Method for Calculating Residual Stresses in the Seam Metal of Welded Pipeline Joints (Variants)

Abstract

Methods for non-destructive testing of engineering materials. In one aspect, a method can be used to calculate residual longitudinal and annular welding stresses in welded joints and can be used to assess the quality of pipeline welds according to the criterion of the level of residual stresses and to determine the initial parameters for the pipeline strength calculation. In some aspects, the method enables independent calculation of the longitudinal and hoop residual stresses. Thus, the stresses can be calculated in the seam metal of the pipelines welds, where they reach their maximum values. The method can be used to test a pipeline section using an ultrasonic echo method to measure the propagation time for longitudinal waves and transverse waves polarized along and across the pipe axis. The measurement results define the distinguishing features of the stress state of a welded joint for a specific type of pipe by numerical modeling.

Claims

1. A method for calculation of residual stresses in the seam metal of welded pipelines joints, consisting in that on the pipeline section under tests the propagation time for longitudinal waves and transverse waves polarized along and across the pipe axis are measured with the ultrasonic echo method, and the measurement results define the distinguishing features of the stress state of a welded joint characterized in that for the specific type of pipe by numerical modeling to pre-define the position of the cross-sections balancing, which balancing the hoop stresses in the base metal reaches the minimum value, and the balancing coefficient value, equal to the ratio of the maximum membrane residual tensile hoop stresses in the seam metal to the value of the minimum residual compressive membrane hoop stresses in the base metal; further, prior to the welded joints completion, measurements of the initial values of the propagation time of the longitudinal wave and transverse waves polarized along and across the pipe axis are performed in the balancing sections are performed; after the welded joints completion at the same measurement points, measurements of the performance values of the propagation time of the same types of waves are performed, according to the results of measurements applying the acoustoelasticity equations for a biaxial stress state: ${\sigma }_z=K_1\left(\frac{t_{01}{t}_3}{t_1{t}_{03}}-1\right)-K_2\left(\frac{t_{02}{t}_3}{t_2{t}_{03}}-1\right)$ ${\sigma }_t=K_1\left(\frac{t_{01}{t}_2}{t_1{t}_{02}}-1\right)-K_2\left(\frac{t_{01}{t}_3}{t_1{t}_{03}}-1\right)$ where t.sub.01, t.sub.02, t.sub.03 are the initial and t.sub.1, t.sub.2, t.sub.3 are the performance values of the propagation times of the transverse waves polarized along and across the generating line of a tube and longitudinal wave, respectively, K.sub.1 and K.sub.2 are the coefficients of the acoustic-elastic linkage, for each section of measurements, the values of membrane longitudinal and hoop stresses are calculated, as well as bending moments, using which, based on the principle of balancing membrane stresses and taking into account the balancing coefficient, the maximum values of residual longitudinal and hoop local stresses in the seam metal are calculated.

2. A method for calculation of residual stresses in the seam metal of welded pipelines joints made of the acoustically isotropic metal, consisting in that on the pipeline section under tests the propagation time for the bulk waves are measured with the ultrasonic echo method, and the measurement results define the distinguishing features of the stress state of a welded joint characterized in that for a specific type of pipe by numerical modeling the position are pre-defined for the cross-sections balancing, which balancing the hoop stresses in the base metal reaches the minimum value, and the balancing coefficient value, equal to the ratio of the maximum membrane tensile hoop stresses in the seam metal to the value of the minimum compressive membrane hoop stresses in the base metal and also the value of the intrinsic acoustic anisotropy of the base metal; and after the welded joint production, in the balancing sections, measurements of the working values of the propagation time of transverse waves polarized along and across the pipe axis are performed, according to the results of measurements using the acoustoelasticity equation for the difference between the longitudinal and hoop membrane stresses the specified difference for each measuring point is calculated: ${\sigma }_z-{\sigma }_t=D\left(2\frac{t_2-t_1}{t_2+t_1}-a_0\right),$ where a.sub.0 is the intrinsic acoustic anisotropy of the base metal, D is the elastic-acoustic coupling coefficient, the separation of longitudinal and hoop membrane stresses is performed using the results of defining the longitudinal stresses in the additional section, then for each measurement section, the values of membrane longitudinal and hoop stresses are calculated, as well as bending moments, using which, based on the principle of balancing membrane stresses and taking into account the balancing coefficient, the maximum values of residual longitudinal and hoop local stresses in the seam metal are calculated.

