Fatigue damage evaluation of metallic components based on the maximum Lyapunov exponent of modified Duffing system

Abstract

Because the Duffing equation is very sensitive to weak signals and noise immunity, the modified Duffing detection system is applied to detect the weak nonlinear signal in nonlinear ultrasonic experiment. Firstly, the Duffing equation is improved to construct detection models to detect the nonlinear ultrasonic signal wave mixing in experiment. Then, the maximum Lyapunov exponent of detection model with state change is calculated to evaluate the fatigue damage. When the collected nonlinear receiving signal in wave mixing experiment is substituted into four detection models, if the phase portraits of Duffing equation changes from the chaotic state into periodic state, the difference frequency signal at 3 MHz can be detected and this states the specimen has fatigue damage. In addition, the maximum Lyapunov exponent of detection model with state change is calculated and less than 0. The damage index is induced and it has a good corresponding relation with fatigue damage of metallic specimen, which the correspondence would be used to quantitatively evaluate the fatigue damage of specimen within a certain range. Therefore this research work is beneficial to extract the weak nonlinear signals for fatigue damage evaluation of metallic components.