CN102297898A

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

Info

Publication number: CN102297898A
Application number: CN2011101259607A
Authority: CN
Inventors: 沈中华; 董利明; 倪辰荫; 阿雷克塞·罗莫诺索夫; 倪晓武
Original assignee: Nanjing University of Science and Technology
Current assignee: Nanjing University of Science and Technology
Priority date: 2011-05-17
Filing date: 2011-05-17
Publication date: 2011-12-28
Anticipated expiration: 2031-05-17
Also published as: CN102297898B

Abstract

The invention discloses a method for accurately measuring the third-order elastic constants of metals by using laser ultrasonic waves. The wave velocities of longitudinal waves, transverse waves and surface waves excited by lasers are respectively measured in stress-free and stressed states; Based on the obtained surface wave, longitudinal wave and shear wave velocity, calculate the second-order elastic constant and density of metal according to the acoustoelastic theory and Rayleigh equation; First-order elastic constants and independently measured linear thermal expansion coefficients, and finally the third-order elastic constants are calculated according to acoustoelastic theory. The invention utilizes the pulsed laser line source to excite the surface acoustic wave, non-contact excitation under the thermoelastic mechanism, avoids the overheating phenomenon of the material, thereby realizing the non-destructive detection; by collecting a large amount of surface acoustic wave data propagated at different distances, and using the correlation function method to calculate The velocity of the surface acoustic wave and the propagation distance of the acoustic wave can greatly reduce the error of the arrival time of the surface acoustic wave, and improve the measurement accuracy of the acoustic wave velocity.

Description

Laser Ultrasonic Determination Method of Metal Third-Order Elastic Constant

技术领域 technical field

本发明涉及一种对金属的三阶弹性常数进行精确测定的方法，具体的说是一种利用激光超声波精确测定金属的三阶弹性常数的方法。The invention relates to a method for accurately measuring the third-order elastic constant of metal, in particular to a method for accurately measuring the third-order elastic constant of metal by using laser ultrasonic waves.

背景技术 Background technique

声弹性效应指固体中的超声波波速会随着施加在固体的变形或应力而变化，该效应在静态的无损检测和残余应力检测中得到广泛应用，这些应用中通常认为波速与应变是线性关系。现有的方法对各种超声模态波速的测量精度可达10^-4甚至更高，见我们先前的研究结果——如文献1[SPIE，Vol.7544，754451(2010)《Measurement of velocitydistribution of laser-generated Rayleigh wave on welded structure》]。而主要的难题是得到声速基于应变变化的关系参数，我们称之为声弹性系数。数学上，声弹性系数是二阶和三阶弹性常数的线性结合，二阶和三阶弹性常数与材料的微观和宏观性能都有密切关系，特别是材料的高阶弹性常数(如三阶弹性常数)对于其特性的定量估计具有重要意义，其中包含有大量材料非线性信息，例如材料的温度膨胀性质、热传导性质以及高频声波的衰减性质等都与高阶弹性常数密切相关。The acoustoelastic effect means that the ultrasonic wave velocity in a solid will change with the deformation or stress applied to the solid. This effect is widely used in static non-destructive testing and residual stress testing. In these applications, it is generally believed that the wave velocity and strain have a linear relationship. Existing methods can measure the wave velocity of various ultrasonic modes up to 10 ^-4 or even higher, see our previous research results - such as literature 1 [SPIE, Vol.7544, 754451 (2010) "Measurement of velocity distribution of laser-generated Rayleigh wave on welded structure "]. The main difficulty is to obtain the relationship parameter of the sound velocity based on the strain change, which we call the acoustoelastic coefficient. Mathematically, the acoustoelastic coefficient is a linear combination of the second-order and third-order elastic constants. The second-order and third-order elastic constants are closely related to the microscopic and macroscopic properties of the material, especially the higher-order elastic constants of the material (such as the third-order elastic Constant) is of great significance for the quantitative estimation of its characteristics, which contains a large amount of material nonlinear information, such as the temperature expansion properties of materials, heat conduction properties and attenuation properties of high-frequency sound waves, etc. are closely related to high-order elastic constants.

