Method for determining plane stresses on in-service steel structure member based on phase spectrum of ultrasonic transverse wave

Abstract

A method for determining plane stresses on an in-service steel structure member based on phase spectrum of ultrasonic transverse wave, including: calibrating stress-spectrum parameters k and c of a replica of the in-service steel structure member; determining a first response frequency of a phase difference and a maximum value of a derivative function of the phase difference of an ultrasonic transverse wave echo of the in-service steel structure member, and obtaining a polarization angle of ultrasonic transverse wave components generated by a birefringence effect; solving a plane normal stress difference and a plane shear stress inside the in-service steel structure member; and separating normal stresses by a shear difference method to obtain three independent plane stress components.

Claims

1. A method for determining plane stresses on an in-service steel structure member based on phase spectrum of ultrasonic transverse wave, comprising: step (1) calibrating stress-spectrum parameters k and c of a replica of the in-service steel structure member; step (2) determining a first response frequency of a phase difference of an ultrasonic transverse wave echo and a maximum value of a derivative function of the phase difference of the in-service steel structure member to obtain a polarization angle of ultrasonic transverse wave components generated by a birefringence effect of the ultrasonic transverse wave; step (3) solving a plane normal stress difference and a plane shear stress inside the in-service steel structure member; and step (4) separating normal stresses by a shear difference method to obtain three independent plane stress components.

2. The method of claim 1, wherein in step (2), the first response frequency of the phase difference and the maximum value of the derivative function of the phase difference are obtained by the steps of: allowing a signal transmitted by a transmitting-receiving ultrasonic transverse wave probe to propagate in the in-service steel structure member and receiving an echo signal by the transmitting-receiving ultrasonic transverse wave probe; collecting the signal by an oscilloscope; processing data to obtain a function curve of the phase difference; and further obtaining a derivative function curve of the phase difference of the ultrasonic transverse wave echo; wherein: a frequency corresponding to a point of a first maximum value in the derivative function curve of the phase difference is the first response frequency of the phase difference; and a value corresponding to a point of a maximum value in the derivative function curve of the phase difference is the maximum value of the derivative function of the phase difference.

3. The method of claim 2, wherein the step of collecting the signal by the oscilloscope comprises the following steps: transmitting a pulse electrical signal by an ultrasonic pulse emission receiver; converting the pulse electrical signal into an ultrasonic transverse wave signal by the transmitting-receiving ultrasonic transverse wave probe; allowing the ultrasonic transverse wave signal to propagate in the in-service steel structure member and to be reflected by a bottom surface of the in-service steel structure member; converting the ultrasonic transverse wave signal to an electrical signal by the transmitting-receiving ultrasonic transverse wave probe; and inputting the electrical signal to the ultrasonic pulse emission receiver by the transmitting-receiving ultrasonic transverse wave probe; and collecting the signal by the oscilloscope.

4. The method of claim 3, wherein a center frequency of the transmitting-receiving ultrasonic transverse wave probe is 5 MHz, and a bandwidth range of the transmitting-receiving ultrasonic transverse wave probe is 0˜10 MHz.

5. The method of claim 2, wherein the phase difference is a difference value between a phase spectrum of an echo received when an incident direction of the ultrasonic transverse wave is rotated by 90 degrees and a phase spectrum of an echo received in an original incident direction of the ultrasonic transverse wave.

6. The method of claim 1, wherein in step (2), the polarization angle of the ultrasonic transverse wave components is obtained by the following steps: recording an incident angle of the ultrasonic transverse wave; capturing an abscissa and an ordinate of the point of the first maximum value in the derivative function curve of the phase difference, and taking the abscissa and the ordinate as the first response frequency of the phase difference and the maximum value of the derivative function of the phase difference, respectively; and obtaining the polarization angle of the ultrasonic transverse wave components by a theory formula for capturing the polarization angle; wherein the theory formula is expressed as follows: $\phi =\theta -\frac{1}{2}\mathrm{arcsec}\frac{{\mathrm{\Delta \phi }}^{\prime }{f}_{\max }}{\pi },$ where, θ is the incident angle of the ultrasonic transverse wave; Δφ′ is the maximum value of the derivative function of the phase difference of the ultrasonic transverse wave echo; f.sub.max is the frequency corresponding to the point of the first maximum value in the derivative function curve of the phase difference i.e., the first response frequency of the phase difference.

