Damage prediction via nonlinear ultrasound: A micro-mechanical approach

J Melchor; W J Parnell; N Bochud; L Peralta; G Rus

doi:10.1016/j.ultras.2018.10.009

Damage prediction via nonlinear ultrasound: A micro-mechanical approach

Ultrasonics. 2019 Mar:93:145-155. doi: 10.1016/j.ultras.2018.10.009. Epub 2018 Oct 28.

Authors

J Melchor¹, W J Parnell², N Bochud³, L Peralta⁴, G Rus⁵

Affiliations

¹ Department of Structural Mechanics, University of Granada, Granada, Spain; IBS Biosanitary Research Institute, Granada, Spain; MNat Scientific Unit of Excellence, University of Granada, Spain. Electronic address: jmelchor@ugr.es.
² School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK.
³ Institut Langevin, ESPCI Paris, CNRS (UMR 7587), PSL Research University, 75005 Paris, France.
⁴ Biomedical Engineering Department, School of Biomedical Engineering and Imaging Sciences, King's College London, London, UK.
⁵ Department of Structural Mechanics, University of Granada, Granada, Spain; IBS Biosanitary Research Institute, Granada, Spain; MNat Scientific Unit of Excellence, University of Granada, Spain.

PMID: 30529738
DOI: 10.1016/j.ultras.2018.10.009

Abstract

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.

Keywords: Homogenization; Micro-cracks; Non-destructive evaluation; Nonlinear acoustics; Nonlinear elasticity; Ultrasound.