CN113899487B - A spatial three-dimensional residual stress ultrasonic testing method - Google Patents

Abstract

The invention discloses a spatial three-dimensional residual stress ultrasonic detection method, which belongs to the technical field of ultrasonic detection. Step 1, deriving the acoustic elasticity equation under the three-dimensional stress state; step 2, determining a spatial three-dimensional residual stress ultrasonic testing scheme according to the acoustoelasticity equation under the three-dimensional stress state. The invention obtains the acoustic elasticity equation under the three-dimensional stress state through theoretical derivation, and further obtains the detection scheme of the residual stress in the three-dimensional space based on this. The three-dimensional residual stress detection method proposed by the invention has the advantages of simple operation, low cost and feasibility, and solves the problem that the existing traditional residual stress can only be detected in a single axis or a plane. At the same time, it also provides some ideas and directions for further research on the follow-up three-dimensional residual stress detection.

Description

A spatial three-dimensional residual stress ultrasonic testing method

technical field

The invention relates to a spatial three-dimensional residual stress ultrasonic detection method, which belongs to the technical field of ultrasonic detection.

Background technique

Residual stress is the elastic stress that maintains its own balance caused by non-uniform plastic deformation inside the material, and can be divided into macroscopic and microscopic stresses. Macroscopic residual stress, that is, the average stress between grains in a material, is the main detection object in engineering applications. In the manufacturing process of various machines and machines, residual stress will be generated inside the component, and the residual stress state generated varies greatly with various processing methods or treatment methods. Residual stress and uneven distribution of residual stress will have a significant impact on the fatigue strength, static strength, structural deformation and service life of components. For example, the influence of the residual stress of the weld runs through the whole life cycle of the welded structure, and the residual stress of the weld will lead to serious stress concentration at the weld, resulting in micro-cracks in the weld, and these cracks will lead to the cracking of the weldment under certain conditions. .

Compared with other non-destructive testing methods for residual stress, ultrasonic non-destructive testing has the advantages of fast detection speed, no radiation damage to the human body, low cost, better spatial resolution and larger detection depth, which can be hand-held and portable on site, and can complete the surface It has many advantages such as the macroscopic participation of the subsurface in the detection of the stress and the tension and compression state, and has been widely concerned by scholars at home and abroad. Beijing Institute of Technology proposed a nonlinear ultrasonic testing method for axial stress of bolts (a nonlinear ultrasonic testing method for axial stress of bolts. Publication number: CN111442869A). The invention provides a nonlinear ultrasonic detection method for axial stress of bolts, and the implementation steps are as follows: Step A: Based on the propagation theory of ultrasonic waves in an isotropic medium, establish a relationship between the amplitude of the second harmonic and the amplitude of the fundamental wave to obtain the expression of relative nonlinear coefficient; step B: perform axial stress loading experiment on the bolt sample and perform nonlinear ultrasonic testing, and calculate the relative nonlinear coefficient under different stress states; step C: load The axial stress and the corresponding relative nonlinear coefficient are fitted to determine the ultrasonic detection coefficient of the axial stress of the bolt, and finally the relationship between the axial stress of the bolt and the relative nonlinear coefficient is obtained; through the above steps, the axial stress of the bolt can be calculated. Non-linear ultrasonic testing, the method can quickly and accurately detect the axial stress of the bolt, and improve the accuracy and practicability of the axial stress detection technology of the bolt. The problem with this method is that it can only realize stress detection in the axial direction of the bolt, and cannot perform three-dimensional spatial characterization of residual stress.

