CN108444920B - Method for nondestructive evaluation of fatigue degree of material by using photoacoustic eigen spectrum analysis method - Google Patents

Method for nondestructive evaluation of fatigue degree of material by using photoacoustic eigen spectrum analysis method Download PDF

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CN108444920B
CN108444920B CN201810057839.7A CN201810057839A CN108444920B CN 108444920 B CN108444920 B CN 108444920B CN 201810057839 A CN201810057839 A CN 201810057839A CN 108444920 B CN108444920 B CN 108444920B
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陶超
郜晓翔
刘晓峻
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    • G01N21/1702—Systems in which incident light is modified in accordance with the properties of the material investigated with opto-acoustic detection, e.g. for gases or analysing solids
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    • G01N21/1702—Systems in which incident light is modified in accordance with the properties of the material investigated with opto-acoustic detection, e.g. for gases or analysing solids
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Abstract

The invention discloses a method for nondestructively evaluating the fatigue degree of a material by utilizing a photoacoustic eigenspectrum analysis method. When the material is fatigued, the elastic characteristic changes, so that the eigenfrequency of the material is changed. Therefore, according to the change of the eigenfrequency and the elasticity parameter of the material obtained by the photoacoustic eigenspectrum analysis method, the fatigue degree of the material can be detected and evaluated without damage. The method for nondestructive testing of the fatigue degree of the material by using the photoacoustic eigen-spectrum analysis method provided by the invention does not need to contact a measuring instrument with the material to be tested, and does not need to carry out any anatomical treatment on the material.

Description

Method for nondestructive evaluation of fatigue degree of material by using photoacoustic eigen spectrum analysis method
Technical Field
The invention relates to a nondestructive measurement method for material fatigue, in particular to a nondestructive evaluation method for nondestructively measuring the eigen spectrum and eigen frequency of a material by utilizing a photoacoustic effect and an optimization algorithm and further carrying out nondestructive evaluation on the fatigue condition of the material according to the relation between the eigen frequency of the material and the fatigue degree of the material.
Background
The non-invasive and non-contact measurement of the fatigue degree of the material is not only the basic research content of material science, but also the fatigue damage detection of the material has wide application prospect in the fields of mechanical manufacture, aerospace, biomedicine and the like, and has important significance on production, life, health and safety. When the material is fatigued, the change of the elasticity of the material is accompanied, and the change of the elasticity of the material is detected to be used as a quantitative evaluation means of the fatigue degree of the material.
Technologies based on the photoacoustic effect have attracted a great deal of attention in material detection. Especially in the last twenty years, photoacoustic imaging has been widely used in the fields of industrial detection and biomedicine due to the advantages of high imaging contrast, high resolution of deep tissue images, high safety, and the like. With photoacoustic techniques, we can successfully extract many biological information including material elasticity, blood oxygen saturation, blood flow velocity, temperature, viscoelasticity, etc.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects in the prior art, the invention provides a method for nondestructively evaluating the fatigue degree of a material by utilizing a photoacoustic eigenspectrum analysis method. The method utilizes the photoacoustic effect to detect the eigenfrequency of the elastomer, and further can evaluate the fatigue degree of the material according to the change of the eigenfrequency of the material under the fatigue condition.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the technical scheme that:
a method for nondestructively evaluating fatigue degree of material by using photoacoustic eigen spectrum analysis method includes utilizing laser pulse to irradiate elastic body to radiate sound wave under action of photoacoustic effect, obtaining photoacoustic eigen spectrum of elastic body by analyzing photoacoustic signal radiated by elastic body, and extracting eigen frequency of elastic body from photoacoustic eigen spectrum. When the material is fatigued, the elastic characteristic changes, so that the eigenfrequency of the material is changed. Therefore, according to the change of the eigenfrequency and the elasticity parameter of the material obtained by the photoacoustic eigenspectrum analysis method, the fatigue degree of the material can be detected and evaluated without damage. The method specifically comprises the following steps:
step 1, irradiating pulse laser to a material to be detected (an elastic body) by using a pulse laser. The material to be measured radiates acoustic waves to surrounding media after being excited by the photoacoustic effect.
