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Contactless monitoring of Surface-Wave Attenuation and Nonlinearity for Evaluating Remaining Life of Fatigued Steels Hirotsugu Ogi, Yoshikiyo Minami, Shinji Aoki, and Masahiko Hirao Graduate School of Engineering Science, Osaka University Machikaneyama 1-3, Toyonaka, Osaka 560-8531, Japan Contact

ABSTRACT

Using surface-skimming shear wave, we studied microstructure evolution in carbon steels exposed to rotating bending fatigue. Specially developed electromagnetic acoustic transducer (EMAT), which operates through the magnetostriction mechanism, enabled us to make a contactless monitoring of the velocity, attenuation and the second-harmonic component of the axial-shear-wave resonance. We obtained the attenuation coefficient from the free-decay amplitude measurement at the resonance. For the nonlinearity, we established a new method relying on the resonance method. The attenuation coefficient always showed peaks before failure. The nonlinearity showed a maximum earlier than the attenuation peak. Observations of surface cracks along with the acoustic measurements indicate that the attenuation peak responds to change in the dislocation structure and the nonlinearity to crack initiation and growth.

INTRODUCTION

Extensive studies of ultrasonic characteristics appeared for nondestructive evaluation of materials degradation due to repeated application of stresses, or fatigue. They include two principal approaches; linear and nonlinear approaches. The former uses sound velocity and attenuation sensitivities to microstructure change. Many researchers reported that velocities decrease and attenuation increases monotonically with the progress of fatigue, responding to increases of dislocation density and crack [1]. The latter is also reported to increase monotonically, mainly responding to crack-closure behavior with passing ultrasonic stress waves [2]. In the present study, however, we found different behaviors of these ultrasonic characteristics. Attenuation shows sharp peaks before failure and the velocity temporarily increases (or pauses) at the attenuation peaks. The nonlinearity exhibits two peaks; the first appears earlier than the attenuation peak and the second just before failure. No study with contact methods reported these observations and, we believe, they are observable only with a contactless method.
For 0.25%C and 0.35%C commercial steels, we monitored the phase velocity, attenuation, and the nonlinearity of surface-skimming shear wave using electromagnetic acoustic resonance (EMAR) [3]. We developed a magnetostrictively coupled electromagnetic acoustic transducer (EMAT) for radiation and detection of an axial shear wave, which propagates in the circumferential direction with an axial polarization. We interpreted our results in terms of dislocation-damping theory [4] and the crack-closure behavior.

MATERIALS

We used commercial steel rods containing 0.25 and 0.35 mass percent carbon. We annealed them at 880 °C for one hour and cooled in air. Specimens were 600 mm long. The specimen diameter was 14 mm at the measuring portion; it continuously increased from 14 mm to 20 mm to cause failure at the minimum diameter. We electrically polished the measured surface before the fatigue test.

MEASUREMENTS

Figure 1 shows the measurement setup for the contactless monitoring of the ultrasonic characteristics. The EMAT consists of a solenoid coil to apply the bias magnetic field in the axial direction and a meander-line coil to induce the dynamic field in the circumferential directions. The total field oscillates about the axial direction at the same frequency as the driving currents and produces the shearing vibration through the magnetostrictive effect to result in the axial-shear-wave excitation. The meander-line then also receives the axial shear wave through the reversed magnetostrictive effect [5].

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 1.4x10⁴ 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 A₁. 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 A₂. Careful investigation of thus determined A₁ and A₂ revealed that their ratio can express the ratio between the usual fundamental and second-harmonic components [6].

RESULTS

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 Nf was 56,000.

Figures 2 (a) and (b) show typical changes of the phase velocity v, the attenuation coefficient a, and the nonlinearity A₂/A₁ for the first axial-shear-wave resonance. Significant observations were that the attenuation coefficient always showed two sharp peaks near 85% and 95% of lifetime, and the nonlinearity showed two broader peaks near 60% and 85%, being independent of the carbon content and the bending stress (Fig. 3). No peak appeared when the bending stress was too small to cause failure. The velocity linearly decreased from the beginning of fatigue and the decreasing rate became larger after the nonlinearity peak. Then, it temporarily increased or paused at the attenuation peaks.
We applied the replica method [5] to monitor surface cracks along with the ultrasonic measurements. Figure 2 (c) shows the result. We defined the crack density as the total crack length divided by the viewing area. Cracks were viewable with an optical microscope as early as at about 30% of lifetime. The crack density increased linearly, while the maximum length remained small until about 70%, and then the crack length rapidly increased for failure. This crack-growth behavior suggests that, at early stages, crack nucleation occurs and the crack density increases. After 70%, crack growth and coalesce are dominant to result in crack growth inward.
Figure 3 plots cycles to failure versus the cycles at the first attenuation peak and the first nonlinearity peak, which demonstrates a pronounced potential for evaluating the remaining life.

Fig 3: Relationship between cycles to failure Nf and the cycles at which the attenuation peak and the nonlinearity peak appear.

DISCUSSION

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.)

CONCLUSION

The linear and nonlinear approaches presented here demonstrated a capability of evaluating the microstructure change related to dislocations and cracks. The attenuation and nonlinearity peaks always appeared at the same fraction of lifetime. Monitoring these ultrasonic characteristics enables us to predict the remaining life of fatigued steels.

REFERENCE

1. W.J. Bratina, in Physical Acoustics IIIA, W. P. Mason, ed., Academic Press, New York, NY, 1966, p. 268.
2. P. B. Nagy, Ultrasonics, 36, 375 (1998).
3. M. Hirao and H. Ogi, Ultrasonics, 35, 413 (1997).
4. A. Granato and K. Lücke, J. Appl. Phys., 27, 583 (1956).
5. H. Ogi, T. Hamaguchi, and H. Hirao, Metal. Material. Trans. A, 31A, 1121 (2000).
6. H. Ogi, S. Aoki, and M. Hirao, Personal communication, to be submitted.
7. A. Hikata, B. B. Chick, and C. Elbaum, J. Appl. Phys., 36, 229 (1965).
8. O. Buck, W. L. Morris, and J. M. Richardson, Appl. Phys. Lett., 33, 371 (1978).

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