Description

[0016] The claimed group of inventions is explained by graphic materials, where

[0017] FIG. 1 shows a graphic chart of the calculated stress distribution,

[0018] FIGS. 2 and 3 show the layout of the measurement points,

[0019] FIG. 4 shows the layout of the measurement points in sections,

[0020] FIGS. 5 and 6 graphically show the results of the defining longitudinal and hoop stresses at the measurement points before and followed by heat treatment of the specimens,

[0021] FIG. 7 shows the results of measurements of acoustic anisotropy values before and followed by the heat treatment (averaged over the measurement cross sections).

[0022] The method comprising a procedure for measuring the propagation times of a longitudinal wave and transverse waves polarized along and across the pipe axis, as well as defining the features of the stress state of a welded joint in the base metal, as per the invention additionally contains the following operations: measurements are performed in certain areas of the base metal adjacent to the seam metal. These areas correspond to the regions of localization of the minimum compressive hoop membrane residual stresses, which balance the maximum tensile hoop membrane residual stresses in the seam metal. The balancing effect that occurs specifically for membrane stresses provides a one-to-one correlation between hoop membrane residual stresses in the weld metal and in the adjacent to-the-weld area. This allows calculating the ratio between them—the balancing coefficient, which is used to calculate the maximum residual stresses in the seam metal based on the results of measurements in the adjacent to-the-weld area.

[0023] The measurements are made in the cross sections of the pipeline located in the specified areas. The position of these sections, as well as the value of the balancing coefficient is defined by the results of preliminary studies or calculations. According to the results of measuring the propagation times of elastic waves before and followed by the welded joint completion by the acoustoelastic method, the values of longitudinal and hoop membrane stresses in the measurement cross sections are obtained.

[0024] The maximum values of longitudinal and hoop local residual stresses in the seam metal are defined from the obtained values of stresses in the measurement cross sections based on the balancing membrane stresses principal using the balancing coefficient.

[0025] In a particular case, when measurements are made on pipelines made of acoustically isotropic materials, the measurement of elastic wave propagation times made prior the welded joint completion is excluded, which makes it possible to evaluate residual stresses not only during assembly, but also on pipelines in operation. The values of longitudinal and hoop membrane stresses in the measurement sections are determined only by the results of measurements performed after the welded joint is made. The distinguishing feature of this procedure is the use of stress measurement results in an additional cross-section located outside the residual stress localization area.

[0026] The method for the embodiment according to the first option is carried out as follows.

[0027] In the method for the calculation of residual stresses in the seam metal of pipelines welds, which consists in the fact that the propagation time of the longitudinal wave and transverse waves polarized along and across the pipe axis is measured using the ultrasonic echo method, and the measurement results define the features of the stress state of the welded joint for a specific type of pipe, the position of the balancing sections is pre-defined by computational modeling. The balancing hoop stresses in the base metal reach minimum values in the specified cross sections. The position of the cross sections is defined by the results of computational modeling of the residual welding stresses or by the results of experimental studies on control welded joints performed after welding but before the heat treatment. Studies are performed for each type of welded joint, which is characterized by the diameter, the pipe wall thickness and the welding technology.

[0028] Also, based on the results of calculated or experimental studies, the balancing coefficient (k), which is equal to the ratio of the maximum tensile membrane hoop stresses in the seam metal (σ.sub.tmax) to the value of the minimum compressive membrane hoop stresses (σ.sub.tmin) in the base metal, is defined. The value of k is defined by the results of computational modeling of the residual welding stresses according to the formula:

[00003]$\begin{array}{cc}k=\frac{{\sigma }_{\mathrm{tmax}}}{{\sigma }_{\mathrm{tmin}}}& \left(1\right)\end{array}$

It is required to precisely apply the acoustoelasticity method for the measurements, which includes the echo method of ultrasonic testing, as the only non-destructive method that provides measurement of the membrane rather than surface stresses [4].

[0029] The measurements shall be performed by devices that implement the measurement method and are certified as instrumentation for single- and bi-axial mechanical stresses.

[0030] Prior the start of the welded joint completion, the initial values of the propagation time of the longitudinal wave and transverse waves polarized along and across the pipe axis are measured in the balancing sections.