Dalian University of Technology proposed an electromagnetic ultrasonic detection method for plane residual stress (an electromagnetic ultrasonic detection method for plane residual stress. Publication number: CN110632177A). The method first assembles an electromagnetic ultrasonic testing system, and uses the ultrasonic coil in the electromagnetic ultrasonic surface wave probe to measure the stress detection ultrasonic signal waveform along three directions, so as to calibrate the acoustic elastic coefficient of the material. By collecting surface wave signals in three directions at the point to be measured, and applying the theoretical formula of ultrasonic testing to calculate the magnitude and direction of plane stress. The method uses a surface wave probe with the function of "three transmissions and three receptions", and realizes the one-time positioning and multi-parameter simultaneous measurement of the two principal stresses and the angle between the principal stresses in the plane stress state. By reducing the number of turns, line width and line spacing of the ultrasonic transmitting and receiving coils, the distance between the transceiver probes is reduced and the spatial resolution of the probes is improved. The RF connector is used to connect the circuit board and the impedance matching network, which is convenient for installation and repeated use, the detection method is simple, and the efficiency is high. The problem with this method is that the method and the detection system are relatively complex and can only complete the plane residual stress detection of the object to be inspected, and cannot perform three-dimensional spatial characterization of the residual stress.

AVIC Beijing Institute of Aeronautical Materials proposed a method for ultrasonic testing of residual stress of aluminum alloy pre-stretched plate by water immersion (a method for ultrasonic testing of residual stress of aluminum alloy pre-stretched board by water immersion. Publication number: CN103543206A). The invention relates to a water immersion ultrasonic testing method for residual stress of an aluminum alloy pre-stretching plate, belonging to the field of non-destructive testing. The method comprises the following steps: making a reference test block; measuring and calibrating; and measuring residual stress. This method adopts the water immersion method. By controlling the water temperature unchanged, the temperature of the stress calibration and the stress measurement process can be ensured to be consistent, thereby eliminating the influence of temperature differences on the ultrasonic velocity and eliminating temperature errors. In addition, an automatic scanning frame is used instead of manual scanning. , which can ensure that the distance between the probe and the surface of the material to be measured remains unchanged during the measurement process, thereby eliminating the influence of the difference in coupling conditions on the sound propagation time and eliminating coupling errors. This method is beneficial to non-destructive evaluation of residual stress near the surface of aluminum alloy pre-stretched sheet. The problem with this method is that this method adopts the water immersion method, the detection environment is relatively limited, and it can only complete the unidirectional residual stress detection of the object to be inspected, and cannot perform three-dimensional spatial characterization of the residual stress.

At present, ultrasonic stress testing for DUTs on the market is often oriented to common structures such as plates, bolts, and welds, and can only detect axial, unidirectional, or planar residual stress. To sum up, there is currently a lack of an ultrasonic testing method that can realize three-dimensional stress in space, and characterize residual stress in three-dimensional space.

SUMMARY OF THE INVENTION

The purpose of the present invention is to propose a method for ultrasonic detection of three-dimensional residual stress in space. Based on the principle of longitudinal wave stress detection, a three-dimensional residual stress detection formula is derived to realize the three-dimensional spatial characterization of residual stress of the object to be measured, so as to solve the problems existing in the prior art.

A method for ultrasonic testing of three-dimensional residual stress in space, the ultrasonic testing method for three-dimensional residual stress in space comprises the following steps:

Step 1. Derive the acoustic elasticity equation under the three-dimensional stress state;

Step 2: Determine a spatial three-dimensional residual stress ultrasonic testing scheme according to the sonoelasticity equation in the three-dimensional stress state.

Further, in step 1, specifically,

Spatial three-dimensional stress ultrasonic testing scheme. Assuming that the propagation direction of the plane wave is along e ₁₁ , the expression of the longitudinal wave velocity represented by the initial coordinates can be obtained by solving the eigenvalues of the acoustic tensor, which can be organized into a common form as:

为常数；e₁₁、e₂₂、e₃₃分别为三个主应变；λ、μ为介质的二阶弹性常数；l、m为介质的三阶弹性常数；σ₁₁、σ₂₂、σ₃₃分别为三个主应力；ν为泊松比，In the formula: v _L is the longitudinal wave velocity in the three-dimensional stress state; ρ0 is the density of the object in the unstressed state; E is the elastic modulus;

are constants; e ₁₁ , e ₂₂ , and e ₃₃ are the three principal strains respectively; λ and μ are the second-order elastic constants of the medium; l, m are the third-order elastic constants of the medium; σ ₁₁ , σ ₂₂ , and σ ₃₃ are respectively three principal stresses; ν is Poisson's ratio,

