CN113899487B - Spatial three-dimensional residual stress ultrasonic detection method - Google Patents

Spatial three-dimensional residual stress ultrasonic detection method Download PDF

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CN113899487B
CN113899487B CN202111037497.0A CN202111037497A CN113899487B CN 113899487 B CN113899487 B CN 113899487B CN 202111037497 A CN202111037497 A CN 202111037497A CN 113899487 B CN113899487 B CN 113899487B
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CN113899487A (en
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赵勃
阚艳
陈婷
史维佳
王丙泉
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Harbin Institute of Technology
State Run Wuhu Machinery Factory
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State Run Wuhu Machinery Factory
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L5/00—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes
    • G01L5/16—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes for measuring several components of force
    • G01L5/173—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes for measuring several components of force using acoustic means
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01L—MEASURING FORCE, STRESS, TORQUE, WORK, MECHANICAL POWER, MECHANICAL EFFICIENCY, OR FLUID PRESSURE
    • G01L5/00—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes
    • G01L5/0047—Apparatus for, or methods of, measuring force, work, mechanical power, or torque, specially adapted for specific purposes measuring forces due to residual stresses

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Abstract

The invention discloses a spatial three-dimensional residual stress ultrasonic detection method, and belongs to the technical field of ultrasonic detection. Step one, deducing an acoustoelastic equation under a three-dimensional stress state; and step two, determining a spatial three-dimensional residual stress ultrasonic detection scheme according to the acoustic-elastic equation in the three-dimensional stress state. According to the invention, the acoustoelastic equation under the three-dimensional stress state is obtained through theoretical derivation, and a detection scheme of the three-dimensional space residual stress is further obtained based on the acoustoelastic equation. The method for detecting the residual stress in the three-dimensional space is simple to operate, low in cost and feasible, and overcomes the defect that the conventional residual stress can only realize single-axis or plane detection. Meanwhile, certain ideas and directions are provided for further research of subsequent three-dimensional space residual stress detection.

Description

Spatial three-dimensional residual stress ultrasonic detection method
Technical Field
The invention relates to a spatial three-dimensional residual stress ultrasonic detection method, and belongs to the technical field of ultrasonic detection.
Background
The residual stress is elastic stress which is caused by uneven plastic deformation in the material and keeps self balance, and is divided into macroscopic stress and microscopic stress. Macroscopic residual stress, i.e. the average stress between grains in a material, is the main test object in engineering applications. In various machines and machines, residual stress is generated in the components, and the generated residual stress state is greatly different according to various processing methods or treatment methods. Residual stress and residual stress maldistribution will have a significant impact on fatigue strength, static strength, structural deformation, and service life of the component. For example, the residual stress of the weld seam, which affects the life cycle of the welded structure, causes severe stress concentration at the weld seam, which leads to microcracks in the weld seam, and the cracks may cause cracking of the welded part under certain conditions.
Compared with other nondestructive testing methods for residual stress, the ultrasonic nondestructive testing method has the advantages of high testing speed, no radiation damage to human bodies, low cost, better spatial resolution, larger detection depth range, capability of realizing on-site hand holding and carrying, capability of completing the detection of the macroscopic participation of surface and subsurface in stress magnitude and tension and compression states, and the like, and has been widely paid attention by scholars at home and abroad. Beijing university of science and engineering proposes a nonlinear ultrasonic detection method of bolt axial stress (a nonlinear ultrasonic detection method of bolt axial stress, publication No. CN 111442869A). The invention provides a nonlinear ultrasonic detection method for axial stress of a bolt, which comprises the following implementation steps: step A: establishing a relation model between the amplitude of the second harmonic and the amplitude of the fundamental wave based on the propagation theory of the ultrasonic wave in the isotropic medium to obtain an expression of a relative nonlinear coefficient; and B: carrying out an axial stress loading experiment on a bolt sample, carrying out nonlinear ultrasonic detection, and calculating relative nonlinear coefficients under different stress states; and C: fitting the loaded axial stress and the corresponding relative nonlinear coefficient, determining the ultrasonic detection coefficient of the axial stress of the bolt, and finally obtaining a relational expression of the axial stress of the bolt and the relative nonlinear coefficient; through the steps, the nonlinear ultrasonic detection of the axial stress of the bolt can be realized, the method can be used for quickly and accurately detecting the axial stress of the bolt, and the accuracy and the practicability of the bolt axial stress detection technology are improved. The method has problems that: only the axial stress detection of the bolt can be realized, and the spatial three-dimensional representation of the residual stress cannot be carried out.
