty into dynamic topology optimization. The approach is applied to single material, composites and multi-scale structures topology optimization. Finally, we develop a topology optimization for dynamic brittle fracture structural resistance, by combining topology optimization with dynamic phase field fracture simulations. This framework is extended to design impact-resistant structures. In contrast to stress-based approaches, the whole crack propagation is taken into account into the optimization process

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Goswami, Somdatta [Verfasser], Timon [Akademischer Betreuer] Rabczuk, Stephane [Gutachter] Bordas, and Magd Abel [Gutachter] Wahab. "Phase field modeling of fracture with isogeometric analysis and machine learning methods / Somdatta Goswami ; Gutachter: Stephane Bordas, Magd Abel Wahab ; Betreuer: Timon Rabczuk." Weimar : Bauhaus-Universität Weimar, 2021. http://d-nb.info/122878924X/34.

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Msekh, Mohammed Abdulrazzak Verfasser], Timon [Akademischer Betreuer] Rabczuk, Lorenzis Laura [Gutachter] De, and Tom [Gutachter] [Lahmer. "Phase Field Modeling for Fracture with Applications to Homogeneous and Heterogeneous Materials / Mohammed Abdulrazzak Msekh ; Gutachter: Laura De Lorenzis, Tom Lahmer ; Betreuer: Timon Rabczuk." Weimar : Bauhaus-Universität Weimar, 2017. http://d-nb.info/1135592950/34.

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Msekh, Mohammed Abdulrazzak Verfasser], Timon [Akademischer Betreuer] [Rabczuk, Lorenzis Laura Gutachter] De, and Tom [Gutachter] [Lahmer. "Phase Field Modeling for Fracture with Applications to Homogeneous and Heterogeneous Materials / Mohammed Abdulrazzak Msekh ; Gutachter: Laura De Lorenzis, Tom Lahmer ; Betreuer: Timon Rabczuk." Weimar : Bauhaus-Universität Weimar, 2017. http://nbn-resolving.de/urn:nbn:de:gbv:wim2-20170615-32291.

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Kramer, Sharlotte Lorraine Bolyard Ravichandran G. (Guruswami) Ravichandran G. (Guruswami) Bhattacharya Kaushik. "Phase-shifting full-field interferometric methods for in-plane tensorial stress determination for fracture studies /cSharlotte Lorraine Bolyard Kramer ; Guruswami Ravichandran, committee chair and advisor ; Kaushik Bhattacharya, co-advisor." Diss., Pasadena, Calif. : California Institute of Technology, 2009. http://resolver.caltech.edu/CaltechETD:etd-05272009-094456.

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Quintanas, Corominas Adrià. "Towards a high-performance computing finite element simulation framework for virtual testing of composite structures." Doctoral thesis, Universitat de Girona, 2019. http://hdl.handle.net/10803/669323.

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his doctoral thesis aims at developing and implementing a computational framework for performing virtual testing of composite structures using a High-Performance Computing (HPC) environment. In this sense, this thesis presents several novel constitutive models based on the continuum damage mechanics theory and their implementation in the HPC-base Finite Element (FE) simulation code called Alya. The verification and validation of the models are performed comparing the numerical predictions with analytical formulations and experimental data. The comparisons demonstrate not only the reliability of the damage models but also the potential of an HPC-based environment for Virtual Testing of COmposite STructures. Therefore, the outcome of this thesis is both the formulation of new fracture models and the numerical framework named Alya-VITECOST
L’objectiu d’aquesta tesis doctoral és el desenvolupament i implementació d’un marc computacional d’alt rendiment (HPC, de les sigles en anglès de High Performance Computing) amb el fi de realitzar proves virtuals d’estructures fetes de materials compòsits. En aquest sentit, aquesta tesis presenta la formulació de diversos models constitutius basats en la teoria de la mecànica de danys continus així com la seva implementació en el codi de simulació HPC anomenat Alya. La verificació i validació dels models i la seva implementació es realitza comparant les prediccions numèriques amb solucions analítiques i dades experimentals. Els resultats demostren la fiabilitat dels models formulats així com el potencial i avantatges oferts pels codis de simulació HPC. Per tant, el resultat d’aquesta tesis és tant la formulació dels models de dany progressiu com el marc numèric de simulació anomenat Alya-VITECOST.

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Staudinger, Ulrike. "Morphologie und Bruchverhalten von Block- und Multipfropfcopolymeren." Doctoral thesis, [S.l. : s.n.], 2007. http://nbn-resolving.de/urn:nbn:de:swb:14-1187261828675-34703.