[0031] After the welded joint completion, the performance values of the propagation time of the same types of waves are measured at the same measurement points. After that, based on the results of the measurements using the acoustoelasticity equations for the biaxial stress state:

[00004]$\begin{array}{cc}{\sigma }_z=K_1\left(\frac{t_{01}{t}_3}{t_1{t}_{03}}-1\right)-K_2\left(\frac{t_{02}{t}_3}{t_2{t}_{03}}-1\right)& \left(2\right)\\ {\sigma }_t=K_1\left(\frac{t_{01}{t}_2}{t_1{t}_{02}}-1\right)-K_2\left(\frac{t_{01}{t}_3}{t_1{t}_{03}}-1\right)& \left(3\right)\end{array}$

where t.sub.01, t.sub.02, t.sub.03 are the initial values, and t.sub.1, t.sub.2, t.sub.3 are the performance values of the propagation times of transverse waves polarized along and across the generating line of a tube and the longitudinal wave, respectively.

[0032] K.sub.1 and K.sub.2 are the elastic-acoustic coupling coefficients calculated in accordance with the standard procedure provided for [5] (for welded elements made of carbon and low-alloy steels, it is allowed not to define the values of K.sub.1 and K.sub.2, but to apply the generalized elastic-acoustic coupling coefficients [6]).

[0033] Based on the results of measurements of time delays according to formulas (2) and (3), the values of longitudinal and hoop stresses at the measurement points are calculated for each section of measurements: [0034] hoop membrane balancing stresses averaged over the measurement cross section (σ.sub.t); [0035] longitudinal membrane stresses averaged over the measurement cross section (σ.sub.z); [0036] total bending moment according to the formula:

M={right arrow over (M.sub.x.sup.2+M.sub.y.sup.2)}  (4)

where M.sub.m,xM.sub.m,y are the components of the moment in Cartesian axials taken for the subject of the survey, calculated using the formulas [7]

[00005]$\begin{array}{cc}{M}_x=\frac{W}{x}{\int }_0^{2\pi }{\sigma }_z\left(\theta \right)\sin \left(\theta \right)d\theta & \left(5\right)\\ M_y=-\frac{W}{x}{\int }_0^{2\pi }{\sigma }_z\left(\theta \right)\cos \left(\theta \right)d\theta W=\frac{{\pi \left(D_{\mathrm{in}}+h\right)}^{2}h}{4},& \left(6\right)\end{array}$

[0037] where W is the resistance moment of a thin-walled pipe; h is the wall thickness of the pipe; D.sub.in is the inner diameter of the pipe; θ is the angular coordinate in the cross-sectional plane, the function of the angular distribution of longitudinal stresses σ.sub.z(θ) is defined by the results of measurements of the values of longitudinal stresses at the measurement points.

[0038] Where the measurements are performed in both sections located on both sides of the seam, the values σz, σ.sub.t and M averaged over both sections are used to define the stresses in the seam metal.

[0039] The maximum hoop tensile stresses in the deposited metal are determined by the value of the minimum balancing hoop membrane stresses in the area of the base metal adjacent to the welded joint. The maximum values of hoop residual stresses in the seam metal (σ.sub.t.s) using the balancing coefficient are calculated according to the formula:

σ.sub.t.s=kσ.sub.t  (7)

[0040] The maximum longitudinal stresses are defined as a superposition of stresses due to tension and bending stresses due to the total bending moment. The maximum values of longitudinal stresses in the seam metal (σ.sub.z,s) calculated according to the formula:

[00006]$\begin{array}{cc}{\sigma }_{z.s}=\frac{M}{W}+\stackrel{\_}{{\sigma }_z}& \left(8\right)\end{array}$

[0041] Where the results of studies on base metal of the welded components representative specimens define that it is acoustically isotropic, that is, the variation of intrinsic acoustic anisotropy of the basic metal (a.sub.0), defined according to the

[00007]$\begin{array}{cc}{a}_0=2\frac{t_{02}-t_{01}}{t_{02}+t_{01}},& \left(9\right)\end{array}$

does not exceed 0.0004, then the second variant of the method for defining residual stresses is implemented.

[0042] The method for the embodiment according to the second option is carried out as follows.

On the pipeline section under study, the bulk waves propagation time is measured applying the ultrasonic echo method, and the features of the stress state of the welded joint are defined based on the measurement results. According to the second option of the method for defining the residual stresses in the pipelines welds metal made of acoustically isotropic metal, for the specific pipes type, pre-determined by the computational modeling: [0043] the position of the balancing sections in which the balancing hoop stresses in the base metal reach the minimum values; [0044] the value of the balancing coefficient (k) according to the formula (1).

[0045] The value of the intrinsic acoustic anisotropy of the base metal (a.sub.0) is also defined.

