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Title: 2D stochastic-integral models for characterizing random grain noise in titanium alloys

We extend our previous work, in which we applied high-dimensional model representation (HDMR) and analysis of variance (ANOVA) concepts to the characterization of a metallic surface that has undergone a shot-peening treatment to reduce residual stresses, and has, therefore, become a random conductivity field. That example was treated as a onedimensional problem, because those were the only data available. In this study, we develop a more rigorous two-dimensional model for characterizing random, anisotropic grain noise in titanium alloys. Such a model is necessary if we are to accurately capture the 'clumping' of crystallites into long chains that appear during the processing of the metal into a finished product. The mathematical model starts with an application of the Karhunen-Loève (K-L) expansion for the random Euler angles, θ and φ, that characterize the orientation of each crystallite in the sample. The random orientation of each crystallite then defines the stochastic nature of the electrical conductivity tensor of the metal. We study two possible covariances, Gaussian and double-exponential, which are the kernel of the K-L integral equation, and find that the double-exponential appears to satisfy measurements more closely of the two. Results based on data from a Ti-7Al sample will be given, andmore » further applications of HDMR and ANOVA will be discussed.« less
Authors:
; ;  [1] ;  [2] ; ; ;  [3]
  1. Victor Technologies, LLC, PO Box 7706, Bloomington, IN 47407-7706 (United States)
  2. University of Dayton Research Institute, 300 College Park Dr., Dayton, OH 45410 (United States)
  3. Air Force Research Laboratory (AFRL/RXC), Wright Patterson AFB OH 45433-7817 (United States)
Publication Date:
OSTI Identifier:
22263807
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 1581; Journal Issue: 1; Conference: 40. annual review of progress in quantitative nondestructive evaluation, Baltimore, MD (United States), 21-26 Jul 2013, 10. international conference on Barkhausen noise and micromagnetic testing, Baltimore, MD (United States), 21-26 Jul 2013; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ANISOTROPY; ELECTRIC CONDUCTIVITY; INTEGRAL EQUATIONS; RESIDUAL STRESSES; SHOT PEENING; STOCHASTIC PROCESSES; TENSORS; TITANIUM ALLOYS