A method for measuring the shear wave velocity of a material

Abstract

The present invention discloses a method for measuring the shear wave velocity of a material. First, the material to be tested is selected and made into a cylindrical specimen. Then, a sensor is respectively pasted on the cylindrical surfaces at both ends of the cylindrical specimen, and the two sensors are spatially staggered at an angle of 90°. Then, one sensor is electrically connected to a signal generator, the other sensor is electrically connected to a lock-in amplifier, and the lock-in amplifier is electrically connected to a signal acquisition device, and the signal generator and the signal acquisition device are started. Then, signal analysis is carried out to obtain the response spectrum of the cylindrical specimen under the scanning excitation. Finally, the first-order torsional natural vibration frequency corresponding to the first peak in the response spectrum is extracted, and the shear wave velocity of the specimen is calculated. The present invention can avoid the error in the selection of the shear wave first arrival time and the influence brought by the ultrasonic time domain measurement noise, improve the convenience and accuracy of the material shear wave velocity measurement, and can provide a theoretical basis and data support for the measurement of the mechanical properties related to the material.

Description

Technical Field

[0001] The present invention relates to a method for measuring the wave velocity of a material under stress, specifically a method for measuring the shear wave velocity of a material, and belongs to the technical field of materials science and technology. Background Art

[0002] In the field of materials science, the measurement of the compression wave velocity and shear wave velocity of materials is an important way to determine the Poisson's ratio elastic constant, shear modulus, bulk modulus, and Young's modulus of materials. In terms of material property evaluation, the shear wave velocity of materials is an important index reflecting the elastic properties and mechanical behaviors of materials. By measuring the shear wave velocity of materials, the mechanical properties such as shear strength and toughness of materials can be evaluated, providing an important basis for the selection and application of materials. In terms of material quality inspection, during the material production process, the measurement of shear wave velocity can also be used to detect internal defects and damages of materials. By comparing the shear wave velocities of different materials, the tiny changes and differences inside them can be found, so as to discover and solve quality problems in a timely manner.

[0003] Traditional wave velocity measurement methods mainly use ultrasonic probes in the time domain and calculate by measuring the propagation distance and propagation time of waves. Since the compression wave is the first wave to arrive and its first arrival time is very easy to judge, the measurement of the compression wave velocity is also the easiest. However, the shear wave is the wave that arrives later. When the propagation distance is long, it separates from the compression wave and is relatively easy to judge. But when the specimen size is small and the propagation distance is very short, since it is integrated into the whole waveform, the first arrival time of the shear wave is often not easy to judge. In addition, the noise during measurement also greatly increases the difficulty of identifying the first arrival moment of the shear wave.

[0004] Currently, there is also a method of approximately inferring the shear wave velocity from the surface wave velocity, believing that the shear wave velocity is approximately equal to the surface wave velocity / 0.87, but this method is an approximate method and is also affected by the Poisson's ratio and elastic modulus of materials. Summary of the Invention

[0005] Aiming at the problems existing in the above-mentioned prior art, the present invention provides a method for measuring the shear wave velocity of a material, which can avoid the error in selecting the first arrival moment of the shear wave and the influence brought by the ultrasonic time domain measurement noise, improve the convenience and accuracy of the measurement of the shear wave velocity of materials, and can provide a theoretical basis and data support for the measurement of the mechanical properties related to materials.

[0006] To achieve the above object, the method for measuring the shear wave velocity of this material specifically includes the following steps:

[0007] Step1, select the material to be tested and make it into a cylindrical specimen;

[0008] Step 2: Paste a sensor on the cylindrical surfaces at both ends of the cylindrical specimen, and the two sensors are spatially staggered at a 90° angle.

[0009] Step 3: Electrically connect one sensor to a signal generator, electrically connect the other sensor to a lock-in amplifier, and electrically connect the lock-in amplifier to a signal acquisition device. Start the signal generator and the signal acquisition device. Transmit a continuous scanning signal through the signal generator, and the signal acquisition device synchronously acquires the signal.