7. The method of claim 1, wherein in step (1), the stress-spectrum parameters k and c are calibrated by the following steps: preparing the replica of the in-service steel structure member; loading an axial stress on the replica of the in-service steel structure member to be calibrated; obtaining a plurality of data pairs of reciprocals of the first response frequency of the phase difference and stresses; and obtaining the stress-spectrum parameters k and c for the plane stress determination by fitting the obtained data pairs; wherein: the stress-spectrum parameters k and c are related to a thickness of the replica of the in-service steel structure member, an elastic coefficient of a material and an anisotropy of the material; and the stress-spectrum parameters k and c are expressed as follows: $k=\frac{1}{4m{t}_0}=\frac{1}{4t_0}.Math.\frac{-8{\mu }^2}{4\mu +n},c=\frac{B_0}{m}=\frac{-8{\mu }^2}{4\mu +n}.Math.B_0,$ where, m is the elastic coefficient of the in-service steel structure member and the replica thereof; t.sub.0 is an acoustic time of the transverse wave propagating in the in-service steel structure member and the replica thereof in an unstressed state; μ is a second order elastic constant; n is a third order elastic constant; B.sub.0 is a birefringence coefficient of the transverse wave when the in-service steel structure member is in the unstressed state.

8. The method of claim 7, wherein the three independent plane stress components σ.sub.x, σ.sub.y and τ.sub.xy satisfy the following equations: ${\sigma }_x-{\sigma }_y=\frac{k\cos 2\phi }{f_{\max }}-c,{\tau }_{xy}=\frac{k\sin 2\phi }{2f_{\max }},$ a separation formula of the normal stress is expressed as: ${\left({\sigma }_x\right)}_p={\left({\sigma }_x\right)}_0-\underset{0}{\overset{p}{.Math.}}\frac{\partial {\tau }_{xy}}{\partial y}\Delta x,$ where, φ is the polarization angle of the transverse wave components and satisfies $\phi =\theta -\frac{1}{2}\mathrm{arcsec}\frac{{\mathrm{\Delta \phi }}^{\prime }{f}_{\max }}{\pi };$ f.sub.max is the frequency corresponding to the point of the first maximum value in the derivative function curve of the phase difference and $f_{\max }=\frac{1}{2P},$ where P is an acoustic time difference of the transverse wave components generated by a birefringence effect and $P=\frac{2l}{v_{31}}-\frac{2l}{v_{32}};$ l represents the thickness of the in-service steel structure member and the replica thereof; v.sub.31 is a velocity of a transverse wave having a propagation direction perpendicular to the stress and a polarization direction perpendicular to the stress; v.sub.32 is a velocity of a transverse wave having a propagation direction perpendicular to the stress and a polarization direction parallel to the stress.

9. The method of claim 1, wherein the derivative function of the phase difference of the ultrasonic transverse wave echo is expressed as: ${\mathrm{\Delta \phi }}^{\prime }=\{\begin{array}{cc}\frac{2\pi P{\sec }^2\left(\pi \mathrm{Pf}\right)\cos \left(2\left(\theta -\phi \right)\right)}{1+{\tan }^2\left(\pi \mathrm{Pf}\right){\cos }^2\left(2\left(\theta -\phi \right)\right)}& \left(f\ne \frac{2N-1}{2P}\right)\\ 2\pi P\sec \left(2\left(\theta -\phi \right)\right)& \left(f=\frac{2N-1}{2P}\right)\end{array},(N=1,2,3,\mathrm{.Math.}),$ where P is the acoustic time difference of the transverse wave components generate by the birefringence effect and $P=\frac{2l}{v_{31}}-\frac{2l}{v_{32}};$ represents the thickness of the in-service steel structure member and the replica thereof; v.sub.31 is the velocity of the transverse wave having a propagation direction perpendicular to the stress and a polarization direction perpendicular to the stress; v.sub.32 is the velocity of the transverse wave having a propagation direction perpendicular to the stress and a polarization direction parallel to the stress; f is the frequency; θ is the incident angle of the ultrasonic transverse wave; and φ is the polarization angle of the transverse wave components.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1 is a schematic diagram showing the birefringence effect of a slightly orthotropic material in a plane stress state.

(2) FIG. 2 schematically shows a Mohr's circle of stresses used in the invention.

(3) FIG. 3 is a schematic diagram of a system in the invention of determining the plane stress on an in-service steel structure member based on an ultrasonic transverse wave phase spectrum.

(4) FIG. 4 is a schematic diagram showing the construction of a plane stress field in the invention.

(5) FIG. 5 shows the fitting relationship between the 1/f.sub.max and σ of a steel plate B obtained by the calibrated stress-spectrum parameters in the invention.