University of major graduates proposes a plane residual stress electromagnetic ultrasonic detection method (a plane residual stress electromagnetic ultrasonic detection method, publication number: CN 110632177A). The method comprises the steps of firstly assembling an electromagnetic ultrasonic detection system, and measuring stress detection ultrasonic signal waveforms along three directions by utilizing ultrasonic coils in an electromagnetic ultrasonic surface wave probe so as to calibrate the acoustic elastic coefficient of the material. The magnitude and the direction of the plane stress are calculated by collecting three directional surface wave signals of a point to be measured and applying an ultrasonic detection theoretical formula. The method adopts a surface wave probe with three-transmitting and three-receiving functions, and realizes one-time positioning and multi-parameter simultaneous measurement of two main stresses and the included angle of the main stresses in a plane stress state. The space between the receiving and transmitting probes is reduced and the spatial resolution of the probes is improved by reducing the turns, the line width and the line distance of the ultrasonic transmitting and receiving coils. The radio frequency connector is adopted to connect the circuit board and the impedance matching network, so that the installation and repeated use are convenient, the detection method is simple, and the efficiency is high. The method has problems that: the method and the detection system are complex, can only complete plane residual stress detection of the to-be-detected part, and cannot perform space three-dimensional representation on the residual stress.
A residual stress water immersion ultrasonic detection method for an aluminum alloy pre-stretching plate is provided by Beijing aviation material research institute of China aviation industry group company (a residual stress water immersion ultrasonic detection method for an aluminum alloy pre-stretching plate, publication No. CN 103543206A). The invention relates to a residual stress water immersion ultrasonic detection method for an aluminum alloy pre-stretching plate, belonging to the field of nondestructive detection, and comprising the following steps: making a reference test block; measuring and calibrating; and measuring the residual stress. The method adopts a water immersion method, can ensure the temperature consistency in the stress calibration and stress measurement process by controlling the water temperature to be constant, thereby eliminating the influence of temperature difference on the ultrasonic speed and eliminating the temperature error, and in addition, adopts an automatic scanning frame to replace manual scanning, can ensure the distance between a probe and the surface of a material to be measured to be constant in the measurement process, thereby eliminating the influence of the coupling condition difference on the sound propagation time and eliminating the coupling error. The method is beneficial to nondestructive evaluation of the near-surface residual stress of the aluminum alloy pre-stretched plate. The method has problems that: the method adopts a water immersion method, the detection environment is limited, only unidirectional residual stress detection of a to-be-detected piece can be completed, and spatial three-dimensional representation of the residual stress cannot be carried out.
At present, ultrasonic stress detection on a to-be-detected part in the market is usually towards common structures such as flat plates, bolts and welding seams, and axial, unidirectional or planar residual stress detection can only be realized. In summary, an ultrasonic detection method capable of realizing spatial three-dimensional stress is absent in the current market, and three-dimensional spatial characterization is performed on residual stress.
Disclosure of Invention
The invention aims to provide a spatial three-dimensional residual stress ultrasonic detection method, which is used for deducing a three-dimensional residual stress detection formula based on a longitudinal wave stress detection principle to realize the three-dimensional representation of the residual stress of a piece to be detected so as to solve the problems in the prior art.
A three-dimensional ultrasonic detection method for residual stress in space comprises the following steps:
step one, deducing an acoustoelastic equation under a three-dimensional stress state;
and step two, determining a spatial three-dimensional residual stress ultrasonic detection scheme according to the acoustic-elastic equation in the three-dimensional stress state.
