Ultrasonics 51 (2011) 974–981

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Ultrasonics

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Cumulative second-harmonic analysis of ultrasonic Lamb waves for ageingbehavior study of modified-HP austenite steel

Yanxun Xiang a, Mingxi Deng b, Fu-Zhen Xuan a,⇑, Chang-Jun Liu a

a Key Laboratory of Safety Science of Pressurized System of MOE, School of Mechanical and Power Engineering, East China University of Science andTechnology, Shanghai 200237, Chinab Department of Physics, Logistics Engineering University, Chongqing 401331, China

a r t i c l e i n f o

Article history:Received 5 January 2011Received in revised form 24 May 2011Accepted 24 May 2011Available online 1 June 2011

Keywords:Lamb wavesSecond-harmonicFerritic Cr–Ni steelPrecipitation kineticsThermal ageing

0041-624X/$ - see front matter � 2011 Elsevier B.V.doi:10.1016/j.ultras.2011.05.013

⇑ Corresponding author. Tel.: +86 21 64252819; faxE-mail address: fzxuan@ecust.edu.cn (F.-Z. Xuan).

a b s t r a c t

The cumulative second-harmonic analysis of ultrasonic Lamb wave has been performed to study the pre-cipitation kinetics and microvoid initiation of ferritic Cr–Ni alloy steel during the ageing process. Ageingof ferritic Cr–Ni alloy materials have been done at 1223 K and 1173 K for different degradation time inter-vals and air cooled. The results show that the normalized acoustic nonlinearity of Lamb wave increaseswith the formation of fine precipitates at the early stage of ageing till about 1000 h and keeps as a plateauwith the precipitates dynamic balance for a long-term ageing, and then decreases gradually at the finalholding time with the coarsening of precipitates and initiation of microvoids. The results also show thatthe variation of nonlinear Lamb wave follows the same trend as that of hardness in materials. Therefore,the cumulative second-harmonic of ultrasonic Lamb waves has been found to be strongly sensitive to theprecipitates behavior and microstructure evolution during the thermal ageing of ferritic Cr–Ni alloy steel.

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1. Introduction

Nonlinear ultrasonic technique has emerged in recent years as apotential tool for non-destructive evaluation (NDE) of the materialproperty degradation. This technique relies on measuring the high-er order harmonics generated by the intrinsic nonlinearity of mate-rials relating to the anharmonicity and imperfection of atomiclattices. The responses in harmonics generation can be related tothe microstructural changes in materials [1–9]. Buck et al. [1] con-ducted experiments of the second-harmonic generation at a flatunbounded interface between two aluminum 1100 cylinders andreported that as the number of fatigue cycles increases, the pres-ence of surface micro-cracks acts as the additional contributionto the nonlinearity. Cantrell and Yost [2,3] experimentally ob-served the change in the acoustic nonlinearity parameter resultingfrom effect of fatigue-induced dislocations, and presented an ana-lytical model that suggested a strong nonlinear interaction of ultra-sonic wave with dislocation dipoles during metal fatigue. Nagy [4]applied cyclic bending to generate fatigue damage in the speci-mens including plastics, metals, composites and adhesives, and re-ported that nonlinear measurements can be provided as an earlierand more sensitive indicator for fatigue damage characterization inmaterials. Jhang and Kim [5] followed to perform the nonlinearultrasonic measurements for materials degradation of SS41 and

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SS45 with stretching and fatigue loading, and they presented thatthe nonlinear parameter b is proportional to the magnitude ofstretching load and the number of fatigue cycles. Recently, Metyaet al. [6] applied higher order harmonic to study the ageing behav-ior of C-250 grade maraging steel. Kim and Lissenden [7] reportedthat the normalized nonlinearity parameter in ferritic 2.25Cr-1Mosteel monotonically increased due to the precipitates and the var-iation in the lattice parameter. Baby et al. [8] and Valluri et al. [9]recently conducted experimental measurements of the higher or-der harmonics in titanium alloy and pure copper, respectively, inorder to evaluate their creep damages. Most previous nonlinearstudies have been confined to longitudinal second-harmonic gen-eration measurements.

When compared to nonlinear ultrasonic techniques that usebulk waves, ultrasonic Lamb waves have obvious advantages, suchas one-side access of pitch-catch configuration and high efficiencyin the long distance propagation, for using as a more suitable can-didate to interrogate large plate- and shell-like structures in thefield applications. Recent studies have presented conditions forthe generation of cumulative second-harmonic of Lamb wavepropagation in materials [10–12], which include phase velocitymatching, nonzero power flux and group velocity matching be-tween the fundamental Lamb waves and the double frequencyLamb waves. Later on, Deng and Pei [13] recently conducted non-linear Lamb wave measurements in aluminum plates subjected tocyclic fatigue loading and reported that the second harmonic signalmonotonically decreases as the fatigue loading progresses. Pruell