A Novel Multi-frequency Nonlinear Ultrasonic Approach for the Characterization of Annealed Polycrystalline Microstructur
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Mechanical properties of polycrystalline materials primarily depend on the grain size.[1] Processes such as cold working or annealing can vary grain size, and the evolved microstructure can be studied using different characterization methods. However, widely used microscopic techniques are limited to laboratory environments. In this context, non-destructive evaluation (NDE) methods such as ultrasonic velocity[2–4] and attenuation[5–9] measurements are used for material characterization even on the industrial scale. Nevertheless, Young’s modulus determines the ultrasonic wave
SAJU T. ABRAHAM, N. SREEVIDYA, C.R. DAS, S.K. ALBERT, and B. VENKATRAMAN are with the Homi Bhabha National Institute, Indira Gandhi Centre for Atomic Research, Kalpakkam, Tamil Nadu, 603 102, India. Contact e-mails: [email protected], [email protected] S. SHIVAPRASAD and KRISHNAN BALASUBRAMANIAM are with the Centre for Non-destructive Evaluation, Indian Institute of Technology, Chennai, 600 036, India. Manuscript submitted June 25, 2019.
METALLURGICAL AND MATERIALS TRANSACTIONS A
velocity and is thus less sensitive to grain size variations.[3,4,8] Power law dependency[10] of the attenuation coefficients limits the measurements to homogeneous fine-grained materials or a lower thickness range. Measurements of attenuation also have limited response toward the identification of phases.[8] A laser-based technique developed by Dong et al.[11] could perform in situ attenuation measurements but with significant error in the standard deviation in the measurements. Overall, the requirements of multiple echoes for the velocity and attenuation measurements limit their implementation on coarse-grained materials as well as thick materials. Despite all these limitations, the nonlinear ultrasonic (NLU) technique is found sensitive to the microstructural changes compared with the linear attenuation and velocity measurements[12] and used in characterizing materials during different processing and degradation mechanisms.[13,14] Nonlinear interaction of a monochromatic elastic wave with a crystalline lattice distorts the waveform and produces harmonics of the fundamental frequency. Measurement of these harmonics provides information about the nonlinear response of the medium and can be quantified by a dimensionless term, the acoustic nonlinearity parameter, b. In a single-phase polycrystalline elastic medium, microstructural features such as grain boundaries induce excess nonlinearity ðbex Þ because of the nonlinear interactions with the ultrasonic waves in addition to the intrinsic nonlinearity blat induced by the elastic constants of the crystalline lattice. A grain boundary is an array of edge dislocations where localized strain is high[15] and has potential sites for nonlinear interactions.[16–18] Since a grain boundary is similar to an infinite dislocation dipole train, the acoustic nonlinearity thus produced from the nonlinear interactions is written as[19] 4 r 3 h dis 2 c2 3 b ¼ Kb 4 XR ð1 tÞ ½1 b l c1 where K is the dislocation density, b is the B
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