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Title: Diffraction Coefficients of a Semi-Infinite Planar Crack Embedded in a Transversely-Isotropic Space

Abstract

We develop a semi-analytical procedure for calculating the diffraction coefficients for cracks perpendicular to the symmetry axis of a transversely-isotropic medium. The problem is of interest in the mathematical modeling of NDE (non-destructive evaluation) of austenitic steels, which are found in claddings and other welds in the nuclear reactors and can be modelled as transversely isotropic.

Authors:
 [1]; ;  [2]
  1. Departament of Mathematics, Iowa State University (United States)
  2. Waves and Fields Research Group, Faculty of Engineering, Science and Built Environment, London South Bank University (United Kingdom)
Publication Date:
OSTI Identifier:
21054976
Resource Type:
Journal Article
Resource Relation:
Journal Name: AIP Conference Proceedings; Journal Volume: 894; Journal Issue: 1; Conference: Conference on review of progress in quantitative nondestructive evaluation, Portland, OR (United States), 30 Jul - 4 Aug 2006; Other Information: DOI: 10.1063/1.2718025; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; AUSTENITIC STEELS; CLADDING; CRACKS; DETECTION; DIFFRACTION; EVALUATION; MATHEMATICAL MODELS; NONDESTRUCTIVE TESTING; NUMERICAL ANALYSIS; REACTOR MATERIALS; SYMMETRY; WELDED JOINTS

Citation Formats

Gautesen, A., Fradkin, L., and Zernov, V.. Diffraction Coefficients of a Semi-Infinite Planar Crack Embedded in a Transversely-Isotropic Space. United States: N. p., 2007. Web. doi:10.1063/1.2718025.
Gautesen, A., Fradkin, L., & Zernov, V.. Diffraction Coefficients of a Semi-Infinite Planar Crack Embedded in a Transversely-Isotropic Space. United States. doi:10.1063/1.2718025.
Gautesen, A., Fradkin, L., and Zernov, V.. Wed . "Diffraction Coefficients of a Semi-Infinite Planar Crack Embedded in a Transversely-Isotropic Space". United States. doi:10.1063/1.2718025.
@article{osti_21054976,
title = {Diffraction Coefficients of a Semi-Infinite Planar Crack Embedded in a Transversely-Isotropic Space},
author = {Gautesen, A. and Fradkin, L. and Zernov, V.},
abstractNote = {We develop a semi-analytical procedure for calculating the diffraction coefficients for cracks perpendicular to the symmetry axis of a transversely-isotropic medium. The problem is of interest in the mathematical modeling of NDE (non-destructive evaluation) of austenitic steels, which are found in claddings and other welds in the nuclear reactors and can be modelled as transversely isotropic.},
doi = {10.1063/1.2718025},
journal = {AIP Conference Proceedings},
number = 1,
volume = 894,
place = {United States},
year = {Wed Mar 21 00:00:00 EDT 2007},
month = {Wed Mar 21 00:00:00 EDT 2007}
}
  • For a three-dimensional semi-infinite transversely isotropic material, Green's functions (that give the full set of coupled fields due to the arbitrarily oriented point force and concentrated generalized point source, that represents either the diffusive chemical substance concentration or heat applied at the boundary of the half-space) are derived in elementary functions in a simple way, using methods of the potential theory. In the course of the analysis we derived the general solution of the field equations, represented in terms of four harmonic potential functions, which may also be relevant to other problems of chemical concentration or heat diffusion. These solutionsmore » constitute generalization of Boussinesq's and Cerruti s problems of elasticity for the chemically diffusive and/or thermoelastic materials.« less
  • the full set of coupled fields due to the arbitrarily oriented point force and concentrated generalized point source, that represents either the diffusive chemical substance concentration or heat applied at the boundary of the half-space) are derived in elementary functions in a simple way, using methods of the potential theory. In the course of the analysis we derived the general solution of the field equations, represented in terms of four harmonic potential functions, which may also be relevant to other problems of chemical concentration or heat diffusion. These solutions constitute generalization of Boussinesq s and Cerruti s problems of elasticitymore » for the chemically diffusive and/or thermoelastic materials.« less
  • Here, we consider the problem of an arbitrary shaped rigid punch pressed against the boundary of a transversely isotropic half-space and interacting with an arbitrary flat crack or inclusion, located in the plane parallel to the boundary. The set of governing integral equations is derived for the most general conditions, namely the presence of both normal and tangential stresses under the punch, as well as general loading of the crack faces. In order to verify correctness of the derivations, two different methods were used to obtain governing integral equations: generalized method of images and utilization of the reciprocal theorem. Bothmore » methods gave the same results. Axisymmetric coaxial case of interaction between a rigid inclusion and a flat circular punch both centered along the z-axis is considered as an illustrative example. Most of the final results are presented in terms of elementary functions.« less