[0010] Step 4: Conduct signal analysis to obtain the response spectrum of the cylindrical specimen under the scanning excitation.

[0011] Step 5: Extract the first-order torsional natural vibration frequency f corresponding to the first peak in the response spectrum t , and calculate the shear wave velocity of the specimen. The calculation formula is as follows:

[0012] V s = 2Lf t

[0013] In the formula: V s is the shear wave velocity; L is the axial length dimension of the cylindrical specimen; f t is the first-order torsional natural vibration frequency corresponding to the first peak.

[0014] Furthermore, in Step 1, the ratio of the axial length dimension L to the diameter dimension D of the cylindrical specimen is in the range of 0.9 to 1.90.

[0015] Furthermore, in Step 2, before pasting the sensors on the cylindrical specimen, measure and record the weight m 1 of the cylindrical specimen, measure and record the weight m 2 of the sensor, and m 2 does not exceed 1% of m 1 .

[0016] Furthermore, in Step 2, after pasting the sensors at both ends of the cylindrical specimen, place the cylindrical specimen flat on a sponge pad.

[0017] Furthermore, in Step 4, first plot the collected original trigger signal and response signal, then correspond the trigger point position in the trigger signal to the data position in the original spectrum, and normalize the original spectrum using the maximum value of the response to obtain the normalized response spectrum of the cylindrical specimen under the scanning excitation.

[0018] Compared with the prior art, the method for measuring the shear wave velocity of this material is convenient to operate and has high measurement accuracy, and has the following beneficial effects:

[0019] 1. Measuring the frequency related to the shear wave velocity through the frequency domain method eliminates the need to extract the arrival time of the first shear wave, greatly improving the convenience and accuracy of the test.

[0020] 2. By setting the ratio range of the axial length to the diameter of the specimen, it is ensured that the first identified frequency is the frequency related to the shear wave velocity, guaranteeing the accuracy of the measurement.

[0021] 3. By restricting the ratio of the mass of the sensor to the specimen, the error influence of the sensor's own weight on the test frequency can be reduced.

[0022] 4. By placing the specimen flat on a sponge pad, on the one hand, it can avoid the test instability caused by placing the specimen vertically or obliquely during traditional tests, and on the other hand, it can significantly reduce the additional constraints on the specimen by placing the sponge pad, ensuring the free vibration of the specimen and the accuracy of the frequency measurement.

[0023] 5. Through the asymmetric arrangement of the sensors, the excitation of the first frequency related to the shear wave velocity can be effectively ensured, thus guaranteeing the accuracy of the measurement. Description of the Drawings

[0024] Figure 1 is a diagram showing the variation of each first-order natural vibration frequency with the length-diameter ratio of the cylindrical specimen;

[0025] Figure 2 is a diagram showing the specimen of the present invention placed flat on a sponge pad after pasting the sensors;

[0026] Figure 3 is a diagram showing the excitation and acquisition connection of the specimen of the present invention;

[0027] Figure 4 is a diagram showing the original trigger signal of the specimen of the present invention;

[0028] Figure 5 is a diagram showing the original response signal of the specimen of the present invention;

[0029] Figure 6 is a diagram showing the normalized response spectrum of the specimen of the present invention;

[0030] Figure 7 is a diagram showing the traditional ultrasonic velocity measurement in the specimen length direction using a dedicated shear wave sensor;

[0031] Figure 8 is a signal time domain diagram of the shear wave sensor;

[0032] Figure 9 is a diagram showing the ultrasonic measurement using a compression wave sensor;

[0033] Figure 10It is the time-domain diagram of the signal of the compression wave sensor;

[0034] Figure 11 It is the diagram of ultrasonic measurement using a piezoelectric wafer sensor;

[0035] Figure 12 It is the time-domain diagram of the signal of the piezoelectric wafer sensor. Specific implementation mode

[0036] The present invention will be further described below with reference to the accompanying drawings.

