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Ray tracing boundary value problems: simulation and SAFT reconstruction for ultrasonic testing
(2016)
The application of advanced imaging techniques for the ultrasonic inspection of inhomogeneous anisotropic materials like austenitic and dissimilar welds requires information about acoustic wave Propagation through the material, in particular travel times between two Points in the material. Forward ray tracing is a popular approach to determine traveling paths and arrival times but is ill suited for inverse problems since a large number of rays have to be computed in order to arrive at prescribed end points.
In this contribution we discuss boundary value problems for acoustic rays, where the ray path between two given points is determined by solving the Eikonal equation. The implementation of such a two Point boundary value ray tracer for sound field simulations through an austenitic weld is described and its efficiency as well as the obtained results are compared to those of a forward ray tracer. The results are validated by comparison with experimental results and commercially available UT simulation tools.
As an application, we discuss an implementation of the method for SAFT (Synthetic Aperture Focusing Technique) reconstruction. The ray tracer calculates the required travel time through the anisotropic columnar grain structure of the austenitic weld. There, the formulation of ray tracing as a boundary value Problem allows a straightforward derivation of the ray path from a given transducer Position to any pixel in the reconstruction area and reduces the computational cost considerably.
Guided waves are increasingly a subject of great interest in nondestructive testing. An example of research in this field is the development of a novel procedure for ultrasonic testing of wheelset-axles using guided waves, which requires to treat the wheelset-axle as a thick walled cylinder with varying thickness. In order to describe ultrasound propagation in a waveguide with non-constant thickness, a multimodal approach, which allows to avoid extensive mesh-based numerical calculations, seems to be promising. The method treats the modes of a corresponding waveguide with constant thickness as a base in which an arbitrary sound field can be expressed. Since the local sound field at any given position in the waveguide with varying thickness will be a combination of these base modes, the problem is reduced to solving the differential equation that governs the evolution of the coefficients in the mode spectrum along the waveguide. Once the description of the sound field along the waveguide is obtained, the time dependence is added by multiplication with a simple oscillating term. Simulations of pulse propagation through the waveguide can then be constructed by adding up a sufficient number of mono-frequent continuous wave solutions. As an early stage in developing a simulation tool for sound propagation in thick walled cylinders with varying thickness, the multimodal approach was implemented and tested for the simple case of plate geometries. In this work, an overview of the simulations carried out for plates with non-constant thickness is presented. The performance of the algorithm based on the multimodal approach and the obtained results are compared to those of mesh-based simulation tools.
Guided waves hold great potential for applications in the field of ultrasonic nondestructive testing. Examples of possible applications are the ultrasonic testing and structural health monitoring of wheelset-axles as used in trains. Depending on the particular type, these axles can be described as either thick cylindrical rods or thick walled hollow cylinders with varying thickness. Wheelset-axles are safety relevant components that have to be inspected on a regular basis. The use of guided waves would allow a full inspection while accessing only the front faces of the axle, thus potentially speeding up the inspection procedure. In order to develop such an inspection technique, however, detailed knowledge of wave propagation through the axle is required. Established mesh-based procedures, like the finite element method, could be used to simulate guided wave propagation in such structures. However, due to the size of the axle itself and the comparatively fine mesh that is dictated by the wavelengths usually applied in ultrasonic testing, these mesh-based procedures would be very expensive in terms of computation times. The multimodal approach seems to be a very promising alternative that can be expected to provide results significantly faster. The multimodal method uses the guided wave modes of a corresponding waveguide with a constant cross-section as basis in which the local sound field at any given position in a waveguide with varying thickness can be expressed. Thereby the numerical effort is reduced to solving the one dimensional differential equations that govern the evolution of the coefficients in the mode spectrum along the waveguide. Once the sound field has been calculated, a time dependence can easily be included, which allows the simulation of pulse propagation through the waveguide. In this thesis, the multimodal approach, as described for the calculation of Lamb-waves in plates with non-constant thickness, is extended to other types of elastic waveguides such as cylindrical rods and thick walled hollow cylinders. For the sake of simplicity, investigations are restricted to axially symmetric wave modes. The results obtained with the multimodal approach are validated against FEM-simulations. It is shown that the multimodal method potentially holds a great advantage in terms of computation time over commercially available software based on the finite element method. Finally, the multimodal method is evaluated with respect to possible future applications on wheelset-axles.