Nonlinear ultrasonics can play a major role in industrial structural health monitoring, since one of its main features is the capability to detect early damage manifestations. The nonlinear constitutive properties of a material, in the sense of deviation from Hooke's law, are recently being shown to be orders of magnitude more sensitive to micro-damage than the linear ones. As a consequence, a number of effects arise in the propagation of the ultrasonic waves as they interact with the material nonlinearity (Ostrovsky & Johnson, 2001; Broda, Staszewski, Martowicz, & Silberschmidt, 2014), namely,
Higher Harmonics Generation: When a sinusoidal wave is emitted, a signal with additional harmonics, multiples of the fundamental, is received.
Hysteretic mechanical behavior, in the stress-strain relationship.
Wave modulations:
In amplitude and phase when two sinusoidal frequencies are propagated.
Cross-Modulation of Waves (Luxemburg-Gorky Effect): Passing modulation from an amplitude modulated excitation to a simultaneous and initially pure sinusoidal excitation.
Amplitude dependent resonant frequency shifts when the material is insonified.
Attenuation that depends on the excitation amplitude.
Acoustic Conditioning: An immediate offset on material property values when insonification is active. The initial transient period time is also referred as fast dynamics.
Relaxation Effects or Fast and Slow Dynamics: When excitation vanishes, material properties has a partial fast recovery and a slow final recovery that last minutes to achieve the original values, before excitation.
Subharmonic generation.
These nonlinear effects, which are originated in the materials’ microscopic and mesoscopic structures, are separable from the linear propagation in the frequency domain by a variety of experimental configurations (Ostrovsky & Johnson, 2001; Zheng, Maev, & Solodov, 1999; Jhang, 2009). Mesoscopic size is the scale of early damage manifestations, and micro-damage has also been shown to be particularly invisible to linear techniques (Nicholson & Bouxsein, 2000). Some recent experimental observations suggest that hysteretic and/or nonlinear mechanical properties may be a key factor to quantify changes and could unveil details of the micro- and meso-structure; both the intrinsic nonlinearity in the material or that of an induced damage. In practice, micro-damage modes such as micro-cracks behave as ultrasonic sources at frequencies different from the excitation, making it a promising tool to clearly locate and quantify damage (Matikas T., 2010). Nonetheless, few studies have been performed on the relationship between crack density and level of nonlinearity (Haupert, et al., 2014; Renaud, Callé, Remenieras, & Defontaine, 2008).