CN102297898B - Laser ultrasonic measuring method for third order elastic constant of metal - Google Patents

Laser ultrasonic measuring method for third order elastic constant of metal Download PDF

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CN102297898B
CN102297898B CN201110125960.7A CN201110125960A CN102297898B CN 102297898 B CN102297898 B CN 102297898B CN 201110125960 A CN201110125960 A CN 201110125960A CN 102297898 B CN102297898 B CN 102297898B
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沈中华
董利明
倪辰荫
阿雷克塞·罗莫诺索夫
倪晓武
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Nanjing University of Science and Technology
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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 method of three rank elastic constants of metal being carried out to Accurate Measurement, specifically a kind of method of utilizing three rank elastic constants of laser ultrasonic Accurate Measurement metal.
Background technology
Acoustoelastic effect refers to that ultrasonic velocity in solid can change along with the distortion that is applied to solid or stress, and this effect is used widely in static Non-Destructive Testing and unrelieved stress detect, and in these application, it has been generally acknowledged that velocity of wave and strain are linear relationships.Existing method can reach 10 to the measuring accuracy of various ultrasound modality velocities of wave -4even 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, we are referred to as sonoelastic coefficient.On mathematics, sonoelastic coefficient is the linearity combination of second order and three rank elastic constants, microcosmic and the macro property of second order and three rank elastic constants and material have substantial connection, particularly the higher 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, all closely related with higher order elastic constant such as attenuation properties of temperature expansion character, heat conduction property and the high frequency sound wave of material etc.
The classic method of measuring three rank elastic constants be adopt calibration load applying to material and measuring speed change, 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 "].It is shaftless to stress and apply longitudinal wave velocity and the shear wave velocity of sound under the axial stress state that this method has been measured solid, 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 to the heart in the sample both sides, so judge that sound wave time of arrival, erroneous judgement easily appearred in (especially for thickness less sample), therefore cause that velocity of wave measuring and calculating and final elastic constant calculate to produce error; Owing to there is no to consider, in the density that applies solid under the axial stress state and axial length, certain variation to be arranged, still adopt density of material and sound wave propagation distance value when unstressed, this brings larger error also 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 method of three rank elastic constants of metal being carried out to Accurate Measurement, 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 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 stress state, measure respectively compressional wave, the shear wave of laser excitation, the velocity of wave of surface wave;
Second step, utilize the surface wave, compressional wave and the transverse wave speed that record under unstress state, according to 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 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, finally according to the theoretical three rank elastic constants that calculate of acoustic elasticity.
Compared with prior art, its remarkable advantage has in the present invention: (1) utilizes the pulse laser line source to excite surface acoustic wave, and under thermoelastic mechanism, noncontact excites, and avoids the material production superheating phenomenon, thereby realizes Non-Destructive Testing; (2) by gathering the surface acoustic wave data of having propagated in a large number different distance, utilize the related function method to calculate surface acoustic wave velocity of wave and sound wave propagation distance, can greatly reduce the error 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 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.
The accompanying drawing explanation
Fig. 1 is used scan laser line source method to calculate respectively the detection system schematic diagram of surface acoustic wave, compressional wave and transverse wave speed in unstress state with when stress state is arranged at metal sample.
Fig. 2 is that the ultrasonic signal figure detected reaches the spectrum analysis figure to surface acoustic wave.
Fig. 3 is the funtcional relationship matched curve figure of 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, the velocity of wave of the ultrasound wave of laser excitation under the Accurate Measurement unstress state (compressional wave, shear wave, surface wave).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 respectively pulsed laser, cylindrical lens, this computer control single channel oscillograph, stepper motor, the single channel oscillograph is connected with ultrasonic sensor, metal sample is placed in the heated at constant temperature container in order to control temperature, pulsed laser, cylindrical lens is fixed on stepper motor so that mobile excitation source, computer control single channel oscillograph, stepper motor, ultrasonic sensor is connected and realizes that acoustical signal converts electric signal to the single channel oscillograph, finally deposit computing machine 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, as shown in Figure 2, the surface acoustic wave signal that the single channel oscillograph is surveyed transducer converts digital signal input computing machine to acoustic waveform, and carries out follow-up data and process.
(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), make 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, records its time of arrival of t l.Control step motor removing LASER Light Source is to X sposition, make from the shear wave pulse of bottom reflection and reach best signal to noise ratio (S/N ratio) (being maximum by the shear wave signal value observation single channel oscillograph), records its time of arrival of t swith light source displacement d.
(4) use waveform related function method relatively to postpone Δ t to time of each step of result of detection acquisition of N step, just can obtain the linear fit relation of 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 obtain 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, according to this velocity of wave, just can obtain X 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 from the propagation distance of bottom reflection compressional wave to be
Figure BSA00000496664900031
just can calculate longitudinal wave velocity
Figure BSA00000496664900032
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 splace, make the noise of shear wave signal best, obtains transverse wave speed
Figure BSA00000496664900033
t sfor 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, calculated density and the second order elasticity constant of metal by Rayleigh equation and Christo Fei Er theory of elasticity, also, according to (1) (3) (4) formula, just can calculate the second order elasticity constant C of metal 11, C 44and density p.
