# Stress Estimation Using the Acoustoelastic Effect of Surface Waves in Weak Anisotropic Materials
## 1 Introduction
Additionally, it is necessary to know the direction of anisotropy in advance, which leads to an inconvenient step of measuring the shear wave velocity in many different polarization directions. In this study, we propose a simpler and more practical method for estimating surface stress using the acoustoelastic effect of surface waves in a plate that has orthogonal anisotropy on its surface. In the proposed method, we modified the isotropic theory, in which the rate of change of surface wave velocity according to the stress is expressed using two acoustoelastic coefficients, two principal stresses and the angle between the principal stress and the wave propagation direction. The difference between the proposed method and isotropic theory is that in isotropic theory, the surface wave velocity at the unstressed state is constant regardless of the propagation direction, while in the proposed method it is dependent on the propagation direction due to anisotropy. Proposed method can estimate not only magnitude but also direction of principal stress by measuring the rate of change of the surface wave velocity in any three directions before and after stress is applied, which does not require any information of stress direction in advance. The requirement to measure the initial surface wave velocities in three directions before stress is applied also will not be a problem at all in the comparison of the stress states before and after the machining such as punching or bending. Furthermore, this method is very simple and practical compared to the previous methods of [PERSON] et al. [8] and [PERSON] et al. [10]. Since there is no need to pre-measure the directional elasticity of the material, or pre-check the direction of anisotropy. In addition, this approach requires measuring only the surface wave velocities in any three directions before and after the stress is applied. For verification of the proposed method, numerical simulations were performed. For the simulation, we generated the surface wave velocity data with respect to the propagation direction using [PERSON]'s model for several typical cases when both anisotropy and stress exist. We then analyzed the error that occurs when the stress is estimated by the proposed method using this data. In the simulation, three different combinations of the anisotropy direction, principal stress direction and measurement direction, and two different stress states, uniaxial stress and biaxial stress, were evaluated. To verify the proposed method experimentally, stresses applied by a tensile testing machine were estimated by measuring the surface wave velocities in three directions. The experiments were carried out for two types of aluminum plates, one nearly isotropic and one with relatively greater anisotropy. Two specimens were prepared for each type where one was used for the measurement of the acoustoelastic coefficients and the other was used for stress estimation. Stress up to 90 MPa was applied and the performance of stress estimation was verified by comparing the estimated stress with the applied stress.