The Effects of Breathing Behaviour on Crack Growth of a Vibrating Beam

Abstract

The effects of breathing behaviour on the dynamic response and crack growth are studied through a cracked cantilever beam. The main goal is to reveal the coupling mechanism of dynamic response and crack growth by employing a plain single-degree-of-freedom (SDOF) lumped system with the breathing crack stiffness and friction damping. The friction damping loss factor is derived by using Coulomb friction model and energy principle. Natural frequency, dynamic stress, dynamic stress intensity factor (DSIF), and crack growth are analyzed by case studies in the end. Results indicate that not only does the stiffness oscillates during crack growth corresponding to the physically open and closed states of the crack, but also stiffness and friction damping oscillate nonlinearly with crack growth. This behaviour induces not only nonlinear dynamic response but also nonlinear crack growth. It provides an approximate description of the nonlinearities introduced by the presence of a breathing crack. Therefore, it can be employed to improve the prediction precision of the crack identification and crack growth life of a cracked cantilever beam.