Further, in step one, specifically,
a spatial three-dimensional stress ultrasonic detection scheme. Assuming the plane wave propagation direction is along e11And obtaining a longitudinal wave velocity expression represented by the initial coordinate by solving the eigenvalue of the sound tensor, and arranging the longitudinal wave velocity expression into a common form expression as follows:
Figure GDA0003616906300000031
in the formula: v. ofLThe longitudinal wave velocity is in a three-dimensional stress state; ρ 0 is the density of the object in an unstressed state; e is the modulus of elasticity;
Figure GDA0003616906300000032
is a constant; e.g. of the type11、e22、e33Three main strains respectively; lambda and mu are second-order elastic constants of the medium; l and m are three-order elastic constants of the medium; sigma11、σ22、σ33Three principal stresses, respectively; v is the poisson ratio,
from the formula (1), the ultrasonic longitudinal sound velocity is the principal stress σ from three directions11、σ22、σ33Jointly determined, the result of the formula (1) provides theoretical support for researching the relation between the ultrasonic wave speed and the stress under the complex stress, an elastic wave sound speed measurement formula of a plane stress field under the combined action of the two-way stress needs to be considered,
to obtainResults in general form, with the symbol e1、e2、e3Expressing principal strain by σ1、σ2、σ3Representing principal stress, assuming plane wave in ξ1The direction of the light is transmitted,
Figure GDA0003616906300000033
suppose the plane wave is xi2The direction of the light is transmitted,
Figure GDA0003616906300000034
suppose the plane wave is xi3The direction of the light is transmitted,
Figure GDA0003616906300000035
the theory of material mechanics shows that for the state of space three-dimensional stress, there are three main stresses perpendicular to each other, which are respectively marked as the first main stress, the second main stress and the third main stress, and the plane wave is in xi1The directional propagation is taken as an example to carry out space three-dimensional stress state analysis, and according to the propagation characteristic of the LCR wave, the LCR wave is in the xi material1-ξ2The surface is small amplitude wave, the propagation direction is parallel to the vibration direction, when the propagation direction of LCR wave is parallel to the first main stress direction, it must be perpendicular to the second and third main stress directions, then the acoustic elastic equation under three-way stress state is simplified into the acoustic elastic equation under plane stress state,
Figure GDA0003616906300000041
substituting the formula (5) into the formula (2),
Figure GDA0003616906300000042
will be provided with
Figure GDA0003616906300000043
Is substituted into the formula (6) to obtain,
Figure GDA0003616906300000044
in the formula:
Figure GDA0003616906300000045
in order to be the bulk modulus,
when e is1＝e2＝e3When the value is 0, the longitudinal wave velocity in the unstressed state is obtained as follows:
Figure GDA0003616906300000046
the formula (7) and the formula (8) are subtracted,
Figure GDA0003616906300000051
since the change in speed is small, the approximation can be made as follows, vL+vL0≈2vL0But due to vL-vL0Not equal to 0, the formula is substituted into the formula (9),
Figure GDA0003616906300000052
Figure GDA0003616906300000053
then the
Figure GDA0003616906300000054
Figure GDA0003616906300000055
Figure GDA0003616906300000056
In the formula: c. C1、c2、c3Respectively, the stress coefficients of three mutually perpendicular directions.
Further, in the step one, specifically, a fixed distance sound time method is adopted in the actual measurement process, the variation of the speed is converted into the measurement of the time variation, and the fixed distance of ultrasonic wave propagation is set as L, tl1Propagation time of LCR wave in stressed state, tl0The LCR wave propagation time is in an unstressed state.
Figure GDA0003616906300000061
Substituting formula (15) for formula (11),
Figure GDA0003616906300000062
suppose σ1＞σ2When the "one-shot" ultrasonic probe is placed, i.e. the propagation direction of the longitudinal wave and the maximum principal stress σ1When the included angle is theta, according to the Morel circle stress theory, the stress in the direction and the stress vertical to the direction are,
Figure GDA0003616906300000063
four different directions theta need to be performed simultaneously1，θ2，θ3，θ4Measurement of the stress magnitude of (c): the first selected measuring direction is regarded as 0 degree, three directions of 30 degrees, 60 degrees and 90 degrees are selected for detection, and four groups of sound time measuring data t are obtainedl1、tl2、tl3And, andtl4. Note tl0-tl1＝Δt1，tl0-tl2＝Δt2，tl0-tl3＝Δt3，tl0-tl4＝Δt4Due to tl4≈tl3≈tl2≈tl1≈tl0However, tl0-tl4≠0，tl0-tl3≠0，tl0-tl2≠0，tl0-tl1When the number is not equal to 0, the method comprises the following steps of,
Figure GDA0003616906300000064
the unknown quantity sigma of the four space three-dimensional stress can be obtained by simultaneous solving1、σ2、σ3And theta.
