Finite element modeling of ultrasonic wave propagation with application to acoustic microscopy

摘要

The development of NDE techniques and the accurate interpretation of measurement signals require a firm understanding of the physical process of energy/defect interactions. This in turn demands an accurate model for the propagation of ultrasonic waves in acoustic and elastic media. Analytical approaches are restricted due to the arbitrary geometries of the discontinuities involved. In this work, a comprehensive numerical model based on the finite element method is developed to simulate ultrasonic wave propagation in ultrasonic NDE systems with emphasis on application to acoustic microscopy;Starting from the governing equations of dynamic elasticity, semi-discretized finite element equations in the space domain are derived according to the variational principle. Direct time integration is carried out through the explicit central difference scheme. Both linear and quadratic elements are implemented with comparison and verifications. Material properties, including anisotrophy, inhomogeneity, viscous damping and arbitrary discontinuities are handled successfully by the model. For ultrasonic systems containing a fluid/solid interface, the governing equations for both the solid and fluid media have to be solved simultaneously with the interfacing boundary conditions properly satisfied. In this case the solid and fluid media are formulated by the displacement vector and pressure scalar respectively. The coefficient matrices are rendered symmetric by introducing a new potential variable for the fluid medium;The transient fields of pulsed transducers in solids and their interaction with flaws are treated in detail. The fields of spherically focused transducers and time-delay arrays are examined. The wave field profiles are compared with those obtained by the classical impulse response method and good agreement is achieved. As an integral part of acoustic microscopy, the visualization of propagation properties of transient leaky Rayleigh waves is also presented. Wave propagation in an acoustic lens and focused waves probing a fluid/solid and solid/solid interfaces as situations in acoustic microscopy are characterized. The finite element model proves to be an effective tool for acoustic device design and ultrasonic NDE.