CN102297898A - Laser ultrasonic measuring method for third order elastic constant of metal - Google Patents

Abstract

The invention discloses a method for utilizing a laser ultrasonic wave to precisely measure a third order elastic constant of metal. The method comprises the following steps: respectively measuring wave velocities of a longitudinal wave, a transverse wave and a surface wave excited by a laser under stress-free state and stress state; utilizing the wave velocities of the longitudinal wave, the transverse wave and the surface wave measured under stress-free state to calculate a second order elastic constant and a density of metal according to a sonic elasticity theory and a Rayleigh equation; utilizing the ultrasonic wave velocities of the longitudinal wave, the transverse wave and the surface wave measured under stress state to introduce an equivalent second order elastic constant and an independently measured linear coefficient of thermal expansion; and lastly, calculating the third order elastic constant according to the sonic elasticity theory. According to the method, a pulse laser source is utilized to excite a sound surface wave, non-contact exciting is performed under a thermal elastic system and an overheated phenomenon of materials is avoided, so as to realize nondestructive measurement. A large amount of sound surface wave data spread for different distances is collected and a correlation function is utilized to calculate a wave velocity of the sound surface wave and a spread distance of sound wave, thereby greatly reducing error of arriving time value of the sound surface wave and promoting the measuring precision of a sound wave velocity.

Description

The laser-ultrasound assay method of metal three rank elastic constants

Technical field

The present invention relates to a kind of three rank elastic constants and carry out accurate method for measuring, a kind of specifically method of utilizing laser ultrasonic accurately to measure three rank elastic constants of metal metal.

Background technology

Acoustoelastic effect refers to that the ultrasonic velocity in the solid can change along with the distortion that is applied to solid or stress, and this effect is used widely in the Non-Destructive Testing of static state and unrelieved stress detect, and these it has been generally acknowledged that velocity of wave and strain are linear relationships in using.Existing method can reach 10 to the measuring accuracy of various ultrasound modality velocities of wave ^-4Even it is higher, see the result of study that we are previous---as document 1[SPIE, Vol.7544,754451 (2010) " Measurement of velocity distribution of laser-generated Rayleigh wave on welded structure "].And a main difficult problem is to obtain the Relation Parameters of the velocity of sound based on strain variation, and we are referred to as sonoelastic coefficient.On the mathematics, sonoelastic coefficient is the linearity combination of second order and three rank elastic constants, the microcosmic and the macro property of second order and three rank elastic constants and material all have substantial connection, particularly the high-order elastic constant of material (as three rank elastic constants) is significant for the quantitative estimation of its characteristic, wherein include the lot of materials nonlinear transformations, for example attenuation properties of temperature expansion character, heat conduction property and the high frequency sound wave of material etc. is all closely related with the high-order elastic constant.

The classic method of measuring three rank elastic constants is to adopt the load of calibration to be applied on the material and the measuring speed variation, this needs complicated huge instrument and equipment, and sample must be specific shape and size, as document 2[Tongji University journal, Vol.23,5 (1995) " ultrasonic measurement methods of three rank elastic constants "].This method has been measured solid does not have axial stress and the longitudinal wave velocity and the shear wave velocity of sound that apply under the axial stress state, utilizes the relation of acoustic velocity and three rank elastic constants to calculate three rank elastic constants.But this method excites and receives ultrasound wave in the sample both sides to the heart, judges that so erroneous judgement appears in sound wave time of arrival (especially for the less sample of thickness) easily, so causes that velocity of wave measuring and calculating and final elastic constant calculate the generation error; Owing to not have to consider certain variation all to be arranged in density that applies solid under the axial stress state and axial length, still adopt density of material and sound wave propagation distance value when unstressed, this also brings bigger error to the measuring and calculating of elastic constant.Therefore develop a kind of accurate measurement acoustic velocity, and then the high reliability technology of accurate Calculation metal three rank elastic constants is very important.

Summary of the invention

The objective of the invention is to invent a kind of three rank elastic constants and carry out accurate method for measuring metal, this method not only makes the acoustic velocity measuring accuracy of various mode higher, can avoid exciting method of reseptance to sound wave value time of arrival error to the heart, and utilize linear thermal expansion to apply hydrostatic stress and avoided causing the metal axial length variations because of applying axial stress, and considered the variable density of metal under the stress state, the precision of three rank elastic constants of therefore calculating metal is higher.