测定三阶弹性常数的传统方法是采用定标的载荷施加到材料上并测量速度变化，这需要复杂庞大的仪器设备，并且样品必须是特定的形状和尺寸，如文献2[同济大学学报，Vol.23，5(1995)《三阶弹性常数的超声测量方法》]。这种方法测量了固体无轴向应力和施加轴向应力状态下的纵波声速和切变波声速，利用声波波速和三阶弹性常数的关系算出三阶弹性常数。但是，这个方法在样品两侧对心激发和接收超声波，如此判断声波到达时间(尤其对于厚度较小的样品)容易出现误判，因此引起波速测算和最终弹性常数计算产生误差；由于没有考虑在施加轴向应力状态下固体的密度和轴向长度都有一定的变化，仍采用无应力时的材料密度和声波传播距离值，这也给弹性常数的测算带来较大的误差。因此开发一种精确测量声波波速，进而精确计算金属三阶弹性常数的高可靠性技术是非常必要的。The traditional method of determining the third-order elastic constant is to apply a calibrated load to the material and measure the velocity change, which requires complex and bulky instruments and equipment, and the sample must be of a specific shape and size, as document 2 [Journal of Tongji University, Vol .23, 5(1995) "Ultrasonic Measurement Method of Third-Order Elastic Constant"]. This method measures the sound velocity of longitudinal wave and shear wave of the solid under the state of no axial stress and applied axial stress, and calculates the third-order elastic constant by using the relationship between the sound wave velocity and the third-order elastic constant. However, this method excites and receives ultrasonic waves on both sides of the sample, so the judgment of the arrival time of the sound wave (especially for samples with small thickness) is prone to misjudgment, thus causing errors in the calculation of the wave velocity and the calculation of the final elastic constant; Under the state of axial stress, the density and axial length of the solid have certain changes, and the material density and acoustic wave propagation distance values without stress are still used, which also brings large errors to the calculation of elastic constants. Therefore, it is very necessary to develop a high-reliability technology that accurately measures the acoustic wave velocity and then accurately calculates the third-order elastic constant of the metal.

发明内容 Contents of the invention

本发明的目的是发明一种对金属的三阶弹性常数进行精确测定的方法，这种方法不但使各种模态的声波波速测量精度更高，可以避免对心激发接收方法对声波到达时间取值误差，而且利用线性热膨胀施加静水应力避免了因施加轴向应力引起金属轴向长度变化，并且考虑了应力状态下金属的密度变化，因此测算金属的三阶弹性常数的精度更高。The purpose of the present invention is to invent a method for accurately measuring the third-order elastic constant of the metal, which not only makes the measurement accuracy of the acoustic wave velocity of various modes higher, but also avoids the acquisition of the arrival time of the acoustic wave by the center excitation receiving method. Value error, and the use of linear thermal expansion to apply hydrostatic stress avoids the change of the axial length of the metal due to the application of axial stress, and considers the density change of the metal under the stress state, so the accuracy of the third-order elastic constant of the metal is higher.

实现本发明目的的技术解决方案为：一种金属三阶弹性常数的激光超声测定方法，步骤如下：The technical solution that realizes the object of the present invention is: a kind of laser ultrasonic measuring method of metal third-order elastic constant, the steps are as follows:

第一步，在无应力状态和有应力状态下，分别测定激光激发的纵波、横波、表面波的波速；The first step is to measure the wave velocities of the longitudinal wave, shear wave and surface wave excited by the laser respectively under the stress-free state and the stressed state;

第二步，利用无应力状态下测得的表面波、纵波和横波波速，根据声弹性理论和瑞利方程计算金属的二阶弹性常数和密度；The second step is to calculate the second-order elastic constant and density of the metal according to the acoustoelastic theory and the Rayleigh equation by using the surface wave, longitudinal wave and shear wave velocity measured in the stress-free state;

第三步，利用有应力状态下测得的纵波、横波、表面波的超声波波速，引入等效二阶弹性常数和独立测量的线性热膨胀系数，最后根据声弹性理论计算三阶弹性常数。The third step is to use the ultrasonic wave velocity of longitudinal wave, shear wave and surface wave measured under the stress state, introduce the equivalent second-order elastic constant and the independently measured linear thermal expansion coefficient, and finally calculate the third-order elastic constant according to the acoustoelastic theory.

本发明与现有技术相比，其显著优点有：(1)利用脉冲激光线源激发声表面波，在热弹机制下非接触激发，避免材料产生过热现象，从而实现无损检测；(2)通过采集大量传播了不同距离的声表面波数据，利用相关函数法计算声表面波波速和声波传播距离，可以大大减小由声表面波到达时间取值的误差，提高了声波波速的测定精度；(3)采用恒温加热法通过样品线性热膨胀施加静水应力不但设备简单实用，而且避免了因施加轴向应力带来金属轴向长度变化，并且考虑了应力状态下金属的密度变化，因此测算金属的三阶弹性常数的精度更高。Compared with the prior art, the present invention has the following significant advantages: (1) the pulsed laser line source is used to excite the surface acoustic wave, and the non-contact excitation is performed under the thermoelastic mechanism, so as to avoid the overheating phenomenon of the material, thereby realizing non-destructive testing; (2) By collecting a large amount of surface acoustic wave data that has propagated at different distances, and using the correlation function method to calculate the velocity of the surface acoustic wave and the propagation distance of the acoustic wave, the error in the value of the arrival time of the surface acoustic wave can be greatly reduced, and the measurement accuracy of the acoustic wave velocity can be improved; (3) Using the constant temperature heating method to apply hydrostatic stress through the linear thermal expansion of the sample is not only simple and practical, but also avoids the change of the axial length of the metal due to the application of axial stress, and considers the density change of the metal under the stress state. The third-order elastic constants are more accurate.