Step 2, receiving the acoustic signal radiated by the material to be measured
And 3, calculating a time-frequency diagram of the acoustic wave signal through the received acoustic wave signal radiated by the material to be detected. Obtaining the eigenfrequency spectral line of the material to be measured at the tail part of the time-frequency diagram, extracting the eigenfrequency spectral line to obtain the eigenfrequency of the material to be measured, and recording the eigenfrequency as the measured eigenfrequency gi。
And 4, a characteristic equation of the vibration of the material to be detected in the inviscid fluid is as follows: i D ═ 0, where D ═ Dij},(i,j＝1,2,3)，
Figure BDA0001554349960000021
d12＝(2n2-ks2a2)Jn(kda)-2kdaJn'(kda)，d13＝2n[ksaJn'(ksa)-Jn(ksa)]，d21＝-kfaHn(1)'(kfa)，d22＝kdaJn'(kda)，d23＝nJn(ksa)，d31＝0，d32＝2n[Jn(kda)–kdaJn'(kda)]，d33＝2ksaJn'(ksa)+[ks2a2-2n2]Jn(ksa)。
Wherein a is the radius of the material to be measured, rhofIs the density of the surrounding medium, psFor the density of the material to be measured, HnIs a Hankel function of order n, JnIs a Bessel function of order n, n is the order of the Hankel function and the Bessel function, kfIs the wave number, k, of the sound wave in the surrounding mediumsIs the wave number, k, of the longitudinal wave in the material to be measureddIs the wave number, k, of transverse waves in the material to be measuredf＝2πf/cf,ks＝2πf/cs,kd＝2πf/cdF is frequency, cfIs the speed of sound of the medium, cdThe velocity of the transverse wave in the elastomer, csIs the velocity of longitudinal waves in the elastomer.
Solving the characteristic equation can obtain the frequency of the material to be measured, and the obtained frequency of the material to be measured is recorded as the eigenfrequency f calculated by the characteristic equationi。
Step 5, the frequency error function F (E, σ) is:
Figure BDA0001554349960000022
wherein E is Young's modulus, sigma is Poisson's ratio, N is the number of eigenfrequencies used for calculating frequency error, fiEigenfrequency, g, calculated for a characteristic equationiFor the measured eigenfrequency, wiAre weighting coefficients. When the error function F (E, sigma) takes the minimum value, the inversion is carried outThe values of E and σ are evaluated.
Step 6, obtaining a fatigue damage parameter D by utilizing the calculated Young modulus E of the material to be detectedd＝1-E/E0Wherein E is0The fatigue damage parameter is a normal elasticity value of the material to be tested, and can be used for evaluating the fatigue degree of the material.
Preferably: in the step 1, a nanosecond pulse laser is used for irradiating the material to be detected with pulse laser.
Preferably: and 2, receiving the acoustic wave signals radiated by the material to be detected by using the ultrasonic transducer, and storing the received acoustic wave signals in a computer after the received acoustic wave signals are amplified by the small signal amplifier and sampled by the digital acquisition card in sequence.
Preferably: the method for obtaining the characteristic equation of the vibration of the material to be detected in the inviscid fluid in the step 4 comprises the following steps:
the wave equation for the material to be tested in a non-viscous fluid satisfies the following equation:
Figure BDA0001554349960000023
where ρ issFor elastomer density, u is the particle displacement vector, t is time, E is Young's modulus, σ is Poisson's ratio,
Figure BDA0001554349960000024
a Hamilton operator;
when the material to be measured is in a non-viscous fluid, 3 boundary conditions are satisfied on the boundary: i) the normal stress in the material to be measured is equal to the pressure in the fluid; ii) the normal displacement within the material to be measured is equal to the normal displacement within the fluid; iii) the tangential component of the internal shear stress of the material to be measured is zero;
and obtaining a characteristic equation of the vibration of the material to be measured in the inviscid fluid according to the above boundary conditions.
Preferably: and 5, solving an inversion result by using a Levenberg-Marquardt algorithm.
Preferably: in step 5 take
Figure BDA0001554349960000031
Compared with the prior art, the invention has the following beneficial effects:
(1) the invention uses the photoacoustic effect to excite the object to be measured to vibrate, and then uses the acoustic transducer to receive the acoustic signal radiated by the object for analysis. The entire process does not require the object to be in contact with the transducer, so the method is non-contact.
