Determination of elastic constants in complex-shaped materials through vibration-mode-pattern-matching-assisted resonant ultrasound spectroscopy

Abstract

The rapid advances in the additive manufacturing technology has led to the emergence of structural materials with arbitrary geometries that were previously challenging to produce using conventional machining techniques. Elastic constants are key mechanical parameters in structural material design; however, their accurate determination becomes challenging when dealing with materials possessing intricate geometries, which make traditional mechanical testing methods less practical. In this study, we accurately determined the elastic constants of a cuboid-shaped SUS304 specimen by combining resonant ultrasonic spectroscopy with the vibration-pattern-pairing method. The proposed method was then applied to a truss-shaped SUS304 specimen. To ensure the consistency of vibration modes, vibration patterns were matched by assessing the cosine similarity between contour plots, which depict the vibration patterns obtained from each of the three planes of the experimental specimen and those generated from a finite element model based on their color map. The measured elastic constants of the truss-shaped specimen were in reasonable agreement with those of the cuboid-shaped specimen and those obtained from tensile tests conducted on specimens obtained from an SUS304 block—the source material for the cuboid- and truss-shaped specimens. The optimization process for the elastic constants exhibited reproducibility, highlighting the efficacy of our approach for quantifying the elastic constants of materials with arbitrary geometries. The proposed method can assist material designers in accurately and efficiently determining the elastic constants of materials with intricate three-dimensional geometries and mechanical anisotropy.