An ultrasonic measurement of stress in steel without calibration: the angled shear wave identity

TL;DR

This paper introduces a calibration-free ultrasonic technique to measure in-plane stress in steel and similar materials by analyzing the speeds of two angled shear waves, validated through simulations.

Contribution

The authors develop a simple, in situ ultrasonic method that does not require prior knowledge of material constants for stress measurement in hard solids.

Findings

Achieves approximately 1% accuracy in stress estimation

Works without calibration or material constants

Validated through finite element simulations

Abstract

Measuring stress levels in loaded structures is crucial to assess and monitor their health, and to predict the length of their remaining structural life. However, measuring stress non-destructively has proved quite challenging. Many ultrasonic methods are able to accurately predict in-plane stresses in a controlled laboratory environment, but struggle to be robust outside, in a real world setting. That is because they rely either on knowing beforehand the material constants (which are difficult to acquire) or they require significant calibration for each specimen. Here we present a simple ultrasonic method to evaluate the in-plane stress in situ directly, without knowing any material constants. This method only requires measuring the speed of two angled shear waves. It is based on a formula which is exact for incompressible solids, such as soft gels or tissues, and is approximately true for compressible "hard" solids, such as steel and other metals. We validate the formula against virtual experiments using Finite Element simulations, and find it displays excellent accuracy, with a small error of the order of 1%.