The technical solution that realizes the object of the invention is: a kind of laser-ultrasound assay method of metal three rank elastic constants, and step is as follows:

The first step at unstress state and having under the stress state, is measured compressional wave, the shear wave of laser excitation, the velocity of wave of surface wave respectively;

In second step, utilize the surface wave, compressional wave and the transverse wave speed that record under the unstress state, according to the second order elasticity constant and the density of acoustic elasticity theory and Rayleigh equation calculating metal;

The 3rd step, utilize the compressional wave that records under the stress state is arranged, the ultrasonic velocity of shear wave, surface wave, introduce the thermal linear expansion coefficient of equivalent second order elasticity constant and independent measurement, at last according to acoustic elasticity Theoretical Calculation three rank elastic constants.

The present invention compared with prior art, its remarkable advantage has: (1) utilizes the pulse laser line source to excite surface acoustic wave, and noncontact excites under thermoelastic mechanism, avoids the material production superheating phenomenon, thereby realizes Non-Destructive Testing; (2) by gathering the surface acoustic wave data of having propagated different distance in a large number, utilize the related function method to calculate surface acoustic wave velocity of wave and sound wave propagation distance, can reduce error greatly by surface acoustic wave value time of arrival, improved the mensuration precision of acoustic velocity; (3) not only equipment is simple and practical to adopt the heated at constant temperature method to apply hydrostatic stress by the sample linear thermal expansion, and avoided bringing the metal axial length variations because of applying axial stress, and considered the variable density of metal under the stress state, the precision of three rank elastic constants of therefore calculating metal is higher.

Below in conjunction with accompanying drawing the present invention is described in further detail.

Description of drawings

Fig. 1 is to use scan laser line source method to calculate the detection system synoptic diagram of surface acoustic wave, compressional wave and transverse wave speed respectively when metal sample is in unstress state and stress state is arranged.

Fig. 2 is the ultrasonic signal figure that detects and to the spectrum analysis figure of surface acoustic wave.

Fig. 3 is the funtcional relationship matched curve figure of the time delay and the ripple propagation distance of N surface acoustic wave signal.

Embodiment

The laser-ultrasound assay method of metal three rank elastic constants of the present invention, its step is as follows:

The first step is accurately measured the velocity of wave of the ultrasound wave (compressional wave, shear wave, surface wave) of laser excitation under the unstress state.Concrete steps comprise:

(1) design detection system, as shown in Figure 1.This detection system comprises pulsed laser, cylindrical lens, stepper motor, ultrasonic sensor (as PZT sensor or interferometer etc.), the metal material sample, the heated at constant temperature container, single channel oscillograph and computing machine, stepper motor connects pulsed laser respectively, cylindrical lens, this computer control single channel oscillograph, stepper motor, the single channel oscillograph links to each other with ultrasonic sensor, metal sample places in the heated at constant temperature container so that the control temperature, pulsed laser, cylindrical lens is fixed on the stepper motor so that mobile excitation source, computer control single channel oscillograph, stepper motor, ultrasonic sensor links to each other with the single channel oscillograph and realizes that acoustical signal converts electric signal to, deposits computing machine at last in.

(2) when constent temperature heater is closed (also sample is in the normal temperature state), the short-pulse laser that utilizes the Nd:YAG laser instrument to produce is focused into line source as the ultrasonic excitation source by cylindrical lens at solid surface, utilize stepper motor that the laser line source is accurately moved vertically, at diverse location X _i(i=N ... 1) locate to excite surface acoustic wave, the sensing point of ultrasonic sensor is fixed on the direction of line source axis, surveys from x _i(i=1 ... N) locate the surface acoustic wave that excites, acoustic waveform as shown in Figure 2, the surface acoustic wave conversion of signals that the single channel oscillograph is surveyed transducer becomes digital signal input computing machine, and carries out follow-up data processing.

