--- 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 <iframe src="https://www.flickr.com/photos/127097364@N03/15149762523/in/photostream/player/" width="501" height="339" frameborder="0" allowfullscreen webkitallowfullscreen mozallowfullscreen oallowfullscreen msallowfullscreen></iframe> 222 selected orientations for cubic polycrystal <iframe src="https://www.flickr.com/photos/127097364@N03/15149225744/in/photostream/player/" width="1024" height="356" frameborder="0" allowfullscreen webkitallowfullscreen mozallowfullscreen oallowfullscreen msallowfullscreen></iframe> ## 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 <iframe src="//www.slideshare.net/slideshow/embed_code/40603090" width="476" height="400" frameborder="0" marginwidth="0" marginheight="0" scrolling="no"></iframe> ## 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 <iframe src="https://www.flickr.com/photos/127097364@N03/15154274114/player/" width="1024" height="695" frameborder="0" allowfullscreen webkitallowfullscreen mozallowfullscreen oallowfullscreen msallowfullscreen></iframe> ## Visualization of the Fourier Coefficients in Real Space #### Test-case for Fiber microstructure (Cross Section) <iframe src="https://www.flickr.com/photos/127097364@N03/15588655258/in/photostream/player/" width="560" height="420" frameborder="0" allowfullscreen webkitallowfullscreen mozallowfullscreen oallowfullscreen msallowfullscreen></iframe> Slice of 3-D microstructure <iframe src="https://www.flickr.com/photos/127097364@N03/15774071615/in/photostream/player/" width="560" height="420" frameborder="0" allowfullscreen webkitallowfullscreen mozallowfullscreen oallowfullscreen msallowfullscreen></iframe> Auto term <iframe src="https://www.flickr.com/photos/127097364@N03/15772198781/in/photostream/player/" width="560" height="420" frameborder="0" allowfullscreen webkitallowfullscreen mozallowfullscreen oallowfullscreen msallowfullscreen></iframe> Cross term #### For Random microstructure <iframe src="https://www.flickr.com/photos/127097364@N03/15588241959/in/photostream/player/" width="560" height="420" frameborder="0" allowfullscreen webkitallowfullscreen mozallowfullscreen oallowfullscreen msallowfullscreen></iframe> Auto term <iframe src="https://www.flickr.com/photos/127097364@N03/15589265060/in/photostream/player/" width="560" height="420" frameborder="0" allowfullscreen webkitallowfullscreen mozallowfullscreen oallowfullscreen msallowfullscreen></iframe> 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