Numerical micromechanical modelling of brittle polycrystalline materials

A generally applicable framework for generating a nite element mesh that is based on the actual micro-structure of a material is developed. The procedure is applied to a microscopic image of a ceramic material. Special attention is paid to the modelling of the interfaces between adjoining grains. Plane strain and plane stress nite element calculations are performed. The observed e ective constants are compared to analytically obtained extreme bounds. A rst attempt is undertaken to simulate crack propagation. Conclusions: The micro-structure of a ceramic material can be numerically modelled by generating a nite element mesh based on a microscopic image of the grain-structure. Finite element analyses show that the overall elastic behaviour is highly dependent on the speci c elastic properties of the individual grains. When averaged over many di erent calculations, the FEM average e ective elastic constants are approximately within analytically obtained extreme bounds. Plane strain calculations result in a relatively high Young's modulus, whereas for plane stress calculations the obtained e ective Young's modulus is relatively low. Crack propagation can be simulated by a node release method, which is however highly mesh dependent. c Philips Electronics N.V. 1998 iii 814/98 Unclassi ed Report iv c Philips Electronics N.V. 1998