(3) utilize stepper motor to move the laser line source to the nearest position X of sensing point _NPlace's (the most close sensing point of line source during this position) makes the compressional wave Signal-to-Noise of detection best, detects from the compressional wave pulse signal of the signal to noise ratio (S/N ratio) maximum of metal sample bottom reflection, writes down its time of arrival of t _LThe control step motor moves LASER Light Source to X _SThe position makes to reach best signal to noise ratio (S/N ratio) (being maximum by the shear wave signal value of observing on the single channel oscillograph) from the shear wave pulse of bottom reflection, writes down its time of arrival of t _SWith light source displacement d.

(4) utilization waveform related function method obtains the relative delay time Δ t in each step to the result of detection in N step, just can obtain the linear fit relation of the change in location Δ x and the Δ t of waveform, as shown in Figure 3, the funtcional relationship by linear fit time delay and wave travel step distance can get surface acoustic wave velocity of wave V _R, the slope of fitting a straight line is 1/V _R, V _RBe the surface acoustic wave velocity of wave, just can get X according to this velocity of wave _NPlace's shot point is from the distance L (being the wave propagation distance) of sensing point.

(5) utilize the thickness h of known L and metal sample to calculate to be from the propagation distance of bottom reflection compressional wave

Just can calculate longitudinal wave velocity

Here t _LIt is the travel-time of compressional wave.Utilize stepper motor to move the laser rays spacing from d to X away from sensing point _SThe place makes the noise of shear wave signal best, obtains transverse wave speed t _SBe the travel-time of shear wave.

Second step, according to the surface acoustic wave of calculating in the first step, compressional wave, transverse wave speed, density and second order elasticity constant by Rayleigh equation and Christo Fei Er theory of elasticity calculating metal also promptly according to (1) (3) (4) formulas, just can calculate the second order elasticity constant C of metal ₁₁, C ₄₄And density p.

Wherein Rayleigh equation is:

${\left(\frac{V_R}{V_S}\right)}^6-8{\left(\frac{V_R}{V_S}\right)}^4+[24-16{\left(\frac{V_S}{V_L}\right)}^2]{\left(\frac{V_R}{V_S}\right)}^2--16[1-{\left(\frac{V_S}{V_L}\right)}^2]=0---\left(1\right)$

V wherein _RMinimum positive real root for equation.For the common metal of isotropic material, Christo Fei Er acoustic elasticity equation can be reduced in one-dimensional plane:

$\left[\begin{array}{cc}{c}_{11}& 0\\ 0& c_{44}\end{array}\right]\left[\begin{array}{c}{P}_x\\ p_y\end{array}\right]=\mathrm{\ρ}{V}^2\left[\begin{array}{c}{P}_x\\ p_y\end{array}\right]---\left(2\right)$

The pass that can get second order elasticity constant and acoustic velocity thus is:

$c_{11}=\mathrm{\ρ}{V}_L^2---\left(3\right)$

$c_{44}=\mathrm{\ρ}{V}_S^2---\left(4\right)$

According to (1) (3) (4) formula, just can calculate the second order elasticity constant c of metal ₁₁, c ₄₄With the density p under the unstress state.

The 3rd step, utilize method measuring and calculating metal sample that linear thermal expansion applies hydrostatic stress at the stress state laser sonic surface wave in following time, compressional wave and transverse wave speed, and the relation of introducing equivalent second order elasticity constant and three rank elastic constants is extrapolated three rank elastic constants of metal.Concrete steps comprise:

(1) metal sample is placed in the constant temperature heating device container (as water-bath), heated sample to a higher temperature (as being higher than room temperature 10-80 ℃) makes sample be in hydrostatic state of stress because of thermal expansion.Here it is different with temperature under the normal temperature just enough only to need to measure differentiation, and does not need to measure the exact value of temperature.Thermal expansion makes sample be in hydrostatic state of stress, and this moment, the strain tensor of metal had following form:

Here α is a thermal expansivity, and T is the temperature variation during for no strain regime.

