CN117214303A - Guided wave nondestructive testing method for elastic modulus of solid material - Google Patents
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- 239000011343 solid material Substances 0.000 title claims abstract description 199
- 238000000034 method Methods 0.000 title claims abstract description 60
- 238000009659 non-destructive testing Methods 0.000 title claims abstract description 14
- 238000001514 detection method Methods 0.000 claims abstract description 38
- 230000005284 excitation Effects 0.000 claims abstract description 24
- 239000006185 dispersion Substances 0.000 claims abstract description 17
- 239000011159 matrix material Substances 0.000 claims description 24
- 230000008569 process Effects 0.000 claims description 15
- 239000000523 sample Substances 0.000 claims description 9
- 238000004458 analytical method Methods 0.000 claims description 6
- 230000008030 elimination Effects 0.000 claims description 6
- 238000003379 elimination reaction Methods 0.000 claims description 6
- 230000004069 differentiation Effects 0.000 claims description 4
- 238000006073 displacement reaction Methods 0.000 claims description 4
- 239000007787 solid Substances 0.000 claims description 4
- 230000009286 beneficial effect Effects 0.000 abstract description 3
- 230000035945 sensitivity Effects 0.000 abstract 1
- 229910000838 Al alloy Inorganic materials 0.000 description 34
- 239000000463 material Substances 0.000 description 8
- 238000005259 measurement Methods 0.000 description 3
- 229910001294 Reinforcing steel Inorganic materials 0.000 description 2
- 238000004364 calculation method Methods 0.000 description 2
- 238000010586 diagram Methods 0.000 description 2
- 239000007769 metal material Substances 0.000 description 2
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- 229910000831 Steel Inorganic materials 0.000 description 1
- 238000005452 bending Methods 0.000 description 1
- 238000012669 compression test Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 230000000644 propagated effect Effects 0.000 description 1
- 239000010959 steel Substances 0.000 description 1
- 238000009864 tensile test Methods 0.000 description 1
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Abstract
The application discloses a guided wave nondestructive testing method for elastic modulus of a solid material, which comprises the following steps: establishing a semi-analytic finite element model for the cross section of the solid material, and setting out a wave characteristic equation of the solid material to obtain a guided wave group velocity dispersion curve of the solid material; establishing a relation model between different elastic model values of the solid material and the guided wave group velocity; analyzing according to the guided wave group velocity dispersion curve of the solid material to obtain the detection frequency and the specific mode of the elastic modulus sensitivity; inputting detection frequency into an ultrasonic guided wave detection system, and carrying out experimental detection on a solid material to respectively obtain a guided wave excitation signal and a guided wave receiving signal of the solid material; and identifying the guided wave excitation signal and the guided wave receiving signal, analyzing and calculating the guided wave group velocity of the solid material, and further obtaining the elastic modulus value of the solid material. The application has the beneficial effects that: the method belongs to nondestructive detection, is safe and simple to operate, can obtain an accurate result by one-time detection, and has low detection cost.
Description
Technical Field
The application relates to the field of ultrasonic guided wave nondestructive testing, in particular to a guided wave nondestructive testing method for elastic modulus of a solid material.
Background
With the continuous progress of technology, various new materials are continuously appeared, and many solid materials need to have mechanical properties such as ultra-high strength, so the detection of various mechanical parameters of the new solid materials is very important. And wherein the elastic modulus is an important physical quantity describing the deformation resistance of the solid material, conventional detection methods such as tensile test method, compression test method, bending test method, ultrasonic detection method, resonance frequency method, and the like. These methods generally have certain drawbacks, such as the fact that they deform or bend by applying a tensile force or pressure to the material, the measuring method and the measuring instrument are relatively complex and cumbersome to operate, and even have certain damage to the solid material. The method of resonance frequency can calculate the elastic modulus by making the material into a sheet or beam with a specific shape, then generating resonance on the sheet or beam by mechanical or electronic excitation, measuring the resonance frequency, and analyzing the resonance frequency and the geometric parameters of the material. The existing ultrasonic detection method needs to be detected and determined for many times in the actual detection process, is complex in process, cannot accurately detect any solid material, has certain error, and is not beneficial to popularization and application.
According to the method, the solid material guided wave characteristic analysis is carried out by a semi-analytic finite element method, and the relation between the guided wave characteristic and the elastic modulus of the material is established; and detecting the guided wave characteristic of the solid material by a guided wave detection system, and reversely pushing out the elastic modulus of the solid material.
