Finite element prediction of acoustoelastic effect associated with Lamb wave propagation in pre-stressed plates

Abstract

The paper presents outcomes of a finite element (FE) study of acoustoelastic effect associated with Lamb wave propagation in plates subjected to homogeneous bi-axial and bending stresses.In particular, the change of the phase velocity of the fundamental Lamb wave modes is obtained for different stress levels, bi-axial stress ratios and wave propagation angles. A comparison of the obtained numerical results with an analytical solution demonstrates a very good agreement.Moreover, the influence of bending stress on the wave velocities and wave front profile is further investigated numerically. There are currently no analytical results for this case. The developed and validated FE modelling approach can help to address several issues in the current non-destructive inspections including: in the investigation of changing stress conditions on the defect detection as well as in an adaptation of the existing Lamb wave-based defect evaluation systems to monitoring of stress too. The latter may have many benefits from sharing the same hardware for the purpose of maintaining structural integrity of thin-walled structural components. . Acoustoelastic effect of Lamb wave propagationAcoustoelastic effect is defined as the effect of the applied stress on the wave propagation in a media. It has been studied since the development of the finite deformation theory by Murnaghan [40], who formulated the material nonlinearity using third order elastic constants. Some pioneering studies in this area include the research of Hughes and Kelly [41], who derived equations relating the wave velocity to the applied stress and experimentally measured the acoustoelastic effect. Another experimental study of Egle and Bray [42] demonstrated how to obtain higher-order elastic constants from experiments with bulk waves. In the literature, many developments and studies in the acoustoelasticity mainly focused on and utilised bulk waves (Pau and Scalea [43]). The acoustoelastic effect is usually quantified = (20) So, equation (19), with the energy function presented in equation (16) can be translated to, ¬ = J -. © © = J -. © © © = J -. %)( ) % ©where T is the second Piola-Kirchhoff (PK2) stress. The stress in VUMAT must be updated with the equation at the end ( + ∆ ) of an integration step and stored in stressNew(i), based on the values of F and U given in the subroutine at the end of previous step ( ). Numerical Case Studies 3D Finite Element ModelA 3D FE model of a 6061-T6 aluminium plate was developed with ABAQUS software and the wave propagation problem was solved by the explicit integration approach [49]. The materialproperties of the 6061-T6 aluminium are listed in Table 1. The thickness of the plate is 3.2mm and the in-plane dimension is 240mm×240mm. The element type used in the model is the 8-

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