Characterization Of Material With Distributed Microcracks Based On Nonlinear Ultrasonic Theory

Due to the limitions of the accuracy and sensitivity, the conventional nondestructive testing techniques, such as ultrasonic inspection, radiographic inspection, acoustic emission inspection and wavelet diagnosis technique, can not be used to quantitatively detect and evaluate material early degradation. However, with the development of electronics and acoustic nonlinear theories, nonlinear ultrasound techniques have attracted amounts of attention. A lot of experiments show that nonlinear elastic behavoir of material constitutive relationship comes from the microstructures, such as microcracks, dislocations and precipitates. Based on the second harmonic generation when elastic wave propagating in nonlinear elastic solids, nonlinear ultrasound techniques can be used to characterize the material nonlinearity. This technique has been widely employed for the evaluation of damages due to fatigue and aging. Particularly in recent years, the industries concern material early degradation caused by fatigue. Microcrack has the close relationship with fatigue damage, however, the researches about the physical mechanism of acoustic nonlinerity due to microcracks have defections. Therefore, it is impormant to study the mechanism, numerical simulations and experiments for nonlinear ultrasonics duo to microcracks.In order to study the quantitative relationship between microcracks and acoustic nonlinear parameter based on bilinear stiffness theory, this paper firstly derives the effective tensile and compressive elastic moduli of cracked solids. Based on the static crack opening displacement of a single crack and the dynamic correction, two micromechanics models using dilute-concentration approach and self-consistent approach are developed to estimate the tensile and compressive elastic moduli of elastic solids containing randomly distributed two-dimensional and three-dimesional microcracks. The theoties show that effective tensile and compressive moduli of a cracked solid are different. These micromechanics models are validated by comparing their predictions with the numerical simulations using the FEM. The dilute-concentration model seems to yield better agreement with the FEM simulations.Next, based on Green function method of wave equation and bilinear stiffness theory using Heaviside function, this paper develops a micromechanics model that relates the crack density to the acoustic nonlinearity parameter. The results show that the amplitude of the second harmonic is linearly related to the one of the fundamental, and is scaled by the tension and compression asymmetry. Detailed numerical simulations of wave propagation in a cracked solid by using the FEM are carried out. The results indicate that the micromechanics model predictions agree well with the FEM simulations.Futhermore, this paper also investigates frequency deviation during imperfect resonant conditions and quasi-collinear condition through FEM simulations and experimental measurements using a one-way mixing technique. It is shown that the waveforms of resonant waves change significantly from a diamond shape to multiple toneburst trains with increasing frequency deviation, the associated waveforms are found to be independent of mixing location and only related to frequency deviation. Due to a quasi-collinear wave source, a special angle between the major axis of the resonant wave and its horizontal axis can cause the test results, which the amplitude of the resonant wave received by the transducer increases linearly with increasing mixing distance.Finally, numerical simulations for collinear wave mixing methods are often limited due to the compromise between computational efficiency and accuracy. Based on spectral finite element formulation using Gauss-Lobatto-Legendre polynomials and ABAQUS/VUEL, 9-node and 48-node spectral finite elements are developed. It is shown that the proposed spectral finite elements are capable of increasing computational efficiency by as much as 14 times while maintaining the same accuracy in comparison with traditional FEM.