Understanding effective elastic constants and elastic symmetry in RUS: From single crystals to textured polycrystals

Resonant Ultrasound Spectroscopy (RUS) is an inverse method used to characterize elastic constants of a sample based on its acoustic or elastic resonance spectrum. Its main stages are the measurement of the resonance frequencies, the choice of a forward model, assuming well-known geometrical properties and uniform density, and an inverse problem methodology that yields material elastic properties. In the forward model, one must assume a certain elastic symmetry class, which represents the symmetry of the sample and defines the number of unknown elastic constants solved for in the inverse problems. We have found that this choice of sample elastic symmetry, and the associated parametrization by elastic constants and Euler angles, is almost always not discussed and sometimes not well understood by practitioners. We find the situation is particularly confusing for textured samples: exactly what elastic constants does RUS determine in that case? In this paper, we aim at clarifying the elastic symmetry choice in the context of polycrystal texture characterization, which has already seen many contributions using RUS. We illustrate this with texture simulations carried out with MTEX to practically show how different textures can lead to elastic symmetries that range from isotropic to triclinic. Finally, we discuss experimental inversions on an additively manufactured 316 L sample under different sample symmetries assumptions and illustrate the aforementioned topic of choosing a symmetry. • Presentation of the fundamentals of the RUS inverse method and what the recovered elastic constants mean, in the case of single crystals as well as in the case of polycrystals. • We discuss the general choices in terms of elastic symmetry and then focus on polycrystals and how the notion of texture translates to the elastic constants using homogenization medols. • We provide results on simulated textures that illustrate how textures of different strengths materialize as different elastic symmetries. • Finally, we provide experimental results on a previously stainless steel polycrystal with a strong texture and use several RUS inverse models, from transverse isotropy to triclinic symmetry, to investigate the right way to model its texture, to which we compare EBSD data.