Browsing by Author "Dattke, Rainer Andreas"

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Modelling the microstructure and simulation of progressive fracturing in brittle granular materials
(2003) Dattke, Rainer Andreas; Kröplin, Bernd (Prof. Dr.-Ing. habil.)
The present thesis is concerned with the initiation and extension of microcracks in brittle, granular materials, particularly in porous ceramics, and with the effect of this microsopic damage on the macroscopic material properties. For an investigation of the damage behaviour, a two-dimensional geometric model of the microstructure and a physical model of its elastic and strength properties is developed. The emerging computer algorithm represents a novel approach to the simulation of microscopic damage since it combines elements of the purely analytical 'micromechanical' models, and ideas of the rather numerical 'mesh models'. The numerical parts are due to the discretization of the actual structure into a grid of grain boundaries, which is seen as a network of potential cracks; the disorder immanent to the microstructure is accounted for via random numbers during the grid generation. The analytical parts are involved in the stress analysis: elementary analytical solutions for the single cavities (cracks, pores) are employed to determine the local stress disturbances; crack interactions are explicitly taken into consideration. The fracture criterion at the microscale relies on an energy balance estimation for the individual grain boundaries ('facets'). This semi-numerical simulation model serves as a tool for investigation of progressive damage under various loading conditions, in particular external compression and internal pore pressure. Crack closure resulting from normal compression, internal friction between sliding crack faces, and structural changes due to microcracking give rise to nonlinear effects which are properly described in the formalism. Exemplary simulations reproduce the various types of damage (unstable crack growth, distributed microcracking, localization) and demonstrate their dependence on the loading modes and on the level of structure heterogeneity. Under internal compression, microcracks grow to connect pores, thus building chains or networks of defects. In the investigations, high interest is focused on the statistical fluctuations of the observables due to the microstructural disorder. The studies span the whole range between nucleation of single microcracks and material failure.