Wherein Rayleigh equation is:
( V R V S ) 6 - 8 ( V R V S ) 4 + [ 24 - 16 ( V S V L ) 2 ] ( V R V S ) 2 - - 16 [ 1 - ( V S V L ) 2 ] = 0 - - - ( 1 )
V wherein rfor the positive real root of the minimum of equation.For the common metal of isotropic material, Christo Fei Er acoustic elasticity equation can be reduced in one-dimensional plane:
c 11 0 0 c 44 P x p y = ρ V 2 P x p y - - - ( 2 )
The pass that can obtain thus second order elasticity constant and acoustic velocity is:
c 11 = ρ V L 2 - - - ( 3 )
c 44 = ρ V S 2 - - - ( 4 )
According to (1) (3) (4) formula, just can calculate the second order elasticity constant c of metal 11, c 44with the density p under unstress state.
The 3rd step, laser sonic surface wave, compressional wave and the transverse wave speed of the method measuring and calculating metal sample that utilizes linear thermal expansion to apply hydrostatic stress under stress state the time, 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 constant temperature heating device container (as water-bath), heated sample to a higher temperature (as higher than room temperature 10-80 ℃), make sample because of thermal expansion in hydrostatic state of stress.Here only need to measure differentiation different from temperature under normal temperature just enough, and do not need to measure the exact value of temperature.Thermal expansion makes sample be in hydrostatic state of stress, and now the strain tensor of metal has following form:
Figure BSA00000496664900045
here α is thermal expansivity, and T is the temperature variation for without strain regime the time.
(2) repeat the mensuration process of the first step, calculate under stress state the laser sonic surface wave velocity of wave
Figure BSA00000496664900046
longitudinal wave velocity
Figure BSA00000496664900051
and transverse wave speed
Figure BSA00000496664900052
(3), under this state, introduce effective second order elasticity constant
Figure BSA00000496664900053
with
Figure BSA00000496664900054
and have
Figure BSA00000496664900055
c 12=c 11-2c 44; Consider that the variable density that strain causes is:
Figure BSA00000496664900056
ρ is the density metal under unstress state.The thermal expansivity that α is metal material.Be similar to second step, now
Figure BSA00000496664900057
for Rayleigh equation
( x V ~ S ) 6 - 8 ( x V ~ S ) 4 + ( 24 - 16 ( V ~ S V ~ L ) 2 ) ( x V ~ S ) 2 - 16 ( 1 - ( V ~ S V ~ L ) 2 ) = 0 - - - ( 5 )
The positive real root of minimum.And can be obtained by the relation of second order equivalent elastic constant and acoustic velocity:
V ~ S = c 44 + αT ( c 144 + 2 c 166 + c 11 + c 44 + 2 c 12 ) ρ / ( 1 + 3 αT ) - - - ( 6 )
V ~ L = c 11 + αT ( c 111 + 2 c 112 + 2 c 11 + 2 c 12 ) ρ / ( 1 + 3 αT ) - - - ( 7 )
(4) in step (3)
Figure BSA000004966649000511
with
Figure BSA000004966649000512
equation be linear, this is to unknown c 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, be very littlely (to see document 3[PRB, 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 to be tested under two temperature conditionss the aluminium sheet sample: 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 and causes error as applying as axial stress.Sample is immersed in the water more than half thickness, and the temperature of water is recorded by thermopair.The solution of equation only depends on different temperature, so it is just enough only need to measure the difference of distinguishing temperature, and does not need to measure the exact value of temperature.Thermalexpansioncoefficientα 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.Shorter distance can well detect the compressional wave pulse from the sample bottom reflection.Utilize the thickness h of known L and sample just can calculate velocity of longitudinal wave
Figure BSA00000496664900061
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
Figure BSA00000496664900062
the result recorded in the aluminium sample is: V r=6361.4m/s; V s=3137.4m/s; V r=2939.9m/s.Then 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 are: c 11=109.6GPa; c 44=26.8GPa; ρ=2709kg/m 3.
Then detect two above-mentioned three rank elastic constants.For this reason, at first we be heated to a higher temperature to sample, then measures R wave velocity of wave at this moment
Figure BSA00000496664900063
transverse wave speed and longitudinal wave velocity
Figure BSA00000496664900065
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 in the value of these constants and existing document, the relevant parameter value of aluminum alloy materials was coincide 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 tested the speed 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 44for 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, therefore the error of calculation of the two introducing is ignored.By formula (3), formula (4),
Figure BSA00000496664900066
with can derive c 11and c 44the maximal value of measuring error is respectively:
δ c 11 = 2 ρ ( L 2 + 4 h 2 ) t L 3 δ ( Δt L ) + 8 ρh t L 2 δh - - - ( 8 )
δc 44 = 2 ρ [ ( L + d ) 2 + 4 h 2 ] t S 3 δ ( Δt S ) + 8 ρh t S 2 δh + 2 ρ ( L + d ) t S 2 δd - - - ( 9 )
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 respectively sample thickness measuring error and measurement shear wave.