下面结合附图对本发明作进一步详细描述。The present invention will be described in further detail below in conjunction with the accompanying drawings.

附图说明 Description of drawings

图1是使用扫描激光线源法在金属样品处于无应力状态和有应力状态时分别测算声表面波、纵波和横波波速的检测系统示意图。Figure 1 is a schematic diagram of a detection system for measuring the velocity of surface acoustic waves, longitudinal waves, and shear waves by using the scanning laser line source method when the metal sample is in an unstressed state and a stressed state.

图2是探测到的超声信号图及对声表面波的频谱分析图。Figure 2 is a graph of the detected ultrasonic signal and a spectrum analysis graph of the surface acoustic wave.

图3是N个声表面波信号的时间延迟和波传播距离的函数关系拟合曲线图。Fig. 3 is a fitting curve diagram of the functional relationship between the time delay of N surface acoustic wave signals and the wave propagation distance.

具体实施方式 Detailed ways

本发明金属三阶弹性常数的激光超声测定方法，其步骤如下：The laser ultrasonic measuring method of metal third-order elastic constant of the present invention, its step is as follows:

第一步，精确测定无应力状态下激光激发的超声波(纵波、横波、表面波)的波速。具体步骤包括：The first step is to accurately measure the wave velocity of the ultrasonic wave (longitudinal wave, transverse wave, surface wave) excited by the laser under the stress-free state. Specific steps include:

(1)设计检测系统，如图1所示。该检测系统包括脉冲激光器、柱面透镜、步进电机、超声探测装置(如PZT传感器或干涉仪等)、金属材料样品、恒温加热容器、单通道示波器和计算机，步进电机分别连接脉冲激光器、柱面透镜，该计算机控制单通道示波器、步进电机，单通道示波器与超声探测装置相连，金属样品置于恒温加热容器内以便控制温度，脉冲激光器、柱面透镜固定在步进电机上以便移动激发光源，计算机控制单通道示波器、步进电机，超声探测装置与单通道示波器相连实现声信号转换成电信号，最后存入计算机。(1) Design the detection system, as shown in Figure 1. The detection system includes a pulsed laser, a cylindrical lens, a stepping motor, an ultrasonic detection device (such as a PZT sensor or an interferometer, etc.), a metal material sample, a constant temperature heating container, a single-channel oscilloscope, and a computer. The stepping motor is respectively connected to the pulsed laser, Cylindrical lens, the computer controls the single-channel oscilloscope and stepping motor, the single-channel oscilloscope is connected with the ultrasonic detection device, the metal sample is placed in a constant temperature heating container to control the temperature, the pulse laser and the cylindrical lens are fixed on the stepping motor for movement The excitation light source, the computer controls the single-channel oscilloscope and the stepper motor, and the ultrasonic detection device is connected with the single-channel oscilloscope to convert the acoustic signal into an electrical signal, which is finally stored in the computer.

(2)在恒温加热器关闭时(也即样品处于常温状态)，利用Nd:YAG激光器产生的短脉冲激光通过柱面透镜在固体表面聚焦成线源作为超声激发源，利用步进电机使激光线源沿轴向精确移动，在不同位置X_i(i＝N，…1)处激发声表面波，超声探测装置的探测点固定在线光源中轴线方向上，探测从x_i(i＝1…N)处激发的声表面波，声波波形如图2所示，单通道示波器把换能器探测的声表面波信号转换成数字信号输入计算机，并进行后续的数据处理。(2) When the constant temperature heater is turned off (that is, the sample is at room temperature), the short-pulse laser generated by the Nd:YAG laser is focused on the solid surface through a cylindrical lens to form a line source as an ultrasonic excitation source, and the laser is driven by a stepping motor. The line source moves precisely along the axial direction, and excites the surface acoustic wave at different positions _Xi ( _i =N, ... 1). The detection point of the ultrasonic detection device is fixed in the direction of the central axis of the line source. The surface acoustic wave excited at N) is shown in Figure 2. The single-channel oscilloscope converts the surface acoustic wave signal detected by the transducer into a digital signal and inputs it into a computer for subsequent data processing.

