Nonlinear ultrasound modelling and validation of fatigue damage

Abstract

Nonlinear ultrasound techniques have shown greater sensitivity to microcracks and they can be used to detect structural damages at their early stages. However, there is still a lack of numerical models available in commercial finite element analysis (FEA) tools that are able to simulate the interaction of elastic waves with the materials nonlinear behaviour. In this study, a nonlinear constitutive material model was developed to predict the structural response under continuous harmonic excitation of a fatigued isotropic sample that showed anharmonic effects. Particularly, by means of Landau's theory and Kelvin tensorial representation, this model provided an understanding of the elastic nonlinear phenomena such as the second harmonic generation in three-dimensional solid media. The numerical scheme was implemented and evaluated using a commercially available FEA software LS-DYNA, and it showed a good numerical characterisation of the second harmonic amplitude generated by the damaged region known as the nonlinear response area (NRA). Since this process requires only the experimental second-order nonlinear parameter and rough damage size estimation as an input, it does not need any baseline testing with the undamaged structure or any dynamic modelling of the fatigue crack growth. To validate this numerical model, the second-order nonlinear parameter was experimentally evaluated at various points over the fatigue life of an Aluminium (AA6082-T6) coupon and the crack propagation was measured using an optical microscope. A good correlation was achieved between the experimental set-up and the nonlinear constitutive model.

Nonlinear ultrasonic stimulated thermography for damage assessment in isotropic fatigued structures

“…As mentioned earlier, further harmonics, at twice and three times the fundamental frequency, have been shown to be generated by damage/defects [19], [20]. The production of these harmonics and subharmonics are generally agreed to be beneficial for crack heating [21].…”

Self-adaptive absorbing boundary conditions for quasilinear acoustic wave propagation

“…We note that, unlike in the derivation of the Westervelt equation in Section 2, here we do not split ψ into a background and oscillatory part, instead we assume ψ ref to be a solution of the equation. This linearization is analogous to the one employed in [52] for the equation in the pressure formulation (8).…”

“…Accurate simulation of nonlinear ultrasound offers a path to a better quality of many procedures in industry and medicine, from non-destructive detection of material damages [8,25,42] to non-invasive treatments of medical disorders [24,35,36,62,66]. When studying such procedures, there is always a region of interest: a kidney stone that will be disintegrated or a propagating fatigue crack in a component of an aircraft.…”

Nonlinear elastic multi-path reciprocal method for damage localisation in composite materials

“…This result in the creation of nonlinear elastic effects such as higher harmonics and sub-harmonics of the excitation frequency, which can be used as signature for micro-damage detection. A number of authors have recently focused their studies on the nonlinear behaviour of ultrasonic waves in composites, both numerically and experimentally [9,10]. Typically, both the second and third order nonlinear elastic responses are used for material damage identification and localisation [11].…”