Chapter 7 A Novel Acoustoelastic-Based Technique for Stress Measurement in Structural Components Mohammad I. Albakri and Pablo A. Tarazaga Abstract The acoustoelastic theory has been widely utilized for nondestructive stress measurement in structural components. Most of the currently available techniques operate at the high-frequency, weakly-dispersive portions of the dispersion curves, and rely on time-of-flight measurements to quantify the effects of stress state on wave speed. This adversely affects the sensitivity and accuracy of such techniques, and renders their accuracy limited by the precision within which time-offlight can be determined. In this work, a novel acoustoelastic-based stress measurement technique is developed by combining dispersion compensation algorithms and numerical optimization schemes. Dispersion compensation allows the use of highly-stresssensitive, low-frequency flexural waves for stress measurement, which in turn enhances the sensitivity of the developed technique. The need for accurate time-of-flight measurements is eliminated in this work by analyzing the entire propagated waveform to reconstruct the dispersion curve over the frequency range of interest. The fact that an entire section of the dispersion curve, as opposed to a single wave speed measurement, is used to calculate the state of stress in the structure enhances the technique’s accuracy and robustness. A criterion for optimal selection of excitation waveform is developed in this work. The effects of material properties uncertainties on the accuracy of stress measurements are also investigated. Keywords Acoustoelasticity • Dispersion compensation • Stress measurement • Reflections • Optimization 7.1 Introduction All structural elements and mechanical components are subjected to internal stresses. Such stresses arise from external loads acting upon the structure, or induced by changes in operation and environmental conditions such as temperature and humidity. Manufacturing processes, such as casting, rolling, and forming, also result in non-uniformly distributed residual stresses in the manufactured parts [1]. Nondestructive, nonintrusive, and accurate solution for measuring the state of stress in structural and mechanical components is of significant importance for structural health monitoring and remaining life predictions. Several theories and techniques have been developed over the last few decades to tackle the problem of stress state measurement, many of them are destructive in nature. Nondestructive techniques, on the other hand, exploit the dependence of mechanical, acoustic, electrical, and magnetic characteristics of the material on the state of stress [2–4]. One particular theory that attracted most of the attention is the acoustoelastic theory; the dependence of propagating waves characteristics on the state of stress [5–9]. Acoustoelastic-based methods involve introducing a low energy, high frequency stress wave in the material and analyzing its propagation and reflections to evaluate the state of stress in the structure. It has been established that dispersion relations depend on the initial state of stress in the structure. For a plane wave propagating in a plate under biaxial stress, in a direction that makes an angle ™ with the 11 direction, the change in ultrasonic plane wave velocity with the application of stress can be expressed as [1]: Cp . / C0 p . / D.K1 11 CK2 22/cos 2 . / C.K3 11 CK4 22/sin 2 . /; (7.1) where Cp is the change in phase velocity due to the application of stress, C0 p is the stress-free phase velocity, is the direction of wave propagation in the principal coordinate system, 11 and 22 are the principal stresses, and the constants M.I. Albakri ( ) • P.A. Tarazaga Vibration, Adaptive Structures and Testing Laboratory, Virginia Tech, 635 Prices Fork Road, Blacksburg, VA 24061, USA e-mail: malbakri@vt.edu © The Society for Experimental Mechanics, Inc. 2016 S. Pakzad, C. Juan (eds.), Dynamics of Civil Structures, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series, DOI 10.1007/978-3-319-29751-4_7 49
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