It can be known from equation (1) that the ultrasonic longitudinal wave sound velocity is jointly determined by the principal stresses σ ₁₁ , σ ₂₂ , and σ ₃₃ in three directions. theoretical support, it is necessary to consider the elastic wave sound velocity measurement formula of the plane stress field under the combined action of bidirectional stress,

In order to obtain the results in general form, the principal strains are denoted by the symbols e ₁ , e ₂ , and e ₃ , and the principal stresses are denoted by σ ₁ , σ ₂ , and σ ₃ , assuming that a plane wave propagates in the ξ ₁ direction,

Assuming that the plane wave propagates in the _ξ2 direction,

Assuming that the plane wave propagates in the _ξ3 direction,

It is known from the theory of material mechanics that for the three-dimensional stress state in space, there are three mutually perpendicular principal stresses, denoted as the _first principal stress, the second principal stress and the third principal stress, respectively. According to the three-dimensional stress state analysis in space, according to the propagation characteristics of the LCR wave, the LCR wave is a small amplitude wave on the surface of the material ξ ₁ -ξ ₂ , and the propagation direction is parallel to the vibration direction. When the propagation direction of the LCR wave is parallel to the first principal stress direction, must be perpendicular to the second and third principal stress directions. Next, the acoustoelasticity equation in the three-dimensional stress state is simplified to the acoustoelasticity equation in the plane stress state,

Substitute equation (5) into equation (2) to get,

代入式(6)中得，Will

Substitute into formula (6) to get,

为体积模量，where:

is the bulk modulus,

When e ₁ =e ₂ =e ₃ =0, the longitudinal wave velocity in the unstressed state is obtained as:

Formula (7) and formula (8) are subtracted to get,

Since the change of speed is small, the following approximation can be made, v _L +v _L0 ≈ 2v _L0 , but since v _L -v _L0 ≠0, substitute the formula into formula (9) to get,

but

where c ₁ , c ₂ , and c ₃ are the stress coefficients in three mutually perpendicular directions, respectively.

Further, in step 1, specifically, in the actual measurement process, a fixed distance acoustic time method is used to convert the change of speed into the measurement of time change, and the fixed distance of ultrasonic propagation is L, and t _l1 is the stress state. The propagation time of the LCR wave, t _l0 is the propagation time of the LCR wave in the unstressed state.

Substitute equation (15) into equation (11) to get,

Assuming that σ ₁ >σ ₂ , when the direction in which the ultrasonic probe is placed, namely the longitudinal wave propagation direction and the maximum principal stress σ ₁ is θ, according to the Mohr circle stress theory, the stress in this direction and perpendicular to the The stress in the direction is,

It is necessary to measure the stress magnitude of four different directions θ ₁ , θ ₂ , θ ₃ , and θ ₄ at the same time: take the measurement direction selected for the first time as 0°, and select three directions of 30°, 60° and 90° The detection is performed to obtain four sets of acoustic time measurement data t _l1 , t _l2 , t _l3 , and t _l4 . Denote t _l0 -t _l1 =Δt ₁ , t _l0 -t _l2 =Δt ₂ , t _l0 -t _l3 =Δt ₃ , t _l0 -t _l4 =Δt ₄ , since t _l4 ≈t _l3 ≈t _l2 ≈t _l1 ≈ t _l0 , but, t _l0 -t _l4 ≠0, t _l0 -t _l3 ≠0, t _l0 -t _l2 ≠0, t _l0 -t _l1 ≠0, then,

Four spatial three-dimensional stress unknowns σ ₁ , σ ₂ , σ ₃ and θ can be obtained by simultaneous solution.