(2) repeat the mensuration process of the first step, calculate under stress state the laser sonic surface wave velocity of wave

Longitudinal wave velocity

And transverse wave speed

(3) under this state, introduce effective second order elasticity constant

With

And have

c ₁₂=c ₁₁-2c ₄₄Consider that the variable density that strain causes is:

ρ is the density metal under the unstress state.α is the thermal expansivity of metal material.Be similar to for second step, at this moment

Be Rayleigh equation

${\left(\frac{x}{{\tilde{V}}_S}\right)}^6-8{\left(\frac{x}{{\tilde{V}}_S}\right)}^4+(24-16{\left(\frac{{\tilde{V}}_S}{{\tilde{V}}_L}\right)}^2){\left(\frac{x}{{\tilde{V}}_S}\right)}^2-16(1-{\left(\frac{{\tilde{V}}_S}{{\tilde{V}}_L}\right)}^2)=0---\left(5\right)$

Minimum positive real root.And can get by the relation of second order equivalent elastic constant and acoustic velocity:

${\tilde{V}}_S=\sqrt{\frac{c_{44}+\mathrm{\αT}(c_{144}+2c_{166}+c_{11}+c_{44}+2c_{12})}{\mathrm{\ρ}/(1+3\mathrm{\αT})}}---\left(6\right)$

${\tilde{V}}_L=\sqrt{\frac{c_{11}+\mathrm{\αT}(c_{111}+2c_{112}+2c_{11}+{2c}_{12})}{\mathrm{\ρ}/(1+3\mathrm{\αT})}}---\left(7\right)$

(4) in the step (3)

With

Equation be linear, this is to the c of the unknown ₁₁₁, c ₁₁₂And c ₁₄₄Three linear equations are just arranged.But because surface acoustic wave velocity of wave and transverse wave speed interdepend, the determinant of this system of equations levels off to zero, so be difficult to try to achieve three three rank elastic constants.Consider the c of common metal material ₁₄₄Than other two three rank elastic constants is (to see document 3[PRB very for a short time, V.79,224102 (2009) " Ab initio calculation of second-, third-, and fourth-order elastic constants for single crystals "]), so we suppose c ₁₄₄=0.The thermal linear expansion coefficient α that utilizes the TMA test to obtain just can try to achieve three rank elastic constant c according to (6) (7) formula ₁₁₁And c ₁₁₂

Embodiment:

We utilize the water-bath heating that the aluminium sheet sample is experimentized under two temperature conditionss: 100 ℃ of the boiling temperatures of 21 ℃-23 ℃ of room temperatures and water.Therefore in this scope, the aluminium sample does not have structural change, can not cause thickness of sample as the axial stress and causes error as applying.Sample immerses more than half thickness in the water, and the temperature of water is recorded by thermopair.Separating of equation only depends on different temperature, so it is just enough only need to measure the difference of distinguishing temperature, and do not need to measure the exact value of temperature.Thermalexpansioncoefficient utilizes TMA test independent measurement.

Concrete steps are as follows: at first, we measure the velocity of wave of all 3 kinds of mode sound waves when room temperature (22 ℃).The velocity of wave of surface acoustic wave is surveyed in short as far as possible distance (approximately 5-6mm).Concrete measuring process is: the waveform that the recording laser source excites on a plurality of positions, and utilize the related function method to measure the time delay of each waveform, and finally the funtcional relationship by linear fit time delay and wave travel step distance calculates velocity of wave.Like this, we can obtain the velocity of wave V of surface acoustic wave _RWith the wave propagation distance L.Short distance can well detect the compressional wave pulse from the sample bottom reflection.Utilize known L and sample thickness h just can calculate velocity of longitudinal wave

Here t _LIt is the travel-time of compressional wave.For the detection of shear wave, we utilize stepper motor to move LASER Light Source and are adjusted at larger distance.The speed that we can measure shear wave in this position is

The result who records in the aluminium sample is: V _R=6361.4m/s; V _S=3137.4m/s; V _R=2939.9m/s.Second order elasticity constant and the density of calculating the aluminium sample according to relational expression (3) and (4) of Rayleigh equation (1) and the velocity of sound and second order elasticity constant is then: c ₁₁=109.6GPa; c ₄₄=26.8GPa; ρ=2709kg/m ³

Then detect two three above-mentioned rank elastic constants.For this reason, we at first are heated to a higher temperature to sample, measure R wave velocity of wave at this moment then

Transverse wave speed

And longitudinal wave velocity

And be 2.4610 with the thermal linear expansion coefficient α of TMA test independent measurement aluminium sample ^-51/K.As mentioned above, we suppose c ₁₄₄=0.Last through type (6) (7) calculates three rank elastic constant: c ₁₁₁=-1130.7GPa, c ₁₁₂=-299.7GPa.

