Nonlinear Acoustic Modeling Of Micro-defects In Solid And Its Application In Non-destructive Evaluation

When finite amplitude wave propagates in solids,there exist many nonlinear phenomena,such as wave distortion,generation of harmonics,etc.The nonlinear phenomena will be more remarkable for inhomogeneous solids,imperfect interfaces,or micro-defects.At present,nonlinear ultrasonic techniques have already been utilized to analyze the feature of microstructure,evaluate the degree of fatigue degradation and locate microscopic imperfections in solids.However,it is crucial for better understanding the mechanisms of nonlinear response induced by the micro-defects.Based on analysis on harmonics and resonance frequencies,several nonlinear acoustic models have been presented to indicate the nature of the nonlinear response.Classical nonlinear theory generally attributed this kind of nonlinear behaviors to the non-harmony of crystal lattice structure inside materials such as dislocation,twist and discontinuities.For example,Hertzian elastic contact model is associated with a kind of elastic-plastic deformation between asperities of rough surface;while contact acoustic nonlinearity(CAN)model describes the physical mechanisms as the alternating transition between opening and closing motion of micro-crack so that the bi-linear stiffness could be applied to model.In recent years,elastic resonance and static stress-strain experiments have demonstrated that the stress-strain relationship in mesoscopic elastic materials or micro-inhomogeneous materials exhibits a hysteresis loop with endpoint memory,and its change is dependent not only on the instant state,but also on the history of the previous process.Preisach-Mayergoyz(PM)space model successfully describes the hysteretic nonlinear behavior of equation of state of stress-strain space in mesoscopic characteristics,which is based on assumption that the elastic properties of a macroscopic sample of material are resulted from the integral response of a large number of individual hysteretic elastic elements.However,analytical solutions of these models are difficult to obtain in the case of two or three-dimensional structures.Consequently,the quantitative relations between nonlinear propagation and defects location remain unclear.This thesis aims to model the nonlinear acoustic responses induced by the micro-defects in solid and its application in non-destructive evaluation.It includes the following works:(1)We studied the vibration characteristics of bonded two-layer plate system associated with the nonlinear bonding condition.The electricity-mechanics-acoustics analogy model was employed to build a nonlinear oscillating circuit model.Then analytical resonant equation of adhesive bonded two-layer plates was derived,which take the nonlinear resonant behavior,the adhesive parameters and the size of plates into account.(2)We investigated the propagation characteristics of non-classical nonlinear acoustic wave in a conical bar embedded with micro-cracks by modifying the stress-strain relationship with hysteresis and discrete memory characteristics.When the variation of the cross section of the bar was insignificant,a one-dimensional model was utilized to solve the problem.In this manner,the general wave equation(in regards to the generation of non-classical nonlinear acoustic wave)was derived,and the analytic harmonic solutions were obtained by using the perturbation theory as well as a variable substitution method.(3)We used Consensus Self-Organizing Models(COSMO)based on clustering and statistical analysis to explore the connections between spectrum distribution and the micro crack growth.The main contributions of this thesis lie in:(1)The nonlinear resonant equation was derived theoretically for adhesively bonded two-layer plates,which showed the nonlinear resonant frequency is intrinsically related to third-order stiffness.Furthermore,the nonlinear resonance is more significant in imperfect adhesive bonds with big linear stiffness.The results indicated that the combination of nonlinear resonant frequency and harmonics would provide sufficient information to evaluate the quality of adhesive layer.(2)The physical mechanism of non-classical nonlinear characteristics in a conical bar was acquired,and the displacement amplitudes were related to the position and width of the micro-cracked region,as well as the strength parameter of the non-classical nonlinearity.These properties thus provided a new method to discern and locate the micro-defects zone embedded in welding seam of bridge,wind power unit and aircraft components.(3)The acoustical COSMO model based on the larger quantity of samples collected from ultrasonic testing,the responding experimental results confirmed that the spectrum amplitude always obeyed some types of probability distribution with parameters,the P(or T)value as significant level indicator could be employed to evaluate the degree of deterioration and predict the remaining life of materials.Therefore,the COSMO model offered great potential in the development of detecting methods for non-destructive evaluation.