IDENTIFICATION OF SINTERED IRONS WITH ULTRASONIC NONLINEARITY

Transcription

1 IDENTIFICATION OF SINTERED IRONS WITH ULTRASONIC NONLINEARITY Y. Ohara 1, K. Kawashima 1, M. Murase 1, and N. Hirose 1 Department of Mechanical Engineering, Nagoya Institute of Technology, Gokiso-cho, Nagoya, , Japan Department of Mechanical Engineering, Tokyo Metropolitan College of Aeronautical Engineering, Tokyo, , Japan ABSTRACT. Two kinds of sinters made of reduced and atomized iron powders were identified by nonlinear ultrasonic measurement to detect higher harmonics generated at micro gaps comparable to the incident wave amplitude using PZT contact transducers of 5 MHz and 10 MHz. Furthermore, the advantage of the nonlinear ultrasonic measurement was demonstrated by the attenuation coefficient measurement for same samples. INTRODUCTION Ultrasonic flaw detection has been widely applied to cracks or voids of some finite volumes. However, the detection of semi-closed cracks such as initial fatigue cracks or initial creep voids appeared grain boundaries is extremely difficult. Through these nearly closed cracks or voids, compressive stress wave is partially transmitted. Therefore we can not detect clear reflection signals, which are visible for open cracks or large voids. One possibility detecting such closed cracks or voids is to use higher harmonics generated by clapping of crack surfaces. For nonlinear continuum, the generation of higher harmonics has been known well and theoretical [1] and experimental [] investigations have been reported. For structural materials including minute cracks, the relation between fatigue damage and the second harmonic was measured [3] and a simple theoretical model of generation of higher harmonics has been derived [4] for elastic half spaces of an infinite crack plane. Russian schools developed a measurement method of higher harmonics of large cracks clapped by an externally excited source [5, 6]. A new concept of Contact Acoustic Nonlinearlity, CAN, has been proposed by Solodov [7] to distinguish it from acoustic nonlinearity of continuum. The most significant feature of CAN is extremely high ultrasonic nonlinearity, namely 100 or 1000 times higher than continuum. This opens new possibility to measure cracks of far small openings by the conventional ultrasonic measurement apparatus. The present authors have been detected a group of minute cracks [8], which were generated under high speed plate impact tests, by measuring the second harmonic with PZT transducers and a pulser exciting large amplitude of some 10 nm. Also, they have confirmed the main feature of the dependence of the second harmonic on the incident

2 wave amplitude and crack openings by FEM wave propagation analyses with contact elements [9]. Furthermore, they have extended the higher harmonic measurement to an artificial crack [10] and a laminated structure model [11] with imperfect bonding. In the present paper, the nonlinear ultrasonic measurement is applied to characterization of sintered iron powder with longitudinal wave. Furthermore, the attenuation measurement for the same samples is performed to show the advantage of the nonlinear ultrasonic measurement. THEORY Compression Tension FIGURE 1. Nonlinear stress-strain curve of continuum. Higher Harmonics Generation in Nonlinear Elastic Solid Assume that a nonlinear stress strain relation shown in Fig.1 is given by Eq. (1). σ = K ε K ε (1) The corresponding solution of wave equation is expressed [1]by u 3 / = U exp i( kx ωt) + ((3K + K 3 ) / 8K ) U k x exp i( kx ωt) where U is the fundamental wave amplitude, K and K 3 are elastic stiffness of the second and third order, (3+K 3 /K ) is the nonlinear parameter of the second harmonic. Eq.() tells us that the second harmonic amplitude is proportional to the square of the fundamental wave amplitude and wave number as well as the propagation distance and. When we use a burst wave of a fixed frequency, the second harmonic amplitude divided by U, the second harmonic ratio, is proportional to U, and x. () Stress-Strain Relationship at Micro Gap For an elastic solid including planar cracks of the opening comparable to the incident wave amplitude, a plane longitudinal wave will close the crack surfaces when the crack opening is smaller than the incident wave amplitude, as show in Fig.. Thereafter compressive stress wave passes partially through the crack surface, however, tensile stress wave is reflected at the crack surface. In gap free area, the stress-strain relationship will be linear as shown in Fig. (a). In gap area which opening is smaller than ultrasonic wave amplitude, tensile stress will not be transmitted, while compression stress will be transmitted after closing the crack by ultrasonic wave in compression phase as shown in Fig. (b, c). In gap area which opening is larger than ultrasonic amplitude, ultrasonic wave will not be transmitted as shown in Fig. (d). Thus, the stress-strain response passing through the micro gap is expressed by superposition of stress-strain relations shown in Fig. (e). The resultant stress-strain curve shows the similar shape shown in Fig. 1. Longitudinal wave velocity is given by E(1 ν) V = ρ(1 + ν)(1 ν) (3)