The present invention has the following beneficial effects: the present invention obtains the acoustic elasticity equation under the three-dimensional stress state through theoretical derivation, and further obtains the detection scheme of the three-dimensional residual stress based on this. The three-dimensional residual stress detection method proposed by the invention has the advantages of simple operation, low cost and feasibility, and solves the problem that the existing traditional residual stress can only be detected in a single axis or a plane. At the same time, it also provides some ideas and directions for further research on the follow-up three-dimensional residual stress detection.

Description of drawings

Figure 1 is a schematic diagram of the principal stress of the material;

2 is a schematic diagram of a three-dimensional stress detection device in space;

FIG. 3 is a schematic diagram of three-dimensional stress detection in space.

Part number in the picture: 1 is the single-array element oblique probe, 2 is the test piece to be inspected.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

A method for ultrasonic testing of three-dimensional residual stress in space, the ultrasonic testing method for three-dimensional residual stress in space comprises the following steps:

Step 1. Derive the acoustic elasticity equation under the three-dimensional stress state;

Step 2: Determine a spatial three-dimensional residual stress ultrasonic testing scheme according to the sonoelasticity equation in the three-dimensional stress state.

Further, referring to FIG. 1 , FIG. 2 and FIG. 3 , the spatial three-dimensional stress ultrasonic detection scheme will be specifically described. Assuming that the propagation direction of the plane wave is along e11, the longitudinal wave velocity expression represented by the initial coordinates can be obtained by solving the eigenvalues of the acoustic tensor.

为常数；e₁₁、e₂₂、e₃₃分别为三个主应变；λ、μ为介质的二阶弹性常数；l、m为介质的三阶弹性常数；σ₁₁、σ₂₂、σ₃₃分别为三个主应力；ν为泊松比，where v _L is the longitudinal wave velocity in the three-way stress state; ρ ⁰ is the density of the object in the unstressed state; E is the elastic modulus;

are constants; e ₁₁ , e ₂₂ , and e ₃₃ are the three principal strains respectively; λ and μ are the second-order elastic constants of the medium; l, m are the third-order elastic constants of the medium; σ ₁₁ , σ ₂₂ , and σ ₃₃ are respectively three principal stresses; ν is Poisson's ratio,

It can be known from equation (1) that the ultrasonic longitudinal wave sound velocity is jointly determined by the principal stresses σ ₁₁ , σ ₂₂ , and σ ₃₃ in three directions. Theoretical support, the Poisson’s ratio ν=0.3 of general aluminum alloy materials, at this time, the longitudinal wave sound speed is mainly affected by the stress in the direction of σ ₁₁ parallel to the propagation direction, and by the stress in the direction of σ ₂₂ and σ ₃₃ perpendicular to the direction of propagation. However, the acoustoelastic effects caused by the σ ₂₂ and σ ₃₃ directional stresses are still not negligible. Therefore, it is necessary to consider the elastic wave sound velocity measurement formula of the plane stress field under the combined action of bidirectional stress,

In order to obtain the results in a general form, the principal strains are denoted by the symbols e ₁ , e ₂ , and e ₃ , and the principal stresses are denoted by σ ₁ , σ ₂ , and σ ₃ . Assuming that the plane wave propagates in the _ξ1 direction,

Assuming that the plane wave propagates in the _ξ2 direction,

Assuming that the plane wave propagates in the _ξ3 direction,

It is known from the theory of material mechanics that for the three-dimensional stress state in space, there are three mutually perpendicular principal stresses, denoted as the _first principal stress, the second principal stress and the third principal stress, respectively. According to the three-dimensional stress state analysis in space, according to the propagation characteristics of the LCR wave, the LCR wave is a small amplitude wave on the surface of the material ξ ₁ -ξ ₂ , and the propagation direction is parallel to the vibration direction. When the propagation direction of the LCR wave is parallel to the first principal stress direction, must be perpendicular to the second and third principal stress directions. Next, the acoustoelasticity equation in the three-dimensional stress state is simplified to the acoustoelasticity equation in the plane stress state,

