Stochastic Geometry, Spatial Statistics and Statistical Physics

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An Analytical Representation of the 2d Generalized Balanced Power Diagram

Tessellations are an important tool to model the microstructure of cellular and polycrystalline materials. Classical tessellation models include the Voronoi diagram and Laguerre tessellation whose cells are polyhedra. Due to the convexity of their cells, those models may be too restrictive to describe data that includes possibly anisotropic grains with curved boundaries. Several generalizations exist. The cells of the generalized balanced power diagram are induced by elliptic distances leading to more diverse structures. So far, methods for computing the generalized balanced power diagram are restricted to discretized versions in the form of label images. In this work, we derive an analytic representation of the vertices and edges of the generalized balanced power diagram in 2d. Based on that, we propose a novel algorithm to compute the whole diagram

Crystal plasticity modeling of Ti-6Al-4V and its application in cyclic and fretting fatigue analysis

Ti-6Al-4V, known for high strength-to-weight ratio and good resistance to corrosion, has been widely used in aerospace, biomedical, and high-performance sports applications. A wide range of physical and mechanical properties of Ti-6Al-4V can be achieved by varying the microstructures via deformation and recrystallization processes. The aim of this thesis is to establish a microstructure-sensitive fatigue analysis approach that can be applied in engineering applications such as fretting fatigue to permit explicit assessment of the influence of microstructure. In this thesis, crystal plasticity constitutive relations are developed to model the cyclic deformation -TiAl has beenabehavior of Ti-6Al-4V. The development of the slip bands within widely reported and has been found to play an important role in deformation and fatigue behaviors of Ti-6Al-4V. The shear enhanced model is used to simulate the formation and evolution of slip bands triggered by planar slip under static or quasi-static loading at room temperature. Fatigue Indicator Parameters (FIPs) are introduced to reflect driving force for the different crack formation mechanisms in Ti-6Al-4V. The cyclic stress-strain behavior and fretting fatigue sensitivity to microstructure and loading parameters in dual phase Ti-6Al-4V are investigated.Ph.D.Committee Chair: David. L. McDowell; Committee Member: Min Zhou; Committee Member: Naresh N. Thadhani; Committee Member: Rami M. Haj-Ali; Committee Member: Richard W. Ne