3 Plane wave σ 1<A <A 3>A A Compression Tension No gap ε (a) No gap (b) 1<A (c) <A (d) 3>A (e) FIGURE. Nonlinear stress-strain response around internal gap. Displacement Compression Incident wave Transmitted wave Time Amplitude A 1 Tension A f f Frequency FIGURE 3. Wave distortion by nonlinear effect. FIGURE 4. Higher harmonics generation. where E is Young's Modulus, is density and is Poisson's ratio. The elastic modulus is higher in compression than in tension. Therefore elastic wave propagates at higher velocity in compressive phase as shown in Fig.3 and higher harmonics appear as shown in Fig.4. This crack surface clapping brings in marked nonlinearity in the transmitted wave as that of acoustic nonlinearity of nonlinear continuum. It should be noted that the stress-strain relation shown in Fig. is extremely simplified. Namely, the real cracks in structural metals have rough surface of the grain size order, therefore, the crack surfaces will contact at some points at first. Under compressive stress, the contact points extend to microscopic contact areas with local plastic deformation. Also, the plastic deformation accompanies hysteresis loop under crack clapping. The stress-strain relations shown in Fig., however, assume that the crack surfaces are perfectly flat and parallel, perfectly bonded after crack closure under compressive stress wave and reopen under tensile stress wave. EXPERIMENTAL SETUP AND METHOD Samples Two kinds of sinters made of reduced and atomized iron powders with porosity shown in Table.1 were used in experiment. The shape of samples is of 9 mm in thickness and 30 mm in diameter. Two kinds of iron powders were pressed under 98 to 886 MPa,

4 (a) Sintered iron of reduced powder FIGURE 5. Microstructure of sintered iron. (b) Sintered iron of atomized powder TABLE 1. Sample. Porosity Sintered iron of reduced powder Sintered iron of atomized powder then sintered in condition to 1473 K in temperature and 5 MPa in pressure in the air of hydrogen[1]. Fig.5 shows the surface micrograph of sinters. For two kinds of sinters of the same porosity, the sinter of reduced iron powders contains more micro gaps suitable for harmonic generation than the sinter of atomized one. Nonlinear Ultrasonic Measurement Fig.6 shows a schematic diagram of an experimental setup constructed to measure precisely the magnitude of fundamental and nd harmonic amplitudes in received ultrasonic wave signals. Ultrasonic signal generator (RAM 5000 SNAP RITEC USA) controlled by a personal computer outputs high voltage, from 98 V to 540 V, to transmitted transducer. A 7.5 MHz PZT transducer (Panametrics V 11, 6.55 mm in diameter) was used as a transmitter. The transmitting signal was a 5 MHz burst longitudinal wave of 0 cycles. The transmitted wave was sensed by a 10 MHz PZT transducer (Ultran KC 5-10, 6.55 mm in diameter). The received signal was processed by super heterodyne frequency analysis system in RITEC SNAP-5000 and the fundamental and second harmonic amplitude were measured. Weight(1.3kg) Personal Computer Signal Generater SNAP Gated Amplifier Super Heterodyne Detector FIGURE 6. Experimental setup. High Z Pre-Amplifier High Power 50Ohm Termination High Pass Filter Attenuator Signal Sampler Low Pass Filter 10MHz Transducer Test Piece Couplant 7.5MHz Transducer

