CN110455919A - A method of solid solid interface contact performance is evaluated using nonlinear effect - Google Patents
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Abstract
The present invention discloses a kind of method using nonlinear effect evaluation solid solid interface contact performance, comprising the following steps: S01 establishes isotropism and adheres border surface model；S02 derives the expression formula of back wave and transmitted wave using perturbation method；S03 defines four nonlinear parameters to evaluate the contact performance of bonding interface admittedly；S04 draws the curve that four nonlinear parameters change with contact stress；S05 utilizes the pumping signal aliasing of supersonic signal generator selection suitable frequency；S06 obtains corresponding spectral image by collected signal by Fast Fourier Transform (FFT), and measurement obtains the nonlinear parameter of test specimen at various pressures；S07, by comparison theoretical value and actual value, analysis obtains nonlinear parameter, and there are monotonic relationshis with test specimen adhesive strength.A kind of method using nonlinear effect evaluation solid solid interface contact performance provided by the invention can preferably evaluate the adhesive strength and contact situation at bond interface, more effectively carry out quality-monitoring and maintenance to bond.
Description
Technical Field
The invention relates to a method for evaluating contact characteristics of a solid-solid interface by utilizing a nonlinear effect, belonging to the technical field of ultrasonic detection and analysis.
Background
The bonding is a method for connecting materials together to form an assembly, the bonded assembly has a series of advantages of no stress concentration, good fatigue resistance, light structure, capability of avoiding electrochemical reaction of metal connection, capability of connecting objects with complex shapes and the like, and is widely and largely applied in the industries of aerospace, electronics, medical appliances, wood, buildings and the like.
However, various micro defects are inevitably formed inside the adhesive or at the bonding interface during the production of the adhesive. Under the influence of the forming process and the working environment, the metal material and the bonding structure thereof are easy to have various defects of early mechanical property degradation. In some very important situations, irreparable consequences can result if the defective bonded assembly cannot be located and replaced in a timely manner. Therefore, nondestructive testing of the adhesive and prediction of the adhesive strength are actual problems to be solved urgently.
Ultrasonic waves are an important means for solving the problem of interfacial adhesion evaluation. The traditional linear ultrasonic flaw detection technology is mainly based on linear parameters generated in the sound wave transmission process to detect flaws in materials. However, in practical application, the detection signal needs to reduce the nonlinear interference of noise, and the ultrasonic wave is severely attenuated when passing through the defect, so that the linear parameter changes insignificantly, and the flaw detection effect is not very ideal.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a method for evaluating the contact characteristic of a solid-solid interface by utilizing a nonlinear effect, which can better evaluate the bonding strength and the contact condition of a bonding piece interface and more effectively monitor and maintain the quality of the bonding piece.
In order to solve the technical problems, the technical scheme adopted by the invention is as follows:
a method for evaluating solid-solid interface contact characteristics by utilizing a nonlinear effect comprises the following steps:
s01, establishing an isotropic solid-solid bonding interface model, and giving a longitudinal wave motion equation and a stress displacement relation;
s02, deriving expressions of reflected waves and transmitted waves by a perturbation method according to a nonlinear wave equation of aliasing incident beams and boundary conditions of a solid-solid interface;
s03, analyzing to obtain a nonlinear effect of an aliasing beam incident on a solid-solid bonding interface, and defining four nonlinear parameters to evaluate the contact characteristics of the solid-solid bonding interface by combining the power law relation of the interface linear rigidity and the contact stress;
s04, drawing a curve of four nonlinear parameters changing along with contact stress under the condition of aliasing of beams with different frequencies according to the numerical calculation result;
s05, selecting excitation signal aliasing with proper frequency by using an ultrasonic signal generator, exciting on the tested piece through an ultrasonic probe, receiving an acquisition signal by using another ultrasonic probe on the other side of the tested piece, and visually acquiring the signal through a signal acquisition device;
s06, carrying out fast Fourier transform on the acquired signals to obtain corresponding frequency spectrum images, and measuring to obtain nonlinear parameters of the test piece under different pressures based on the theoretical basis of S03;
and S07, comparing the theoretical value with the actual value, and analyzing to obtain the monotonic relation between the nonlinear parameter and the bonding strength of the test piece.