(6) FIG. 6 is a schematic diagram showing positions of plane stress determination points in the invention.

(7) FIG. 7 shows horizontal normal stress values in the plane stress determination of an in-service steel structure member in the invention.

(8) FIG. 8 shows vertical normal stress values in the plane stress determination of the in-service steel structure member in the invention.

(9) FIG. 9 shows shear stress values in the plane stress determination of the in-service steel structure member in the invention.

(10) FIG. 10 shows the layout of a strain gauge in the plane stress verification of the in-service steel structure member in the invention.

(11) FIG. 11 shows the comparison between the horizontal normal stresses measured according to an embodiment of the invention and the horizontal normal stresses measured by the strain gauge method.

(12) FIG. 12 shows the comparison between the vertical normal stresses measured according to an embodiment of the invention and the vertical normal stresses measured by the strain gauge method.

(13) FIG. 13 shows the comparison between shear stresses measured according to an embodiment of the invention and shear stresses measured by the strain gauge method.

(14) FIG. 14 shows the comparison between the normal stress difference measured according to embodiment of the invention and the normal stress difference measured by the strain gauge method.

(15) FIG. 15 shows a derivative function curve of the phase difference of the ultrasonic transverse wave echo at different incident angles according to the invention.

DETAILED DESCRIPTION OF EMBODIMENTS

(16) This application will be further illustrated below with reference to the embodiments.

(17) The principle of the method for determining plane stresses on an in-service steel structure member based on phase spectrum of ultrasonic transverse wave provided herein is described as follows.

(18) The coordinate system used in the theoretical formula derivation of the invention is schematically shown in FIG. 1. The origin is a position where the ultrasonic transverse wave probe is in contact with the in-service steel structure member. Under the action of the plane stress, transverse wave components generated by birefringence rotate from an orthotropic symmetry axis of the in-service steel structure member to a principal stress direction. θ is an incident angle of the ultrasonic transverse wave, φ is a polarization angle of the ultrasonic transverse wave components, α is an angle between the principal stress and the horizontal axis of the in-service steel structure member, and x.sub.3 direction is the propagation direction of the ultrasonic transverse wave.

(19) The ultrasonic transverse wave transmitted by the ultrasonic transverse wave probe enters the in-service steel structure member, and then decomposed into two transverse wave components under the action of plane stresses, where the two transverse wave components have perpendicular polarization directions and different propagation velocities. The propagation direction of the two transverse wave components is perpendicular to the stress plane. Under the action of the plane stress, the polarization direction of the two transverse wave components does not follow the orthotropic symmetry axis of the in-service steel structure member, but has a certain angle with the orthotropic symmetry axis. This phenomenon is named as the birefringence which is unique to the ultrasonic transverse wave. In the invention, the angle between the incident direction and the polarization direction is referred to as an azimuth of the transverse wave.

(20) In the invention, y(t) represents the vibration amplitude of the vibration source o; t represents the acoustic time of the wave; l represents the thickness of the in-service steel structure member and the replica thereof; v.sub.31 is the velocity of a transverse wave having a propagation direction perpendicular to the stress, and a polarization direction perpendicular to the stress; v.sub.32 is the velocity of a transverse wave having a propagation direction perpendicular to the stress and a polarization direction parallel to the stress.

(21) An ultrasonic echo vibration equation synthesized by the two transverse wave components generated by the birefringence effect after being reflected from the bottom surface of the in-service steel structure member to the probe can be obtained in the combination of the birefringence effect and spectral analysis technique with the existing wave equation. The ultrasonic echo vibration equation is expressed as follows:

(22) $\begin{array}{cc}{u}_r\left(t\right)=y\left(t-\frac{2l}{v_{31}}\right){\cos }^2\left(\theta -\phi \right)+y\left(t-\frac{2l}{v_{32}}\right){\sin }^2\left(\theta -\varphi \right)& \left(1\right)\end{array}$

(23) for simplicity,

(24) 0$\begin{array}{cc}a=\frac{2l}{v_{31}}& \left(2\right)\\ b=\frac{2l}{v_{32}}& \left(3\right)\\ P=\frac{2l}{v_{32}}-\frac{2l}{v_{31}}& \left(4\right)\\ Q=\frac{2l}{v_{31}}+\frac{2l}{v_{32}}& \left(5\right)\end{array}$