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Cheng, Zifeng. "Modelling Brittle Fractures with Finite Elements: A Time-independent Phase-field Model." Thesis, Faculty of Engineering, School of Civil Engineering, 2020. https://hdl.handle.net/2123/29350.

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The objective of this paper is to propose a 2-D time-independent phase-field model with validating its performance as well as applying it for simulating existing representative experiments. Firstly, the section of the literature review provides an overview of quasi-brittle material and brittle fracture behaviours, as well as the existing FE models from both discontinuous and continuous approaches for simulating fracture behaviours. Next, the governing equations of the proposed phase-field model are determined, which are based on traditional Griffith’s theory as well as a specific variational method evolved from that. The proposed model is implemented in Abaqus. In particular, the implementation is achieved by using the User Subroutine in order to take the phase-field into account. The proposed model is validated by simulating a pure-tension and a pure shear test. In this part, not only the effect of discretisation but also the effects of length parameter and energy release rate has been discussed, of which the latter effect is exclusive in phase-field method. Finally, the validated model is used for simulating two sets of existing experiments, including a mixed-mode test and a series of Brazilian disks test. The results in both validation and simulation part indicate that the proposed model can successfully simulate both crack initiation and propagation in these cases, and good qualitative agreement with theoretical or experimental results can be observed.

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Sommer, Liesel [Verfasser], and Christian [Akademischer Betreuer] Engwer. "An unfitted discontinuous Galerkin scheme for a phase-field approximation of pressurized fractures / Liesel Sommer ; Betreuer: Christian Engwer." Münster : Universitäts- und Landesbibliothek Münster, 2019. http://d-nb.info/1201729483/34.

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Borden, Michael Johns. "Isogeometric analysis of phase-field models for dynamic brittle and ductile fracture." Thesis, 2012. http://hdl.handle.net/2152/ETD-UT-2012-08-6113.

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To date, efforts to model fracture and crack propagation have focused on two broad approaches: discrete and continuum damage descriptions. The discrete approach incorporates a discontinuity into the displacement field that must be tracked and updated. Examples of this approach include XFEM, element deletion, and cohesive zone models. The continuum damage, or smeared crack, approach incorporates a damage parameter into the model that controls the strength of the material. An advantage of this approach is that it does not require interface tracking since the damage parameter varies continuously over the domain. An alternative approach is to use a phase-field to describe crack propagation. In the phase-field approach to modeling fracture the problem is reformulated in terms of a coupled system of partial differential equations. A continuous scalar-valued phase-field is introduced into the model to indicate whether the material is in the unfractured or fractured ''phase''. The evolution of the phase-field is governed by a partial differential equation that includes a driving force that is a function of the strain energy of the body in question. This leads to a coupling between the momentum equation and the phase-field equation. The phase-field model also includes a length scale parameter that controls the width of the smooth approximation to the discrete crack. This allows discrete cracks to be modeled down to any desired length scale. Thus, this approach incorporates the strengths of both the discrete and continuum damage models, i.e., accurate modeling of individual cracks with no interface tracking. The research presented in this dissertation focuses on developing phase-field models for dynamic fracture. A general formulation in terms of the usual balance laws supplemented by a microforce balance law governing the evolution of the phase-field is derived. From this formulation, small-strain brittle and large-deformation ductile models are then derived. Additionally, a fourth-order theory for the phase-field approximation of the crack path is postulated. Convergence and approximation results are obtained for the proposed theories. In this work, isogeometric analysis, and particularly T-splines, plays an important role by providing a smooth basis that allows local refinement. Several numerical simulations have been performed to evaluate the proposed theories. These results show that phase-field models are a powerful tool for predicting fracture.
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(9312344), Xiaorong Cai. "PHASE FIELD MODELING OF MICROSTRUCTURE EVOLUTION IN CRYSTALLINE MATERIALS." Thesis, 2020.

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The material responses and the deformation pattern of crystals are strongly influ- enced by their microstructure, crystallographic texture and the presence of defects of various types.

In electronics, Sn coatings are widely used in circuits to protect conductors, reduce oxidation and improve solderability. However, the spontaneous growth of whiskers in Sn films causes severe system failures. Based on extensive experimental results, whiskers are observed to grow from surface grains with shallow grain boundaries. The underlying mechanism for these surface grains formation is crucial to predict potential whisker sites. A phase field model is coupled with a single crystal plasticity model and applied to simulate the grain boundary migration as well as the grain rotation process in Sn thin film, which are two possible mechanisms for surface grain formation. The grain boundary migration of three columnar grains is modeled and no surface grain is formed due to large plastic dissipation. In polycrystal Sn thin film, the nucleation of subgrains with shallow grain boundaries is observed for certain grain orientations on the film surface and the location of which corresponds to the regions with high strain energy density. From these simulations, it can be concluded that the grain rotation is the mechanism for whisker grain formation and the nucleated subgrains may be the potential whisker sites.

