For ultrasonic imaging closed cracks, unable by traditional ultrasonic techniques, the subharmonic phased array for crack evaluation (SPACE) has been developed. However, a simulation model for optimizing inspection conditions and for scientific understanding of subharmonic waves is required. In this paper, by extending the finite-difference time-domain (FDTD) model with damped double nodes (DDNs) to realistic testing conditions and comparing the simulation with the experiment, the availability of this model is demonstrated.
To model a compact tension specimen with a fatigue crack extended from a notch, the DDN model was extended to the vertical closed crack mode. When the tensile stress of incident ultrasonic wave at the closed crack is larger than the compression residual stress Tth at the crack, the crack changes to the open state with particle velocity nodes separated to dual nodes. Moreover, to suppress the numerical noise due to the contact vibration, the damping term is introduced.
In the experiment with small amplitude incident waves, only the notch response was observed, whereas in the experiment with large amplitude incident waves, the crack response was observed. The latter behavior was reproduced by the simulation when the tensile stress of the incident wave was larger than Tth. The experimental image of the crack tip obtained by the SPACE was also reproduced by the simulation, indicating the usefulness of the DDN model.
Moreover, in both experiment and simulation, a scattered wave was observed at the crack face between the crack tip and the notch in the subharmonic images. Since only “reflection” takes place on a crack face with no singularity, whereas “scattering” takes place at a crack tip with singularity, the scattering at a crack face with no singularity is surprising. Therefore, we examined the cause of this phenomenon and found that the crack was continuously opened until the crack closure point (CCP) where the tensile stress of incident wave became less than Tth. The scattered wave was generated at the CCP as a new singularity formed at the crack face. This is a novel finding and will be useful in evaluation of local compression residual stress at cracks, which plays important role in prediction of lifetime of structures.