·Table of Contents ·Materials Characterization and testing | Contactless monitoring of Surface-Wave Attenuation and Nonlinearity for Evaluating Remaining Life of Fatigued SteelsHirotsugu Ogi, Yoshikiyo Minami, Shinji Aoki, and Masahiko HiraoGraduate School of Engineering Science, Osaka University Machikaneyama 1-3, Toyonaka, Osaka 560-8531, Japan Contact |
Fig 1: Magnetostrictively coupled EMAT for axial shear wave and measurement setup of the four-point bending fatigu test. |
The meander-line coil was wrapped around the minimum diameter of the specimen. The axial length was 20 mm. The meander-line spacing was 0.9 mm. We rotated the specimen at 240 rpm (4 Hz). The bias field was fixed to 1.4x10^{4} A/m. Four-point bending configuration produced bending stresses at the measuring portion, which were 280 MPa for the 0.25%C steel, and 357 MPa and 382 MPa for the 0.35%C steel. We measured the ultrasonic characteristics by interrupting the rotation and releasing the stresses. Then, we restarted fatiguing. We repeated this process until failure occurred.
Driving the meander-line coil with long tone bursts causes interference among the axial shear waves traveling around the surface. By sweeping the frequency, we find the resonance frequencies, at which all the waves overlap coherently to produce large amplitudes. We used the first resonance mode, whose amplitude shows the maximum at the surface and rapidly decays inward; the penetration depth is estimated within 0.5 mm [5]. We determined the resonance frequency by fitting a Lorentzian function to the measured spectrum and the attenuation coefficient by fitting an exponential function to the free-decay amplitude at the resonance. Details for obtaining these linear ultrasonic characteristics appear in references 3 and 5.
Concerning the nonlinearity, we propose a new method. First, we measured the resonance frequency by sweeping the burst frequency and measuring the received signal amplitude of the same frequency component as the bursts. We defined the maximum amplitude as the fundamental component A_{1}. Then, we excited the axial shear wave by driving the meander-line coil with a half frequency of the resonance frequency. In this case, the fundamental component of the axial shear wave fails to cause a resonance. However, the second-harmonic component satisfies the resonance condition and the power spectrum of the received signal involves an amplitude peak at the original resonance frequency. We defined the peak amplitude as the second-harmonic component A_{2}. Careful investigation of thus determined A_{1} and A_{2} revealed that their ratio can express the ratio between the usual fundamental and second-harmonic components [6].
Fig 2: Evolutions of (a) the phase velocity and attenuation coefficient, (b) the nonlinearity, and (c) surface cracks with progress of the fatigue test for 0.25%C steel. Bending stress was 280 MPa and the cycle number of failure N_{f} was 56,000. |
Fig 3: Relationship between cycles to failure N_{f} and the cycles at which the attenuation peak and the nonlinearity peak appear. |
Velocity and attenuation
Because cracks cause failure, one may attribute the velocity and attenuation evolutions to crack growth. However, the crack evolution in Fig. 2 (c) fails to explain the attenuation decrease after taking the maximum, because the crack evolution would have caused monotonous attenuation increase throughout the life. The velocity increase (or pause) at the attenuation peak also denies crack's dominant contribution. We consider dislocation damping as a major factor that can cause such a complicated change in the ultrasonic property. According to the string model of vibrating dislocations [4], a increases and v decreases with the increase of free dislocations, which can vibrate responding to the acoustic wave. Dislocations multiply from the beginning of fatigue until failure. Since they pile up to obstacles and tangle each other, they become less mobile and the free dislocations decrease as the fatigue progresses. The increase of the dislocation density and decrease of the dislocation mobility balance and keep the attenuation coefficient unchanged for a long time. But, cracks coalesce at the later stages, which produces high stress region around the crack tips, where the rearrangement of dislocation structure, the release of the piling dislocations from obstacles, and dislocation multiplication occur. This event will be sufficient to raise the attenuation coefficient several times as large as the initial value. The attenuation coefficient, however, decreases soon because of the dislocation tangling and piling up again. The velocity change is also understandable with this process. Thus, we attribute the attenuation peak to the rapid dislocation-structure change caused by the crack growth into inside of the material. We have reported more detailed discussions of the crack-dislocation interaction to give rise to the attenuation peak using 0.45%C steel and aluminum alloy in reference 5.
Nonlinearity
We consider that the second (later) nonlinear peak is also caused by the crack-dislocation evolution as described above, because it appears at the same lifetime fraction with the attenuation peak. The free dislocations can increase the nonlinearity with the similar way as the attenuation case [7]. Concerning the first (earlier) peak, we adopt the crack-closure behavior responding to the ultrasonic stress wave [8] for interpretation. With the compressive stress, the crack becomes tightly closed and the local modulus approaches that of the matrix. With the tension stress, the crack fully opens to decrease the local modulus. Thus, this crack-closure behavior produces the nonlinearity. Indeed, the crack density in Fig. 2 (c) well corresponds to the nonlinearity change before the peak. Because the sensitivity of the nonlinearity to such a behavior depends on the crack size and the number of cracks in the shear-wave penetration region, the nonlinearity shows an maximum with the progress of fatigue. (The resulting nonlinearity will vanish for the large (or entirely open) cracks.)
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