(2) The invention does not need the transducer to contact with the object to be detected, so that the non-invasive detection of deep tissues can be conveniently realized.
(3) The method for nondestructive testing of the fatigue degree of the material by using the photoacoustic eigen-spectrum analysis method provided by the invention does not need to contact a measuring instrument with the material to be tested, and does not need to carry out any anatomical treatment on the material.
Drawings
FIG. 1 is a system diagram of the method for nondestructive evaluation of material fatigue by photoacoustic eigenspectrum analysis of the present invention.
Fig. 2 shows the acoustic signal radiated by the brass wire after being excited by laser.
FIG. 3 is a time-frequency diagram of a brass wire whole-segment acoustic signal.
FIG. 4 is a spectral diagram of a bow wave and a wake wave.
The elasticity evaluation values of the different fatigue-free wire samples of fig. 5 are compared with the actual values.
Figure 6 eigen spectrum of steel wires of different fatigue levels.
Fig. 7 is a graph showing the elasticity and fatigue damage parameters of steel wires with different degrees of fatigue, in which fig. 7(a) shows a graph showing the elasticity (young's modulus) of steel wires with different degrees of fatigue, and fig. 7(b) shows a graph showing the fatigue damage parameters of steel wires with different degrees of fatigue.
Detailed Description
The present invention is further illustrated by the following description in conjunction with the accompanying drawings and the specific embodiments, it is to be understood that these examples are given solely for the purpose of illustration and are not intended as a definition of the limits of the invention, since various equivalent modifications will occur to those skilled in the art upon reading the present invention and fall within the limits of the appended claims.
A method for nondestructively evaluating the fatigue degree of a material by utilizing a photoacoustic eigenspectrum analysis method comprises the following steps of:
(1) as shown in figure 1, a metal wire is immersed in water, a Nd: YAG laser is used for radiating laser pulses to irradiate the metal wire, the pulse width of the laser is about 10ns, namely between 9 ns and 11ns, and the laser gives a trigger to a digital acquisition card. The metal wire radiates sound waves after being excited by the photoacoustic effect.
(2) After the wire radiates the acoustic wave, the acoustic signal is received by the ultrasonic transducer. The ultrasonic transducer has a center frequency of 4.39MHz and a 6dB bandwidth of 4.4 MHz. The sound wave signal is amplified by a signal amplifier, sampled by a digital acquisition card with the sampling rate of 60MHz and finally stored in a computer.
(3) And calculating a time-frequency diagram of the sound wave signal through signal processing software. Obtaining the eigenfrequency spectral line of the elastomer at the tail part of the time-frequency diagram, extracting the spectral line to obtain the eigenfrequency of the metal wire sample, and recording the eigenfrequency as the measured eigenfrequency gi。
The acoustic signals received by the transducers are processed by a computer. As shown in fig. 2, it shows the acoustic signal radiated from the brass wire after being excited by the laser. The front amplitude of the signal is strong and this segment of the signal is called the bow wave. The head wave is a photoacoustic signal radiated by the metal wire directly excited by laser, and an enlarged view of the head wave is shown in the figure. The head wave is followed by a relatively long period of acoustic signal of continuously decreasing amplitude, which is called the wake wave. The tail wave is the sound wave radiated by the wire to keep vibrating due to its own inertia after the laser disappears.
The time-frequency diagram of the whole acoustic signal is shown in fig. 3. The signals of the front section broadband of the time-frequency diagram correspond to head waves, and the narrow-band resonance spectral lines of the rear section are corresponding to tail waves. The wake signal is composed of multiple eigenfrequencies in the frequency domain, indicating that the wake signal is not random, but periodic. The resonance line of the tail wave signal corresponds to the eigenfrequency of the metal wire.
Fig. 4 is a frequency spectrum of a head wave and a tail wave. The head wave is a broad band spectrum, and the tail wave is composed of a plurality of resonance peaks, namely, the resonance lines in a time-frequency diagram.
(4) The wave equation of the elastic body satisfies the following formula
Figure BDA0001554349960000041
Where ρ issFor elastomer density, u is the particle displacement vector, t is time, E is Young's modulus, σ is Poisson's ratio,
Figure BDA0001554349960000042
is Hamilton operator.