What the relevant parameter value of aluminum alloy materials was coincide in the value of these constants and the existing document is fine, as document 4[Nondestructive testing and Evaluation, V.18,2 (2002) " Propagation of surface waves in deformed anisotropic thin layered solids "] in the relevant parameter value be respectively :-1100GPa and-315GPa, therefore also proved the correctness of this measurement material three rank constant new methods.

The existing error of measuring system depends primarily on the error of measuring compressional wave, shear wave and surface wave speed, and the error that tests the speed then depends primarily on and surveys long error is L, d and the time determination error of thickness measuring h and shot point and sensing point distance.

With c ₁₁, c ₄₄Be example, consider that the distance L of initial shot point and sensing point is calculated gained by waveform related algorithm and surface wave velocity of wave by program, so the error of calculation of the two introducing is ignored.Then by formula (3), formula (4),

With

Can derive c ₁₁And c ₄₄The maximal value of measuring error is respectively:

$\mathrm{\&delta;}{c}_{11}=\frac{2\mathrm{\&rho;}({\mathrm{<figure-callout\; id="2"\; label="L"\; filenames="HSA00000496665000012.png,HSA00000496665000021.png"\; state="\{\{state\}\}">L</figure-callout>}}^2+4h^2)}{t_L^3}\mathrm{\&delta;}\left({\mathrm{\&Delta;t}}_L\right)+\frac{8\mathrm{\&rho;<figure-callout\; id="2"\; label="h\; t\; L"\; filenames="HSA00000496665000012.png,HSA00000496665000021.png"\; state="\{\{state\}\}">h</figure-callout>}}{t_L^{}}\mathrm{\&delta;h}---\left(8\right)$

${\mathrm{\&delta;c}}_{44}=\frac{2\mathrm{\&rho;}[{(L+d)}^2+4h^2]}{t_S^3}\mathrm{\&delta;}\left({\mathrm{\&Delta;t}}_S\right)+\frac{8\mathrm{\&rho;<figure-callout\; id="2"\; label="h\; t\; S"\; filenames="HSA00000496665000012.png,HSA00000496665000021.png"\; state="\{\{state\}\}">h</figure-callout>}}{t_S^{}}\mathrm{\&delta;h}+\frac{2\mathrm{\&rho;}(L+d)}{{\mathrm{<figure-callout\; id="2"\; label="t\; S"\; filenames="HSA00000496665000012.png,HSA00000496665000021.png"\; state="\{\{state\}\}">t</figure-callout>}}_S^{}}\mathrm{\&delta;d}---\left(9\right)$

Here, δ c ₁₁With δ c ₄₄It is the error of second order elasticity constant; δ (Δ t _L) and δ (Δ t _S) be respectively the travel-time measuring error of compressional wave and shear wave; Light source displacement error when δ h and δ d are sample thickness measuring sum of errors measurement shear wave respectively.

In the test, δ (Δ t _L)=δ (Δ t _S)=0.5ns, δ h=0.01mm, δ d=1.25 μ m then can be got by formula (8) and formula (9):

δc ₁₁＝0.248GPa， $\frac{{\mathrm{\&delta;c}}_{11}}{c_{11}}=0.226\%;$

δc ₄₄＝0.046GPa， $\frac{\mathrm{\&delta;}{c}_{44}}{c_{44}}=0.164\%$

And under stress state, equivalence second order elasticity constant adopts identical experimental technique to record, therefore with above-mentioned second order elasticity constant identical error range is arranged, because three rank elastic constants are to carry out the algebraically Conversion Calculation and obtain by introducing equivalent second order elasticity, ignore the error of calculation and can get the measuring error of three rank elastic constants also less than 0.3%.The analysis showed that this system has higher measuring accuracy, the second order of the aluminium sample of surveying and the measuring error of three rank elastic constants are less, can satisfy the requirement of engineering and scientific research permissible error.