(3)利用步进电机移动激光线源至探测点最近的位置X_N处(此位置时线源最靠近探测点)，使探测的纵波信号信噪比最好，探测到从金属样品底部反射的信噪比最大的纵波脉冲信号，记录其到达时间t_L。控制步进电机移动激光光源至X_S位置，使得从底部反射的横波脉冲达到最好的信噪比(通过观察单通道示波器上的横波信号值为最大)，记录其到达时间t_S和光源移动距离d。(3) Use a stepping motor to move the laser line source to the nearest position X _N of the detection point (at this position, the line source is closest to the detection point), so that the signal-to-noise ratio of the detected longitudinal wave signal is the best, and the reflection from the bottom of the metal sample is detected Record the arrival time t _L of the longitudinal wave pulse signal with the largest signal-to-noise ratio. Control the stepper motor to move the laser light source to the X _S position, so that the shear wave pulse reflected from the bottom reaches the best signal-to-noise ratio (by observing the maximum value of the shear wave signal on the single-channel oscilloscope), record its arrival time t _S and light source movement distance d.

(4)运用波形相关函数法对N步的探测结果获得各步的时间相对延迟Δt，便可得到波形的位置变化Δx与Δt的线性拟合关系，如图3所示，通过线性拟合延迟时间和波形传播步进距离的函数关系可得声表面波波速V_R，拟合直线的斜率为1/V_R，V_R即为声表面波波速，根据此波速便可得X_N处激发点离探测点的距离L(即波的传播距离)。(4) Using the waveform correlation function method to obtain the relative time delay Δt of each step from the detection results of N steps, the linear fitting relationship between the position change Δx and Δt of the waveform can be obtained, as shown in Figure 3, through the linear fitting delay The function relationship between time and waveform propagation step distance can be the surface acoustic wave velocity V _R , the slope of the fitted line is 1/V _R , _VR is the surface acoustic wave velocity, and the excitation point at X _N can be obtained according to this wave velocity The distance L from the detection point (that is, the propagation distance of the wave).

(5)利用已知的L和金属样品的厚度h计算得到从底面反射纵波的传播距离为

便可计算纵波波速

这里t_L是纵波的传播时间。利用步进电机远离探测点移动激光线源距离d至X_S处，使横波信号的信噪最好，得到横波波速t_S为横波的传播时间。(5) Using the known L and the thickness h of the metal sample, the propagation distance of the reflected longitudinal wave from the bottom surface is calculated as

The longitudinal wave velocity can be calculated

Here t _L is the travel time of the longitudinal wave. Use a stepper motor to move the laser line source distance d to X _S away from the detection point, so that the signal-to-noise of the shear wave signal is the best, and the shear wave velocity is obtained t _S is the propagation time of the shear wave.

第二步，根据第一步中测算的声表面波、纵波、横波波速，由瑞利方程和克里斯托菲尔弹性理论计算金属的密度和二阶弹性常数，也即根据(1)(3)(4)式，便可计算金属的二阶弹性常数C₁₁、C₄₄和密度ρ。In the second step, according to the surface acoustic wave, longitudinal wave, and shear wave velocity measured in the first step, the density and second-order elastic constant of the metal are calculated by the Rayleigh equation and Christopher's elastic theory, that is, according to (1)(3 )(4), the second-order elastic constants C ₁₁ , C ₄₄ and density ρ of the metal can be calculated.

其中瑞利方程为：where the Rayleigh equation is:

${((\frac{{V V}_{R R}}{{V V}_{S S}}))}^{66} - - 88 {((\frac{{V V}_{R R}}{{V V}_{S S}}))}^{44} + + [[24 twenty four - - 1616 {((\frac{{V V}_{S S}}{{V V}_{L L}}))}^{22}]] {((\frac{{V V}_{R R}}{{V V}_{S S}}))}^{22} - - - - 1616 [[11 - - {((\frac{{V V}_{S S}}{{V V}_{L L}}))}^{22}]] = = 00 - - - - - - ((11))$

其中V_R为方程的最小正实根。对于各向同性材料的常见金属，克里斯托菲尔声弹性方程在一维平面内可简化为：Where _VR is the smallest positive real root of the equation. For common metals, which are isotropic materials, the Christopher's acoustoelastic equation can be simplified in a one-dimensional plane as:

$[\begin{matrix} {c c}_{1111} & 00 \\ 00 & {c c}_{4444} \end{matrix}] [\begin{matrix} {P P}_{x x} \\ {p p}_{y the y} \end{matrix}] = = ρ ρ {V V}^{22} [\begin{matrix} {P P}_{x x} \\ {p p}_{y the y} \end{matrix}] - - - - - - ((22))$

由此可得二阶弹性常数与声波波速的关系为：From this, the relationship between the second-order elastic constant and the acoustic wave velocity can be obtained as:

${c c}_{1111} = = ρ ρ {V V}_{L L}^{22} - - - - - - ((33))$

${c c}_{4444} = = ρ ρ {V V}_{S S}^{22} - - - - - - ((44))$

根据(1)(3)(4)式，便可计算金属的二阶弹性常数c₁₁、c₄₄和无应力状态下的密度ρ。According to formulas (1)(3)(4), the second-order elastic constants c ₁₁ and c ₄₄ of the metal and the density ρ in the unstressed state can be calculated.

