Ultrasonic determination of crystallographic texture by transmitted field fitting regardless of medium dispersivity

Abstract

The determination of crystallographic texture through elastic wave propagation offers a cost-effective, nondestructive means of obtaining through-thickness information with minimal sample preparation. Existing ultrasonic approaches rely on either bulk-wave or guided-wave velocity measurements for texture inversion. These strategies impose geometric constraints: bulk-wave methods become impractical for thin specimens, whereas guided-wave techniques are limited to relatively small thicknesses. Furthermore, many formulations assume orthotropic symmetry of the aggregate, thereby restricting their applicability to materials with higher anisotropy. In this work, a full-field wave fitting strategy is developed in which the transmitted ultrasonic field is simulated and directly compared to experimental measurements. Because the approach does not rely on bulk-wave or plate-wave approximations, it remains applicable across a broad range of specimen thicknesses. Furthermore, no macroscopic symmetry assumptions are imposed on the aggregate, enabling the characterization of generally anisotropic materials. The effective elastic response is computed using a Hashin-Shtrikman homogenization framework, which provides tighter bounds than classical Voigt-Reuss-Hill averages and constrains the admissible search space during optimization, thereby improving convergence. The nonlinear inverse problem is solved using a GPU-accelerated optimization scheme. The methodology is validated on materials with hexagonal and cubic crystal symmetry over a range of specimen thicknesses. The inferred texture coefficients show consistent agreement with independent diffraction measurements. Additionally, textures with weak elastic anisotropy are successfully recovered, demonstrating the robustness and versatility of the proposed method. Complete measurement and inversion are achieved within approximately 10 minutes.