Fitting the grain orientation distribution of a polycrystalline material conditioned on a Laguerre tessellation
Abstrakt
The description of distributions related to grain microstruc-ture helps physicists to understand the processes in materials and their properties. This paper presents a general statistical methodology for the analysis of crystallographic orientations of grains in a 3D Laguerre tessellation dataset which represents the microstructure of a polycrystalline material.
We introduce complex stochastic models which may substitute expensive lab-oratory experiments: conditional on the Laguerre tessellation, we suggest interaction models for the distribution of cubic crystal lattice orientations, where the interaction is between pairs of ori-entations for neighbouring grains in the tessellation. We discuss parameter estimation and model comparison methods based on maximum pseudolikelihood as well as graphical procedures for model checking using simulations.
Our methodology is applied for analysing a dataset representing a nickel-titanium shape memory alloy.(c) 2023 Elsevier B.V. All rights reserved.