(25) equations (2) and (3) are substituted into (1) to obtain the following equation:
u.sub.r(t)=y(t−a)cos.sup.2(θ−φ)+y(t−b)sin.sup.2(θ−φ)  (6)
u.sub.r(f), u.sub.0(f) are defined as Fourier transforms of u.sub.r(t) and y(t), the time domain relationship among parameters is converted into the frequency domain relationship, and the following equation is obtained:
u.sub.r(f)=u.sub.0(f)cos.sup.2(θ−φ)e.sup.−i2πfa+u.sup.0(f)sin.sup.2(θ−φ)e.sup.−i2πfb  (7)

(26) φ.sub.r(f) and φ.sub.0(f) are defined as phases respectively corresponding to u.sub.r(f) and u.sub.0 (f), and phases corresponding to each frequency point are obtained through the following equation:
φ.sub.r(f)=φ.sub.0(f)−(πfQ+arctan(tan(πfP)cos(2(θ−φ))))  (8).

(27) According to formula (8), the phase value of the echo received from the bottom surface of the in-service steel structure member when the ultrasonic transverse wave probe is rotated by 90 degrees can be obtained as follows:
φ′.sub.r(f)=φ.sub.0(f)−πfQ+arctan(tan(πfP)cos(2(θ−φ)))  (9).

(28) According to the above formulas (8) and (9), the phase difference function is shown as follows:
Δφ=φ′.sub.r(f)−φ.sub.r(f)=2 arctan(tan(πfP)cos(2(θ−φ)))  (10).(9).

(29) The relationship between the phase difference and the acoustic time difference P of the transverse wave components is analyzed. It is found that when the acoustic time difference of the transverse wave components increases, the slope of the phase difference function becomes larger, that is, the derivative function of the phase difference and the acoustic time difference of the transverse wave components have a certain positive correlation. Due to the acousto elastic theory, the propagation velocity of the transverse wave components will be affected by the stresses of the in-service steel structure member. Therefore, the acoustic time difference of the transverse wave components and the stresses are closely related. Theoretical formula of the stress determination is explored by analyzing the derivative function of the phase difference of the ultrasonic transverse wave echo. In the actual determination, when the ultrasonic transverse wave probe is fixed on the in-service steel structure member, the acoustic time difference P of the transverse wave birefringence components is also determined. In the theoretical analysis, the derivative function curve of the phase difference is obtained as shown in FIG. 15 by assuming that P is 100.

(30) It can be found from FIG. 15 that when the incident angle of the transverse wave is determined, the derivative function of the phase difference has periodic maximum values. In the invention, the frequency corresponding to the maximum point is referred to as the response frequency. The relationship between the response frequency and the acoustic time difference of the transverse wave components is shown as follows:

(31) $\begin{array}{cc}{f}_{\max }=\frac{2N-1}{2P},(N=1,2,3,\mathrm{.Math.}).& \left(11\right)\end{array}$

(32) It is required to handle the formula (11) in the stress determination based on the phase spectrum for the in-service steel structure member, where a period parameter N exists and needs to be determined. By processing the phase difference of the ultrasonic transverse wave echo obtained by test, it is found that the first maximum value point in the derivative function curve of the phase difference is obvious in a frequency band of 0 to 10 MHz. Since it is finally necessary to capture the frequency corresponding to the maximum value of the derivative function of the phase difference to achieve the determination of stresses, the target frequency band is selected to be 0˜10 MHz to facilitate the data reading and analysis in this embodiment. Therefore, N is set to 1, and the theoretical formula for calculating the first response frequency of the phase difference curve is shown as follows:

(33) $\begin{array}{cc}{f}_{\max }=\frac{1}{2P}& \left(12\right)\end{array}$

(34) where, f.sub.max is the frequency corresponding to the first maximum value point in the derivative function curve of the phase difference. It can be seen from equation (12) that the acoustic time difference of the in-service steel structure member shows a linear relationship with the reciprocal of the first response frequency.

(35) At present, it is shown in the researches on stress determination based on spectrum of ultrasonic transverse wave that the two transverse wave components generated by the birefringence effect are driven to rotate from an orthotropic symmetry axis to principal stress direction of the in-service steel structure member under the action of the plane stresses. Therefore, in order to adopting the phase spectrum to solve the problem of plane stress determination, the values of the polarization angle must be obtained in the phase spectrum. The invention has further explored to determine the values of the polarization angle.