第三步，利用线性热膨胀施加静水应力的方法测算金属样品在应力状态下时的激光声表面波、纵波和横波波速，并引入等效二阶弹性常数与三阶弹性常数的关系推算出金属的三阶弹性常数。具体步骤包括：The third step is to use the method of linear thermal expansion to apply hydrostatic stress to measure the laser surface acoustic wave, longitudinal wave and shear wave velocity of the metal sample under stress, and introduce the relationship between the equivalent second-order elastic constant and the third-order elastic constant to calculate the metal Third-order elastic constants. Specific steps include:

(1)把金属样品置于恒温加热装置容器(如水浴锅)内，加热样品至一个较高的温度(如高于室温10-80℃)，使样品因热膨胀处于静水应力状态。这里只需测量区分与常温下温度不同便已足够，而不需要测量温度的精确值。热膨胀使样品处于在静水应力状态，此时金属的应变张量有如下的形式：

这里α是热膨胀系数，T是对于无应变状态时的温度变化。(1) Place the metal sample in a container of a constant temperature heating device (such as a water bath), and heat the sample to a higher temperature (such as 10-80°C higher than room temperature), so that the sample is in a state of hydrostatic stress due to thermal expansion. Here, it is sufficient to measure the difference between the temperature and the normal temperature, and it is not necessary to measure the precise value of the temperature. Thermal expansion puts the sample in a state of hydrostatic stress. At this time, the strain tensor of the metal has the following form:

Here α is the coefficient of thermal expansion and T is the temperature change for the unstrained state.

(2)重复第一步的测定过程，测算得在应力状态下激光声表面波波速

纵波波速

和横波波速

(2) Repeat the measurement process of the first step to measure and calculate the velocity of the laser surface acoustic wave under the stress state

P wave velocity

and shear wave velocity

(3)在该状态下，引入有效二阶弹性常数

和

且有

c₁₂＝c₁₁-2c₄₄；考虑到应变引起的密度变化为：

ρ为无应力状态下的金属密度。α为金属材料的热膨胀系数。类似于第二步，此时

为瑞利方程(3) In this state, the effective second-order elastic constant is introduced

and

and have

c ₁₂ ＝c ₁₁ -2c ₄₄ ; considering the density change caused by strain is:

ρ is the metal density in the unstressed state. α is the thermal expansion coefficient of the metal material. Similar to the second step, this time

is the Rayleigh equation

${((\frac{x x}{{\overset{~ ~}{V V}}_{S S}}))}^{66} - - 88 {((\frac{x x}{{\overset{~ ~}{V V}}_{S S}}))}^{44} + + ((24 twenty four - - 1616 {((\frac{{\overset{~ ~}{V V}}_{S S}}{{\overset{~ ~}{V V}}_{L L}}))}^{22})) {((\frac{x x}{{\overset{~ ~}{V V}}_{S S}}))}^{22} - - 1616 ((11 - - {((\frac{{\overset{~ ~}{V V}}_{S S}}{{\overset{~ ~}{V V}}_{L L}}))}^{22})) = = 00 - - - - - - ((55))$

的最小正实根。而由二阶等效弹性常数与声波波速的关系可得：The smallest positive real root of . And from the relationship between the second-order equivalent elastic constant and the acoustic wave velocity:

${\overset{~ ~}{V V}}_{S S} = = \sqrt{\frac{{c c}_{4444} + + αT αT (({c c}_{144144} + + 22 {c c}_{166166} + + {c c}_{1111} + + {c c}_{4444} + + 22 {c c}_{1212}))}{ρ ρ / / ((11 + + 33 αT αT))}} - - - - - - ((66))$

${\overset{~ ~}{V V}}_{L L} = = \sqrt{\frac{{c c}_{1111} + + αT αT (({c c}_{111111} + + 22 {c c}_{112112} + + 22 {c c}_{1111} + + {22 c c}_{1212}))}{ρ ρ / / ((11 + + 33 αT αT))}} - - - - - - ((77))$

