Quantitative evaluation of defects in anisotropic media using the far-field radiation characteristics of vibrating sources

Understanding the nature of wave radiation and propagation within anisotropic materials, such as fiber-reinforced composites, columnar-grained weld structures and certain ceramic materials, is an essential step in the development of efficient NDE techniques. However, many models require extensive computational efforts due to the increasing complexity of analytical expressions and to numerical difficulties. Also, relationships which would allow to exploit analogies to the isotropic material case are generally not available. In this contribution, explicit far-field formulations for wavefields generated by vibrating planar sources are presented, applicable to both transducer radiation and wave scattering at defects. Integral equations for circular and rectangular sources are solved using a far-field approximation. For the propagating bulk waves with single-valued group velocities, expressions are obtained similar to the isotropic case and validated via comparison with exact calculations using point source superposition. On this basis, the scattering behavior of globular and crack-like defects is examined using explicit expressions for pulse-echo amplitude locus curves. Quantitative defect evaluation, where - in addition to the times-of-flight and the maximum amplitudes - the dynamic behavior of the flaw signal is used, is performed in the following way: first, spherical and disk-shaped defects are discriminated with the help of their isolated directivities, then the amplitude locus curves are inverted to yield the respective defect dimensions. This procedure is illustrated using simulated as well as experimental data for a unidirectional composite material.