In S01, the one-dimensional elastic longitudinal wave propagates in the X-axis direction, and the reference plane positions of the contact surfaces are set to X ═ X, respectively-,x＝X+In the region X < X-Incident one-dimensional longitudinal wave fincTo obtain a reflected wave frefIn the region X > X+Obtaining a transmitted wave ftra；
The one-dimensional longitudinal wave is positively propagated along the x axis, and the relation between the motion equation and the stress displacement is as follows:
wherein u (x, t) represents the displacement of the acoustic wave propagating along the x direction; σ (x, t) represents the stress variation; sigma0Two solid contact static stresses; t represents time; ρ represents the density of the medium.
In S02, the aliased beam nonlinear wave equation expression is as follows:
where phi is the velocity potential and the velocity expression of the acoustic wave is
Wherein, c0The propagation velocity of small-amplitude sound waves in ideal gas is constant and depends on a medium; gamma is the ratio of specific heat at constant pressure to specific heat at constant volume; p is pressure, P0Is the initial pressure; rho0Is the initial density.
In S02, the solid-solid interface boundary condition satisfies:
when the elastic wave has interaction across the boundary, the displacement and stress conditions are as follows:
when the elastic waves do not interact across the boundary, i.e. there is no contact between the two solids at this time, the displacement and stress conditions are as follows:
wherein u (+0, t) is acoustic wave in region X > X+Displacement of (2); u (-0, t) is acoustic wave in region X < X-Displacement of (2); σ (+0, t) is that sound wave is in area X > X+The stress of (a); sigma (-0, t) is that sound wave is in region X < X-Of the stress of (c).
The specific steps of deriving the expressions of the reflected wave and the transmitted wave by using the perturbation method are as follows:
the solutions of step a, formula (1) and formula (2) are as follows:
u(x,t)＝finc(x-ct)+fref(x+ct)x＜X- (7)
u(x,t)＝ftra(x-ct)x＞X+ (8)
in the formula, function finc(x-ct),fref(x + ct) and ftra(x-ct) represents an expression of an incident wave propagating right along the x-axis on the left side of the interface, a reflected wave propagating left along the x-axis, and a transmitted wave propagating right along the x-axis on the right side of the interface, respectively, and the wave velocity c of the acoustic wave is (λ/ρ)1/2λ is the elastic constant;
step b, in order to solve the equations of the formula (1) and the formula (2), introducing the following variables:
Z(t)＝[u(X+,t)+u(X-,t)]/2 (9)
Y(t)＝u(X+,t)-u(X-,t)＝h(t)-h0 (10)
one-dimensional elastic longitudinal wave propagates along the direction of the X axis, and the reference plane positions of the contact surfaces are respectively set as X ═ X-,x＝X+(ii) a Wherein u (+0, t) is an acoustic wave at the interface X ═ X+A displacement of (a); u (-0, t) is acoustic wave at the interface X ═ X-A displacement of (a); h (t) is the gap distance between the contact surfaces when the sound waves are transmitted; h is0The gap distance between the contact surfaces is constant when the contact surface is silent, and is related to the roughness of the solid medium and the contact surface; z represents the displacement between both ends of the contact interfaceY represents the difference in displacement across the interface;
the derivation of equations (10) and (11) yields:
wherein, σ (h)0+ Y) is the stress at the contact interface when the acoustic wave propagates;
and solving to obtain an expression of the reflected wave and the transmitted wave:
wherein Y represents the displacement difference between the two ends of the interface;
c, exciting to obtain a frequency f1，f2Two ultrasonic waves will generate nf due to the nonlinear interaction between the two ultrasonic waves at the interface1，nf2，f1+f2Sum frequency wave sum f1-f2The difference frequency wave of (a) is,
regardless of the acoustic wave attenuation and the initial phase difference, the introduced excitation signal expression is as follows:
in the formula, A1And A2，ω1And ω2Respectively the amplitude and angular frequency of the two excited sound waves,