(4)步骤(3)中

和

的方程式是线性的，这对未知的c₁₁₁、c₁₁₂和c₁₄₄就有三个线性方程。但由于声表面波波速和横波波速相互依赖，这个方程组的行列式趋近于零，所以难以求得三个三阶弹性常数。考虑到常见金属材料的c₁₄₄相比于其他两个三阶弹性常数是很小的(见文献3[PRB，V.79，224102(2009)《Ab initio calculation of second-，third-，and fourth-order elastic constants for single crystals》])，因此我们假设c₁₄₄＝0。利用TMA测试得到的线性热膨胀系数α，根据(6)(7)式便可求得三阶弹性常数c₁₁₁和c₁₁₂。(4) In step (3)

and

The equation of is linear, and there are three linear equations for unknown c ₁₁₁ , c ₁₁₂ and c ₁₄₄ . However, since the surface acoustic wave velocity and the shear wave velocity depend on each other, the determinant of this equation is close to zero, so it is difficult to obtain the three third-order elastic constants. Considering that the c ₁₄₄ of common metal materials is very small compared to the other two third-order elastic constants (see literature 3 [PRB, V.79, 224102 (2009) "Ab initio calculation of second-, third-, and fourth -order elastic constants for single crystals "]), so we assume c ₁₄₄ =0. Using the linear thermal expansion coefficient α obtained from the TMA test, the third-order elastic constants c ₁₁₁ and c ₁₁₂ can be obtained according to equations (6) and (7).

实施例：Example:

我们利用水浴锅加热法对铝板样品在两个温度情况下进行实验：室温21℃-23℃和水的沸点温度100℃。这个范围内，铝样品没有结构变化，因此不会像施加轴向应力般引起样品厚度而导致误差。样品浸入水中过半的厚度，水的温度由热电偶测得。方程的解仅仅依赖于不同的温度，所以只需测量区分温度的不同便已足够，而不需要测量温度的精确值。热膨胀系数α利用TMA测试独立测量。We used the water bath heating method to conduct experiments on aluminum plate samples at two temperatures: room temperature 21°C-23°C and water boiling point temperature 100°C. In this range, there is no structural change in the aluminum sample, so there will be no error caused by the sample thickness caused by the application of axial stress. The sample is submerged to half its thickness in water, the temperature of which is measured by a thermocouple. The solution of the equation depends only on the difference in temperature, so it is sufficient to measure the difference in temperature rather than the exact value of the temperature. The coefficient of thermal expansion α was independently measured using the TMA test.

具体步骤如下：首先，我们测量在室温(22℃)时所有3种模态声波的波速。声表面波的波速在尽可能短的距离(大约5-6mm)探测。具体的测量过程为：记录激光源在多个位置上激发的波形，且利用相关函数法测定每个波形的延迟时间，并最终通过线性拟合延迟时间和波形传播步进距离的函数关系计算得到波速。这样，我们可以得到声表面波的波速V_R和波的传播距离L。较短的距离可以很好的探测到从样品底部反射的纵波脉冲。利用已知的L和样品的厚度h就可以计算得到纵波速度

这里t_L是纵波的传播时间。对于横波的探测，我们利用步进电机移动激光光源调整在较远的距离。在这个位置我们可以测量到横波的速度是

在铝样品中测得的结果是：V_R＝6361.4m/s；V_S＝3137.4m/s；V_R＝2939.9m/s。然后根据瑞利方程(1)和声速与二阶弹性常数的关系式(3)和(4)计算铝样品的二阶弹性常数和密度为：c₁₁＝109.6GPa；c₄₄＝26.8GPa；ρ＝2709kg/m³。The specific steps are as follows: First, we measure the wave velocities of all three modes of sound waves at room temperature (22°C). The wave velocity of the SAW is detected at the shortest possible distance (approximately 5-6 mm). The specific measurement process is: record the waveforms excited by the laser source at multiple positions, and use the correlation function method to measure the delay time of each waveform, and finally calculate the functional relationship between the delay time and the waveform propagation step distance by linear fitting wave speed. In this way, we can get the wave velocity V _R of the surface acoustic wave and the propagation distance L of the wave. Shorter distances allow good detection of longitudinal wave pulses reflected from the bottom of the sample. Using the known L and the thickness h of the sample, the longitudinal wave velocity can be calculated

Here t _L is the travel time of the longitudinal wave. For the detection of shear waves, we use stepper motors to move the laser light source and adjust it at a longer distance. At this position we can measure the velocity of the shear wave as

The results measured in the aluminum sample are: V _R =6361.4m/s; V _S =3137.4m/s; V _R =2939.9m/s. Then calculate the second-order elastic constant and density of the aluminum sample according to the Rayleigh equation (1) and the relationship between the sound velocity and the second-order elastic constant (3) and (4): c ₁₁ =109.6GPa; c ₄₄ =26.8GPa; ρ =2709 kg/m ³ .

接着检测上述的两个三阶弹性常数。为此，我们首先把样品加热到一个较高的温度，然后测量这时的瑞利波波速

横波波速

和纵波波速

并用TMA测试独立测量铝样品的线性热膨胀系数α为2.46·10^-51/K。正如上文所述，我们假设c₁₄₄＝0。最后通过式(6)(7)计算得三阶弹性常数：c₁₁₁＝-1130.7GPa，c₁₁₂＝-299.7GPa。Next, the above-mentioned two third-order elastic constants are detected. To do this, we first heated the sample to a higher temperature and then measured the Rayleigh wave velocity at this time

Shear wave velocity

and longitudinal wave velocity

And the linear thermal expansion coefficient α of the aluminum sample was independently measured by TMA test to be 2.46·10 ^-5 1/K. As mentioned above, we assume c ₁₄₄ =0. Finally, the third-order elastic constants are calculated by formulas (6) (7): c ₁₁₁ =-1130.7GPa, c ₁₁₂ =-299.7GPa.