[0046] The position of the balancing sections should be specified after the weld is made during preliminary measurements performed at points located along the generating lines of a pipeline.

[0047] After the welded joint completion, the performance values of the propagation time of the transverse waves polarized along and across the pipe axis are measured in the balancing sections. Based on the results of measurements using the acoustoelasticity equation for the difference between longitudinal and hoop membrane stresses, the values of the specified difference are determined for each measurement point:

[00008]$\begin{array}{cc}{\sigma }_z-{\sigma }_t=D\left(2\frac{t_2-t_1}{t_2+t_1}-a_0\right)& \left(10\right)\end{array}$

where D is the elastic-acoustic coupling coefficient for the uniaxial stress state, defined in accordance with the standard procedure provided for [5] (for welded components made of carbon and low-alloy steels, it is allowed not to define the values of D, but to use the generalized elastic-acoustic coupling coefficient [6]).

[0048] Separation of the longitudinal and hoop membrane stresses is performed using the results of defining the longitudinal stresses in the additional section. Therefor, based on the results of measurements in the additional section located outside the area of residual welding stresses, σ.sub.z—the average values of longitudinal membrane stresses (σ.sub.z) at the measurement points are calculated. The values σ.sub.z, therefore, are calculated according to the formula (10), provided that there are no residual stresses in the cross section of additional measurements and, consequently, at all measurement points σ.sub.t=0.

[0049] The values of the membrane hoop stresses are defined in accordance with the compensation principle for bending longitudinal stresses in the cross section, and also taking into account the fact that the average values of the longitudinal membrane stresses are the same along the entire length of the cylindrical component. For each measurement cross-section, the values of σ.sub.t—the average values of the hoop membrane balancing stresses (σ.sub.t) over the measurement cross-section. The hoop membrane stresses at the measurement points, in accordance with (10), are calculated according to the formula:

[00009]$\begin{array}{cc}{\sigma }_t=\stackrel{\_}{{\sigma }_z}-D\left(2\frac{t_2-t_1}{t_2+t_1}-a_0\right).& \left(11\right)\end{array}$

The total bending moment M and its components M.sub.x and M.sub.y are calculated according to the formulas (4, 5 and 6), respectively.

[0050] Where the measurements are performed in both sections located on both sides of the seam, the values σ.sub.z, σ.sub.t and M averaged over both sections are used to define the stresses in the seam metal.

[0051] The maximum values of residual longitudinal and hoop local stresses in the seam metal σ.sub.t.s and σ.sub.z.s are calculated according to the formulas (7) and (8) c applying the balancing coefficient.

[0052] The claimed group of inventions is explained by the following examples.

[0053] Example 1. Calculation of the maximum residual welding stresses in the welded joint of a split-design coil made of pipe billets DN850x70 (steel 10GN2MFA).

[0054] Acoustoelasticity parameters were measured using the IN-5101A device, certified as a instrument for single- and bi-axial mechanical stresses. The measurements were performed in accordance with the requirements of [5].

[0055] The position of cross sections for the pipes type and the value of the balancing coefficient were defined based on the results of the computational modeling of the residual welding stresses prior the heat treatment using the “SVARKA” software package developed at the Technologies of Welding and Diagnostics Department of Bauman Moscow State Technical University.

[0056] FIG. 1 shows the diagram for defining the measurement cross sections (1A and 1B) based on the results of calculations of hoop membrane stresses in a welded joint by the finite element technique.

[0057] According to the calculation results (FIG. 1), it is found that the measurement sections 1A and 1B are located at a distance of ±50 mm from the weld central axis, and the balancing coefficient according to the formula (1): k=−3.25.

[0058] Further, the measurement points were indicated. The measurement points layout on the monitored object in sections 1A and 1B is shown on FIGS. 2 and 3.

[0059] The initial values of the propagation times (t.sub.01, t.sub.02, t.sub.03) of acoustic signals were calculated at all measurement points prior to welding.

[0060] The performance values (t.sub.1, t.sub.2, t.sub.3) were defined twice: prior and followed by the heat treatment. The results of defining the cross-section averaged measurements applying formulas (2) and (3) of longitudinal and hoop stresses at the measurement points prior (curve a) and followed by (curve b) the heat treatment are shown on FIG. 4.

[0061] To calculate the stresses, the elastic-acoustic coupling coefficients obtained in accordance with the requirements of [5] for 10GN2MFA steel were applied: [0062] K.sub.1=−116300 MPa; K.sub.2=−12000 MPa; D=−128300 MPa.

