A study of the noncollinear ultrasonic-wave-mixing technique under imperfect resonance conditions.

Geometrical and material property changes cause deviations in the resonant conditions used for noncollinear wave mixing. These deviations are predicted and observed using the SV(ω1)+L(ω2)→L(ω1+ω2) interaction, where SV and L are the shear vertical and longitudinal waves, respectively, and ω1, ω2 are their frequencies. Numerical predictions, performed for the scattered secondary field in the far field zone, show three field features of imperfect resonance conditions: (1) rotation of a scattered beam, (2) decrease in the beam amplitude, and (3) beam splitting. The response of the nonlinear ultrasonic wave mixing technique is verified experimentally in two ways: (1) detection of a kissing bond between two polyvinyl chloride (PVC) plates, and (2) detection of subsurface micro-cracks in polymethyl methacrylate (PMMA). A predominant decrease in nonlinear wave energy is observed in both experiments. Beam rotation and splitting is observed in the kissing-bond experiment, while a minor increase in the nonlinear wave energy up to 100% is observed in the micro-cracked PMMA specimen.

Possible second-order nonlinear interactions of plane waves in an elastic solid.

There exist ten possible nonlinear elastic wave interactions for an isotropic solid described by three constants of the third order. All other possible interactions out of 54 combinations (triplets) of interacting and resulting waves are prohibited, because of restrictions of various kinds. The considered waves include longitudinal and two shear waves polarized in the interacting plane and orthogonal to it. The amplitudes of scattered waves have simple analytical forms, which can be used for experimental setup and design. The analytic results are verified by comparison with numerical solutions of initial equations. Amplitude coefficients for all ten interactions are computed as functions of frequency for polyvinyl chloride, together with interaction and scattering angles. The nonlinear equation of motion is put into a general vector form and can be used for any coordinate system.

Noncollinear wave mixing for measurement of dynamic processes in polymers: physical ageing in thermoplastics and epoxy cure.

Elastic wave mixing using an immersion method has shown effective monitoring and scanning capabilities when applied to thermoplastic ageing, epoxy curing, and non-destructive testing. In water, excitation and reception of waves do not require physical contact between the tools and the specimen, making the acquisition of high-resolution C-scans possible. The nonlinear material parameters exhibit a much higher sensitivity to the specimen state compared to linear ones. Thus, the nonlinear data for polymethyl methacrylate (PMMA) have a 40% difference between zones of "young" and "aged" material, while the linear data show no difference at all. Methodology and logistics of the immersion wave-mixing method are discussed in detail. Monitoring of epoxy curing has also revealed a good sensitivity of the method to this complex process including several characteristic stages, such as the time of maximal viscosity, the gel time, and the vitrification time. These stages are independently verified in separate rheometry measurements. The presented method allows for a number of possibilities: wave-mode and frequency separations, elimination of surrounding medium influence, "steering" (scanning) a scattered wave, controlling the location of the intersection volume, single-sided or double-sided measurements, and operation in detector mode.