Details

Autor(en) / Beteiligte

• Andersson, Jenny

Titel

Point processes and convex sets: Applications in fatigue

Ort / Verlag

ProQuest Dissertations & Theses

Erscheinungsjahr

2003

Link zum Volltext

• ProQuest

Quelle

ProQuest Dissertations & Theses A&I

Beschreibungen/Notizen

• Two modelling approaches from stochastic geometry that can be applied to fatigue problems are introduced.First, the grain structure of the surface of a metal is modelled as a Voronoi tessellation of Poisson points in the plane. As an example of this approach, we study the influence of grain structure on fatigue life. A crack growth model is applied to simulated grain structures. The conclusion is that the fatigue life decreases, compared to a model with grains of equal size. Also the life variation, due to the random grain structure, can be estimated.The second approach is to describe inclusions in steel by two models of non-overlapping convex sets, which are generalisations of Matern's hard-core models. In both cases, we start with a Poisson process and assign a convex set to each point. The point process is then thinned so that no set intersects another set. We derive the second-order product density for convex sets with the same orientation. The product density can be used to compare the models to a homogeneous Poisson process. For spherical sets of equal radii, there can be no point within a distance of less than two times the radius to another point. Pairs of points at distance between two and four times the radius are more frequent than in a Poisson process. For larger distances, the frequency of point pairs is the same as for a Poisson process.