The material to be measured in a non-viscous fluid meets 3 boundary conditions on the boundary: i) the normal stress in the material to be measured is equal to the pressure in the fluid; ii) the normal displacement within the material to be measured is equal to the normal displacement within the fluid; iii) the tangential component of the shear stress in the material to be measured is zero. From the above boundary conditions, a characteristic equation of the vibration of the infinite cylindrical elastic solid (material to be measured) in the inviscid fluid can be obtained, where | D | ═ 0, where D ═ Dij},(i,j＝1,2,3)，
Figure BDA0001554349960000043
Figure BDA0001554349960000044
d12＝(2n2-ks2a2)Jn(kda)-2kdaJn'(kda)，d13＝2n[ksaJn'(ksa)-Jn(ksa)]，d21＝-kfaHn(1)'(kfa)，d22＝kdaJn'(kda)，d23＝nJn(ksa)，d31＝0，d32＝2n[Jn(kda)–kdaJn'(kda)]，d33＝2ksaJn'(ksa)+[ks2a2-2n2]Jn(ksa) In that respect Wherein a is the radius of the material to be measured, rhofIs given byDensity of surrounding medium, psFor the density of the material to be measured, HnIs a Hankel function of order n, JnIs a Bessel function of order n, n is the order of the Hankel function and the Bessel function, kfIs the wave number, k, of the acoustic wave in the mediumsIs the wave number, k, of the longitudinal wave in the material to be measureddIs the wave number, k, of transverse waves in the material to be measuredf＝2πf/cf,ks＝2πf/cs,kd＝2πf/cdF is frequency, cfIs the speed of sound of the medium, cdIs the transverse wave velocity of the elastomer, csIs the longitudinal wave velocity of the elastomer.
Solving the characteristic equation can obtain the frequency of the material to be measured, and the obtained frequency of the material to be measured is recorded as the eigenfrequency f calculated by the characteristic equationi。
(5) Defining the frequency error function F (E, σ) as:
Figure BDA0001554349960000051
wherein E is Young's modulus, sigma is Poisson's ratio, N is the number of eigenfrequencies used for calculating frequency error function, giFor the measured eigenfrequency, fiEigenfrequency, w, calculated for a characteristic equationiFor weighting factors, it is common to take
Figure BDA0001554349960000052
When the error function F (E, σ) takes a minimum value, the inverted E and σ are evaluation values. And solving an inversion result by utilizing a Levenberg-Marquardt algorithm.
The eigenfrequency g measured in FIG. 4iEigenfrequency f calculated from a characteristic equationiAnd (3) substituting the formula (2) and calculating the Young modulus and the Poisson ratio when the error function is minimum by using a Levenberg-Marquardt algorithm.
(6) Using the calculated material elastic modulus (young's modulus) E, the fatigue damage parameter D is obtained as 1-E/E0Wherein E is0Is the normal elasticity value of the material, and the fatigue damage parameter can be used for evaluating the fatigue degree of the material.
And repeating the experiment and the calculation steps on the metal wires of different materials, and calculating the evaluation values of the Young modulus and the Poisson ratio of the different materials. Fig. 5 shows a comparison of the evaluation value and the actual value.
The implementation is as follows:
applying 100N of pulling force to the steel wire, and respectively stretching for 200, 400 and 600 cycles to obtain the steel wires with different fatigue degrees. The eigen spectrum of the steel wires of different degrees of fatigue was measured according to the procedure of example 1. As shown in fig. 6, the photoacoustic eigen spectrum of steel wires with different degrees of fatigue. Young's modulus values were calculated, and fatigue damage parameters D of different degrees of fatigue were obtained from the Young's modulus values, and the results are shown in FIGS. 7(a) and (b).