Substitute equation (5) into equation (2) to get,

代入式(6)中得，Will

Substitute into formula (6) to get,

为体积模量，where:

is the bulk modulus,

When e ₁ =e ₂ =e ₃ =0, the longitudinal wave velocity in the unstressed state is obtained as:

Formula (7) and formula (8) are subtracted to get,

Since the change of speed is small, the following approximation can be made, v _L +v _L0 ≈ 2v _L0 , but since v _L -v _L0 ≠0, substitute the formula into formula (9) to get,

but

where c ₁ , c ₂ , and c ₃ are the stress coefficients in three mutually perpendicular directions, respectively.

Further, due to the smallness of the sonoelastic effect, the direct sound speed change is not easy to measure. Under fixed conditions, the sound speed is inversely proportional to the LCR wave propagation time, so the fixed distance sound time method is used in the actual measurement process. The amount of change is converted into a measurement of time change. Let the ultrasonic propagation fixed distance be L, t _l1 is the propagation time of the LCR wave in the stress state, and t _l0 is the propagation time of the LCR wave in the unstressed state.

Substitute equation (15) into equation (11) to get,

In the actual inspection process, the principal stress direction of a stress-tested part is unknown, so it cannot be guaranteed that the "one-shot-one-receive" ultrasonic probe is placed parallel to the σ ₁ direction or parallel to the σ ₂ direction, assuming σ ₁ > σ _2. When the direction in which the "one send and one receive" ultrasonic probe is placed, that is, the angle between the longitudinal wave propagation direction and the maximum principal stress σ ₁ is θ, according to the Mohr circle stress theory, the stress in this direction and the stress perpendicular to this direction are,

For the quasi-isotropic composite material in the state of stress, only one measurement is not enough to obtain the four unknown quantities of σ ₁ , σ ₂ , σ ₃ and θ, so this method needs to simultaneously perform four different directions θ ₁ , θ . ₂ , θ ₃ , θ ₄ stress measurement, in order to facilitate the measurement, this paper regards the first selected measurement direction as 0°, and selects 30°, 60° and 90° for testing, and obtains four groups of Acoustic time measurement data t _l1 , t _l2 , t _l3 , and t _l4 . Denote t _l0 -t _l1 =Δt ₁ , t _l0 -t _l2 =Δt ₂ , t _l0 -t _l3 =Δt ₃ , t _l0 -t _l4 =Δt ₄ , since t _l4 ≈t _l3 ≈t _l2 ≈t _l1 ≈ t _l0 , but, t _l0 -t _l4 ≠0, t _l0 -t _l3 ≠0, t _l0 -t _l2 ≠0, t _l0 -t _l1 ≠0, then,

Four spatial three-dimensional stress unknowns σ ₁ , σ ₂ , σ ₃ and θ can be obtained by simultaneous solution.

The above implementation examples are only used to help understand the method of the present invention and its core idea. For those skilled in the art, according to the idea of the present invention, several improvements and modifications can be made in the specific implementation and application scope. These improvements and retouching should also be regarded as the protection scope of the present invention.

Claims (2)

1. a spatial three-dimensional residual stress ultrasonic detection method, is characterized in that, described space three-dimensional residual stress ultrasonic detection method comprises the following steps: Step 1. Derive the acoustic elasticity equation under the three-dimensional stress state; Step 2: According to the sonoelasticity equation in the three-dimensional stress state, determine a spatial three-dimensional residual stress ultrasonic detection scheme, In step 1, specifically, Spatial three-dimensional stress ultrasonic testing scheme: Assuming that the plane wave propagation direction is along e ₁₁ , the longitudinal wave velocity expression represented by the initial coordinates can be obtained by solving the eigenvalues of the acoustic tensor, and the common form expression is:

where v _L is the longitudinal wave velocity in the three-way stress state; ρ ⁰ is the density of the object in the unstressed state; E is the elastic modulus;

