Nonlinear Guided Waves for Thermal Stress Measurement in Constrained Solids

Abstract

Nonlinear guided waves have drawn considerable interest in the last few decades for interrogating long waveguide-like structures as they efficiently combine high sensitivity to peculiar structural conditions, typical of nonlinear parameters, with large inspection ranges, characteristic of wave propagation in confined media. Their mathematical treatment, however, becomes extremely challenging when characterized to waveguides that are complex in either material and/or geometry. Therefore the successful use of nonlinear guided waves as a structural diagnostic tool is not always a trivial task. The classical mathematical framework governing nonlinear wave propagation in solids relies on finite strain theory. The present work presents a constitutive model to expand the topic of nonlinear wave propagation to the case solid under constrained thermal expansion. The origin of nonlinear effects in this case is explained on the basis of the anharmonicity of interatomic potentials, and the absorption of the potential energy corresponding to the (prevented) thermal expansion. Such “residual†energy is, at least, cubic as a function of strain, hence leading to a nonlinear wave equation and higher-harmonic generation. The model predicts a decrease in longitudinal wave speed and a corresponding increase in nonlinear parameter with increasing temperature, as a result of the thermal stresses caused by the prevented thermal expansion of the solid. This theoretical framework is applied for the prediction of thermal stresses in Continuous-Welded Rail (CWR). The almost total absence of joints makes these structures prone to breakage in cold weather and, more importantly, buckling in hot weather. Field tests were performed at the Transportation Technology Center (TTC) in Pueblo, CO. The collected results suggest the potential of the proposed nonlinear ultrasonic measurement technique to quantify thermal stresses from prevented thermal expansion and prevent catastrophic failures for buckling-prone structures.