solving a reflected wave equation and a transmitted wave equation by using a perturbation method according to a wave equation and an incident wave expression; considering that, when the displacement of the incident wave is small, the gap distance changes little,in this case, the function σ (h) may be determined by the function σ (h) when h is equal to h0The nearby taylor expansion is replaced, taking the second order term, the expression is as follows:
σ(h)＝σ(h0+Y)＝σ0-K1Y+K2Y2 (16)
wherein,K1represents linear stiffness;K2representing the nonlinear rigidity of the contact surface, namely the second-order rigidity; h is the gap distance of the contact interface;
and d, substituting the formula (15) and the formula (16) into the formula (12) to obtain a first-order nonlinear ordinary differential equation related to Y, wherein the expression form is as follows:
e, solving an approximate solution by using a perturbation method as follows:
consider an approximate solution of the equation Y ═ Y1+Y2Wherein Y is1Is a first order trace, Y2Is a second order trace, is an approximate solution of the equation, and, at the same time, Y1,Y2The following equation is satisfied:
obtaining by solution:
wherein,δ1＝arctan(ω1/a)，δ2＝arctan(ω2/a)
wherein, take Δ ω ═ ω2-ω1，Σω＝ω1+ω2，ψ1＝θ1+δ1-δ2，ψ2＝θ2-δ1-δ2，θ1＝arctan[a/(Δω)]，θ2＝arctan(a/Σω)；
Step f, finally obtaining an expression of the reflected wave and the transmitted wave:
in S03, the expression of the power law relationship between the interface linear stiffness and the contact stress is as follows:
K1＝Cσ0 m (24)
wherein C and m are normal numbers, willAndand substituting to obtain a relation function of second-order rigidity and contact pressure:
defining a non-linearity parameter beta1,β2Is a difference frequency component in the transmitted wave,The ratio of the amplitude of the sum frequency component to the amplitude of the fundamental frequency, the non-linear parameter gamma1,γ2The ratio of the amplitude of the difference frequency component and the sum frequency component in the reflected wave to the amplitude of the fundamental frequency is:
the invention has the beneficial effects that: the invention provides a method for evaluating the contact characteristic of a solid-solid interface by utilizing a nonlinear effect, which is used for evaluating the contact characteristic of the solid-solid bonding interface by comparing a measured value of a nonlinear parameter with a reference value to analyze the bonding strength at the solid-solid bonding interface. In practical application, the detection signal needs to reduce the nonlinear interference of noise, and meanwhile, the ultrasonic wave can be seriously attenuated when passing through the defect, so that the linear parameter change is not obvious, and the linear ultrasonic flaw detection effect is not ideal directly. Compared with the single beam serving as an excitation source, the nonlinear ultrasonic detection technology can better make up the defect, and compared with the single beam serving as an excitation source, the aliasing beam with any frequency serving as an excitation source can more easily see different frequency components when receiving response signals, and can more easily measure nonlinear parameters, the defect of linear ultrasonic detection is well made up, so that the sensitivity of nonlinear ultrasonic detection using the aliasing beam as the excitation source is higher. Meanwhile, the method for evaluating the contact characteristic of the solid-solid bonding interface based on the nonlinear parameters has stronger practicability.
Drawings
FIG. 1 is a schematic representation of a model of the present invention;
figure 2 is a graph of the present invention at different difference frequencies,coefficient of non-linearity beta1Graph against stress (theoretical value);
FIG. 3 shows the nonlinear coefficient β of the present invention at different sum frequencies2Graph against stress (theoretical value);
FIG. 4 shows the nonlinear coefficient γ of the present invention at different difference frequencies1Pressure dependence (theoretical);
FIG. 5 shows the nonlinear coefficient γ of the present invention at different sum frequencies2Pressure dependence (theoretical);
FIG. 6 is a schematic view of the experimental set-up of the present invention;
FIG. 7 is a graph of the spectrum of a transmitted signal without applied pressure in an example of the invention;
FIG. 8 is a graph of the spectrum of the transmission signal when pressure is applied in an example of the present invention;
FIG. 9 is a graph comparing the curves of the theoretical values and the actual measured values of the present invention.