Disclosure of Invention
In order to overcome the defects in the prior art, the application aims to provide a guided wave nondestructive testing method for the elastic modulus of a solid material, which is used for simply, safely and accurately detecting the elastic modulus of the solid material, and is suitable for accurately detecting the elastic modulus of homogeneous solid materials with various cross section types and various thin rod-shaped metal materials such as plates, pipes, reinforcing steel bars, guys and steel rails.
In order to achieve the above purpose, the present application adopts the following technical scheme: a guided wave nondestructive testing method for elastic modulus of solid material comprises the following steps:
step S1, a semi-analytic finite element model is established for the cross section of a solid material, an improved wave characteristic equation of the solid material is obtained, and a guided wave group velocity dispersion curve of the solid material is obtained;
step S2, according to the wave characteristic equation of the solid material improved in the step S1, solving the guided wave group velocity of the solid material, and establishing a relation model between different elastic modulus values and the guided wave group velocity of the solid material;
s3, analyzing according to the guided wave group velocity dispersion curve of the solid material in the step S1 to obtain detection frequency and a specific mode which are sensitive to the elastic modulus;
s4, inputting the detection frequency sensitive to the elastic modulus of the solid material obtained in the step S3 into an ultrasonic guided wave detection system to carry out experimental detection on the solid material, and respectively obtaining a guided wave excitation signal and a guided wave receiving signal of the solid material;
and S5, identifying the guided wave excitation signal and the guided wave receiving signal of the solid material in the step S4, and solving the guided wave group velocity of the solid material through the relation model in the step S2 to obtain the elastic modulus value of the solid material.
Further, in step S1, a semi-analytical finite element model is built for the cross section of the solid material, and an improved wave characteristic equation of the solid material is obtained, which is shown in formula (1);
（1）；
wherein:；
wherein:；
wherein:；
in the method, in the process of the application,、/>and->Three different elimination for solid material +.>Is>Is the total mass matrix of the solid material, +.>Is imaginary number and is->For wave number, < >>Is angular frequency; />For guiding the displacement vector of each node in the solid material, < >>、/>And->Three different elimination for solid material +.>Is a cell stiffness matrix, ">Cell mass matrix of solid material, +.>Is a weak elastic matrix of solid material, +.>Unit number for solid material, +.>Total number of units of solid material, +.>Andcell strain matrix of solid material, respectively +.>And->Transpose of the unit strain matrix of solid material, respectively,/->Is a set of unit numbers of solid material, +.>Differentiation of the set of units as solid material, +.>Is a unit-shaped function of solid material, +.>Transpose of the unit shape function of the solid material, +.>Is the density of the solid material->Is the modulus of elasticity of the solid material,poisson's ratio for solid materials.
Further, in step S2, a relation model between different elastic modulus values of the solid material and the guided wave group velocity is established; the specific formula is shown in formula (2);
（2）；
wherein:；
in the method, in the process of the application,group velocity of guided waves for solid material, +.>Is->Eliminate imaginary number->Is>Left eigenvector of the solid material and right eigenvector of the solid material, respectively, +.>For guiding wave and elastic modulus in solid material guiding wave propagation>An irrelevant correlation vector.
Further, in step S3, the optimal excitation frequency of the solid material is obtained by analyzing the dispersion curve of the solid material, and the specific mode of the solid material corresponding to the optimal excitation frequency is obtained.
Further, in step S4, the ultrasonic guided wave detection system detects by using a transceiver-integrated sensor probe, and a transceiver-integrated sensor probe is mounted on the solid material. And (3) inputting the detection frequency sensitive to the elastic modulus of the solid material obtained in the step (S3) into an ultrasonic guided wave detection system, and carrying out experimental detection on the solid material to obtain a guided wave excitation signal and a guided wave receiving signal of the solid material respectively.
Further, in step S5, the guided wave excitation signal and the guided wave receiving signal of the solid material in step S4 are identified, so as to obtain the guided wave group velocity of the solid material, which specifically includes:
（3）；
in the method, in the process of the application,is the guided wave group velocity of the solid material, L is the thickness of the plate or the distance between the transceiver integrated sensor probe and the end of the solid material, < >>Time of receiving signal for acquired solid material guided wave,/->The moment for acquiring the solid material guided wave excitation signal;
and (2) obtaining the guided wave group velocity of the solid material through experimental analysis, and establishing a relation model between different elastic modulus values and the guided wave group velocity of the solid material in the step (S2), thereby obtaining the elastic modulus value of the solid material.