[0037] The method for measuring the shear wave velocity of this material specifically includes the following steps:

[0038] Step1, select the material to be tested and make it into a cylindrical specimen.

[0039] If the dimensions of the specimen are not made properly, it may cause the first-order bending natural vibration frequency of the specimen perpendicular to the axial direction or the radial direction to be lower than the first-order shear mode frequency required by the present invention, resulting in an error in calculating the shear wave velocity by directly selecting the first main frequency from the spectrum.

[0040] The first-order bending natural vibration frequency f of the cylindrical specimen perpendicular to the axial direction b is expressed as follows:

[0041]

[0042] In the formula: k 1 is the first-order bending mode constant perpendicular to the axial direction, with a value of 4.730041; E is the elastic modulus of the material; ρ is the material density.

[0043] The first-order bending natural vibration frequency f of the cylindrical specimen perpendicular to the radial direction p is expressed as follows:

[0044]

[0045] In the formula: β 1 is the first-order bending mode constant perpendicular to the radial direction, β 1 is related to the Poisson's ratio μ of the material. When μ = 0.3, β 1 = 3.00052.

[0046] The first-order torsional natural vibration frequency f of the cylindrical specimen t (The detailed derivation process can be seen in the subsequent step6) is expressed as follows:

[0047]

[0048] In the formula: G is the shear modulus of the material.

[0049] Set μ = 0.3, plot the first-order frequencies of cylindrical specimens under a series of different L / D conditions, and use the first-order torsional natural vibration frequency f t Normalize it, and the variation of different modal frequencies can be obtained as shown in Figure 1 shown. It can be seen from the figure that when μ = 0.3, only when the length-diameter ratio is within a certain limited range (0.42 - 2.87), the first-order torsional natural vibration frequency f t will be the smallest among all kinds of first-order natural vibration frequencies. Considering that the Poisson's ratio of conventional solid materials usually varies between 0.10 and 0.40, and in order to make the test interval as far away from the corresponding frequencies at the intersection as possible, the present invention limits the length-diameter ratio range of the cylindrical specimen to 0.9 - 1.90, so as to fully avoid other interference frequency bands and ensure that the first-order mode of the specimen is the torsional mode, which can ensure that the first identified frequency is the frequency related to the shear wave velocity and guarantee the measurement accuracy.

[0050] In the test example, the material to be tested is selected as concrete, and it is made into a cylindrical specimen with an axial length dimension L of 3.756 cm and a diameter dimension D of 2.468 cm, D:L = 1.52.

[0051] Step2, measure and record the weight m of the specimen 1 , measure and record the weight m of the sensor 2 , m 2 should not exceed 1% of m 1 . The sensor can be a piezoelectric piece or other ultrasonic probes.

[0052] There is usually the following relationship between the natural vibration frequency f of the cylindrical specimen and the mass m 1 :

[0053]

[0054] From the relative error formula ( it can be seen that when the weight m of the sensor attached to the cylindrical specimen 2 does not exceed 1% of the weight m of the cylindrical specimen 1 , the resulting relative error is less than 0.5%. At this time, the frequency measurement error caused by the additional mass can be ignored. Therefore, the present invention limits that m 2 should not exceed 1% of m 1 to reduce the error influence on the test frequency caused by the weight of the sensor itself.

[0055] The weight m of the specimen in the test example 1 is 43.02 g, and the weight m of the sensor 2 is 0.18 g. It is calculated that m 2 / m 1= 0.42%, not exceeding 1% of the weight of the test piece.

[0056] Step3, paste a sensor on the cylindrical surfaces at both ends of the test piece respectively, and the two sensors are spatially staggered at a 90° angle, then place the test piece flat on the sponge pad.

[0057] After the sensors are pasted on the test piece in the test example, it is placed flat on the sponge pad as Figure 2 shown.

