Evaluation of effective wave velocities in polycrystalline materials using the ultrasonic reflection matrix
In-depth characterization of heterogeneous materials has long been a challenge in non-destructive testing. Here, a method is proposed to determine the elastic constants of metallic polycrystalline materials using back-scattered ultrasound. The waves scattered by the microstructure are analyzed to image the effective bulk velocities. To this end, a reflection matrix is acquired with an array of transducers. The projection of this matrix onto a focused basis is used to estimate an average point spread function. Optimizing this function with respect to the propagation model leads to an estimation of the longitudinal velocity. Additional treatments are developed to adapt the method to map the shear wave velocity. The local Poisson's ratio is then deduced from the ratio between those two velocities. Young's modulus and shear modulus can also be obtained assuming known densities. This matrix approach is experimentally validated on different polycrystalline materials. A sample displaying heterogeneous mechanical properties is then simulated to assess the accuracy and the resolution of the method. Its strengths and limitations are discussed, demonstrating its potential for quantitative non-destructive material characterization.