Nonlinear Ultrasonic Evaluation Of Microcrack Damage In A Metal Plate

Plate-like structures have been widely used in key components in the energy,transportation,and aerospace industries,and the reliability and integrity of plate-like structures have become more and more important.Due to improper manufacturing process,or under the influence of external load,fatigue effect,structural aging and other unfavorable factors,cracks will be developed within the solid plate,which will affect the normal function of the structure or even cause serious accidents.Therefore,it is necessary to detect and evaluate the damage state of the solid plate structure effectively and quickly.The nonlinear ultrasonic Lamb wave has the characteristics of propagation in high speed,long propagation distance and sensitivity to changes of internal microstructure.Lamb wave based nonlinear ultrasonic nondestructive testing method has therefore received more and more attention nowadays.It is of great significance to study the propagation of nonlinear Lamb waves in solid plates and the interaction between Lamb waves and damage caused by cracks in the plates.In this paper,the nonlinear ultrasonic damage evaluation of crack damage in metal plates is carried out numerically and experimentally.Firstly,by solving the dispersion equation of Lamb wave,the phase velocity and group velocity dispersion curve of Lamb wave in a single-layer aluminum plate are thereafter plotted.Then the analytical solution of the second harmonic is derived by using the second-order perturbation approximation and the wave mode expansion method,and the necessary conditions for generating the second hrarmonic are thus obtained.On this basis,the propagation process of Lamb wave in aluminum plate is numerically simulated.The influence of phase velocity and group velocity matching on the second harmonic generation of Lamb wave is studied.Furthermore,influence of the microcrack in the plate on nonlinear Lamb wave propagation is thereafter investigated,the effects of different depth cracks on nonlinear parameters and the variation of nonlinear parameters with propagation distance of Lamb waves after passing through the crack are compared in the case of exciting S1-s2 mode pair and S2-s4 mode pair.Finally,the relationship between the acoustic nonlinear parameter of the nonlinear Lamb wave and the microcrack depth is experimentally studied.The study shows that:(1)The necessary conditions for generating accumulated second harmonics of nonlinear Lamb wave in a solid plate are a non-zero power flux flowing frorm the fundamental frequency to the second harmonic and phase velocity matching between the fundamental frequency and the second harmonic.When the phase velocity is matching,the second harmonic amplitude increases linearly with the propagation distance;when the phase velocity is not matching,the amplitude of second harmonic varies with the propagation distance in a sinusoidal form and has a maximum value.When the phase velocity is approximately matching,the amplitude of second harmonic approximately satisfies the linear cumulative growth law within the effective distance.(2)For a perfect single-layer aluminum plate,both the second harmonic amplitude of the S1-s2 mode pair and the S2-s4 mode pair exhibit a linear cumulative growth with the propagation distance on condition that there is non-zero power flux flowing from the fundamental wave to the second harmonic and phase velocity matching,while group velocity matching is not a necessary condition for linear cumulative growth.For an aluminum plate with microcrack,the acoustic nonlinear parameter of the nonlinear Lamb wave S1-s2 mode pair and the S2-s4 node pair increase with the increase of the crack depth,but in the case of the same crack depth,the acoustic nonlinear parameter of the S1-s2 modal pair is more sensitive to changes in crack depth,and the S1-s2 mode is more effective for detecting crack damage in aluminum plates.(3)In the experimental aspect,the S1 mode Lamb wave can be selectively excited by using an oblique wedge transducer at a certain incident angle and excitation frequency.The acoustic nonlinear parameter of the S1-s2 mode pair increases linearly with the propagation distance under the condition that the phase velocity is matching and the non-zero power flux flow from the fundamental frequency to the double frequency.The nonlinear ultrasonic experimental study on aluminum plates with different depth cracks shows that when the crack depth is within a certain range,the local nonlinearity of the cracks and the cumulative nonlinearity of the aluminum plates overlap,which increases the local nonlinear parameter of the crack region.At the same propagation distance,the nonlinear parameters of the S1-s2 mode increase with increasing crack depth.Therefore,the S1-s2 mode in the nonlinear Lamb wave can be used to effectively evaluate the crack depth propagation and evolution process in a metal plate.