Acoustic nonlinearity parameters for transversely isotropic polycrystalline materials

Abstract

This article considers polycrystalline materials with macroscopic elastic anisotropy and the effect of the anisotropy on the quadratic nonlinearity parameter used to describe second harmonic generation in solids. The polycrystal is assumed to have transversely isotropic elastic symmetry, which leads to a directional dependence of the nonlinearity parameters. Additionally, the anisotropy leads to second harmonic generation from an input shear wave. Estimates of the longitudinal and shear wave nonlinearity parameters are given as a function of single-crystal elastic constants, macroscopic anisotropy constants, and propagation direction. An inverse model is presented that relates measured nonlinearity parameters to the macroscopic anisotropy constants. The estimates of the nonlinearity parameters can be used to approximate the damage-free or baseline nonlinearity parameter of structural components, which helps the effort toward absolute measures of material damage.

Second-order harmonic generation of Lamb wave in prestressed plates

“…The material nonlinearity has been a subject of many theoretical and experimental studies [26], [46]- [48]. According to the work of Pruell et al [49] and Kim [50], plastic deformations and fatigue damage can be a source of the material non-linearities, in addition to the intrinsic non-linearity due to the inter-atomic and molecular forces.…”

Structural state awareness through integration of global dynamic and local material behavior

“…A modeling effort to include the grain fragmentation and development of preferential grain orientations into a theory of nonlinear ultrasound was performed. Namely, the quadratic nonlinearity parameter, β , was formulated using the microstructures orientation distribution function (Kube and Turner, 2015, 2016)…”

“…A major driver of NDI/SHM research is detection of damage earlier in service life in order to prevent failures, change use, or schedule repair (Farrar and Worden, 2007; Rabiei et al, 2016; Sangid, 2013). Examples of measureable precursors to fatigue crack development may involve changes in acoustic energy (Arguelles et al, 2016; Baby et al, 2008; Kube and Turner, 2015, 2016; Lissenden et al, 2014; Malfense-Fierro, 2014; Patra and Banerjee, 2017), electric and magnetic field lines (Atulasimha and Flatau, 2011; Clark, 2000; Dobmann et al, 2006; Gao et al, 2009; Garcia-Martin et al, 2011; Haile et al, 2016; Matlack et al, 2014; Nagy and Hu, 1998; Scheidler et al, 2015), material compliance (Cole et al, 2017a, 2017b; Wakha et al, 2005), optical changes (Pang et al, 2012, 2013), or electromagnetic scattering (Patra and Banerjee, 2016; Si et al, 2011; Weder, 2009).…”