Albach, Peter Heinrich; (1990) Three-dimensional scattering of time harmonic elastic waves from axisymmetric surface indentations in a half-space. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

This thesis reports a study with the aim of assessing the possibilities of detecting and characterising the early stages of pitting corrosion, which is located on the remote side a thick aluminium plate. The work concentrated on the use of ultrasonic techniques. An incoming ultrasound plane wave is scattered from a corrosion pit, and the scattered field can provide information about the size and the shape of the surface perturbation and therefore of the extent of corrosion present on the surface. The corrosion pit can be represented as an axisymmetric indentation in the stress free surface of an elastic half-space, and the three-dimensional nature of pits requires numerical models capable of simulating three-dimensional elastic wave scattering processes. The numerical method used here is an indirect boundary method. The incident compressional or shear wave is expanded in into an infinite series of spherical vector functions. The scattered field can also be described as an infinite series of outgoing spherical waves with unknown coefficients. For numerical purposes both series are truncated to a finite number of terms. The boundary conditions of vanishing normal stress components along the free boundary are applied using a least squares matching method which gives the coefficients for the outward travelling waves. The axisymmetric nature of the surface obstacle allows a decomposition of the three-dimensional scattering problem to a set of two-dimensional subproblems with a given angular dependence, which can be solved separately and the solutions are then superimposed to give the full three-dimensional solution. The results obtained with the numerical model are compared with experimental data and support the findings of the theoretical predictions.

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