Detailed Description
The present invention is further described with reference to the accompanying drawings, and the following examples are only for clearly illustrating the technical solutions of the present invention, and should not be taken as limiting the scope of the present invention.
Nonlinear ultrasonic detection techniques can clearly see different frequency components when receiving a response signal. In addition to the fundamental frequency signal in the incident wave, higher harmonics are present in the received acoustic wave. Compared with the fundamental wave signal harmonic wave, the attenuation is very small, the defect of linear ultrasonic detection is well compensated, and therefore the sensitivity of nonlinear ultrasonic detection is higher.
The method of beam aliasing is controllable, so that any space can be selected, different waveforms can be converted, sound waves with different frequencies and different propagation directions can be selected, and the effect of avoiding nonlinear interference on a system can be achieved. The method for measuring the nonlinear effect of the system by adopting one path of incident sound wave response summation not only can remove the nonlinearity of the system, but also has higher sensitivity to the tiny change of the internal structure of the detection material and better application prospect. Therefore, compared with the single beam serving as the excitation source, harmonic signals of different frequencies can be more easily received by using the aliasing beam of any frequency as the excitation source, the nonlinear parameter can be more easily measured, and the method has higher accuracy and higher practicability.
The invention discloses a method for evaluating solid-solid interface contact characteristics by utilizing nonlinear effect, which is characterized in that two signals with different frequencies are input, the generated nonlinear effect of difference frequency and sum frequency signals is utilized, and the solid-solid interface contact characteristics are evaluated by introducing nonlinear coefficients, and the method mainly comprises the following steps:
step one, establishing a corresponding isotropic solid-solid bonding interface model according to actual conditions. As shown in fig. 1, which is a schematic diagram of a model of the present invention, a one-dimensional longitudinal elastic wave propagates along an X-axis direction, and reference plane positions of contact surfaces are set to X ═ X, respectively-,x＝X+In the region X < X-Incident one-dimensional longitudinal wave fincTo obtain a reflected wave frefIn the region X > X+Obtaining a transmitted wave ftra。
The one-dimensional longitudinal wave is positively propagated along the x axis, and the relation between the motion equation and the stress displacement is as follows:
wherein u (x, t) represents the displacement of the acoustic wave propagating along the x direction; σ (x, t) represents the stress variation; sigma0Two solid contact static stresses; t represents time; ρ represents the density of the medium.
And step two, deriving expressions of reflected waves and transmitted waves by using a perturbation method according to a nonlinear wave equation of aliasing incident beams and the boundary conditions of a solid-solid interface.
Wherein, the expression of the aliasing beam nonlinear wave equation is as follows:
where phi is the velocity potential and the velocity expression of the acoustic wave is
Wherein, c0The propagation velocity of small-amplitude sound waves in ideal gas is constant and depends on a medium; gamma is the ratio of specific heat at constant pressure to specific heat at constant volume; p is pressure, P0 is initial pressure; rho0Is the initial density.
Wherein, the boundary condition of the solid-solid interface satisfies:
when the elastic wave has interaction across the boundary, the displacement and stress conditions are as follows:
when the elastic waves do not interact across the boundary, i.e. there is no contact between the two solids at this time, the displacement and stress conditions are as follows:
one-dimensional elastic longitudinal wave propagates along the direction of the X axis, and the reference plane positions of the contact surfaces are respectively set as X ═ X-,x＝X+. Wherein u (+0, t) is acoustic wave in region X > X+Displacement of (2); u (-0, t) is acoustic wave in region X < X-Displacement of (2); σ (+0, t) is that sound wave is in area X > X+The stress of (a); sigma (-0, t) is that sound wave is in region X < X-Of the stress of (c). The specific steps of deriving the expressions of the reflected wave and the transmitted wave by using the perturbation method are as follows:
the solutions of step a, formula (1) and formula (2) are as follows:
u(x,t)＝finc(x-ct)+fref(x+ct)x＜X- (7)
u(x,t)＝ftra(x-ct)x＞X+ (8)
in the formula, function finc(x-ct),fref(x + ct) and ftra(x-ct) respectively represent expressions of incident waves propagating to the right along the x-axis on the left side of the entrance interfaceThe expression of the reflected wave propagating to the left along the x-axis and the expression of the transmitted wave propagating to the right along the x-axis on the right side of the interface, the wave speed c of the acoustic wave being (λ/ρ)1/2And λ is the elastic constant.
