--- layout: post title: 2 point statistics using GSH basis function --- ## Details of New Synthetic dataset for developing Structure-Property Linkages + Details of structure dataset obtained from Yuksel (GT) can be found in [this paper](http://www.sciencedirect.com/science/article/pii/S1359645414006235) + Structure dataset for cubic polycrystal is chosen (Cu) + 3-D Microstructure is of size 21x21x21 with cyrstal orientation associated with each voxel + 222 orientations on surface of Fundamental zone were chosen + Total 3600 microstructures, 1200 each of random, delta and equiaxed + FEM elastic deformation simulations were done on 3600 microstructures to simulate uniaxial strain with periodic boundary conditions + Property data (Elastic stiffness) will be calculated from simulation results 222 selected orientations for cubic polycrystal ## Reason for discarding binning + Binning of Fundamental Zone leads to large number of discrete local states for orientations + Indicator basis function is not compact for representing orientations + Continuous basis function is needed for compact representation of orientations 2-point statistics from EBSD data using binning ## Building microstructure function using GSH basis (continuous basis function) for computing 2-point statistics + Generalized Spherical Harmonics (GSH) [1-4] to represent orientation distribution function over the Fundamental zone + GSH provides compact representaion of orientations ## Visualization of the Fourier Coefficients in Real Space #### Test-case for Fiber microstructure (Cross Section) Slice of 3-D microstructure Auto term Cross term #### For Random microstructure Auto term Cross term ## Current issues and Futue work + Redundancy in the fourier coefficients + Performing PCA + Calculation of elastic stiffness from simulation results + Develop structure-property linkages using regression ## References - [1] http://www.sciencedirect.com/science/article/pii/S1359645414006235 - [2] http://www.sciencedirect.com/science/article/pii/S1359645414005394 - [3] Texture analysis in Materials Science, H.J. Bunge, 1993 - [4] Microstructure-sensitive Design for Performance Optimization (2013), Authors: Brent L. Adams, Surya Kalidindi, David T. Fullwood