(36) On the basis that the first response frequency of the phase difference has been captured, the polarization angle of the transverse wave components can be directly obtained as follows using the phase difference derivative function value corresponding to the first response frequency of the phase difference and the known incident angle:

(37) $\begin{array}{cc}\phi =\theta -\frac{1}{2}\mathrm{arc}\sec \frac{{\mathrm{\Delta \phi }}^{\prime }{f}_{\max }}{\pi }.& \left(13\right)\end{array}$

(38) The velocities of various forms of ultrasonic wave propagating in solid changes correspondingly with the stress in the solid. This phenomenon is called the acousto elastic effect, and the related theory derived from the acousto elastic effect is called the acousto elastic theory. Through the acousto elastic theory, a relationship between some characteristic parameters of ultrasonic wave and stress can be established. When the in-service steel structure member is subjected to plane stress, the relationship between the propagation velocity of the ultrasonic transverse wave and the plane stresses is shown as follows:

(39) $\begin{array}{cc}B=\sqrt{{\left[B_0+m\left({\sigma }_1-{\sigma }_2\right)\cos 2\alpha \right]}^2+{\left[m\left({\sigma }_1-{\sigma }_2\right)\sin 2\alpha \right]}^2}& \left(14\right)\\ \tan 2\phi =\frac{m\left({\sigma }_1-{\sigma }_2\right)\sin 2\alpha }{B_0+m\left({\sigma }_1-{\sigma }_2\right)\cos 2\alpha }& \left(15\right)\end{array}$

(40) where, B is a birefringence coefficient of the transverse wave, which characterizes a relative velocity of the transverse wave components and can represent acoustic anisotropy, and its expression is as follows:

(41) $\begin{array}{cc}B=\frac{v_{31}-v_{32}}{\left(v_{31}+v_{32}\right)\text{/}2}.& \left(16\right)\end{array}$

(42) When the member is in an unstressed state, the acoustic anisotropy of the material itself is generated by the factors such as the texture of the material. The birefringence coefficient of the transverse wave obtained at this time is B.sub.0. m is composed of second-order and third-order elastic coefficients, indicating the characteristics of the material itself.

(43) Since the direction of the principal stress remains unknown before the determination, the principal stress cannot be directly determined. Therefore, the mathematical processing by means of the Mohr's circle is necessary to indirectly obtain the formulas of the normal stress and the shear stress, and the process is schematically shown in FIG. 2. The relationships between normal stress and principal stress, shear stress and principal stress can be obtained from the Mohr's circle:
(σ.sub.1−σ.sub.2)cos 2α=σ.sub.x−σ.sub.y  (17),
(σ.sub.1−σ.sub.2)sin 2a=2τ.sub.xy  (18).

(44) The formulas (17) and (18) are substituted into the formulas (14) and (15) to obtain determination formulas of the normal stresses and the shear stress through necessary mathematical processing:

(45) $\begin{array}{cc}{\sigma }_x-{\sigma }_y=\frac{B\cos 2\phi -B_0}{m},& \left(19\right)\\ {\tau }_{\mathrm{xy}}=\frac{B\sin 2\phi }{2m}.& \left(20\right)\end{array}$

(46) Since the material is assumed to be elastic during the deformation process and the steel has a large elastic modulus, the dimensional change in the direction of ultrasonic propagation is small when the member is stressed in the elastic range. Therefore, the thickness l can be approximately considered to be invariable, that is:

(47) $\begin{array}{cc}\frac{l}{v_0}=t_0& \left(21\right)\end{array}$

(48) where, t.sub.0 is the acoustic time of the transverse wave in the in-service steel structure member under the unstressed state; v.sub.0 is the propagation velocity of the transverse wave in the in-service steel structure member under the unstressed state.

(49) When the in-service steel structure member is stressed, a stress of 100 MPa only causes the wave velocity to change by about 0.1%, so that the transverse wave velocity is actually less affected, and the following approximation can be made:
v.sub.32≈v.sub.31≈v.sub.0  (22).

(50) The relationship between the acoustic time difference P of the transverse wave components and the birefringence coefficient B of the transverse wave is established as follows based on equations (21) and (22):
P=2Bt.sub.0  (23).

(51) Equation (23) is substituted into equations (19) and (20) to obtain the following equations through the necessary mathematical processing:
σ.sub.x−σ.sub.y=2kP cos 2φ−c  (24)
τ.sub.xy=kP sin 2φ  (25)

(52) where, k and c are related to a thickness of the in-service steel structure member, elastic coefficients of a material and anisotropy of the material itself, and are respectively expressed as follows:

(53) $\begin{array}{cc}k=\frac{1}{4m{t}_0}=\frac{1}{4t_0}.Math.\frac{-8{\mu }^2}{4\mu +n},& \left(26\right)\\ c=\frac{B_0}{m}=\frac{-8{\mu }^2}{4\mu +n}.Math.B_0.& \left(27\right)\end{array}$

