Description of creep damage by means of stochastic geometry
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In this paper, some ideas concerning the statistical modelling of damage on a microstructural level and its relation to macroscopic quantities are given.
Two examples using different kinds of approaches for the damage modelling are presented. In the first part, creep damage of an austenitic steel is modelled in a phenomenological way according to experimental observations. This leads to patterns of simulated grain boundary failure, which are in qualitative agreement with experimental findings. A method is indicated how to incorporate micromechanical models in macroscopic relations for creep behavior.
In the second part, a micromechanical model for creep damage of alumina is incorporated into the simulated grain boundary structure. Characteristic patterns of the different simulation procedures are shown.
As a first step, the results seem to be encouraging. The advantages of the use of stochastic geometry methods in the light of the possible inclusion of more sophisticated models for grain boundary failure and the interaction effects of cavitated grain boundary facets are twofold:
Any kind of grain boundary failure can be handled by the stochastic model which is therefore applicable for different kinds of material.
Interaction effects of cavitated grain boundary facets can be handled in a very efficient way, which allows the simulation of realistic configurations without a prohibitively large amount of computing time.
The framework of the stochastic geometry seems therefore to be a very efficient tool for the development of micromechanical damage models and their relation to a macroscopic description of damage.
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