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Nonlinear Acoustic Modeling and Measurements during the Fatigue Process in Metals

1,2,3, 1,2,* and 3
State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China
University of Chinese Academy of Sciences, Beijing 100049, China
Université Polytechnique Hauts-de-France, CNRS, Univ. Lille, YNCREA, Centrale Lille, UMR 8520IEMN-DOAE, F-59313 Valenciennes CEDEX 9, France
Author to whom correspondence should be addressed.
Materials 2019, 12(4), 607;
Received: 11 January 2019 / Revised: 9 February 2019 / Accepted: 15 February 2019 / Published: 18 February 2019
(This article belongs to the Special Issue Non-destructive Inspection)
PDF [3501 KB, uploaded 18 February 2019]


The nonlinear spring model combined with dislocation dipole theory was applied to describe the acoustic nonlinearity during the fatigue process in metals. The spring stiffness changes with fatigue degree. For the early stage, spring stiffness approaches infinity, and the heavier nonlinearity mainly results from the increase of dislocation density. Further fatigue leads to the occurrence of micro-cracks, during which spring stiffness begins to decrease. Abundant micro-crack sprouting accelerates the crack’s expansion, and spring stiffness drops quickly, which causes the obvious decline in the transmitted harmonic amplitudes. Solutions obtained from the nonlinear wave equation with dislocation terms were added into the spring model. Varying spring stiffness was chosen for simulating the fatigue process. Then, nonlinear harmonic variation during this process was observed, which was classified into three stages: (I) the early dislocation fatigue stage; (II) the micro-crack sprouting stage; (III) the crack expansion stage. Nonlinear acoustic measurements were carried out on an aluminum alloy specimen during its fatigue process until cracks could be seen clearly. Harmonic variations in experiments can also be classified into the same three stages as the numerical results, which provides a theoretical and experimental reference for fatigue evaluation in metals using the nonlinear acoustic method. View Full-Text
Keywords: nonlinear spring model; dislocation dipoles; fatigue evaluation nonlinear spring model; dislocation dipoles; fatigue evaluation

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Lyu, W.; Wu, X.; Xu, W. Nonlinear Acoustic Modeling and Measurements during the Fatigue Process in Metals. Materials 2019, 12, 607.

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