(54) It can be seen from the plane stress determination formulas (24) and (25) that the normal stress difference and the shear stress can be solved by capturing the first response frequency of the phase difference and the maximum value of the derivative function of the phase difference and then calibrating the stress-spectrum parameters k and c. Finally, the normal stresses are separated to obtain all of the three independent stress components through the following shear difference method:

(55) $\begin{array}{cc}{\left({\sigma }_x\right)}_p={\left({\sigma }_x\right)}_0-\underset{0}{\overset{p}{.Math.}}\frac{\partial {\tau }_{xy}}{\partial y}\Delta x.& \left(28\right)\end{array}$

(56) According to the formulas (12), (13), (24), (25) and (28), theoretical formulas for the plane stress determination of the in-service steel structure member based on phase spectrum can be obtained as follows:

(57) 0$\begin{array}{cc}\phi =\theta -\frac{1}{2}\mathrm{arcsec}\frac{{\mathrm{\Delta \phi }}^{\prime }{f}_{\max }}{\pi }& \left(29a\right)\\ {\left({\sigma }_x\right)}_p={\left({\sigma }_x\right)}_0-\underset{0}{\overset{p}{.Math.}}\frac{\partial {\tau }_{xy}}{\partial y}\Delta x& \left(29b\right)\\ {\sigma }_x-{\sigma }_y=\frac{k\cos 2\phi }{f_{\max }}-c& \left(29c\right)\\ {\tau }_{xy}=\frac{k\sin 2\phi }{2f_{\max }}& \left(29d\right)\end{array}$

(58) where, k and c which can be obtained by parameter calibration are related to a thickness of the in-service steel structure member, elastic coefficients of a material and anisotropy of the material itself, and are expressed in equations (26) and (27). θ is the incident angle of the ultrasonic transverse wave, which is measurable. f.sub.max and Δφ′ can be captured from the derivative function curve of the phase difference. Finally, the normal stresses are separated by the shear difference method to achieve the derivation of theoretical formulas for the plane stress determination of the in-service steel structure member based on the phase spectrum.

(59) It can be concluded from the above theoretical derivation that the method provided herein mainly includes five steps: (1) preparing a replica of the in-service steel structure member; (2) calibrating the stress-spectrum parameters k and c under axial stress state; (3) capturing the first response frequency of the phase difference and the maximum value of the phase difference derivative function of the ultrasonic transverse wave echo; (4) solving a normal stress difference and a shear stress inside the in-service steel structure member; and separating normal stresses by a shear difference method to obtain three independent plane stress components. The five steps are specifically described as follows, respectively.

(60) In step (1), since the in-service steel structure member is generally non-detachable, and the stress-spectrum parameters k and c are required to be calibrated herein, a steel structure member with the same material and thickness as the in-service steel structure member is used as a replica for the calibration of stress-spectrum parameters.

(61) In step (2), the stress-spectrum parameters k and c are calibrated under axial stress. In the plane stress determination formula, the normal stress in one direction and shear stress are set as 0. The principal stress direction is coincided with the orthotropic symmetry axis of the steel structure member, so the polarization angle generated by the transverse wave birefringence is 0. The determination formula of axial stress can be directly obtained as follows:

(62) $\begin{array}{cc}\sigma =\frac{k}{f_{\max }}-c& \left(30\right)\end{array}$

(63) It can be found that the simplified axial stress formula contains all the undetermined parameters in the plane stress determination formula, so the calibration of the stress-spectrum parameters can be converted into the determination of axial stress, and the specific process is described as follows.

(64) (1) The surfaces of the in-service steel structure member and the replica thereof are treated, where the position where the ultrasonic transverse wave probe is placed is polished to ensure that the ultrasonic transverse wave probe and the steel structure member are in close contact. Then the in-service steel structure member and the replica thereof are painted after the measurement.

(65) (2) As shown in FIG. 3, the instruments are connected and the stress measurement system is debugged to ensure that the ultrasonic signal displayed by the instruments is clear and effective.

(66) (3) The ultrasonic transverse wave probe is fixed on the surface of a test sample. It can be concluded from theoretical analysis that there are obvious frequency domain signal characteristics when the incident angle of the ultrasonic transverse wave is controlled at around 45°, where in the invention, the incident angle of the ultrasonic transverse wave is maintained at 30°.

(67) (4) A set of axial forces are discretely applied to the replica of the in-service steel structure member, where each stress state is kept for 5 min, and the determination data points are ensured to be random. The ultrasonic transverse wave echo signals and corresponding stresses are recorded.

