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The authors leverage full-field ultrasonic reflection matrices acquired from transducer arrays to map effective bulk wave velocities and local elastic moduli in heterogeneous polycrystalline materials. Resolving these constants non-destructively has historically been difficult due to severe phase aberrations and microstructural scattering. By optimizing an average point spread function derived from a focused reflection basis against a propagation model, the framework accurately reconstructs both longitudinal and shear velocities to map local Poisson's ratios and stiffness parameters.
Microstructural scattering noise can be directly inverted into a signal: projecting ultrasonic reflection matrices onto focused bases isolates point spread functions to map full elastic tensors non-destructively.
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.