The invention has the following beneficial effects: according to the invention, the acoustoelastic equation under the three-dimensional stress state is obtained through theoretical derivation, and a detection scheme of the three-dimensional space residual stress is further obtained based on the acoustoelastic equation. The method for detecting the residual stress in the three-dimensional space is simple to operate, low in cost and feasible, and overcomes the defect that the conventional residual stress can only realize single-axis or plane detection. Meanwhile, certain ideas and directions are provided for further research of subsequent three-dimensional space residual stress detection.
Drawings
FIG. 1 is a schematic diagram of principal stress of a material;
FIG. 2 is a schematic diagram of a spatial three-dimensional stress detection apparatus;
fig. 3 is a schematic diagram of spatial three-dimensional stress detection.
Part number in the figure: 1 is a single-array element oblique probe, and 2 is a test piece to be detected.
Detailed Description
The technical solutions in the embodiments of the present invention will be described clearly and completely with reference to the accompanying drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
A three-dimensional ultrasonic detection method for residual stress in space comprises the following steps:
step one, deducing an acoustoelastic equation under a three-dimensional stress state;
and step two, determining a spatial three-dimensional residual stress ultrasonic detection scheme according to the acoustic-elastic equation in the three-dimensional stress state.
Further, the spatial three-dimensional stress ultrasonic detection scheme is specifically described with reference to fig. 1, 2 and 3. Assuming that the propagation direction of the plane wave is along e11, a longitudinal wave velocity expression represented by the initial coordinates can be obtained by solving the eigenvalues of the sound tensor, and the longitudinal wave velocity expression is arranged into a common form expression:
Figure GDA0003616906300000081
in the formula: v. ofLThe longitudinal wave velocity is in a three-dimensional stress state; rho0Density of the object in an unstressed state; e is the modulus of elasticity;
Figure GDA0003616906300000082
is a constant; e.g. of the type11、e22、e33Three main strains respectively; lambda and mu are second-order elastic constants of the medium; l and m are three-order elastic constants of the medium; sigma11、σ22、σ33Three principal stresses, respectively; v is the poisson ratio,
from the formula (1), the ultrasonic longitudinal sound velocity is the principal stress σ from three directions11、σ22、σ33Together, the result of the formula (1) provides theoretical support for researching the relation between the ultrasonic wave speed and the stress under complex stress, and the poisson ratio v of the aluminum alloy material is 0.3 generally, and at the moment, the longitudinal wave sound speed is mainly influenced by sigma parallel to the propagation direction11The influence of the directional stress is influenced by σ perpendicular to its propagation direction22、σ33The influence of the directional stress is0.3 times of, nevertheless, a22、σ33The acoustic elastic effect caused by the directional stress is still not negligible. Therefore, the elastic wave sound velocity measurement formula of the plane stress field under the combined action of the two-way stress needs to be considered,
to obtain the result in general form, the symbol e is used later1、e2、e3Expressing principal strain by σ1、σ2、σ3Indicating the principal stress. Suppose a plane wave is xi1The direction of the light beam is transmitted,
Figure GDA0003616906300000083
suppose the plane wave is xi2The direction of the light is transmitted,
Figure GDA0003616906300000084
suppose the plane wave is xi3The direction of the light is transmitted,
Figure GDA0003616906300000085
the theory of material mechanics shows that for the state of space three-dimensional stress, there are three main stresses perpendicular to each other, which are respectively marked as the first main stress, the second main stress and the third main stress, and the plane wave is in xi1The directional propagation is taken as an example to carry out space three-dimensional stress state analysis, and according to the propagation characteristic of the LCR wave, the LCR wave is in the xi material1-ξ2The surface is small amplitude wave, the propagation direction is parallel to the vibration direction, when the propagation direction of LCR wave is parallel to the first main stress direction, it must be perpendicular to the second and third main stress directions, then the acoustic elastic equation under three-way stress state is simplified into the acoustic elastic equation under plane stress state,
Figure GDA0003616906300000091
substituting the formula (5) into the formula (2),
Figure GDA0003616906300000092
will be provided with
Figure GDA0003616906300000093
Is substituted into the formula (6) to obtain,
Figure GDA0003616906300000094
in the formula:
Figure GDA0003616906300000095
in order to be the bulk modulus,
when e is1＝e2＝e3When the value is 0, the longitudinal wave velocity in the unstressed state is obtained as follows:
Figure GDA0003616906300000096
the formula (7) and the formula (8) are subtracted,
Figure GDA0003616906300000101
since the change in speed is small, the approximation can be made as follows, vL+vL0≈2vL0But due to vL-vL0Not equal to 0, the formula is substituted into the formula (9),
Figure GDA0003616906300000102
Figure GDA0003616906300000103
then
Figure GDA0003616906300000104
Figure GDA0003616906300000105
Figure GDA0003616906300000106
In the formula: c. C1、c2、c3Respectively, the stress coefficients of three mutually perpendicular directions.