(68) (5) Fourier transform is performed on the ultrasonic signal to convert the time domain ultrasonic transverse wave echo signal into the frequency domain signal to obtain the derivative function curves of the phase difference, from which the first response frequencies respectively corresponding to each stress are extracted.

(69) (6) The reciprocals of the first response frequencies are calculated according to the data obtained in step (5) and the corresponding stresses are obtained. The reciprocals of the first response frequency of the phase difference are linearly fitted with the stress values by least square method to obtain the parameters k and c in equation (30).

(70) In step (3), the process is specifically implemented as follows.

(71) (1) Firstly, the position where the ultrasonic transverse wave probe is placed is polished with sandpaper to remove the paint from the surface and make the surface smooth, so as to ensure that the ultrasonic transverse wave probe and the surface of the in-service steel structure member are in close contact. Then the polished portion is painted after Step (3) is completed.

(72) (2) A strain rosette is stuck on the position where the ultrasonic transverse wave probe is placed and connected to a strain collecting box to obtain the plane stress condition of the determination point.

(73) (3) Coupling agent is applied to the determination portion of the in-service steel structure member. The ultrasonic transverse wave probe is fixed on the in-service steel structure member and connected to the instruments. The determination system is debugged until a stable ultrasonic signal is displayed on the screen of the oscilloscope.

(74) (4) The incident angle of the ultrasonic transverse wave probe is set at 30°, where the adjustment of the angle is completed by an angle fixing plate.

(75) (5) The in-service steel structure member is loaded by a manual hydraulic pump. The stress value can be obtained by the strain rosette, and the signal is collected and saved.

(76) (6) The determination points are kept unchanged, and the ultrasonic transverse wave probe is rotated by 90°, that is, the incident angle is 120°. The signal is collected and saved after it is stable. At this time, a set of data of this determination point has been collected.

(77) (7) The collected signals are processed by a software system to complete the time-frequency domain conversion of the signals, obtaining the derivative function curve of the phase difference of the ultrasonic signals and capturing the first response frequency of the phase difference and the maximum value of the derivative function of the phase difference.

(78) (8) The same operation is subsequently performed on other determination points to obtain the results of signal processing at each point.

(79) In step (4), on the premise that the stress-spectrum parameters k and c are obtained in step (2) and the transverse wave incident angle θ is 30°, the first response frequency of the phase difference and the maximum value of the derivative function of the phase difference of the ultrasonic transverse wave echo of the in-service steel structure member obtained in step (3) are substituted into the formula (29) to calculate the normal stress difference and the shear stress inside the in-service steel structure member.

(80) In step (5), the normal stresses are separated by the shear difference method to obtain all of the three independent plane stress components.

(81) Described below is the determination for the absolute stress of the in-service steel structure member using the method provided herein for determining plane stresses on an in-service steel structure member based on ultrasonic transverse wave phase spectrum. In order to further verify the accuracy of the method, the test for determining the plane stress of a steel structural member and comparative tests are performed below.

Example 1

(82) A steel plate A made of Q235B is used herein as the research object to construct the plane stress field. It can be found from the analysis about the factors affecting the axial stress that a smaller thickness will result in a larger amplification parameter of the determination error. However, the thickness of the research object cannot be limitlessly reduced to control the determination error. The thickness of the steel plate A is empirically selected to 1 cm. At the same time, the steel plate A is provided with a rectangular opening to avoid the field having a stress uniformity similar to the axial stress field. Then the steel plate A is loaded in a direction parallel to the plate by placing a hydraulic jack at the rectangular opening. The final plane stress field is schematically shown in FIG. 4, and the plane stress determining system is shown in FIG. 3. In order to ensure that the results are sufficiently reliable, a small test sample B with a size of 45.00 mm×30.00 mm×10.00 mm is produced from portion cut during the opening process for the calibration. The determination was carried out in accordance with the procedures mentioned above.

(83) In step (1), a replica of the in-service steel structure member is prepared. The steel plate A is assumed as the in-service steel structure member, and in the manufacturing of the steel plate A, a small test sample B with a size of 45.00 mm×30.00 mm×10.00 mm is derived from the portion cut during the opening process and used for the calibration, thereby ensuring the consistence with the steel plate A in thickness and material. The test sample B, i.e., the replica of the in-service steel structure member, is used for the calibration of axial stress, and the plane stress determination for the in-service steel structure member is performed on the steel plate A. In step (2), the calibration of the stress-spectrum parameters k and c under plane stress is replaced by the calibration under axial stress. The test sample B is stepwise loaded, and the first response frequencies and stress values of the derivative function curve of the phase difference under each load are recorded and listed in Table 1. The stress values in Table 1 and the reciprocals of the first response frequencies are fitted using the least square method to obtain a linear relationship between the stress values and the reciprocals of the first response frequencies, as shown in FIG. 5. It can be seen that the stress values of the replica of the in-service steel structure member have a good linear relationship with the reciprocals of the first response frequencies.