Step b, in order to solve the equations of the formula (1) and the formula (2), introducing the following variables:
Z(t)＝[u(X+,t)+u(X-,t)]/2 (9)
Y(t)＝u(X+,t)-u(X-,t)＝h(t)-h0 (10)
one-dimensional elastic longitudinal wave propagates along the direction of the X axis, and the reference plane positions of the contact surfaces are respectively set as X ═ X-,x＝X+. Wherein u (+0, t) is an acoustic wave at the interface X ═ X+A displacement of (a); u (-0, t) is acoustic wave at the interface X ═ X-A displacement of (a); h (t) is the gap distance between the contact surfaces when the sound waves are transmitted; h is0The gap distance between the contact surfaces in the case of a non-acoustic wave is constant and depends on the roughness of the solid medium and the contact surfaces. Z represents half of the sum of displacements at both ends of the contact interface, and Y represents the difference in displacement between both ends of the interface.
The derivation of equations (10) and (11) yields:
wherein, σ (h)0+ Y) is the stress at the contact interface as the acoustic wave propagates.
And solving to obtain an expression of the reflected wave and the transmitted wave:
where Y represents the difference in displacement between the two ends of the interface.
C, exciting to obtain a frequency f1，f2Two ultrasonic waves due to the non-linear motion of the two ultrasonic wavesNon-linear interaction will occur at the interface, resulting in nf1，nf2，f1+f2Sum frequency wave sum f1-f2The difference frequency wave of (1).
Regardless of the acoustic wave attenuation and the initial phase difference, the introduced excitation signal expression is as follows:
in the formula, A1And A2，ω1And ω2The amplitude and angular frequency of the two excited sound waves respectively.
And solving the equations of the reflected wave and the transmitted wave by using a perturbation method according to the wave equation and the incident wave expression. Considering that the gap distance changes very little when the displacement of the incident wave is small, the function σ (h) may be derived from this in this case when h is h0The nearby taylor expansion is replaced, taking the second order term, the expression is as follows:
σ(h)＝σ(h0+Y)＝σ0-K1Y+K2Y2 (16)
wherein,K1represents linear stiffness;K2representing the nonlinear rigidity of the contact surface, namely the second-order rigidity; h is the gap distance of the contact interface.
And d, substituting the formula (15) and the formula (16) into the formula (12) to obtain a first-order nonlinear ordinary differential equation related to Y, wherein the expression form is as follows:
e, solving an approximate solution by using a perturbation method as follows:
consider an approximate solution of the equation Y ═ Y1+Y2. Wherein, Y1Is a first order of a micronAmount, Y2Is a second order trace and is an approximate solution to the equation. At the same time, Y1,Y2The following equation is satisfied:
obtaining by solution:
wherein,δ1＝arctan(ω1/a)，δ2＝arctan(ω2/a)
wherein, take Δ ω ═ ω2-ω1，Σω＝ω1+ω2， ψ1＝θ1+δ1-δ2，ψ2＝θ2-δ1-δ2，θ1＝arctan[a/(Δω)]，θ2＝arctan(a/Σω)。
Step f, finally obtaining an expression of the reflected wave and the transmitted wave:
and step three, analyzing and obtaining the nonlinear effect of the aliasing wave beam incident on the solid-solid bonding interface according to the expression of the reflected wave and the transmitted wave obtained by deduction in the step two, and defining four nonlinear parameters to evaluate the contact characteristic of the solid-solid bonding interface by combining the power law relation of the linear rigidity and the contact stress of the interface.
