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In dieser Arbeit wird ein Ansatz zur Simulation von Initiierung und Wachstum von Rissen in spröden Materialien, basierend auf diffusen Grenzflächen, um seinen Anwendungsbereich erweitert. Durch die Ergänzung der inneren Energie eines bestehenden Phasenfeldmodells um einen zusätzlichen Anteil wird das Beschreiben von Ermüdungsrisswachstum
ermöglicht. Außerdem wird durch das Modifizieren des Gradienten des Phasenfeldparameters in der regularisierten Rissenergie erreicht, dass das entstehende Modell anisotropes
Risswachstum abbilden kann.
Einleitend werden die benötigten Grundlagen aus verschiedenen Feldern der Mechanik
beschrieben sowie die Phasenfeld Methode zur Simulation von Risswachstum eingeführt.
Danach werden die Modifikationen, welche im Rahmen dieser Arbeit eingebracht wurden
begründet. Es wird im Weiteren detailliert beschrieben, wie die entsprechenden Erweiterungen eingearbeitet wurden und die Evolutionsgleichungen der neuen Phasenfeldmodelle,
in Form von Ginzubug-Landau Gleichungen werden hergeleitet.
Das resultierende gekoppelte Differentialgleichungssystem wurde, unter Verwendung von
impliziter Zeitintegration, als ebenes nichtlineares Finite Elemente Problem implementiert.
Die starke als auch die schwache Form der beschreibenden Gleichungen des Phasenfeld
Modells werden beschrieben.
Verschiedene Test Szenarien wurden simuliert, um zu Untersuchen inwieweit reale Ergebnisse mit dem Modell erzielt werden können. Die Ergebnisse zeigen, dass Brüche in
anisotropen Medien beschrieben werden können. Außerdem erzielt das entwickelte Ermüdungsmodell reales Verhalten für wichtige Größen wie die Risswachstumsgeschwindigkeit
und Phänomene wie Mittelspannungseinfluss oder Reihenfolge Einflüsse werden korrekt
abgebildet. Simulationsergebnisse von beiden Modellen werden mit experimentellen Ergebnissen verglichen, wobei eine gute Übereinstimmung nachgewiesen werden kann.
Recently, phase field modeling of fatigue fracture has gained a lot of attention from many researches and studies, since the fatigue damage of structures is a crucial issue in mechanical design. Differing from traditional phase field fracture models, our approach considers not only the elastic strain energy and crack surface energy, additionally, we introduce a fatigue energy contribution into the regularized energy density function caused by cyclic load. Comparing to other type of fracture phenomenon, fatigue damage occurs only after a large number of load cycles. It requires a large computing effort in a computer simulation. Furthermore, the choice of the cycle number increment is usually determined by a compromise between simulation time and accuracy. In this work, we propose an efficient phase field method for cyclic fatigue propagation that only requires moderate computational cost without sacrificing accuracy. We divide the entire fatigue fracture simulation into three stages and apply different cycle number increments in each damage stage. The basic concept of the algorithm is to associate the cycle number increment with the damage increment of each simulation iteration. Numerical examples show that our method can effectively predict the phenomenon of fatigue crack growth and reproduce fracture patterns.
Within this work, we utilize the framework of phase field modeling for fracture in order to handle a very crucial issue in terms of designing technical structures, namely the phenomenon of fatigue crack growth. So far, phase field fracture models were applied to a number of problems in the field of fracture mechanics and were proven to yield reliable results even for complex crack problems. For crack growth due to cyclic fatigue, our basic approach considers an additional energy contribution entering the regularized energy density function accounting for crack driving forces associated with fatigue damage. With other words, the crack surface energy is not solely in competition with the time-dependent elastic strain energy but also with a contribution consisting of accumulated energies, which enables crack extension even for small maximum loads. The load time function applied to a certain structure has an essential effect on its fatigue life. Besides the pure magnitude of a certain load cycle, it is highly decisive at which point of the fatigue life a certain load cycle is applied. Furthermore, the level of the mean load has a significant effect. We show that the model developed within this study is able to predict realistic fatigue crack growth behavior in terms of accurate growth rates and also to account for mean stress effects and different stress ratios. These are important properties that must be treated accurately in order to yield an accurate model for arbitrary load sequences, where various amplitude loading occurs.
Phase field modeling of fracture has been in the focus of research for over a decade now. The field has gained attention properly due to its benefiting features for the numerical simulations even for complex crack problems. The framework was so far applied to quasi static and dynamic fracture for brittle as well as for ductile materials with isotropic and also with anisotropic fracture resistance. However, fracture due to cyclic mechanical fatigue, which is a very important phenomenon regarding a safe, durable and also economical design of structures, is considered only recently in terms of phase field modeling. While in first phase field models the material’s fracture toughness becomes degraded to simulate fatigue crack growth, we present an alternative method within this work, where the driving force for the fatigue mechanism increases due to cyclic loading. This new contribution is governed by the evolution of fatigue damage, which can be approximated by a linear law, namely the Miner’s rule, for damage accumulation. The proposed model is able to predict nucleation as well as growth of a fatigue crack. Furthermore, by an assessment of crack growth rates obtained from several numerical simulations by a conventional approach for the description of fatigue crack growth, it is shown that the presented model is able to predict realistic behavior.