are constants; e ₁₁ , e ₂₂ , and e ₃₃ are the three principal strains respectively; λ and μ are the second-order elastic constants of the medium; l, m are the third-order elastic constants of the medium; σ ₁₁ , σ ₂₂ , and σ ₃₃ are respectively three principal stresses; ν is Poisson's ratio, It can be known from equation (1) that the ultrasonic longitudinal wave sound velocity is jointly determined by the principal stresses σ ₁₁ , σ ₂₂ , and σ ₃₃ in three directions. theoretical support, it is necessary to consider the elastic wave sound velocity measurement formula of the plane stress field under the combined action of bidirectional stress, In order to obtain the results in general form, the principal strains are denoted by the symbols e ₁ , e ₂ , and e ₃ , and the principal stresses are denoted by σ ₁ , σ ₂ , and σ ₃ , assuming that a plane wave propagates in the ξ ₁ direction,

Assuming that the plane wave propagates in the _ξ2 direction,

Assuming that the plane wave propagates in the _ξ3 direction,

It is known from the theory of material mechanics that for the three-dimensional stress state in space, there are three mutually perpendicular principal stresses, denoted as the _first principal stress, the second principal stress and the third principal stress, respectively. According to the three-dimensional stress state analysis in space, according to the propagation characteristics of the LCR wave, the LCR wave is a small amplitude wave on the surface of the material ξ ₁ -ξ ₂ , and the propagation direction is parallel to the vibration direction. When the propagation direction of the LCR wave is parallel to the first principal stress direction, must be perpendicular to the second and third principal stress directions. Next, the acoustoelasticity equation in the three-dimensional stress state is simplified to the acoustoelasticity equation in the plane stress state,

Substitute equation (5) into equation (2) to get,

Will

Substitute into formula (6) to get,

where:

is the bulk modulus, When e ₁ =e ₂ =e ₃ =0, the longitudinal wave velocity in the unstressed state is obtained as:

Formula (7) and formula (8) are subtracted to get,

Since the change of speed is small, the following approximation can be made, v _L +v _L0 ≈ 2v _L0 , but since v _L -v _L0 ≠0, substitute the formula into formula (9) to get,

but

where c ₁ , c ₂ , and c ₃ are the stress coefficients in three mutually perpendicular directions, respectively. 2. A method for ultrasonic testing of three-dimensional residual stress in space according to claim 1, characterized in that, in step 1, specifically, in the actual measurement process, a fixed-distance acoustic time method is used to convert the variation of the speed into a pair of For the measurement of time change, let the ultrasonic propagation fixed distance be L, t _l1 is the propagation time of the LCR wave in the stress state, t _l0 is the propagation time of the LCR wave in the unstressed state,

Substitute equation (15) into equation (11) to get,

Assuming σ ₁ >σ ₂ , when the direction in which the ultrasonic probe is placed, that is, the angle between the longitudinal wave propagation direction and the maximum principal stress σ ₁ is θ, according to the Mohr circle stress theory, the stress in this direction and the vertical The stress in the direction is,

It is necessary to measure the stress magnitude of four different directions θ ₁ , θ ₂ , θ ₃ , θ ₄ at the same time: take the measurement direction selected for the first time as 0°, and select three directions of 30°, 60° and 90° Carry out detection to obtain four sets of acoustic time measurement data t _l1 , t _l2 , t _l3 , and t _l4 , denote t _l0 -t _l1 =Δt ₁ , t _l0 -t _l2 =Δt ₂ , t _l0 -t _l3 =Δt ₃ , t _l0 -t _l4 =Δt ₄ , since t _l4 ≈t _l3 ≈t _l2 ≈t _l1 ≈t _l0 , but, t _l0 -t _l4 ≠0, t _l0 -t _l3 ≠0, t _l0 -t _l2 ≠ 0, t _l0 -t _l1 ≠ 0, then

Four spatial three-dimensional stress unknowns σ ₁ , σ ₂ , σ ₃ and θ can be obtained by simultaneous solution.

Images