The expression of the power law relation of the interface linear rigidity and the contact stress is as follows:
K1＝Cσ0 m (24)
wherein C and m are normal numbers, willAndand substituting to obtain a relation function of second-order rigidity and contact pressure:
defining a non-linearity parameter beta1,β2The nonlinear parameter gamma is the ratio of the amplitude of the difference frequency component and sum frequency component to the amplitude of the fundamental frequency in the transmitted wave1,γ2The ratio of the amplitude of the difference frequency component and the sum frequency component in the reflected wave to the amplitude of the fundamental frequency is:
the four non-linear parameters (beta) for evaluating the contact characteristics of the solid-solid bonding interface are obtained by the steps of theoretical calculation1,β2,γ1,γ2)。
And step four, under the condition that wave beams with different frequencies are aliased, drawing a change curve of the four nonlinear parameters along with the contact stress according to the numerical calculation result, and analyzing the nonlinear characteristics of the solid-solid interface. Meanwhile, the dependence of the harmonic on the contact stress of the solid-solid bonding interface was evaluated.
And fifthly, selecting the excitation signal aliasing with proper frequency by using the ultrasonic signal generator. The ultrasonic probe is used for exciting the test piece, and then the signal collector is used for collecting signals on the other side of the test piece.
And sixthly, the acquired signals are subjected to fast Fourier transform to obtain corresponding frequency spectrum images. And measuring to obtain the nonlinear parameters of the test piece under different pressures based on the theoretical basis of the third step.
And seventhly, analyzing to obtain that the nonlinear parameter has a monotonic relation with the bonding strength of the test piece by comparing the theoretical value with the actual value, so that the contact characteristic of the solid-solid bonding interface can be evaluated by using the nonlinear parameter, and the correctness and the feasibility of the method can be verified.
According to the theoretical calculation, under the condition of analyzing aliasing of beams with different frequencies, the change curves of four nonlinear parameters along with the contact stress are specifically as follows: as shown in fig. 2, the nonlinear coefficient β is obtained at different difference frequencies1The change curve of stress; as shown in fig. 3, the nonlinear coefficient β is different at different sum frequencies2The change curve of stress; as shown in fig. 4, the nonlinear coefficient γ is obtained at different difference frequencies1The change curve of stress; as shown in fig. 5, the nonlinear coefficient γ is different for different sum frequencies2And the change curve of stress. The following conclusions were reached: the non-linear parameter decreases with increasing pressure; the larger the difference of the incident frequencies is, the smaller the nonlinear parameter is; the non-linearity parameter is smaller as the sum of the incident frequencies is larger. Thus, through theoretical analysis, nonlinear parameters and experiments are foundThe piece bonding strength has a monotonous relation and can be used for evaluating the contact characteristics of a solid-solid bonding interface.
Finally, the feasibility of the method of the invention was verified by experimental practical measurements. FIG. 6 is a schematic diagram of the experimental apparatus. In the experiment, two rows of sine waves with frequencies of 2MHz and 2.5MHz respectively are selected, mixed by an ultrasonic signal generator and used as an excitation source, the two rows of sine waves are excited on a tested piece by an ultrasonic probe, and then signals are collected by a signal collector on the other side. The acquired signals are subjected to fast fourier transform to obtain spectral images as shown in fig. 7 and 8. The measurement results in the nonlinear parameters of the test piece under different pressures. As shown in fig. 9, by comparing the theoretical value and the actual value, the nonlinear parameter obtained by analysis has a monotonic relationship with the bonding strength of the test piece, and the fitting degree of the actual measurement curve and the theoretical curve is high. Therefore, the feasibility and the reliability of evaluating the contact characteristics of the solid-solid bonding interface by utilizing the nonlinear parameters are verified.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.
