Stress inversion in waveguides with arbitrary cross sections with acoustoelastic guided waves

Abstract

Acoustoelasticity or the change in elastic wave speeds with stress is promising for prestress measurements in waveguides. The theory of guided wave propagation in initially isotropic materials with arbitrary cross sections and under homogeneous biaxial stresses is developed using Semi-Analytical Finite Element (SAFE) modeling in this article. Based on the anisotropic effect induced by the applied biaxial load, an inversion method for biaxial force was developed. The acoustoelastic response for a particular mode and frequency is described by only two constants, which can be determined from known uniaxial loading experiments. The magnitude and direction of the biaxial force can be obtained by further coefficient fitting. Stress inversion can be obtained without considering the shape of the cross section and applies to multiple guided wave modes. The inversion has been verified by the results of SAFE and 3D Sweeping Frequency Finite Element Modeling (SFFEM) method, and the Mean Absolute Errors of stresses obtained by different methods are all within 1%. The 3D SFFEM was combined with the Matrix Pencil Method using the time domain information to extract the dispersion curve. Unlike previous finite element modeling, here the inheritance of the solution between the two solvers was set instead of approximating static load conditions by shortening the guided wave travel time. It guarantees the steady state of the force in the time-variant study, ensuring the high precision required for the study of the acoustoelastic effect.