Possible uses and limits of probability models in connection with the reliability of large scale plants

The existing probability models and failure theories were compiled and discussed, where the main point was a study of previous literature on brittle and ductile fracture. In order to describe ductile failure, analytical models of growth of isolated hollow spaces were developed, when looking at the formation of micro-cracks and later failure. Due to the observed pore formation with great plastic deformation, material laws were developed, which started from the assumption of incompressible plastic deformation. From taking into account the phenomenon of formation, growth and combination of hollow spaces by suitable material laws, it was found that one has to start from a non-homogeneous distribution of the hollow spaces, which can lead to unstable plastic deformation in the form of shear strips between large hollow spaces in the material. Numerical methods (e.g. FEM) were used in the development and testing of the models. In describing brittle fracture, models based on the work of Weibull and the model of the weakest member are used, which were expanded by various modifications. (orig./DG)