Counter-directional mixing of longitudinal guided waves for fatigue damage detection in pipes

Accurate detection and localization of fatigue damage in pipes are essential for ensuring safety and reliability. Nonlinear ultrasonic guided waves offer significant advantages for material damage detection owing to their high sensitivity to microstructural evolution. Combined harmonics generated from the counter-directional mixing of guided waves are expected to guarantee a high spatial resolution in identifying multiple damage zones in pipes due to the limited interaction zone, which have been rarely reported. This study investigates the combined harmonic generation, spatial localization and discrimination of fatigue damage zones through physical analysis, numerical simulations and experimental measurements on the counter-directional mixing of two axisymmetric longitudinal guided waves in pipes. The physical mechanisms underlying counter-directional mixing and combined harmonic generation were first examined based on resonance conditions obtained from theoretical analysis. Obvious resonance phenomena of the selected mode triplet were observed in simulations and experiments. For both the cases with the damage zone longer or shorter than the wave mixing zone, fatigue damage was accurately localized with the peak nonlinearity parameter occurring at its center. Moreover, high spatial resolution was achieved in distinguishing two fatigue damage zones by optimizing the number of wave cycles in the primary waves. The findings of this study pave the way for damage detection and localization in pipes by counter-directional wave mixing in the field of nondestructive evaluation and structural health monitoring.