Claims (4)

1. the laser-ultrasound assay method of metal three rank elastic constants is characterized in that step is as follows:

The first step at unstress state and having under the stress state, is measured compressional wave, the shear wave of laser excitation, the velocity of wave of surface wave respectively;

In second step, utilize the surface wave, compressional wave and the transverse wave speed that record under the unstress state, according to the second order elasticity constant and the density of acoustic elasticity theory and Rayleigh equation calculating metal;

The 3rd step, utilize the compressional wave that records under the stress state is arranged, the ultrasonic velocity of shear wave, surface wave, introduce the thermal linear expansion coefficient of equivalent second order elasticity constant and independent measurement, at last according to acoustic elasticity Theoretical Calculation three rank elastic constants.

2. the laser-ultrasound assay method of metal three rank elastic constants according to claim 1 is characterized in that in the first step, measures unstressed and has the method for compressional wave under the stress state, shear wave, surface wave velocity of wave to be:

(1) design detection system, this detection system comprises pulsed laser, cylindrical lens, stepper motor, ultrasonic sensor, metal material sample, single channel oscillograph and computing machine, stepper motor connects pulsed laser, cylindrical lens respectively, this computer control single channel oscillograph, stepper motor, the single channel oscillograph links to each other with ultrasonic sensor, and the short-pulse laser that pulsed laser excites passes through cylindrical lens focus line source irradiation at metal material sample surfaces x _i(i=1 ... N) position, as the excitaton source of the surface acoustic wave of metal material surface, after metal material absorbs pulsed laser energy, in the laser aggregation zone of sample surfaces, produce the thermal stress of the short pulse of a part, inspire the surface acoustic wave in broadband, and propagate along the surface;

(2) pulsed laser and cylindrical lens are fixed on the translation stage of stepper motor, and computer-controlled stepper motor moves laser line light source vertically, at different position x _i(i=1 ... N) locate to excite surface acoustic wave, the sensing point of ultrasonic sensor is fixed on the direction of line source axis, surveys from x _i(i=1 ... N) locate the surface acoustic wave that excites, the surface acoustic wave conversion of signals that the single channel oscillograph is surveyed ultrasonic sensor becomes digital signal input computing machine, and carries out follow-up data processing;

(3) utilization waveform related function method is calculated the relative delay time Δ t in each step to the result of detection in N step, funtcional relationship by linear fit time delay and wave travel step distance calculates the surface acoustic wave velocity of wave, and calculates the wave propagation distance L according to step distance; At laser line source and sensing point (X the most nearby _NThe place) the best compressional wave signal of detectable noise utilizes the thickness h of known L and metal sample to calculate from the propagation distance of bottom reflection compressional wave, just can calculate longitudinal wave velocity time of arrival according to compressional wave; Utilize stepper motor to move the laser line source to X _SThe place obtains the best shear wave signal of signal to noise ratio (S/N ratio), according to the shear wave propagation distance with obtain transverse wave speed time of arrival.

3. the laser-ultrasound assay method of metal three rank elastic constants according to claim 1, it is characterized in that in second step, second order elasticity constant at unstressed shape body measurement metal, its method is: based on the acoustic elasticity theory, Christo Fei Er equation is simplified the relational expression that can obtain second order elasticity constant and acoustic velocity in one-dimensional plane With

Introduce Rayleigh equation then, by Simultaneous Equations, by the V that has recorded _R, V _LAnd V _SJust can try to achieve the second order elasticity constant of metal.

4. the laser-ultrasound assay method of metal three rank elastic constants according to claim 1 is characterized in that in the 3rd step, utilized thermal expansion to make metal be in the method for measuring three rank elastic constants under the hydrostatic state of stress to be:

(1) metal sample is carried out heated at constant temperature, metal is under the hydrostatic state of stress, measure the speed of laser sonic surface wave, compressional wave and the shear wave of this moment;

(2) utilize TMA test independent measurement metal sample in temperature variant inflection curves, and then obtain the thermal linear expansion coefficient of metal material;

(3) consider that thermal expansion causes variable density

Introduce the relation of equivalent second order elasticity constant and acoustic velocity, utilize calculated second order elasticity constant of second step, acoustic velocity, thermal expansivity, density calculation three rank elastic constants.

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