Sn-based solders are also widely used in electronics packaging. The reliability and the performance of SAC (Sn-Ag-Cu) solders are of key importance for the miniaturiza- tion of electronics. The interfacial reaction between Cu substrates and Sn-based sol- ders forms two types of brittle intermetallic compounds (IMCs), Cu6Sn5 and Cu3Sn.

During the operation, the interconnecting solders usually experience thermal loading and electric currents. These environmental conditions result in the nucleation of voids in Cu3Sn layer and the growth of the IMCs. A phase field damage model is applied to model the fracture behavior in Cu/Sn system with different initial void densities and different Cu3Sn thickness. The simulation results show the fracture location is dependent on the Cu3Sn thickness and the critical stress for fracture can be increased by lowering the void density and Cu3Sn thickness.

In alloys, the stacking fault energy varies with the local chemical composition. The effects of the stacking fault energy fluctuation on the strengthening of alloys are studied using phase field dislocation method (PFDM) simulations that model the evolution of partial dislocations in materials at zero temperature. Some examples are shown to study the dependency of the yield stress on the stacking fault energy, the decorrelation of partial dislocations in the presence of impenetrable and penetrable particles. Simulations of the evolution of partial dislocations in a stacking fault energy landscape with local fluctuations are presented to model the responses of high entropy alloys. A strong size dependency is observed with a maximum strength when the mean region size approaches the average equilibrium stacking fault width. The strength of high entropy alloys could be improved by controlling the disorder in the chemical misfit.

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Kramer, Sharlotte Lorraine Bolyard. "Phase-Shifting Full-Field Interferometric Methods for In-Plane Tensorial Stress Determination for Fracture Studies." Thesis, 2009. https://thesis.library.caltech.edu/2176/3/02A_chap2.pdf.

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Anisotropic fracture criteria can be established with understanding of full-field stresses near a crack. The anisotropy of the stresses implies that the full in-plane tensorial stress is required, but current experimental optical techniques only give the sum or difference of principal stresses, motivating development of experimental methods that combines two experimental techniques to determine all of the stress components, such as the proposed hybrid experimental method of phase-shifting photoelasticity and transmission Coherent Gradient Sensing (CGS). This thesis establishes this method for stress determination around cracks in photoelastic materials.

This experimental method first requires a new theory for the use of CGS, a wavefront shearing interferometry technique, for photoelastic materials. The first analysis of transmission wavefront shearing interferometry for photoelastic materials is experimentally demonstrated using CGS in full field for a compressed polycarbonate plate with a side V-shaped notch with good agreement with theoretical data. For the hybrid experimental method, a six-step phase-shifting photoelasticity method determines principal stress directions and the difference of principal stresses, and the transmission CGS method utilizes a standard four-step phase-shifting method to measure the x and y first derivatives of the sum of principal stresses, which are numerically integrated for the sum of principal stresses. The full-field principal stresses may then be separated, followed by the Cartesian and polar coordinate stresses using the principal stress directions and the polar angle. The method is first demonstrated for in-plane tensorial stress determination for a compressed polycarbonate plate with a side V-shaped notch with good comparison to theoretical stress fields. The CGS-photoelasticity experimental method is then applied to determine stresses around Mode I-dominant cracks in Homalite-100. The experimental stress fields have excellent agreement with the full-field 2D asymptotic crack solution using the Mode I and Mode II stress intensity factor values calculated from the experimental data. With this foundation of stress determination around cracks in photoelastic materials and with some future analysis, this experimental method can be extended to determine stresses in anisotropic crystals for fracture studies.

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Arriaga, e. Cunha Miguel Torre do Vale. "Stability Analysis of Metals Capturing Brittle and Ductile Fracture through a Phase Field Method and Shear Band Localization." Thesis, 2016. https://doi.org/10.7916/D8RX9HPR.