[0063] Based on the results of the stress measurement, the following parameters are defined:

the averaged values of hoop stresses in the measurement cross sections prior and followed by the heat treatment (σ.sub.t.sub.wld and σ.sub.t.sub.HT, respectively): [0064] σ.sub.t.sub.wld=−190 MPa; σ.sub.t.sub.HT=−1 MPa;
according to the formulas (4-6), the values of the bending moment in the weld section prior and followed by the heat treatment (M.sub.wld and M.sub.HT, respectively): [0065] M.sub.wld=0.14 mN*m; M.sub.HT=0.04 mN*m.

[0066] Due to the split-design coil ends fixing absence, the averaged longitudinal stresses (σ.sub.z) were assumed to be identically equal to zero, which corresponds to the results of measurements for which the averaged longitudinal stresses are within the measurement error limit.

[0067] The maximum hoop tensile stresses in the welded joint, calculated according to the formula (13), prior and followed by the heat treatment (wld and HT, respectively) are equal to: [0068] σ.sub.t.s.sub.wld=615 MPa and σ.sub.t.s.sub.HT=5 MP.

[0069] The maximum longitudinal stresses in the welded joint, calculated according to the formula (14), prior and followed by the heat treatment (σ.sub.z.s.sub.Wld and σ.sub.z.s.sub.HT, respectively) are equal to: [0070] σ.sub.z.s.sub.wld=3 MPa and σ.sub.z.s.sub.HT=1 MPa

[0071] Example 2. Calculation of the maximum residual welding stresses in the welded joint of a split-design coil made of pipe billets DN850x70 (10GN2MFA steel), for which preliminary studies of the acoustic features of the metal were performed.

[0072] According to the results of studies on base metal of the welded components representative specimens define that the values of the intrinsic acoustic anisotropy are in the range of 0.0001±0.0003, that is, the base metal of the coil is acoustically isotropic. The initial value of the intrinsic acoustic anisotropy is assumed to be: [0073] a.sub.0=0.0001.

[0074] To clarify the position of the measurement sections, additional measurements of acoustic anisotropy were performed after the welded joint completion at points located along the pipeline generators (see FIG. 4, where the layout of the location of the measurement points (O1-4) on the generating lines I and II of a pipeline is shown).

[0075] Based on the measurement results, it was found that the minimum values of the intrinsic acoustic anisotropy correspond to O2 points located at a distance of 50 mm from the weld line, which corresponds to the results of the computational modeling.

[0076] Thus, the position of the cross sections of measurements 1A and 1B and the value of the balancing coefficient are taken similarly to Example 1. The location of the stress measurement points is also similar to Example 1. Since, due to the split-design coil ends fixing absence, the averaged longitudinal stresses (σ.sub.z) were assumed to be identically equal to zero, measurements in section 2 intended for the calculation of σ.sub.z were not performed.

[0077] The performance values (t.sub.1, t.sub.2, t.sub.3) were defined twice: prior and followed by the heat treatment. The results of calculation the values of acoustic anisotropy (averaged over the measurement cross-sections) at the measurement points prior and followed by the heat treatment are shown on FIGS. 5 and 6.

[0078] Based on the results of acoustic anisotropy measurement, the following values were calculated:

according to the formula (10) the averaged values of hoop stresses in the measurement cross sections prior and followed by the heat treatment (σ.sub.t.sub.wld and σ.sub.t.sub.HT, respectively): [0079] tσ.sub.t.sub.wld=−199 MPa; σ.sub.t.sub.HT=−6 MPa
according to the formulas (11-12), the values of the bending moment in the weld section prior and followed by the heat treatment (M.sub.wld and M.sub.HT, respectively): [0080] M.sub.wld=0.11 mN*m; M.sub.HT=0.09 mN*m.

[0081] The maximum hoop tensile stresses in the welded joint, calculated according to the formula (13), prior and followed by the heat treatment (wld and HT, respectively) are equal to: [0082] wld=646 MPa and HT=20 MPa

[0083] The maximum longitudinal stresses in the welded joint, calculated according to the formula (14), prior and followed by the heat treatment (σ.sub.z.s.sub.wld and σ.sub.z.s.sub.HT, respectively) are equal to: [0084] σ.sub.t.s.sub.wld=2.4 MPa and σ.sub.t.s.sub.HT=1.9 MPa

REFERENCES

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