这些常数的值和现有文献中铝合金材料的相应参数值吻合的很好，如文献4[Nondestructive testing and Evaluation，V.18，2(2002)《Propagation of surface waves indeformed anisotropic thin layered solids》]中相应参数值分别为：-1100GPa和-315GPa，因此也证明了这种测量材料三阶常数新方法的正确性。The values of these constants are in good agreement with the corresponding parameter values of aluminum alloy materials in the existing literature, such as literature 4 [Nondestructive testing and Evaluation, V.18, 2 (2002) "Propagation of surface waves deformed anisotropic thin layered solids"] The corresponding parameter values are: -1100GPa and -315GPa, respectively, so it also proves the correctness of this new method for measuring the third-order constant of materials.

测量系统所存在的误差主要取决于测量纵波、横波及表面波速度的误差，而测速的误差则主要取决于测长误差即测厚h和激发点与探测点距离的L、d以及测时误差。The error of the measurement system mainly depends on the error of measuring the velocity of longitudinal wave, shear wave and surface wave, while the error of velocity measurement mainly depends on the error of length measurement, that is, the error of thickness measurement h, the distance between the excitation point and the detection point L, d and the error of time measurement .

以c₁₁、c₄₄为例，考虑初始激发点与探测点的距离L由波形相关算法与表面波波速由程序计算所得，故二者引入的计算误差忽略不计。则由式(3)、式(4)、

和

可推导出c₁₁和c₄₄测量误差的最大值分别为：Taking c ₁₁ and c ₄₄ as examples, considering that the distance L between the initial excitation point and the detection point is calculated by the waveform correlation algorithm and the surface wave velocity by the program, the calculation error introduced by the two is negligible. Then by formula (3), formula (4),

and

It can be deduced that the maximum values of the measurement errors of c ₁₁ and c ₄₄ are respectively:

$δ δ {c c}_{1111} = = \frac{22 ρ ρ (({L L}^{22} + + 44 {h h}^{22}))}{{t t}_{L L}^{33}} δ δ (({Δt Δt}_{L L})) + + \frac{88 ρh ρh}{{t t}_{L L}^{22}} δh δh - - - - - - ((88))$

${δc δ c}_{4444} = = \frac{22 ρ ρ [[{((L L + + d d))}^{22} + + 44 {h h}^{22}]]}{{t t}_{S S}^{33}} δ δ (({Δt Δt}_{S S})) + + \frac{88 ρh ρ h}{{t t}_{}} δh δh + + \frac{22 ρ ρ ((L L + + d d))}{{t t}_{S S}^{22}} δd δd - - - - - - ((99))$

这里，δc₁₁和δc₄₄是二阶弹性常数的误差；δ(Δt_L)和δ(Δt_S)分别是纵波和横波的传播时间测量误差；δh和δd分别是样品测厚误差和测量横波时的光源移动距离误差。Here, δc ₁₁ and δc ₄₄ are the errors of the second-order elastic constants; δ(Δt _L ) and δ(Δt _S ) are the measurement errors of the travel time of longitudinal waves and shear waves, respectively; The light source movement distance error.

测试中，δ(Δt_L)＝δ(Δt_S)＝0.5ns，δh＝0.01mm，δd＝1.25μm，则由式(8)和式(9)可得：In the test, δ(Δt _L )=δ(Δt _S )=0.5ns, δh=0.01mm, δd=1.25μm, then it can be obtained from formula (8) and formula (9):

δc₁₁＝0.248GPa， $\frac{{δc}_{11}}{c_{11}} = 0.226 %;$ δc ₁₁ =0.248GPa, $\frac{{δ c}_{11}}{c_{11}} = 0.226 %;$

δc₄₄＝0.046GPa， $\frac{δ c_{44}}{c_{44}} = 0.164 %$ δc ₄₄ =0.046GPa, $\frac{δ c_{44}}{c_{44}} = 0.164 %$

而在应力状态下，等效二阶弹性常数采用相同的实验方法测得，因此与上述二阶弹性常数有相同的误差范围，由于三阶弹性常数是通过引入等效二阶弹性进行代数换算计算得到，忽略计算误差可得三阶弹性常数的测量误差也小于0.3％。分析表明，该系统具有较高的测量精度，所测铝样品的二阶和三阶弹性常数的测量误差较小，能满足工程及科学研究允许误差的要求。In the state of stress, the equivalent second-order elastic constant is measured by the same experimental method, so it has the same error range as the above-mentioned second-order elastic constant, because the third-order elastic constant is calculated by introducing the equivalent second-order elastic algebraic conversion It is obtained that, ignoring the calculation error, the measurement error of the third-order elastic constant is also less than 0.3%. The analysis shows that the system has high measurement accuracy, and the measurement errors of the second-order and third-order elastic constants of the measured aluminum samples are small, which can meet the requirements of engineering and scientific research allowable errors.