Claims (6)
1. A method for evaluating the contact characteristic of a solid-solid interface by utilizing a nonlinear effect is characterized by comprising the following steps: the method comprises the following steps:
s01, establishing an isotropic solid-solid bonding interface model, and giving a longitudinal wave motion equation and a stress-displacement relation;
s02, deriving expressions of reflected waves and transmitted waves by a perturbation method according to a nonlinear wave equation of aliasing incident beams and boundary conditions of a solid-solid interface;
s03, analyzing to obtain a nonlinear effect of an aliasing beam incident on a solid-solid bonding interface, and defining four nonlinear parameters to evaluate the contact characteristics of the solid-solid bonding interface by combining the power law relation of the interface linear rigidity and the contact stress;
s04, drawing a curve of four nonlinear parameters changing along with contact stress under the condition of aliasing of beams with different frequencies according to the numerical calculation result;
s05, selecting excitation signal aliasing with proper frequency by using an ultrasonic signal generator, exciting on the tested piece through an ultrasonic probe, receiving an acquisition signal by using another ultrasonic probe on the other side of the tested piece, and visually acquiring the signal through a signal acquisition device;
s06, carrying out fast Fourier transform on the acquired signals to obtain corresponding frequency spectrum images, and measuring to obtain nonlinear parameters of the test piece under different pressures based on the theoretical basis of S03;
and S07, comparing the theoretical value with the actual value, and analyzing to obtain the monotonic relation between the nonlinear parameter and the bonding strength of the test piece.
2. The method for evaluating the contact characteristic of the solid-solid interface by utilizing the nonlinear effect as claimed in claim 1, wherein: in the step S01, the first step,
one-dimensional elastic longitudinal wave propagates along the direction of the X axis, and the reference plane positions of the contact surfaces are respectively set as X ═ X-,x＝X+In the region X < X-Incident one-dimensional longitudinal wave fincTo obtain a reflected wave frefIn the region X > X+Obtaining a transmitted wave ftra；
The one-dimensional longitudinal wave is positively propagated along the x axis, and the relation between the motion equation and the stress displacement is as follows:
wherein u (x, t) represents the displacement of the acoustic wave propagating along the x direction; σ (x, t) represents the stress variation; sigma0Two solid contact static stresses; t represents time; ρ represents the density of the medium.
3. The method for evaluating the contact characteristic of the solid-solid interface by utilizing the nonlinear effect as claimed in claim 2, wherein: in S02, the aliased beam nonlinear wave equation expression is as follows:
where phi is the velocity potential and the velocity expression of the acoustic wave is
Wherein, c0The propagation velocity of small-amplitude sound waves in ideal gas is constant and depends on a medium; gamma is the ratio of specific heat at constant pressure to specific heat at constant volume; p is pressure, P0Is the initial pressure; rho0Is the initial density.
4. The method for evaluating the contact characteristic of the solid-solid interface by utilizing the nonlinear effect as claimed in claim 2, wherein: in S02, the solid-solid interface boundary condition satisfies:
when the elastic wave has interaction across the boundary, the displacement and stress conditions are as follows:
when the elastic waves do not interact across the boundary, i.e. there is no contact between the two solids at this time, the displacement and stress conditions are as follows:
wherein u (+0, t) is acoustic wave in region X > X+Displacement of (2); u (-0, t) is acoustic wave in region X < X-Displacement of (2); σ (+0, t) is that sound wave is in area X > X+The stress of (a); sigma (-0, t) is that sound wave is in region X < X-Of the stress of (c).
