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.
Highlights
Conventional ultrasonic non-destructive evaluation (NDE) methods are sensitive to gross defects, but are generally much less sensitive to distributed micro-cracks [1,2,3,4]
It should be stressed that micro-mechanics can be employed in the context of linear and nonlinear acoustics described here because we are well into the so-called separation of scales regime, where propagating wavelengths are much larger than the defect or crack under consideration
This relationship is formulated by establishing a bilinear clapping constitutive law, which is subsequently approximated by a Taylor expansion, from which the second order constitutive nonlinearity stems
Summary
Conventional ultrasonic non-destructive evaluation (NDE) methods are sensitive to gross defects, but are generally much less sensitive to distributed micro-cracks [1,2,3,4]. It should be stressed that micro-mechanics can be employed in the context of linear and nonlinear acoustics described here because we are well into the so-called separation of scales regime, where propagating wavelengths are much larger than the defect or crack under consideration.
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