Further, in the step S1, a semi-analytical finite element model is established for the cross section of the solid material, and a wave characteristic equation of the solid material is listed, and is shown in a formula (4);
（4）；
wherein:；
wherein:；
wherein:；
in the method, in the process of the application,、/>and->Three different total stiffness matrices for solid material, < > j->Is the total mass matrix of the solid material, +.>Is imaginary number and is->For wave number, < >>Is angular frequency; />For guiding the displacement vector of each node in the solid material, < >>、/>Andthree different cell stiffness matrices for solid material, < > j->Cell mass matrix of solid material, +.>Elastic matrix of solid material>Unit number for solid material, +.>Total number of units of solid material, +.>And->Cell strain matrix of solid material, respectively +.>And->Transpose of the unit strain matrix of solid material, respectively,/->Is a set of unit numbers of solid material, +.>Differentiation of the set of units as solid material, +.>Is a unit-shaped function of solid material, +.>Transpose of the unit shape function of the solid material, +.>Is the density of the solid material->Elastic modulus of solid material +.>Poisson's ratio for solid materials;
in the step S1, the guided wave group velocity dispersion curve of the solid material is obtained according to the fluctuation characteristic equation of the solid material, and the calculation formula of the guided wave group velocity dispersion curve of the solid material is shown as follows;
（5）；
in the method, in the process of the application,is the guided wave group velocity of aluminum alloy plate, +.>The left characteristic vector of the aluminum alloy plate and the right characteristic vector of the aluminum alloy plate are respectively.
In step S2, the wave characteristic equation of the solid material is improved, a relation model between different elastic modulus values and guided wave group velocities of the solid material is established, and a theoretical basis is provided for judging the elastic modulus value of the solid material by the guided wave group velocities obtained by actual measurement of the solid material to be measured.
The application has the beneficial effects that: the method belongs to nondestructive detection, is safe and simple to operate, can obtain accurate results by one-time detection, has low detection cost, and is suitable for accurate detection of the elastic modulus of solid materials with various cross section types and thin rod-shaped metal materials such as various plates, pipes, reinforcing steel bars, inhaul cables and the like.
Drawings
FIG. 1 is a schematic flow chart of the method of the present application.
FIG. 2 is a graph showing the group velocity dispersion curve of aluminum alloy sheet in accordance with an embodiment of the present application.
FIG. 3 is a graph of a model of the relationship between different elastic moduli and guided wave group velocities of aluminum alloy sheet material in accordance with an embodiment of the present application.
FIG. 4 is a schematic diagram of an ultrasonic guided wave detection system for aluminum alloy sheet in an embodiment of the application.
FIG. 5 is a schematic representation of excitation signals and received signals obtained by an aluminum alloy sheet in an embodiment of the application.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present application more apparent, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application, and it is apparent that the described embodiments are some embodiments of the present application, but not all embodiments of the present application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
FIG. 1 is a schematic flow chart of the method of the present application, in which a method for nondestructive testing of elastic modulus of solid material is provided, the analysis of the guided wave characteristics of the solid material is performed by a semi-analytical finite element method, and the relation between the guided wave characteristics and the elastic modulus of the material is established; and detecting the guided wave group velocity of the solid material by an ultrasonic guided wave detection system, and calculating the elastic modulus of the solid material.
Further, in step S1, a semi-analytical finite element model is built for the cross section of the solid material, and a wave characteristic equation of the solid material is listed, as shown in formula (4);
（4）；
wherein:；
wherein:；
wherein:；
in the method, in the process of the application,、/>and->Three different total stiffness matrices for solid material, < > j->Is the total mass matrix of the solid material, +.>Is imaginary number and is->For wave number, < >>Is angular frequency; />For guiding the displacement vector of each node in the solid material, < >>、/>Andthree different cell stiffness matrices for solid material, < > j->Cell mass matrix of solid material, +.>Is an elastic matrix of a solid material which,/>unit number for solid material, +.>Total number of units of solid material, +.>And->Cell strain matrix of solid material, respectively +.>And->Transpose of the unit strain matrix of solid material, respectively,/->Is a set of unit numbers of solid material, +.>Differentiation of the set of units as solid material, +.>Is a unit-shaped function of solid material, +.>Transpose of the unit shape function of the solid material, +.>Is the density of the solid material->Elastic modulus of solid material +.>Poisson's ratio for solid materials.
Further, in step S1, the group velocity dispersion curve of the guided wave of the solid material is obtained according to the wave characteristic equation of the solid material, and the calculation formula of the group velocity dispersion curve of the guided wave of the solid material is shown as follows;
（5）；
in the method, in the process of the application,is the guided wave group velocity of aluminum alloy plate, +.>The left characteristic vector of the aluminum alloy plate and the right characteristic vector of the aluminum alloy plate are respectively.
