Propagation And Control Of Interfacial Cracks In Piezoelectric Materials

With the rapid development of modern high technology,piezoelectric materials are widely used in precision instruments,aerospace,automatic control,biomedicine,precision positioning and micro-mechanical systems.In manufacturing and use,the existence of defects at the interface of piezoelectric materials will affect the safety of the device itself.However,the inherent electromechanical coupling characteristics of piezoelectric bodies make the study of damage and fracture characteristics at the interface extremely complicated and difficult,so in order to improve the fracture resistance and from the perspective of safety,it is of great scientific significance to study the characteristics of piezoelectric structures,especially the dynamic behavior of interface cracks and the control of crack defects.Therefore,this paper takes the interface crack of piezoelectric materials as the research object,and analyzes the propagation law of interface crack and the effective method of defect control from the constitutive relation of electromechanical coupling.The main research work of this paper is as follows:1.Considering the effect of crack propagation speed,dynamic crack propagation at semi-infinite interface of piezoelectric materials is studied.Based on the principle of energy conservation and the mechanical and electrical coupling constitutive relation,the dynamic crack propagation model of semi-infinite interface is established.After Laplace transformation,the Wiener-Hopf method was used to study the model,and the expressions of dynamic stress intensity factor and electrodynamic displacement intensity factor at the interface crack tip were obtained.The effectiveness of the method is verified by numerical simulation,and the parameters affecting the dynamic crack growth such as time,electromechanical coupling coefficient and crack growth rate are discussed in detail.It is found that the crack propagation will accelerate with the increase of time in a certain range,and the electromechanical coupling coefficient can affect the nonlinear strength of the material,and then affect the crack propagation,and there is a critical speed in the crack propagation.2.Considering the influence of crack shape,the dynamic propagation of circular interfacial crack of piezoelectric materials is further studied.Based on the electroelastic theory and the constitutive relationship in polar coordinate system,a dynamic model of piezoelectric double-material circular interfacial crack is established.（After analyzing the equilibrium equation,constitutive equation and boundary conditions,the expression of elastic displacement and potential of the upper and lower materials is established,which is the key to solve the problem.）Combined with Laplace transform and Hankel transform method,the model is theoretically analyzed,and the analytical solution of Crack Opening Displacement（COD）strength factor is obtained.The effects of material thickness,material parameters,electric field and time on the dynamic propagation of circular interfacial cracks are discussed,and the effectiveness of the method is verified.It is found that the thinner the thickness of the material,the easier it is to detect crack growth.At the same time,whenh₁/a（28）2,the influence of electric field on crack growth is significantly increased,and time will induce a high amplitude of crack growth,which decreases after reaching the peak and gradually tends to be flat,and the gentle value is the strength factor value at static state.3.Considering the existence of electric waves during elastic wave propagation,the scattering of SH waves（waves whose particle vibration occurs in a plane parallel to the wave propagation plane）by an orthotropic interface crack in piezoelectric materials is studied.Taking the piezoelectric ceramic polymer as the research object,a dynamic model of the anisotropic interfacial crack scattering of SH wave was established by Laplace and Fourier transforms combined with the constitutive equation of the piezoelectric ceramic polymer.The expression of scattering field intensity factor is obtained by using series method and Schmidt method.The effectiveness of the method is verified by analyzing the piezoelectric ceramic materials.It is found that the piezoelectric ceramic polymer PMN-PT/PVDF will accelerate crack propagation.Meanwhile,when the frequency is constant,the initial peak value of the left end point on the back wave surface will decrease with the increase of the Angle,and the initial peak value of the right end point on the forward wave surface will increase with the increase of the Angle.When the Angle is fixed,the field intensity factor will have both high amplitude and low amplitude with the increase of frequency.4.Considering the effect of film thickness,the dynamic propagation of multiple cracks at the interface of piezoelectric materials is studied.Piezoelectric film.Firstly,the dynamic expansion model of multiple cracks at the interface was established,and theoretical analysis was carried out by Laplace transform and Fourier transform and Chebyshev place method to obtain the stress field and electric displacement field near the crack tip.The effect of film thickness,time and the interaction between cracks on the propagation in the case of double and triple cracks is discussed.On the basis of the above model,the influence of stress and electric displacement on energy release rate is further analyzed.It is found that when the ratio of film thickness to substrate thickness is constant,the crack propagation under PVDF/PZT-4is slower,and the crack propagation under PVDF/PZT-5H is faster,and the dynamic crack propagation is easier to detect when the film thickness is thinner.From the dynamic expansion in the time domain,it can be found that when the action time becomes longer,the crack growth will first increase,reach the peak,then decline and finally tend to be flat,and the value of flat is the static stress intensity value.At the same time,regardless of the number of cracks,the stress value of the inner tip of the crack is greater than that of the outer tip.The normal stress will accelerate crack growth,and the negative stress will inhibit crack growth within a certain range.The effect of the electric displacement on the energy release rate is parabolic.The positive displacement accelerates crack propagation within a certain range,and then inhibits crack propagation,and the negative displacement load can inhibit crack propagation.5.Considering the influence of material properties,the dynamic propagation of orthotropic interface cracks in piezoelectric materials is studied.Taking the piezoelectric film substrate as the research object,the expressions of dynamic stress and electric displacement intensity factor at the crack tip of the orthotropic interface were obtained by Laplace transform and Fourier transform and Chebyshev placement method.The effects of material size ratio,film thickness and material elastic constant on dynamic crack propagation are discussed.It is found that the stress intensity value whend₁d₂（28）0.01is smaller than the stress intensity value whend₁d₂（28）0.0125,and the crack growth is more easily detected when the film is thinner,and the dynamic stress intensity factor value of the crack is smaller when the material elastic constant（?）_c（28）2,and the reduction amplitude is lower,that is,the increase of the material elastic constant has a control effect on the crack growth.6.Considering the necessity of quantitative crack analysis,the problem of central rectangular crack at the interface of piezoelectric materials is studied.Based on the constitutive relation and equilibrium equation of rectangular crack,a three-dimensional piezoelectric material model with central rectangular crack at the interface is established.The stress,displacement and potential of rectangular central crack of piezoelectric material are quantified by finite element method in ABAQUS software.It is found that the crack propagation can be controlled by adjusting the force load and electric field.The longer the crack length,the greater the change of tip growth,the smaller the residual strength of the device itself,and the ability to resist fracture;The stress value near the crack tip is much larger than other areas,and gradually becomes smaller and smaller towards the position of the rectangular crack Angle,which is the difference between the rectangular crack and other cracks.