An ultrasonic guided wave method to estimate applied biaxial loads

Abstract

Guided waves propagating in a homogeneous plate are known to be sensitive to both temperature changes and applied stress variations. Here we consider the inverse problem of recovering homogeneous biaxial stresses from measured changes in phase velocity at multiple propagation directions using a single mode at a specific frequency. Although there is no closed form solution relating phase velocity changes to applied stresses, prior results indicate that phase velocity changes can be closely approximated by a sinusoidal function with respect to angle of propagation. Here it is shown that all sinusoidal coefficients can be estimated from a single uniaxial loading experiment. The general biaxial inverse problem can thus be solved by fitting an appropriate sinusoid to measured phase velocity changes versus propagation angle, and relating the coefficients to the unknown stresses. The phase velocity data are obtained from direct arrivals between guided wave transducers whose direct paths of propagation are oriented at different angles. This method is applied and verified using sparse array data recorded during a fatigue test. The additional complication of the resulting fatigue cracks interfering with some of the direct arrivals is addressed via proper selection of transducer pairs. Results show that applied stresses can be successfully recovered from the measured changes in guided wave signals.