In step S2, the wave characteristic equation of the solid material is improved, a relation model between different elastic modulus values and guided wave group velocities of the solid material is established, and a theoretical basis is provided for judging the elastic modulus value of the solid material by the guided wave group velocities of the solid material obtained by actual measurement of the solid material to be measured. The specific steps are as follows:
（1）；
wherein:；
wherein:；
wherein:；
in the method, in the process of the application,、/>and->Three different elimination for solid material +.>Is>、/>And->Three different elimination for solid material +.>Is a cell stiffness matrix, ">Is a weak elastic matrix of solid material.
Further, in step S2, the guided wave group velocity of the solid material is obtained according to the improved wave characteristic equation of the solid material, and a relation model between different elastic modulus values of the solid material and the guided wave group velocity is established, specifically shown in formula (2);
（2）；
wherein:；
in the method, in the process of the application,is->Eliminate imaginary number->Is>For guiding wave and elastic modulus in solid material guiding wave propagation>An irrelevant correlation vector.
Taking an aluminum alloy plate as an example, carrying out analysis on the guided wave characteristics of the aluminum alloy plate by a semi-analytic finite element method, and establishing a relation between the guided wave characteristics and the elastic modulus of the material; and detecting the guided wave group velocity of the aluminum alloy plate by an ultrasonic guided wave detection system, and calculating the elastic modulus of the aluminum alloy plate. The elastic modulus of the aluminum alloy plate is between 68GPa and 73GPa, and the elastic modulus E=70GPa of the aluminum alloy plate is assumed, and the Poisson ratio is calculated=0.33, density->=2700kg/m 3 And (3) carrying the parameters of the aluminum alloy plate into the formula (1) to obtain a guided wave group velocity dispersion curve of the aluminum alloy plate, as shown in figure 2. The excitation frequency is required to be selected to have a small number of modes, and the group velocities of the guided waves of the modes at the frequency are greatly different from each other, so that the receiving and distinguishing of experimental signals are facilitated. From the dispersion curves, each dispersion curve represents the same guided wave propagation mode. For the same guided wave mode, the propagation speed tends to be stable along with the increase of the frequency, namely the dispersion phenomenon is weakened. And as the frequency increases, the number of guided wave modes which can be propagated in the solid material at the same frequency gradually increases. From this, it can be seen that the excitation frequency is 1MHz, which is suitable for elastic modulus measurement, and fig. 2 shows a total of 5 modes at this frequency. The guided wave group velocities of the aluminum alloy sheets at the different elastic moduli are also different, and table 1 shows the guided wave group velocity values of each mode at the different elastic moduli for the aluminum alloy sheets at an excitation frequency of 1 MHz.
TABLE 1 group velocity of guided waves of various modes at excitation frequency of 1MHz
Further, in step S2, a relation model between different elastic modulus values and guided wave group velocities of the aluminum alloy sheet may be established, and from table 1, the 3 rd mode may be obtained to conform to the mode of guided wave propagation of the aluminum alloy sheet. FIG. 3 is a graph showing the relationship between the elastic modulus value and the guided wave group velocity of the aluminum alloy sheet. Providing a basis for judging the elastic modulus value of the guided wave group velocity obtained by actually measuring the aluminum alloy plate to be measured.
In the embodiment, as shown in fig. 4, which is a schematic diagram of an ultrasonic guided wave detection system, the ultrasonic guided wave detection system can detect by adopting the simplest transceiver-integrated sensor probe, and only one transceiver-integrated sensor probe needs to be installed on the aluminum alloy plate to be detected, so that the operation is simple and convenient. Inputting the obtained aluminum alloy plate detection frequency of 1MPa into an ultrasonic guided wave detection system to perform experimental detection on the aluminum alloy plate to be detected, and respectively obtaining a guided wave excitation signal and a guided wave receiving signal of the aluminum alloy plate to be detected.
Further, in step S5, the guided wave excitation signal and the guided wave receiving signal of the aluminum alloy sheet in step S4 are identified, as shown in fig. 5, to obtain the guided wave group velocity of the aluminum alloy sheet, specifically:
（3）；
in the method, in the process of the application,is the guided wave group velocity of the aluminum alloy plate, L is the thickness of the plate or the distance from the probe to the end of the solid material, +.>Time of receiving signal for acquired solid material guided wave,/->The moment for acquiring the solid material guided wave excitation signal;
the guided wave group velocity of the aluminum alloy plate can be obtained through experimental analysis, and the elastic modulus value of the aluminum alloy plate can be accurately obtained through the relation between different elastic moduli of the aluminum alloy plate and the guided wave group velocity, which is established in the step S2 and the step 4.
