Tensorial nature of [formula omitted]-rafting evolution in nickel-based single crystal superalloys

Abstract

Our work aims at providing a tensorial analysis of directional γ′ rafting state in a nickel based single crystal superalloy, for several orientations. According to a visco-plasticity modeling accounting for microstructure evolution during creep (including rafting), different —even— order fabric tensor representations are provided, respectively for γ channel width, primary γ′ cuboidal particles and microstructure periodicity λ. Several image processing algorithms are presented and used to best measure these quantities, particularly the AutoCorrelation Method (ACM) and the Rotational Intercept Method (RIM). Each method is developed for a specific purpose: the AutoCorrelation Method yields information about principal directions and pattern periodicity, while RIM method provides a polar distribution of a physical quantity. A methodology is proposed and applied to measure the Rose diagrams and the corresponding fabric tensors of order 2, 4, 6 and 8, starting by the best fitting Fourier series coefficients of the experimental data. When RIM method is possible to apply, fabric tensors up to order 8 are considered. In any case a 2ndorder tensor representation of single crystals γ′ rafting state is provided.