Diffuse ultrasonic backscatter in a two-dimensional domain

The scattering of elastic waves in polycrystalline materials is relevant for ultrasonic materials characterization and nondestructive evaluation (NDE). Diffuse ultrasonic backscatter measurements are used widely to extract the microstructural parameters such as grain size and also to detect flaws in materials. Accurate interpretation of experimental data requires robust scattering models. Line transducers are often used for ultrasonic experiments such that an appropriate model for these two-dimensional problems is needed. Here, a theoretical expression for the temporal diffuse backscatter is derived for such domains under a single-scattering assumption. The result is given in terms of transducer and microstructural parameters. In addition, the problem is examined in terms of numerical simulations using Voronoi polycrystals that are discretized using finite elements in a plane-strain formulation. The material properties of the individual Voronoi cells are chosen according to appropriate material distributions. Such numerical models also allow scattering theories, including the one discussed here, to be examined for well-controlled microstructures. Example numerical results for materials with varying degrees of scattering that are of common interest are presented. The numerical results are compared with the theory developed with good agreement. These results are anticipated to impact ultrasonic NDE of polycrystalline media.