Estimation of Stresses in a Plate with a Concentrator through Ultrasonic Measurements of Acoustic Anisotropy

Introduction . Acoustic anisotropy is measured during ultrasonic nondestructive testing. It estimates the magnitude of stresses by the acoustoelasticity method. The literature describes in detail the application of this approach in the case of a biaxial strength of extended structures: main pipelines, rail strings, steam generators, and others. They assume the presence of a uniform field with zero or weak gradients of stresses and deformations. However, the problem of timely detection and assessment of critical stresses caused by local concentrators through ultrasonic testing has not been solved. The presented material is intended to fill this gap. The work is aimed at determining the possibilities of the acoustoelasticity method to estimate the difference in the main biaxial stresses around the concentrator — a circular cutout in a rectangular plate. Materials and Methods . A 510×120×15 mm plate with a central hole of 40 mm in diameter was cut from a sheet of commercial-purity aluminum of the AMc brand (AW-3003 according to ISO) across the rolling direction, and subjected to uniaxial step loading in an Instron-8850 testing machine. For ultrasonic measurements, an acoustic sensor with a carrier frequency of 5 MHz was used. The stresses were calculated by solving the problem of stretching an isotropic linear-elastic plate in the ANSYS finite element modeling package and by the relations of the plane Kirsch problem obtained in the polar coordinate system. Results . The research allows us to state that the results of analytical and numerical calculations largely coincide only for points located near the zone of greatest stress concentration. In all other cases, the indicators differ several times in sign and modulus. The difference is explained by the fact that Kirsch's approach assumes the action of compressive stresses in the area of location of some points, but this factor is absent if we are talking about a real plate. It has been established that in the area of material with predominant tensile stresses, the acoustoelasticity method allows for a quantitative estimate of their difference with an error not exceeding the engineering one. Calculations based on the Kirsch relations correlate with the others only at points with the maximum concentration of tensile stresses. Discussion and Conclusion . The results of the study provide applying the acoustoelasticity method to estimate the magnitude of tensile biaxial stresses in the area around the fabrication holes. They are consistent with well-known scientific results and make it possible to rationally select the measurement points of acoustic anisotropy. The results of this scientific work can be applied in ultrasonic non-destructive testing using the acoustoelasticity method.