5. The method for evaluating the contact characteristic of the solid-solid interface by utilizing the nonlinear effect as claimed in claim 2, wherein: the specific steps of deriving the expressions of the reflected wave and the transmitted wave by using the perturbation method are as follows:
the solutions of step a, formula (1) and formula (2) are as follows:
u(x,t)＝finc(x-ct)+fref(x+ct) x＜X- (7)
u(x,t)＝ftra(x-ct) x＞X+ (8)
in the formula, function finc(x-ct),fref(x + ct) and ftra(x-ct) represents an expression of an incident wave propagating right along the x-axis on the left side of the interface, a reflected wave propagating left along the x-axis, and a transmitted wave propagating right along the x-axis on the right side of the interface, respectively, and the wave velocity c of the acoustic wave is (λ/ρ)1/2λ is the elastic constant;
step b, in order to solve the equations of the formula (1) and the formula (2), introducing the following variables:
Z(t)＝[u(X+,t)+u(X-,t)]/2 (9)
Y(t)＝u(X+,t)-u(X-,t)＝h(t)-h0 (10)
one-dimensional elastic longitudinal wave propagates along the direction of the X axis, and the reference plane positions of the contact surfaces are respectively set as X ═ X-,x＝X+(ii) a Wherein u (+0, t) is an acoustic wave at the interface X ═ X+A displacement of (a); u (-0, t) is acoustic wave at the interface X ═ X-A displacement of (a); h (t) is the gap distance between the contact surfaces when the sound waves are transmitted; h is0The gap distance between the contact surfaces is constant when the contact surface is silent, and is related to the roughness of the solid medium and the contact surface; z represents the half of the displacement sum of the two ends of the contact interface, and Y represents the displacement difference of the two ends of the contact interface;
the derivation of equations (10) and (11) yields:
wherein, σ (h)0+ Y) is the stress at the contact interface when the acoustic wave propagates;
and solving to obtain an expression of the reflected wave and the transmitted wave:
wherein Y represents the displacement difference between the two ends of the interface;
c, exciting to obtain a frequency f1，f2Two ultrasonic waves will generate nf due to the nonlinear interaction between the two ultrasonic waves at the interface1，nf2，f1+f2Sum frequency wave sum f1-f2The difference frequency wave of (a) is,
regardless of the acoustic wave attenuation and the initial phase difference, the introduced excitation signal expression is as follows:
in the formula, A1And A2，ω1And ω2Respectively the amplitude and angular frequency of the two excited sound waves,
solving a reflected wave equation and a transmitted wave equation by using a perturbation method according to a wave equation and an incident wave expression; considering that the gap distance changes very little when the displacement of the incident wave is small, the function σ (h) may be derived from this in this case when h is h0The nearby taylor expansion is replaced, taking the second order term, the expression is as follows:
σ(h)＝σ(h0+Y)＝σ0-K1Y+K2Y2 (16)
wherein,K1represents linear stiffness;K2representing the nonlinear rigidity of the contact surface, namely the second-order rigidity; h is the gap distance of the contact interface;
and d, substituting the formula (15) and the formula (16) into the formula (12) to obtain a first-order nonlinear ordinary differential equation related to Y, wherein the expression form is as follows:
e, solving an approximate solution by using a perturbation method as follows:
consider an approximate solution of the equation Y ═ Y1+Y2Wherein Y is1Is a first order trace, Y2Is a second order trace, is an approximate solution of the equation, and, at the same time, Y1,Y2The following equation is satisfied:
obtaining by solution:
wherein,δ1＝arctan(ω1/a)，δ2＝arctan(ω2/a)
wherein, take Δ ω ═ ω2-ω1，Σω＝ω1+ω2，ψ1＝θ1+δ1-δ2，ψ2＝θ2-δ1-δ2，θ1＝arctan[a/(Δω)]，θ2＝arctan(a/Σω)；
Step f, finally obtaining an expression of the reflected wave and the transmitted wave:
6. the method for evaluating the contact characteristic of the solid-solid interface by utilizing the nonlinear effect as claimed in claim 4, wherein: in S03, the expression of the power law relationship between the interface linear stiffness and the contact stress is as follows:
K1＝Cσ0 m (24)
wherein C and m are normal numbers, willAndand substituting to obtain a relation function of second-order rigidity and contact pressure:
defining a non-linearity parameter beta1,β2The nonlinear parameter gamma is the ratio of the amplitude of the difference frequency component and sum frequency component to the amplitude of the fundamental frequency in the transmitted wave1,γ2As a difference frequency in the reflected waveRatio of the amplitude of the component, sum frequency component, to the amplitude of the fundamental frequency:
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