A stochastic approach applied to directionally solidified turbine blades

This paper addresses the situation where the size of a representive volume element is considerably larger than the characteristic lengths of the structure, using as an example the case of directionally solidified low pressure turbine blades. The statistical effects of grain boundaries on these blades are investigated by explicitly meshing the columnar microstructure of grains in the blade and then crystallographic orientations are assigned to each grain in the blades. A Crystal Plasticity Finite Element simulation is then performed for each configuration. Since the shape of grains and the crystallographic orientations change from one component to another, 1050 statistical components are generated and computed. Initial results show only the effects of crystallographic orientations of grains on the localisation of stress and plastic strain at grain boundaries. Other analyses are then conducted using different polycrystalline meshes to introduce the effect of the grain boundary location on field fluctuations. For example, we can investigate the crystallographic configurations which generate maximum values for the equivalent stress or plastic strain at different positions of the blade.