Noncontact determination of elastic moduli by two-dimensional Fourier transformation and laser ultrasonic technique

Abstract

Broadband laser ultrasonics and two dimensional Fourier transformation are used to characterize the properties of varieties of foils and plates. Laser ultrasonics generation is achieved by use of a pulsed laser which deposits pulsed laser energy on the surface of the specimen. The displacement amplitude of the resulting broadband ultrasonic modes are monitored using a two wave mixing photo-refractive interferometer. By applying a two dimensional Fourier transformation to the detected spatial and temporal displacement waveforms, the images of density of state (DOS) for the excited ultrasounds are obtained. Results are presented for a 150 µm thick paper sample, a 52.8 µm stainless steel foil and a 1.27 mm thick aluminum plate. The DOS image demonstrates the ability to measure the properties of each generated ultrasonic modes and provides a direct, non destructive, measure of elastic moduli of the tested specimens.Techniques that have been used successfully for non-destructive elastic properties evaluation in films fall into two basic categories [1]: laser based ultrasonic methods [2-4] and techniques utilizing Brillouin scattering [5][6][7]. In laser ultrasonics (LU) experiments, ultrasonic waves are externally generated, and either the dispersion of surface propagation modes is measured or the acoustic pulses propagating out of the plane of the specimens are monitored. Brillouin scattering probes the thermally induced vibration modes and measures their dispersions.The LU metrology uses pulsed laser irradiation to induce ultrasounds in a test object via three mechanisms: thermal-elastic, ablation and plasma. The resulting ultrasonic wave packets are often measured in a non-contact, nondestructive manner using an optical interferometer. LU techniques can provide information about the mechanical, thermal, and electronic properties of materials, and can also be used to detect surface and subsurface flaws in structures [2].LU often monitors an ultrasonic waveform in the time domain. From the obtained time-domain waveform, a technique, like phase velocity calculation, can be used to obtain indirectly the phase velocity dispersion curve as a function of frequency [8][9][10]. Using a fit to this curve one can extract the physical properties of the sample. The conventional technique to obtain phase velocity dispersion requires skill, knowledge and knowhow in data processing. In addition, previous knowledge of material properties is also necessary.In this letter, we describe a two dimensional fast Fourier transformation (2D FFT) technique to avoid most problems confronted by the conventional method. It is implemented by taking incremental measurements in separation distance between ultrasound emitter and receiver to obtain a second spatial dimension, correspond to wavevector ( k ) domain in Fourier transformation. The method automatically produces density of state ( DOS ) image as function of frequency ( f ) and wavevector for the generated ultrasounds with minimum human involvement in the process. The DOS image not only b...

Evidence of surface acoustic wave band gaps in the phononic crystals created on thin plates

“…They are classified as longitudinal or transverse characterized standing modes. 15,16,19 And their Fourier magnitudes are weaker than A0's and S0's in the 2DFT image. Figure 2͑b͒ illustrates the results for an aluminum plate with a square lattice of air-filled holes.…”

“…The image displays the dispersion relations for the A0 ͑the lowest-order asymmetric Lamb mode͒, S0 ͑the lowest order symmetric Lamb mode, next to A0͒, and higher-order Lamb modes ͑the rest of the weak modes͒. 15,16,19 A0 mode has a large out-ofplane displacement component and hence is observed easily by the current laser ultrasonics setup. The S0 is an in-plane mode at low frequencies ͑below 1 MHz͒, however it becomes visible at high frequencies because its out-of-plane component increases with frequency.…”

“…A laser ultrasonics instrument 18,19 was utilized to characterize the SAW band properties of the phononic crystals. The detail of current setup was described elsewhere.…”

“…The detail of current setup was described elsewhere. 19 Briefly, the broadband surface ultrasonic waves are generated by a point focused pulsed laser beam. The generated broadband ultrasonic waves propagate along the sample surface, travel through structures such as phononic crystals, and are a͒ Electronic mail: xinya.zhang@ipst.gatech.edu then probed by the detector.…”

Characterization of guided acoustic waves in an arbitrary direction with full-field instantaneous maps of the acoustic displacement

“…The laser generation of guided waves is usually performed by focusing the beam from a pulsed laser at the plate surface, so that broadband waves are generated, whereas the detection of guided wavetrains is usually performed by optical means, typically pointwise interferometers. [20][21][22][23][24] The applicability of the 2D FT method is not limited to plates. In fact, several authors have reported the use of this method to calculate the frequency spectrum of guided waves in other structures, for example, cylinders 25,26 or wedge tips.…”