Furthermore, due to the tiny acoustic elastic effect, direct sound velocity change is not easy to measure, and under a fixed condition, the sound velocity is inversely proportional to the LCR wave propagation time, so that a fixed distance sound time method is adopted in the actual measurement process, the speed variation is converted into the measurement of time change, the fixed distance of ultrasonic wave propagation is set as L, and t is set asl1Propagation time of LCR wave in stressed state, tl0The LCR wave propagation time is in an unstressed state.
Figure GDA0003616906300000111
The formula (15) is substituted for the formula (11),
Figure GDA0003616906300000112
in the actual detection process, the main stress direction of a stress to-be-detected piece is unknown, so that the condition that the 'one-sending-one-receiving' ultrasonic probe is parallel to the sigma cannot be ensured1Direction is placed or parallel to sigma2Directional placement, assuming σ1＞σ2When the "one-shot" ultrasonic probe is placed, i.e. the propagation direction of the longitudinal wave and the maximum principal stress σ1When the included angle is theta, according to the Morel circle stress theoryThe stress in that direction and the stress perpendicular to that direction are,
Figure GDA0003616906300000113
for quasi-isotropic composites in a stressed state, a measurement of only one time is not sufficient to obtain σ1、σ2、σ3And theta are four unknowns, so the method requires four different directions theta to be performed simultaneously1，θ2，θ3，θ4For convenience of measurement, the first selected measurement direction is regarded as 0 °, and three directions of 30 °, 60 ° and 90 ° are selected for detection, so as to obtain four groups of acoustic time measurement data tl1、tl2、tl3And tl4. Note tl0-tl1＝Δt1，tl0-tl2＝Δt2，tl0-tl3＝Δt3，tl0-tl4＝Δt4Due to tl4≈tl3≈tl2≈tl1≈tl0However, tl0-tl4≠0，tl0-tl3≠0，tl0-tl2≠0，tl0-tl1If the number is not equal to 0, then,
Figure GDA0003616906300000121
the unknown quantity sigma of the four space three-dimensional stress can be obtained by simultaneous solving1、σ2、σ3And theta.
The above embodiments are only used to help understanding the method of the present invention and the core idea thereof, and a person skilled in the art can also make several modifications and decorations on the specific embodiments and application scope according to the idea of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.