5 Couplant Transducer u C u B u Buffer h Sample FIGURE 7. Attenuation measurement setup. Attenuation Measurement An attenuation measurement method [13, 14] with inserted buffer rod between transducer and sample was used. As shown in Fig.7, the absolute amplitude of reflected wave is expressed by A = UR, B = UT T exp( αh), C = UT RT exp( 4αh) BS SB where is attenuation coefficient of sample, U is common factor for three sample, eg, incident wave amplitude and attenuation in buffer rod, R is the reflected coefficient at interface between buffer rod and sample, T BS (T SB ) is the transmitted coefficient to sample(buffer rod) from buffer rod(sample). By using relationship between eq.(4) and R +T BS T SB =1, attenuation coefficient is expressed by 1 R = ln h, C / B α R BS SB (4) AC = (5) AC + B 5 MHz and 10 MHz PZT transducers were used to measure the attenuation coefficient at these frequencies. Pulse waves were transmitted to the samples through buffer rod by the transducers connected to pulser-receiver (Panametrics, Model 5900PR). Reflected wave signals (u A, u B, u C ) are processed by FFT analysis and each absolute amplitude (A, B, C) at 5 MHz and 10 MHz signal were measured. Calibration of Displacement of Amplitude of Free Surface The output of the PZT transducer was calibrated by a laser interferometer, then the received signal was transformed displacement. Free surface amplitude was measured by laser interferometer. A schematic diagram of an experimental setup is illustrated in Fig.8. Input voltage is proportional to displacement amplitude as shown in Fig.9. We use an experimental formula; Displacement [nm] = [nm/v]input voltage [V]0.369 [nm]

6 0 Laser Interferometer Band Pass Filter Specimen Digital Oscilloscope Transducer itude[nm] Wave ampl Exciting voltage[v] FIGURE 8. Amplitude measurement on free surface. FIGURE 9. and wave amplitude. Relation between exciting voltage RESULTS Dependence of the nd Harmonics on Porosity and Kinds of Iron Powder The second harmonic ratio, the second harmonic amplitude divided by the fundamental one, is plotted against the incident wave amplitude in Fig.10. For every value of porosity, the ratio is nearly proportional to the fundamental wave amplitude. The slopes are higher for low porosity. At nearly same porosity, the reduced iron powder gives higher second harmonic than the atomized one as shown in Fig.10. The former includes small voids as shown in Fig.5, while the latter does include only large voids. To excite the second harmonic, the gap distance or crack opening should be comparable to the incident wave amplitude. Large voids or gaps remain open under compressive wave, therefore no clapping occurs. It should be noted that the sensitivity of the second harmonic ratio is about 0.01%. A /A 1 [%] Porosity Reduced powder Atomized powder Incident wave amplitude [nm] FIGURE 10. Second harmonic ratios.

7 Attenuation coeffi cient [1/cm] Reduced Atomized 10 MHz 5 MHz Porosity FIGURE 11. Attenuation coefficients at 5 MHz and 10 MHz. / 5MHz 10MHz Reduced Atomized Porosity FIGURE 1. Attenuation coefficients 10MHz / 5MHz. Comparison Between nd Harmonic Ratio and Attenuation Measured attenuation coefficients at 5 MHz and 10 MHz are shown in Fig.11. The attenuation coefficients do not show clear dependence on iron powder and porosity. Thus, it is difficult to identify the porosity on the same powder as well as the kind of iron powder at nearly same porosity. The attenuation coefficient ratio, in which the attenuation coefficient at 10 MHz 10MHz is divided by the 5 MHz one 5MHz, is plotted against the porosity in Fig.1. The attenuation coefficient ratio of sintered iron of reduced powder is larger than the atomized one. Therefore, this result shows that the difference of nd harmonic ratio shown in Fig.10 is not caused by the attenuation. Thus, the nonlinear ultrasonic method is more suitable for the identification of sintered iron than attenuation coefficient measurement. CONCLUSIONS The effectiveness of the nonlinear ultrasonic measurement, the second harmonic amplitude, for nearly closed cracks was demonstrated for sintered iron of internal gaps, as compared to attenuation coefficient measurement. In these measurements, the conventional PZT contact transducer was combined with commercial ultrasonic pulser and receiver. The resolution of the second harmonic ratio, A /A 1, is about 0.1%. This method can detect the set of nearly closed cracks or gaps of the opening comparable to incident wave amplitude, however, there is a detectable range of the crack opening, which depends on the incident wave amplitude. ACKNOWLEDGEMENT This work has been supported by Grant-in-Aids for Scientific Research (B , B ) from the Ministry of Education, Science, Sports and Culture, Japan.

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