In test, δ (Δ t l)=δ (Δ t s)=0.5ns, δ h=0.01mm, δ d=1.25 μ m can be obtained by formula (8) and formula (9):
δc 11=0.248GPa, δc 11 c 11 = 0.226 % ;
δc 44=0.046GPa, δ 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 measuring error that the error of calculation can obtain three rank elastic constants and also be less than 0.3%.The analysis showed that, this system has higher measuring accuracy, and the second order of the aluminium sample of surveying and the measuring error of three rank elastic constants are less, can meet the requirement of engineering and scientific research permissible error.

Claims (3)

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 stress state, measure respectively compressional wave, the shear wave of laser excitation, the velocity of wave of surface wave;
Second step, utilize the surface wave, compressional wave and the transverse wave speed that record under unstress state, according to 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 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, finally, according to the theoretical three rank elastic constants that calculate of acoustic elasticity, concrete steps comprise:
(1) metal sample is carried out to heated at constant temperature, make metal under hydrostatic state of stress, measure the surface acoustic wave velocity of wave of laser excitation now
Figure FSB0000111701770000011
longitudinal wave velocity
Figure FSB0000111701770000012
and transverse wave speed
Figure FSB0000111701770000013
thermal expansion makes sample be in hydrostatic state of stress, and now the strain tensor of metal has following form: e = αT 1 0 0 0 1 0 0 0 1 , Here α is thermal expansivity, and T is the temperature variation for without strain regime the time;
(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 the calculated second order elasticity constant of acoustic velocity, thermal expansivity and second step, density calculation three rank elastic constants,, under this state, introduce equivalent second order elasticity constant c ~ 11 = c 11 + αT ( c 111 + 2 c 112 + 2 c 11 + 2 c 12 ) With c ~ 44 = c 44 + αT ( c 144 + 2 c 166 + c 11 + c 44 + 2 c 12 ) , And have
Figure FSB0000111701770000018
c 12=c 11-2c 44; Consider that the variable density that strain causes is:
Figure FSB0000111701770000019
ρ is the density metal under unstress state, now
Figure FSB00001117017700000110
for Rayleigh equation
( x V ~ S ) 6 - 8 ( x V ~ S ) 4 + ( 24 - 16 ( V ~ S V ~ L ) 2 ) ( x V ~ S ) 2 - 16 ( 1 - ( V ~ S V ~ L ) 2 ) = 0
The positive real root of minimum, and can be obtained by the relation of second order equivalent elastic constant and acoustic velocity:
V ~ S = c 44 + αT ( c 144 + 2 c 166 + c 11 + c 44 + 2 c 12 ) ρ / ( 1 + 3 αT )
V ~ L = c 11 + αT ( c 111 + 2 c 112 + 2 c 11 + 2 c 12 ) ρ / ( 1 + 3 αT )
Wherein,
Figure FSB0000111701770000022
with
Figure FSB0000111701770000023
equation be linear, this is to unknown c 111, c 112and c 144three linear equations are just arranged, 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 front formula 111and c 112.
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 have the method for compressional wave under 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 respectively pulsed laser, cylindrical lens, this computer control single channel oscillograph, stepper motor, the single channel oscillograph is connected 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 iposition, i=1...N, as the excitaton source of the surface acoustic wave of metal material surface, after metal material absorbs pulsed laser energy, produce the thermal stress of the short pulse of a part in the laser aggregation zone of sample surfaces, inspire the surface acoustic wave in broadband, and propagate along 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 iplace excites surface acoustic wave, i=1...N, and the sensing point of ultrasonic sensor is fixed on the direction of line source axis, surveys from x ithe surface acoustic wave that place excites, i=1...N, the surface acoustic wave signal that the single channel oscillograph is surveyed ultrasonic sensor converts digital signal input computing machine to, and carries out follow-up data and process;
(3) use waveform related function method relatively to postpone Δ t to result of detection respectively time of step of calculating of 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 the most nearby, i.e. X nlocate the best compressional wave signal of detectable noise, utilize the thickness h of known L and metal sample to calculate from the propagation distance of bottom reflection compressional wave, according to compressional wave, just can calculate longitudinal wave velocity time of arrival; Utilize stepper motor to move the laser line source to X splace, obtain 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, measure the second order elasticity constant of metal at unstress state, 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
Figure FSB0000111701770000031
with
Figure FSB0000111701770000032
then introduce Rayleigh equation, by Simultaneous Equations, by the velocity of wave V of the surface acoustic wave recorded r, velocity of longitudinal wave V lwith shear wave velocity V sjust can try to achieve the second order elasticity constant of metal.
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