CN116822294A - Method for calculating critical elastoplastic buckling pressure of steel pipeline containing irregular corrosion defects - Google Patents

Method for calculating critical elastoplastic buckling pressure of steel pipeline containing irregular corrosion defects Download PDF

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CN116822294A
CN116822294A CN202310782697.1A CN202310782697A CN116822294A CN 116822294 A CN116822294 A CN 116822294A CN 202310782697 A CN202310782697 A CN 202310782697A CN 116822294 A CN116822294 A CN 116822294A
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武行
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Dalian Minzu University
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Abstract

A calculation method for critical elastoplastic buckling pressure of a steel pipeline containing irregular corrosion defects belongs to the technical field of deep sea oil gas development, production and transportation. According to the method, based on a classical Timoshenko shell buckling theory, a tangential modulus theory is introduced, the influence of irregular corrosion defect size on the buckling response of the pipeline is considered, and a critical elastoplastic buckling pressure calculation equation of the pipeline containing the irregular corrosion defects is deduced. And the buckling response of the pipeline in two buckling modes of positive symmetry or negative symmetry is considered, and a method for calculating the critical external pressure of the corroded pipeline is deduced; and the accuracy of the calculation method is verified by comparing the calculation method with the previous experiment and the finite element result.

Description

Method for calculating critical elastoplastic buckling pressure of steel pipeline containing irregular corrosion defects
Technical Field
The invention relates to a calculation method of critical elastoplastic buckling pressure of a steel pipeline containing irregular corrosion defects, and belongs to the technical field of deep sea oil gas development, production and transportation.
Background
Subsea pipelines are an important component of offshore oil and gas development projects. The external pressure of the submarine pipeline gradually increases with the increase of the water depth. The large external pressure may cause buckling, fracture or even collapse of the pipeline, which is a significant cause of subsea pipeline accidents. The existence of corrosion defects leads to the thinning of the wall thickness of the pipeline, and the compressive bearing capacity of the pipeline is greatly reduced. Therefore, the research of corrosion defects has important significance for evaluating the stability of the pipeline.
Aiming at a critical buckling load calculation formula of a steel pipeline under the action of external pressure, an elastoplastic buckling calculation formula of a perfect pipeline and a double-corrosion pipeline is available at present. Corrosion is a complex and random electrochemical reaction process. As the time of use of the pipe increases, adjacent corrosion defects overlap to form new irregular corrosion defects. An irregular etch defect is one that has one or more major peaks in the circumferential or axial distribution of defect depths, which can be reduced to a large top layer defect combination of small bottom layer defects. At present, no calculation formula for the elastoplastic buckling pressure of the pipeline with irregular corrosion defects exists at home and abroad.
Disclosure of Invention
In order to make up for the defects of research technology in the aspect of corrosion defect forms of deep sea pipelines, the invention provides a calculation method of the external pressure critical elastoplastic buckling pressure of the pipelines with irregular corrosion defects under the condition that adjacent corrosion defects are overlapped into an irregular corrosion defect, which has higher accuracy and practicability.
The invention adopts the scheme for solving the technical problems that:
based on the classical Timoshenko shell buckling theory, a tangential modulus theory is introduced, the influence of the size of the irregular corrosion defect on the buckling response of the pipeline is considered, and a critical elastoplastic buckling pressure calculation equation of the pipeline containing the irregular corrosion defect is deduced. And deducing a critical external pressure calculation method of the corrosion pipeline by considering buckling response of the pipeline in two buckling modes of positive symmetry or negative symmetry; and the accuracy of the calculation method is verified by comparison with the previous experiment and the finite element result.
A calculation method for critical elastoplastic buckling pressure of a steel pipeline containing irregular corrosion defects comprises the following steps:
s1, an irregular defect pipeline with the average radius of R and the wall thickness t is assumed to be long enough, and the irregular defect pipeline is influenced by external pressure p. When the pipe and defect are long enough, any point displacement on each section along the pipe axis is the same, and buckling of the pipe can be reduced to a two-dimensional plane problem. Thus, the deformation problem of the corrosion defective pipe can be analyzed based on the planar strain assumption, the displacement is only related to the polar angle θ, and the radial displacement of any point of the pipe section is w. In addition, the circumferential displacement v caused by the centerline extension is very small and therefore negligible. The irregular defects of the pipe consist of bottom layer defects (large defects) and top layer defects (small defects). According to symmetry, half of a circular ring of the pipeline section is taken for research, the ring of the half pipe section can be divided into three parts, and the polar angle range is as follows:
theta is the angle, theta 1 Angle theta is the included angle of the defect of the half bottom layer 2 The sum of the angles of the corrosion defects of the half bottom layer and the half top layer;
the thickness of the walls and average radius of the underlying, top, and intact zones are different and can be expressed as:
wherein t is the thickness of the pipeline, t 1 Is the wall thickness of the pipeline at the defect of the bottom layer, t 2 Is the wall thickness of the pipeline at the defect of the top layer, t 3 Is the thickness of the wall of the intact part of the pipeline, R is the radius of a curved surface in the pipeline, R 1 Is the radius of a curved surface in a pipeline at the defect of the bottom layer, R 2 Is the radius of a curved surface in the pipeline at the defect of the top layer, R 3 Is the radius of the curved surface in the intact part of the pipeline.
S2, adopting a Ramberg-Osgood equation for a stress-strain curve:
wherein the method comprises the steps ofEpsilon is strain, sigma is stress, E is elastic modulus, epsilon y For strain, sigma y Is the yield stress and β is the strain hardening exponent.
The tangential modulus of each segment of the ring is:
E t1 ，E t2 ，E t3 the tangential moduli of the bottom layer, top layer and intact tubing, respectively.
S3, the resultant moment M of the middle curved surface can be obtained through balance analysis:
M ＝ M 0 + pR(w-w 0 ) (8)
wherein w is 0 And M 0 Is a small radial displacement and bending moment caused by a small initial displacement. Then, by combining equations (2) - (9) with the classical theory of Timoshenko (1961), it is possible to obtain the critical buckling pressures (p) of the pipeline with irregular defects in symmetric and antisymmetric buckling modes b ) Is defined by the differential equation:
1) Symmetric buckling mode
2) Anti-symmetric buckling mode
S4, boundary conditions of the two buckling modes are respectively as follows:
1) Symmetric buckling mode
2) Anti-symmetric buckling mode:
by solving the characteristic equations (10) - (12), the following solutions can be obtained
Combining equations (16) - (18) with the boundary conditions for the symmetric buckling modes yields the following equation:
wherein:
I 11 ＝-sin(k 2 θ 1 )；
I 12 ＝0；
I 13 ＝cos(k 1 θ 1 )；
I 14 ＝-cos(k 2 θ 1 )；
I 21 ＝sin[k 2 θ 2 ]；
I 22 ＝-sec(k 3 π)cos[k 3 (π-θ 2 )]；
I 23 ＝0；
I 24 ＝cos[k 2 θ 2 ]；
I 31 ＝-k 2 cos(k 2 θ 1 )；
I 32 ＝0；
I 33 ＝-k 1 sin(k 1 θ 1 )；
I 34 ＝k 2 sin(k 2 θ 1 )；