(84) TABLE-US-00001 TABLE 1 First response frequencies of the test sample B under different stress values σ f.sub.max σ f.sub.max (MPa) (MHz) (MPa) (MHz) 9.41634 9.688984 108.09634 9.257545 20.13807 9.662769 116.56131 9.229349 28.35157 9.594167 132.33847 9.165063 39.25879 9.495774 143.19373 9.119095 51.3882 9.502993 152.87618 9.06454 64.28101 9.433962 165.24317 9.014694 75.22575 9.386146 175.8973 8.959771 84.66946 9.344048 188.77001 8.90948 96.33056 9.300595 198.83364 8.845644

(85) In step (3), the first response frequencies of the phase difference and the maximum values of the derivative function of the phase difference of the ultrasonic transverse wave echoes are obtained. The positions of the determination points on the in-service steel structure member provided herein are shown in FIG. 6. The distance between the determination point 1 and the lower surface of the in-service steel structure member is 2 cm, and the determination points 2, 3, and 4 are selected at an interval of 2 cm. The upper and lower determination points are symmetrically arranged with respect to the horizontal central axis of the in-service steel structure member. The steel plate is determined under the loading state according to the method mentioned above, and the ultrasonic echo signals of each determination point are recorded. The collected signals are processed with the software system to complete the conversion of the time-frequency domain of the signals and obtain the derivative function curves of the phase difference of the ultrasonic wave signals, capturing the first response frequencies of the phase difference and the maximum values of the derivative function curve of the phase difference.

(86) In step (4), the normal stress difference and the shear stress value inside the in-service steel structure member are solved as follows. The stress-spectrum parameters k and c obtained in step (2), the transverse wave incident angle θ of 30°, the first response frequencies of the phase difference and the derivative function curve maximum values of the phase difference of the ultrasonic transverse wave echo of the in-service steel structure obtained in step (3) are substituted into the formula (29) to calculate the normal stress difference and the shear stress inside the in-service steel structure member.

(87) In step (5), the normal stresses are separated by the shear difference method to obtain all of the three independent plane stress components. The normal stress difference and the shear stress value of respective determination points have been obtained through the test. In order to obtain three independent plane stress values, the invention adopts the shear difference method to realize the separation of the normal stresses by solving the plane stress differential equation. The shear difference method is originally used in the photoelastic determination of the plane stress, and its application is relatively full-blown.

(88) The invention realizes the separation of the normal stresses by the shear difference method, thereby realizing the solution of three independent plane stress values. The plane stresses of each determination point are shown in FIGS. 7-9.

Comparative Example 1 Determination of Internal Stress of Steel Sheet by Strain Gauge Method

(89) In step (3) of Example 1, when an unknown force is applied to the steel plate A, the unknown force can be measured by the strain gauge method, where the arrangement of the strain gauges is shown in FIG. 10. The results determined by the method provided herein are compared with the stress values collected by the strain gauges, and the comparison results are shown in FIGS. 11-14. It can be found from FIGS. 11-14 that the overall error of the plane stress values obtained by the method of the invention with respect to the true stress values is under control. The determined plane stress trend is consistent with the true plane stress trend, and can reflect the distribution of the plane stresses along a straight line, which demonstrates the effectiveness of the method of the invention.

(90) It can be seen from the comparison between Embodiment 1 and Comparative Embodiment 1 that the method for determining plane stresses on an in-service steel structure member based on phase spectrum of ultrasonic transverse wave proposed herein can realize the non-destructive determination for the plane stress of the in-service steel structure member. There is no extra requirement for the sampling rate of the data acquisition system during the determining. In addition, this method is less affected by the high-frequency noise of the environment and the obtained results are demonstrated to be valid. The instruments employed in the method have simple installation and operation and low cost. Therefore, the method provided herein is suitable for the determination of plane stress of a steel structure member in construction and in service, and can also be used for the determination of welding residual stress and loading stress of other metal components.

(91) Described above are merely preferred embodiments of the invention, which are not intended to limit the invention. Various variations and replacements made by those skilled in the art without departing from the spirit of the invention should fall within the scope of the invention.