Damage prediction via nonlinear ultrasound: A micro-mechanical approach
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AuthorMelchor Rodríguez, Juan Manuel; Parnell, W. J.; Bochud, Nicolás; Peralta, L.; Rus Carlborg, Guillermo
Non-destructive evaluationNonlinear elasticityUltrasoundHomogenizationMicro-cracksNonlinear acoustics
J. Melchor et al. Damage prediction via nonlinear ultrasound: A micro-mechanical approach. Ultrasonics 93 (2019) 145–155 [https://doi.org/10.1016/j.ultras.2018.10.009]
SponsorshipThe authors acknowledge the Spanish Ministerio de Economía y Competitividad for project DPI2014-51870-R and Junta de Andalucía for projects P11-CTS-8089 and GGI3000IDIB. Melchor is grateful to the University of Manchester for funding via the Engineering and Physical Science Research Council (EPSRC) grant reference EP/I01912X/1. Parnell is grateful to the EPSRC for his research fellowship (EP/L018039/1).
Nonlinear constitutive mechanical parameters, predominantly governed by micro-damage, interact with ultrasound to generate harmonics that are not present in the excitation. In principle, this phenomenon therefore permits early stage damage identification if these higher harmonics can be measured. To understand the underlying mechanism of harmonic generation, a nonlinear micro-mechanical approach is proposed here, that relates a distribution of clapping micro-cracks to the measurable macroscopic acoustic nonlinearity by representing the crack as an effective inclusion with Landau type nonlinearity at small strain. The clapping mechanism inside each micro-crack is represented by a Taylor expansion of the stress-strain constitutive law, whereby nonlinear terms arise. The micro-cracks are considered distributed in a macroscopic medium and the effective nonlinearity parameter associated with compression is determined via a nonlinear Mori-Tanaka homogenization theory. Relationships are thus obtained between the measurable acoustic nonlinearity and the Landau-type nonlinearity. The framework developed therefore yields links with nonlinear ultrasound, where the dependency of measurable acoustic nonlinearity is, under certain hypotheses, formally related to the density of micro-cracks and the bulk material properties.