The foregoing is merely exemplary of the present application and is not intended to limit the present application. Various modifications and variations of the present application will be apparent to those skilled in the art. Any modification, equivalent replacement, improvement, etc. which come within the spirit and principles of the application are to be included in the scope of the claims of the present application.
Claims (6)
1. A guided wave nondestructive testing method for elastic modulus of solid material is characterized in that: the method comprises the following steps:
step S1, a semi-analytic finite element model is established for the cross section of a solid material, an improved wave characteristic equation of the solid material is obtained, and a guided wave group velocity dispersion curve of the solid material is obtained;
step S2, according to the wave characteristic equation of the solid material improved in the step S1, solving the guided wave group velocity of the solid material, and establishing a relation model between different elastic modulus values and the guided wave group velocity of the solid material;
s3, analyzing according to the guided wave group velocity dispersion curve of the solid material in the step S1 to obtain detection frequency and a specific mode which are sensitive to the elastic modulus;
s4, inputting the detection frequency sensitive to the elastic modulus of the solid material obtained in the step S3 into an ultrasonic guided wave detection system to carry out experimental detection on the solid material, and respectively obtaining a guided wave excitation signal and a guided wave receiving signal of the solid material;
and S5, identifying the guided wave excitation signal and the guided wave receiving signal of the solid material in the step S4, and solving the guided wave group velocity of the solid material through the relation model in the step S2 to obtain the elastic modulus value of the solid material.
2. The guided wave nondestructive testing method of the elastic modulus of the solid material according to claim 1, wherein the method comprises the following steps: in the step S1, a semi-analytic finite element model is established for the cross section of the solid material, and an improved wave characteristic equation of the solid material is obtained, wherein the wave characteristic equation is shown in a formula (1);
（1）；
wherein:；
wherein:；
wherein:；
in the method, in the process of the application,、/>and->Three different elimination for solid material +.>Is>Is the total mass matrix of the solid material, +.>Is imaginary number and is->For wave number, < >>Is angular frequency; />For guiding the displacement vector of each node in the solid material, < >>、/>Andthree different elimination for solid material +.>Is a cell stiffness matrix, ">Cell mass matrix of solid material, +.>Is a weak elastic matrix of solid material, +.>Unit number for solid material, +.>Total number of units of solid material, +.>And->Cell strain matrix of solid material, respectively +.>And->Transpose of the unit strain matrix of solid material, respectively,/->Is a set of unit numbers of solid material, +.>Differentiation of the set of units as solid material, +.>Is a unit-shaped function of solid material, +.>Transpose of the unit shape function of the solid material, +.>Is the density of the solid material->Elastic modulus of solid material +.>Poisson's ratio for solid materials.
3. The guided wave nondestructive testing method of the elastic modulus of the solid material according to claim 2, wherein the method comprises the following steps:
in the step S2, a relation model between different elastic modulus values of the solid material and the guided wave group velocity is established; the specific formula is shown in formula (2);
（2）；
wherein:；
in the method, in the process of the application,group velocity of guided waves for solid material, +.>Is->Eliminate imaginary number->Is>Left eigenvector of the solid material and right eigenvector of the solid material, respectively, +.>For guiding wave and elastic modulus in solid material guiding wave propagation>An irrelevant correlation vector.
4. A guided wave nondestructive testing method of elastic modulus of solid material according to claim 3, wherein: in step S3, the optimal excitation frequency of the solid material is obtained by analyzing the dispersion curve of the solid material, and the specific mode of the solid material corresponding to the optimal excitation frequency is obtained.
5. The guided wave nondestructive testing method for the elastic modulus of the solid material according to claim 4, wherein the method comprises the following steps of: in step S4, the ultrasonic guided wave detection system detects by using a transceiver-integrated sensor probe, and a transceiver-integrated sensor probe is installed on the solid material.
6. The guided wave nondestructive testing method for the elastic modulus of the solid material according to claim 5, wherein the method comprises the following steps of: in step S5, the guided wave excitation signal and the guided wave receiving signal of the solid material in step S4 are identified, so as to obtain the guided wave group velocity of the solid material, which specifically includes:
（3）；
in the method, in the process of the application,is the guided wave group velocity of the solid material, L is the thickness of the plate or the distance between the transceiver integrated sensor probe and the end of the solid material, < >>Time of receiving signal for acquired solid material guided wave,/->The moment for acquiring the solid material guided wave excitation signal;
and (2) obtaining the guided wave group velocity of the solid material through experimental analysis, and establishing a relation model between different elastic modulus values and the guided wave group velocity of the solid material in the step (S2), thereby obtaining the elastic modulus value of the solid material.
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