Fraunhofer-Institut für Techno- und Wirtschaftsmathematik ITWMDescription
From the 3D stochastic modeling point of view, the challenge consists in defining models for the regular point process of particle centers and the typical particle. Standard models using spherical, ellipsoidal or cylindrical particles cannot be applied since the AMC particles show complicated non-convex shapes as well as a high variance of particle sizes. A starting point for this project is the work by Zangmeister (2013) where a first model for the materials under investigation was introduced. The thesis suggested here aims at a refinement of the model and at the development of statistical model fitting techniques based on the image data. The formulation of packing algorithms for non-convex particles is highly complicated, especially if the particle process is not stationary. For fitting the model to real data, relations between the model parameters and important geometric characteristics of the model will be derived analytically or by Monte-Carlo simulation. For the latter, a fast simulation algorithm for the model has to be developed.
The estimation of model parameters from the image data is complicated by the fact that the materials under consideration are not tractable to tomographic imaging. Alternative 3D imaging techniques such as FIB-tomography are laborious and costly. Hence, the required information should be estimated from two-dimensional SEM images. This implies that stereological methods have to be applied to estimate the model parameters. However, FIB-tomography images will be used to derive suitable assumptions on the shape of the typical particle and to validate the estimation techniques.
In a second step, a spatio-temporal model describing the deformation behavior will be developed. The main goal is to link this behavior to specific microstructural features, e.g. to identify critical points for crack initiation.