Reference-free absolute strain estimation using longitudinal waves and relative strain measurements

Abstract

The absolute strain, which is the total strain experienced by a structure when the loading increases from zero to the current loading level, is an important physical quantity for evaluating the integrity of a structural component. To measure the absolute strain, a strain sensor, such as a strain gauge or fiber Bragg grating, must be installed at a target structure when no loading or strain is present. Subsequently, loading is applied, and the absolute strain can be measured from the variation in the strain sensor reading. However, measuring absolute strain is difficult because the strain sensors are not installed on most in-service structures before any loading is applied or any strain occurs. In this study, a reference-free absolute strain estimation technique is developed based on the acoustoelastic effect of longitudinal waves. First, the relationship between the absolute strain and longitudinal wave velocity is explicitly derived. Subsequently, the absolute strain is estimated based on the linear relationship between the absolute strain and the velocity ratio of the longitudinal wave propagating in the loading direction to that propagating in the transverse direction. The uniqueness of the developed technique includes (1) a theoretical derivation of the linear relationship between the absolute strain and the velocity ratio of longitudinal waves propagating in parallel and perpendicular directions of uniaxial loading, (2) absolute strain estimation without any prior sensor installation or any absolute strain measurement at a known loading level, and (3) automated temperature compensation for in-service structures without any temperature measurement. The performance of the developed technique is experimentally evaluated using an aluminum plate and steel rod specimens. The evaluation results show that the developed technique estimates absolute strain within an 8.8% maximum relative error and a 6.1% normalized root-mean-square error.