Influence of residual stress on the free vibrations of an elastic solid; application to resonant ultrasound spectroscopy (RUS)

Abstract

Resonant ultrasound spectroscopy (RUS) is a standard technique for experimentally measuring the elastic constants of anisotropic elastic materials. Traditionally, the influence of internal or residual stresses on the measurement of elastic constants is not taken into consideration. However, it is well-known that residual stress can impart a small variation in the phase velocity of ultrasonic bulk waves, which is known as the acoustoelastic effect. Thus, it is plausible that residual stress will influence the resonances of samples measured during RUS. In this presentation, the elastodynamic theory for describing free vibrations is reformulated by using a stress-dependent constitutive relationship. The model culminates in an eigenvalue problem with a stiffness matrix being dependent on the spatially varying residual stress field within the domain of the sample. The model is evaluated by considering a realistic residual stress distribution. Results show the degree at which frequencies of resonance depend on the residual stress. While accounting for residual stress is expected to improve the estimates of elastic constants, there is also potential to use RUS as a tool to assess and characterize the residual stress present in samples.