[0058] Step4, as Figure 3 shown, electrically connect one sensor to the signal generator, electrically connect the other sensor to the lock-in amplifier, and electrically connect the lock-in amplifier to the signal acquisition device. Start the signal generator and the signal acquisition device, and transmit a continuous scanning signal through the signal generator. The signal acquisition device synchronously acquires the signal.

[0059] The excitation and acquisition parameters of the test piece in the test example are shown in Table 1 below:

[0060] Table 1 Excitation and acquisition parameters

[0061]

[0062]

[0063] Step5, perform signal analysis to obtain the response spectrum of the test piece under the scanning excitation.

[0064] For the test piece in the test example, first plot the acquired original trigger signal and response signal as Figure 4 , Figure 5 shown, then correspond the trigger point position in the trigger signal (the data point 203677 at the vertical line position in Figure 3 ) to the data position in the original spectrum, and normalize the original spectrum using the maximum value of the response to obtain the normalized response spectrum of the test piece under the scanning excitation as Figure 6 shown.

[0065] Step6, extract the frequency f corresponding to the first peak in the response spectrum 1 , and calculate the shear wave velocity of the test piece.

[0066] The propagation of waves in a medium can establish a wave equation through the relationship between strain and displacement:

[0067] Strain-displacement relationship: The relationship between the displacement u(x,t) and strain ε of the material is expressed as follows:

[0068]

[0069] Stress-strain relationship: During the torsion of an elastic material, the relationship between the shear stress τ and the shear strain ε is described by the shear modulus G as follows:

[0070] τ = Gε

[0071] Equation ②

[0072] Force balance: Considering the force balance within a unit volume, assuming the shear force per unit length is τ and the density of the material is ρ, then we have:

[0073]

[0074] Substituting Equation ② into Equation ③, we get

[0075]

[0076] Substituting Equation ① into Equation ④, we get

[0077]

[0078] Equation ⑤ can be rewritten as

[0079]

[0080] Dividing both sides of Equation ⑥ by ρ and rearranging, we can obtain the wave equation:

[0081]

[0082] Solving the above wave equation of Equation ⑦, assuming the solution of the displacement is in the form of separated variables, that is

[0083] u(x, t) = X(x)T(t) Equation ⑧

[0084] Substituting Equation ⑧ into the wave equation of Equation ⑦, we get:

[0085]

[0086] Dividing both sides of Equation ⑨ by XT, we get:

[0087]

[0088] where: λ is the separation constant.

[0089] Among them, the equation of the time part is expressed as:

[0090]

[0091] Its solution is:

[0092]

[0093] where: A and B are constants.

[0094] The equation for the spatial part is expressed as:

[0095]

[0096] Its solution is:

[0097]

[0098] Where: C and D are constants.

[0099] For equation Applying the boundary conditions, for a freely vibrating cylinder, the boundary conditions are free at both ends (displacement is 0), that is, X(0) = 0, X(L) = 0. From X(0) = 0, we can get C = 0. Therefore For X(L) = 0, we can get The above equation always holds, which means: That is For the first-order mode n = 1, we can get

[0100] Substitute into equation For the solution of the time part, we can get:

[0101]

[0102] From this, the corresponding first-order torsional natural vibration frequency f t is:

[0103]

[0104] Furthermore, we can get:

[0105] V s = 2Lf t Equation

[0106] Where: V s is the shear wave velocity; L is the axial length dimension of the cylindrical specimen; f t is the first-order torsional natural vibration frequency corresponding to the first peak.

[0107] For the test example specimen, extract the first-order torsional natural vibration frequency f t corresponding to the first peak in the response spectrum. It is 35.47 kHz. Using equation calculate the shear wave velocity of the specimen to be 2664.51 m / s.

