The influence of stress state multiaxiality on the propagation velocity of Rayleigh waves is explored through a detailed numerical study. The study uses the Murnaghan model to capture nonlinear elastodynamics in the material behavior, necessitating consideration of third-order elastic constants. Various invariant stress variables are compared for their suitability to describe the relationship between multiaxiality of the stress state and change in propagation velocity. The results are interpreted physically and provide information about the interaction between stress state multiaxiality and wave propagation. Finite element simulations are conducted using Abaqus/Explicit, with the material behavior implemented via a VUMAT user subroutine. Transformation relations for rotated axes are used to understand how the stress state affects the directional dependence of wave velocity. This study offers valuable insights into the complex relationship between stress state and Rayleigh wave propagation, essential for applications in reconstruction of residual stress fields. The results show that the change in propagation velocity is best described by models that include the principal stresses. Different stress states lead to different distortion of the propagation front. The numerical results are compared and validated with the semianalytical solution. The results show good agreement.

Residual stresses play a crucial role in the maintenance and longevity of engineering structures. However, continuous monitoring of these stresses remains a challenge due to cost, implementation complexity, and reliability concerns. The present contribution proposes a novel method for continuous long-term residual stress monitoring by tracking the effect of residual stress changes on the propagation velocity of surface acoustic waves (SAWs) due to the acoustoelastic effect via a fixed setup of piezoelectric patch transducers (PETs). The applicability of patch transducers to stress measurement using SAW was experimentally validated using tensile and bending tests on 25CrMo4 (1.7218) steel specimens. The tensile tests exhibited a consistent decrease in wave velocity with increasing stress, enabling straightforward determination of the acoustoelastic coefficient (AEC). The bending tests confirmed the method’s applicability, highlighting the need for multiple excitation frequencies to improve reliability and detect inconsistencies. Finally, it is briefly outlined how to separate residual and load stresses during long-term measurements. The results demonstrate that this approach provides a cost-effective solution for continuous monitoring of residual stresses in metallic materials, offering potential applications in structural health monitoring and predictive maintenance.