Claims (2)

1. The ultrasonic detection method for the spatial three-dimensional residual stress is characterized by comprising the following steps of:
step one, deducing an acoustoelastic equation under a three-dimensional stress state;
secondly, determining a spatial three-dimensional residual stress ultrasonic detection scheme according to the acoustoelastic equation under the three-dimensional stress state,
in step one, specifically,
the spatial three-dimensional stress ultrasonic detection scheme comprises the following steps: assuming the plane wave propagation direction is along e11And obtaining a longitudinal wave velocity expression represented by the initial coordinate by solving the eigenvalue of the sound tensor, and arranging the longitudinal wave velocity expression into a common form expression as follows:
Figure FDA0003616906290000011
in the formula: v. ofLThe longitudinal wave velocity is in a three-dimensional stress state; rho0Density of the object in an unstressed state; e is the modulus of elasticity;
Figure FDA0003616906290000012
is a constant; e.g. of the type11、e22、e33Three main strains respectively; lambda and mu are second-order elastic constants of the medium; l and m are three-order elastic constants of the medium; sigma11、σ22、σ33Three principal stresses, respectively; v is the poisson ratio,
from the formula (1), the ultrasonic longitudinal sound velocity is the principal stress σ from three directions11、σ22、σ33Jointly determined, the result of the formula (1) provides theoretical support for researching the relation between the ultrasonic wave speed and the stress under the complex stress, an elastic wave sound speed measurement formula of a plane stress field under the combined action of the two-way stress needs to be considered,
to obtain the result in general form, the symbol e is used1、e2、e3Expressing principal strain by σ1、σ2、σ3Representing principal stress, assuming plane wave in ξ1Direction transmissionThe broadcast is carried out by a broadcast station,
Figure FDA0003616906290000013
suppose the plane wave is xi2The direction of the light beam is transmitted,
Figure FDA0003616906290000014
suppose the plane wave is xi3The direction of the light is transmitted,
Figure FDA0003616906290000015
the theory of material mechanics shows that for the state of space three-dimensional stress, there are three main stresses perpendicular to each other, which are respectively marked as the first main stress, the second main stress and the third main stress, and the plane wave is in xi1The directional propagation is taken as an example to carry out space three-dimensional stress state analysis, and according to the propagation characteristic of the LCR wave, the LCR wave is in the xi material1-ξ2The surface is small amplitude wave, the propagation direction is parallel to the vibration direction, when the propagation direction of LCR wave is parallel to the first main stress direction, it must be perpendicular to the second and third main stress directions, then the acoustic elastic equation under three-way stress state is simplified into the acoustic elastic equation under plane stress state,
Figure FDA0003616906290000021
substituting the formula (5) into the formula (2),
Figure FDA0003616906290000022
will be provided with
Figure FDA0003616906290000023
Is substituted into the formula (6) to obtain,
Figure FDA0003616906290000024
in the formula:
Figure FDA0003616906290000025
in order to be the bulk modulus,
when e is1＝e2＝e3When the value is 0, the longitudinal wave velocity in the unstressed state is obtained as follows:
Figure FDA0003616906290000031
the formula (7) and the formula (8) are subtracted,
Figure FDA0003616906290000032
since the change in speed is small, the approximation can be made as follows, vL+vL0≈2vL0But due to vL-vL0Not equal to 0, the formula is substituted into the formula (9),
Figure FDA0003616906290000033
Figure FDA0003616906290000034
then
Figure FDA0003616906290000035
Figure FDA0003616906290000036
Figure FDA0003616906290000041
In the formula: c. C1、c2、c3Respectively, the stress coefficients of three mutually perpendicular directions.
2. The ultrasonic testing method for the three-dimensional residual stress in the space according to claim 1, wherein in the step one, specifically, a fixed distance sound time method is adopted in the actual measurement process, the speed variation is converted into the measurement of the time variation, and the fixed distance of ultrasonic wave propagation is set as L, tl1Propagation time of LCR wave in stressed state, tl0For the propagation time of the LCR wave in the unstressed state,
Figure FDA0003616906290000042
substituting formula (15) for formula (11),
Figure FDA0003616906290000043
suppose σ1＞σ2When the "one-shot" ultrasonic probe is placed, i.e. the propagation direction of the longitudinal wave and the maximum principal stress σ1When the included angle is theta, according to the Morel circle stress theory, the stress in the direction and the stress vertical to the direction are,
Figure FDA0003616906290000044
four different directions theta need to be performed simultaneously1，θ2，θ3，θ4Measurement of the stress magnitude of (c): the first selected measuring direction is regarded as 0 degree, three directions of 30 degrees, 60 degrees and 90 degrees are selected for detection, and four groups of sound time measuring data t are obtainedl1、tl2、tl3And tl4Let us remember tl0-tl1＝Δt1，tl0-tl2＝Δt2，tl0-tl3＝Δt3，tl0-tl4＝Δt4Due to tl4≈tl3≈tl2≈tl1≈tl0However, tl0-tl4≠0，tl0-tl3≠0，tl0-tl2≠0，tl0-tl1If the number is not equal to 0, then,
Figure FDA0003616906290000051
the unknown quantity sigma of the four space three-dimensional stress can be obtained by simultaneous solving1、σ2、σ3And theta.
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