[0108] To verify the accuracy of the shear wave velocity of the test example specimen, a dedicated shear wave sensor is used to perform traditional ultrasonic velocity measurement in the axial length direction of the specimen as Figure 7As shown, the excitation and acquisition parameters are as shown in Table 2 below:

[0109] Table 2 Ultrasonic Excitation and Acquisition Parameters

[0110] Excitation and acquisition parameters Value Excitation frequency 500 kHz Excitation amplitude 100V Acquisition trigger type Edge Trigger level 1V Amplification gain 20 dB Signal acquisition frequency 10 MHz Signal acquisition duration 0.001s Number of sampling points 10000

[0111] The obtained ultrasonic response signal is as Figure 8 shown. Although the dedicated shear wave sensor has sufficiently suppressed the compression wave, it is noted that Figure 8 the compression wave signal still exists in P and the signal t Figure 8 first arriving at 0.079 ms is the compression wave signal. The first arrival time of the shear wave in s is t s = 0.0142 ms. The shear wave velocity calculated by Vs = L / t is 2645.07 m / s, which is in good agreement with the shear wave velocity of 2664.51 m / s obtained by using the method proposed in the present invention, with a relative error of 0.73%.

[0112] Figures 9 to 12 The layout form of ultrasonic measurement using a compression wave sensor and a piezoelectric wafer and the ultrasonic response signal are also given. From the signal time domain diagrams in Figure 9 and Figure 12 , it can be seen that the first arrival time of the compression wave of the specimen is clearly distinguishable, but the arrival time of the shear wave is basically indistinguishable from the waveform diagram, and at this time, the shear wave velocity cannot be directly obtained.

[0113] Compared with the time domain measurement method used in traditional wave velocity measurement, the measurement method of the shear wave velocity of this material does not require the extraction of the first arrival time of the shear wave, thereby avoiding the error in the selection of the first arrival time of the shear wave and the influence of the ultrasonic time domain measurement noise, and can greatly improve the convenience and accuracy of the measurement of the shear wave velocity of the material, providing a theoretical basis and data support for the measurement of the mechanical properties related to the material.

Claims

1. A method for measuring shear wave velocity of a material, characterized in that: The specific steps include: Step 1, select the material to be tested and make it into a cylindrical specimen, the ratio of the axial length dimension L to the diameter dimension D of the cylindrical specimen is in the range of 0.9 to 1.90; Step 2, affix a sensor to the cylindrical surface at both ends of the cylindrical specimen, and the two sensors are staggered at a 90° angle; Step 3, electrically connect one sensor to the signal generator, electrically connect another sensor to the phase-locked amplifier, and electrically connect the phase-locked amplifier to the signal acquisition device, start the signal generator and the signal acquisition device, emit a continuous scanning signal through the signal generator, and the signal acquisition device synchronously acquires the signal; Step 4, perform signal analysis to obtain the response spectrum of the cylindrical specimen under scanning excitation; Step 5: Extract the first-order torsional natural frequency f corresponding to the first peak in the response spectrum. t , the shear wave velocity of the specimen is calculated, and the calculation formula is as follows: <h2 style=";text-align:left;direction:ltr">V<h2 style=";text-align:left;direction:ltr"> s <h2 style=";text-align:left;direction:ltr"> <2Lf<h2 style=";text-align:left;direction:ltr"> t Where: V s is the shear wave velocity; L is the axial length of the cylindrical specimen; f t is the first-order torsional natural frequency corresponding to the first peak.

2. The method for measuring the shear wave velocity of a material according to claim 1, characterized in that: In Step 2, before attaching the sensor to the cylindrical specimen, measure and record the weight m1 of the cylindrical specimen, and measure and record the weight m2 of the sensor, and m2 shall not exceed 1% of m1.

3. The method for measuring the shear wave velocity of a material according to claim 1, characterized in that: In Step 2, after attaching sensors to both ends of the cylindrical specimen, place the cylindrical specimen flat on the sponge pad.

4. The method for measuring the shear wave velocity of a material according to claim 1, characterized in that: In Step 4, the collected original trigger signal and response signal are first plotted, and then the trigger point position in the trigger signal is matched with the data position in the original spectrum, and the original spectrum is normalized using the maximum value of the response to obtain the normalized response spectrum of the cylindrical specimen under scanning excitation.

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