Claims

1. a laser ultrasonic measuring method of metal third-order elastic constant, is characterized in that step is as follows:

The first step is to measure the wave velocities of the longitudinal wave, shear wave and surface wave excited by the laser respectively under the stress-free state and the stressed state;

The second step is to calculate the second-order elastic constant and density of the metal according to the acoustoelastic theory and the Rayleigh equation by using the surface wave, longitudinal wave and shear wave velocity measured in the stress-free state;

The third step is to use the ultrasonic wave velocity of longitudinal wave, shear wave and surface wave measured under the stress state, introduce the equivalent second-order elastic constant and the independently measured linear thermal expansion coefficient, and finally calculate the third-order elastic constant according to the acoustoelastic theory.

2. the laser ultrasonic measuring method of metal third-order elastic constant according to claim 1 is characterized in that in the first step, the method for measuring the longitudinal wave, shear wave, surface wave velocity under stress-free and stressed state is:

(1) design detection system, this detection system comprises pulse laser, cylindrical lens, stepper motor, ultrasonic detection device, metal material sample, single-channel oscilloscope and computer, stepper motor connects pulse laser, cylindrical lens respectively, and this computer Control the single-channel oscilloscope and stepping motor, and the single-channel oscilloscope is connected with the ultrasonic detection device. The short pulse laser excited by the pulse laser is irradiated on the position x _i (i=1...N) on the surface of the metal material sample through the cylindrical lens focused line light source , as the excitation source of the surface acoustic wave on the surface of the metal material, after the metal material absorbs the pulsed laser energy, a local short-pulse thermal stress is generated in the laser concentration area on the sample surface, and a broadband surface acoustic wave is excited, and along the surface spread;

(2) The pulsed laser and the cylindrical lens are fixed on the translation stage of the stepping motor, and the computer controls the stepping motor to move the laser line light source along the axial direction, and excite the acoustic surface at different positions x _i (i=1...N) wave, the detection point of the ultrasonic detection device is fixed in the direction of the central axis of the line light source, and detects the surface acoustic wave excited from x _i (i=1...N), and the single-channel oscilloscope converts the surface acoustic wave signal detected by the ultrasonic detection device into digital The signal is input into the computer for subsequent data processing;

(3) Use the waveform correlation function method to calculate the time relative delay Δt of each step for the detection results of N steps, and calculate the surface acoustic wave velocity by linearly fitting the functional relationship between the delay time and the waveform propagation step distance, and according to the step distance Calculate the propagation distance L of the wave; the longitudinal wave signal with the best signal and noise can be detected at the closest point between the laser line source and the detection point (X _N ), and the propagation of the longitudinal wave reflected from the bottom surface is calculated by using the known L and the thickness h of the metal sample Distance, the longitudinal wave velocity can be calculated according to the longitudinal wave arrival time; use the stepper motor to move the laser line source to _XS to obtain the shear wave signal with the best signal-to-noise ratio, and obtain the shear wave velocity according to the shear wave propagation distance and arrival time.

3. the laser ultrasonic measuring method of metal third-order elastic constant according to claim 1 is characterized in that in the second step, measures the second-order elastic constant of metal in stress-free shape, and its method is: based on acoustoelasticity theory , the Christopher equation can be simplified in a one-dimensional plane to obtain the relationship between the second-order elastic constant and the sound wave velocity and

Then introduce the Rayleigh equation, through the simultaneous equations, the second-order elastic constant of the metal can be obtained from the measured _VR , V _L and V _S.

4. the laser ultrasonic measuring method of metal third-order elastic constant according to claim 1 is characterized in that in the 3rd step, utilizes thermal expansion to make metal be in the method for measuring third-order elastic constant under the hydrostatic stress state:

(1) Heating the metal sample at a constant temperature, so that the metal is in a state of hydrostatic stress, and measuring the speed of the laser surface acoustic wave, longitudinal wave and transverse wave at this time;

(2) Use the TMA test to independently measure the deformation curve of the metal sample changing with temperature, and then obtain the linear thermal expansion coefficient of the metal material;

(3) Consider the density change caused by thermal expansion

The relationship between the equivalent second-order elastic constant and the acoustic wave velocity is introduced, and the third-order elastic constant is calculated by using the second-order elastic constant, acoustic wave velocity, thermal expansion coefficient, and density calculated in the second step.