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 (5)

1. A method for nondestructively evaluating the fatigue degree of a material by utilizing a photoacoustic eigenspectrum analysis method is characterized by comprising the following steps of:
step 1, irradiating pulse laser to a material to be detected by using a pulse laser; the material to be measured radiates sound waves to surrounding media after being excited by the photoacoustic effect; the material to be detected is a cylindrical elastic solid;
step 2, receiving an acoustic signal radiated by a material to be detected;
step 3, calculating a time-frequency diagram of the sound wave signal through the received sound wave signal radiated by the material to be detected; obtaining the eigenfrequency spectral line of the material to be measured at the tail part of the time-frequency diagram, extracting the eigenfrequency spectral line to obtain the eigenfrequency of the material to be measured, and recording the eigenfrequency as the measured eigenfrequency gi；
Step 4, the wave equation of the material to be measured in the inviscid fluid satisfies the following formula:
Figure FDA0002941911040000011
where ρ issFor elastomer density, u is the particle displacement vector, t is time, E is Young's modulus, σ is Poisson's ratio,
Figure FDA0002941911040000012
a Hamilton operator;
a cylindrical elastic solid in a non-viscous fluid, which satisfies 3 boundary conditions at the boundary: i) normal stress in the cylindrical elastic solid is equal to pressure in the fluid; ii) the normal displacement within the cylindrical elastic solid is equal to the normal displacement within the fluid; iii) the tangential component of the internal shear stress of the cylindrical elastic solid is zero;
obtaining a characteristic equation of the vibration of the cylindrical elastic solid in the inviscid fluid according to the above boundary conditions;
the characteristic equation for the vibration of a cylindrical elastic solid in a inviscid fluid is as follows: i D ═ 0, where D ═ Dij},i,j＝1,2,3，d11＝(ρf/ρs)ks 2a2Hn(1)(kfa)，d12＝(2n2-ks2a2)Jn(kda)-2kdaJn'(kda)，d13＝2n[ksaJn'(ksa)-Jn(ksa)]，d21＝-kfaHn(1)'(kfa)，d22＝kdaJn'(kda)，d23＝nJn(ksa)，d31＝0，d32＝2n[Jn(kda)–kdaJn'(kda)]，d33＝2ksaJn'(ksa)+[ks2a2-2n2]Jn(ksa)；
Wherein a is the radius of the material to be measured, rhofIs the density of the surrounding medium, psFor the density of the material to be measured, HnIs a Hankel function of order n, JnIs a Bessel function of order n, subscript n is the order of the Hankel function and the Bessel function, kfIs the wave number, k, of the acoustic wave in the mediumsFor longitudinal waves in the material to be measuredWave number, k ofdIs the wave number, k, of transverse waves in the material to be measuredf＝2πf/cf,ks＝2πf/cs,kd＝2πf/cdF is frequency, cfIs the speed of sound of the medium, cdIs the transverse wave velocity of the elastomer, csIs the longitudinal wave velocity of the elastomer;
solving the characteristic equation to obtain the frequency of the material to be tested, and recording the obtained frequency of the material to be tested as the eigenfrequency f calculated by the characteristic equationi；
Step 5, the frequency error function F (E, σ) is:
Figure FDA0002941911040000013
wherein E is Young's modulus, sigma is Poisson's ratio, N is the number of eigenfrequencies used for calculating frequency error, fiEigenfrequency, g, calculated for a characteristic equationiFor the measured eigenfrequency, wiIs a weighting coefficient; when the error function F (E, sigma) takes the minimum value, E and sigma obtained by inversion are evaluated values;
step 6, obtaining a fatigue damage parameter D by utilizing the calculated Young modulus E of the material to be detectedd＝1-E/E0Wherein E is0The fatigue damage parameter is used for evaluating the fatigue degree of the material.
2. The method for non-destructively assessing the degree of fatigue of a material using photoacoustic eigen-spectroscopy as set forth in claim 1, wherein: in the step 1, a nanosecond pulse laser is used for irradiating the material to be detected with pulse laser.
3. The method for non-destructively assessing the degree of fatigue of a material using photoacoustic eigen-spectroscopy as set forth in claim 1, wherein: and 2, receiving the acoustic wave signals radiated by the material to be detected by using the ultrasonic transducer, and storing the received acoustic wave signals in a computer after the received acoustic wave signals are amplified by the small signal amplifier and sampled by the digital acquisition card in sequence.
4. The method for non-destructively assessing the degree of fatigue of a material using photoacoustic eigen-spectroscopy as set forth in claim 1, wherein: and 5, solving an inversion result by using a Levenberg-Marquardt algorithm.
5. The method for non-destructively assessing the degree of fatigue of a material using photoacoustic eigen-spectroscopy as set forth in claim 1, wherein: in step 5, take wi＝1/gi 2。
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