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Dynamic fracture of metals is a fascinating multiphysics-multiscale problem that often results in brittle and/or ductile fracture of structural components. Additionally, under high strain rates such as impact or blast loads, a failure phenomena known as shear banding may also occur, which is a common precursor to fracture. Both fracture and shear banding are instability processes leading to strong discontinuities and strain localization, respectively. Namely, shear bands are zones of highly localized plastic deformation, while brittle/ductile cracks are material discontinuities due to cleavage and/or void coalescence. Furthermore, while fracture events are mostly driven by triaxial tensile loading, shear bands are driven by shear heating caused by inelastic deformations and high temperature rise. In this work, fracture is modeled through a phase field formulation coupled to a set of equations that describe shear bands. While fracture is governed by a strong length scale that propagates at a fast time scale, shear bands are dominated by a weak length scale and propagate slower. These are two different failure modes with distinct spatial and temporal scales. This thesis is aimed at the development of analytical and numerical methods to determine the onset of both shear band localization and fracture. The main contribution of this thesis is the formulation of analytical criteria, based on the linear perturbation method, for the onset of fracture and shear band instabilities. We first propose a stability framework for shear bands that account for a non-constant Taylor Quinney coefficient. In addition, we apply the linear perturbation method to the phase field formulation of fracture to study the onset of unstable crack growth. The derivations lead to an analytical, energy based criterion for the phase field method in linear elastic and visco-plastic materials. The stability criterion not only recovers the critical stress value reported in the literature for simple elastic cases but also provides a criterion for visco-plastic materials with a general degradation function and fracture induced by cold-work. Finally, we analyze the physical stability of both failure modes and their interaction. The analysis provides insight into the dominant failure mode and can be used as a criterion for mesh refinement. Several numerical results with different geometries and a range of strain rate loadings demonstrate that the stability criterion predicts well the onset of failure instability in dynamic fracture applications. For the example problems considered, if a fracture instability precedes shear banding, a brittle-like failure mode is observed, while if a shear band instability is initiated significantly before fracture, a ductile-like failure mode is expected. In any case, fracture instability is stronger than a shear band instability and if initiated will dominate the response. Another contribution of this thesis is the development of numerical type stability methods based on the discretized model which can be employed within any finite element method. In this approach, a novel methodology to determine the onset of shear band localization is proposed, by casting the instability analysis as a generalized eigenvalue problem with a particular decomposition of the element Jacobian matrix. We show that this approach is attractive, as it is applicable to general rate dependent multidimensional cases and no special simplifying assumptions ought to be made. Furthermore, this technique is also applied to the fully coupled dynamic fracture problem and is shown to agree well with the analytical criteria. Finally, we propose an alternative for identifying the instability point following a generalized stability analysis concept. In this framework, a stability measure is obtained by computing the instantaneous growth rate of the vector tangent to the solution. Such an approach is more appropriate for non-orthogonal problems and is easier to generalize to difficult dynamic fracture problems.

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Carka, Dorinamaria. "Non-Linear Analysis of Ferroelastic/Ferroelectric Materials." 2012. http://hdl.handle.net/2152/19499.

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Abstract Ferroelectric/ferroelastic ceramics are used in a range of smart structure applications, such as actuators and sensors due to their electromechanical coupling properties. However, their inherent brittleness makes them susceptible to cracking and understanding their fracture is of prominent importance. A numerical study for a stationary, plane strain crack in a ferroelastic material is performed as part of this work. The stress and strain fields are analyzed using a constitutive law that accounts for the strain saturation, asymmetry in tension versus compression, Bauschinger effects, reverse switching, and remanent strain reorientation that can occur in these materials due to the non-proportional loading that arises near a crack tip. The far-field K-loading is applied using a numerical method developed for two-dimensional cracks allowing for the true infinite boundary conditions to be enforced. The J -integral is computed on various integration paths around the tip and the results are discussed in relation to energy release rate results for growing cracks and for stationary cracks in standard elastic–plastic materials. In addition to the fracture studies, we examine the far field electromechanical loading conditions that favor the formation, existence and evolution of stable needle domain array patterns, using a phase-field modeling approach. Such needle arrays are often seen in experimental imaging of ferroelectric single crystals, where periodic arrays of needle-shaped domains of a compatible polarization variant coexist with a homogeneous single domain parent variant. The infinite arrays of needles are modeled via a representative unit cell and the appropriate electrical and mechanical periodic boundary conditions. A theoretical investigation of the generalized loading conditions is carried out to determine the sets of averaged loading states that lead to stationary needle tip locations. The resulting boundary value problems are solved using a non-linear finite element method to determine the details of the needle shape as well as the field distributions around the needle tips.
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Dissertations / Theses on the topic 'Phase Field Fracture'

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