To realize the high selectivity of closed cracks, we propose a fundamental wave amplitude difference (FAD) method based on the threshold behavior of fundamental waves caused by the contact vibration of closed cracks. This is realized by the subtraction of a fundamental array (FA) image at a small input amplitude multiplied by the amplification factor from that at a large input amplitude. The formulation clarified that FAD can selectively image closed cracks while eliminating other linear scatterers, which cannot be completely eliminated by the subharmonic wave amplitude difference (SAD) method. Furthermore, FAD was experimentally verified in a closed fatigue crack specimen using the closed-crack-imaging method of subharmonic phased array for crack evaluation (SPACE). Thus, we demonstrated that FAD is useful for achieving the higher selectivity of closed cracks against other linear scatterers than previous amplitude difference methods without filtering out the subharmonic or superharmonic waves.

To solve the underestimation of closed-crack depth, we have developed an imaging method, subharmonic phased array for crack evaluation (SPACE). However, a single-array SPACE can image only the vicinity of a transmission focal point (TFP) when the TFP is fixed. In this study, we have developed a confocal SPACE that defines multiple TFPs for imaging closed cracks over a wide area. We demonstrated its usefulness by measuring a stress corrosion crack (SCC). Moreover, we proposed a radarlike display that shows single-focus images with a line indicating the incident direction. By applying it to the SCC specimen, a moving crack response (MCR) was observed with varying incident angles. To analyze this behavior, we performed a simulation using a finite-difference time-domain (FDTD) method with a damped double node (DDN) model. Furthermore, we examined the ratio of the subharmonic to fundamental responses depending on the stress ratio between input wave stress and crack closure stress (σ c ).

Crack closure stress (CCS) is an important parameter that affects crack propagation rate. However, the method for measuring CCS in practical fields has yet to be developed. In this study, we propose a practical method of estimating CCS. In our experiment, a closed fatigue crack was imaged by a linear phased array (PA) method during crack opening by global preheating and local cooling (GPLC). Here, we assumed that the crack appears in PA images after the thermal stress induced by GPLC exceeds CCS. Therefore, we calculated the thermal stress induced by GPLC using an analytical solution and thereby estimated CCS. Then, to validate the CCS estimation method, we simulated the PA images by a finite difference time domain (FDTD) method with a damped double node (DDN) model, where CCS was relieved by the calculated thermal stress. Consequently, the temporal variation in crack depth observed in the PA image was successfully reproduced in the simulation. Thus, the CCS estimation method was verified by comparing experimental results with analysis results.

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 T th 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 T th . 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 T th . 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.