I 35 ＝0；
I 36 ＝0；
I 41 ＝cos[k 2 θ 2 ]；
I 42 ＝-k 3 sec(k 3 π)sin[k 3 (π-θ 2 )]；
I 43 ＝0；
I 44 ＝-k 2 sin[k 2 θ 2 ]；
I 45 ＝0；
I 46 ＝0；
I 61 ＝I 62 ＝0；
I 63 ＝1；
I 64 ＝0；
[I]is a matrix containing critical buckling pressures. Obviously A 12 、A 21 、A 22 、A 32 、w 0 And M 0 Are non-zero parameters. Thus, matrix [ I ]]The determinant value of (2) is zero. I.e.
The critical buckling pressure of the irregularly corroded defective pipe in the symmetric buckling mode of i=0 (20) can be obtained by solving equation (20).
S5, for the anti-symmetrical buckling mode, by solving equations (13) - (15), we can obtain
w 2 ＝ C 21 sink 2 θ+ C 22 cosk 2 θ, for θ 1 ≤ θ ≤ θ 2 (22)
w 3 ＝ C 31 sink 3 θ +C 32 cosk 3 θ, for θ 2 ≤ θ ≤ π (23)
Combining equations (21) - (23) with the boundary conditions for the anti-symmetric buckling mode, the following equation can be derived:
wherein the elements in [ J ] are:
J 11 ＝sin(k 1 θ 1 )；
J 12 ＝-sin(k 2 θ 1 )；
J 13 ＝-cos(k 2 θ 1 )；
J 14 ＝0；
J 21 ＝0；
J 22 ＝sin[k 2 (θ 1 +θ 2 )]；
J 23 ＝cos[k 2 θ 2 ]；
J 24 ＝(cos[k 3 θ 2 ]-sin[k 3 (π-θ 2 )]/sink 3 π；
J 31 ＝k 1 cos(k 1 θ 1 )；
J 32 ＝-k 2 cos(k 2 θ 1 )；
J 33 ＝k 2 sin(k 2 θ 1 )；
J 34 ＝0；
J 41 ＝0；
J 42 ＝k 2 cos[k 2 θ 2 ]；
J 43 ＝-k 2 sin[k 2 θ 2 ]；
J 44 ＝-Sin[k 3 θ 2 ]+k 3 cos[k 3 (π+θ 2 )]/sink 3 π.
obviously, the determinant of [ J ] is also zero:
|J| ＝ 0 (25)
the critical buckling pressure of the irregular corrosion defective pipe in the anti-symmetric buckling mode can be obtained by solving equation (25).
Compared with the prior art, the invention has the following advantages:
1. under the condition of considering the mutual influence among corrosion defects, the calculation method of the elastoplastic buckling pressure of the irregular corrosion defect pipeline is deduced on the basis of elastoplastic buckling of the single corrosion defect pipeline, and the calculation result is more accurate than that of the double corrosion defect pipeline.
2. The buckling response formula of the pipeline is further improved by considering the influence of the complex shape of the irregular corrosion defect on the critical buckling pressure.
Drawings
FIG. 1 is a graph of the curve in a cross section of an irregularly corroding pipe.
Fig. 2 is a finite element model.
Fig. 3 is a graph comparing finite element results with theoretical results.
Detailed Description
Consider a sufficiently long irregular defect tube with an average radius R and wall thickness t, and subject to an external pressure p. When the pipe and defect are long enough, any point displacement on each section along the pipe axis is the same, and buckling of the pipe can be reduced to a two-dimensional plane problem. Thus, the deformation problem of the corrosion defective pipe can be analyzed based on the planar strain assumption, the displacement is only related to the polar angle θ, and the radial displacement of any point of the pipe section is w. In addition, the circumferential displacement v caused by the centerline extension is very small and therefore negligible. The irregular defects of the pipe consist of bottom layer defects (large defects) and top layer defects (small defects). According to symmetry, half of a circular ring of the pipeline section is taken for research, the ring of the half pipe section can be divided into three parts, and the polar angle range is as follows:
theta is the angle, theta 1 Angle theta is the included angle of the defect of the half bottom layer 2 The sum of the angles of the corrosion defects of the half bottom layer and the half top layer;
the segmentation case according to equation (1), where the wall thickness and average radius of the bottom layer defect, the top layer defect and the complete area are different, can be expressed as:
wherein, the liquid crystal display device comprises a liquid crystal display device,t is the thickness of the pipeline, t 1 Is the wall thickness of the pipeline at the defect of the bottom layer, t 2 Is the wall thickness of the pipeline at the defect of the top layer, t 3 Is the thickness of the wall of the intact part of the pipeline, R is the radius of a curved surface in the pipeline, R 1 Is the radius of a curved surface in a pipeline at the defect of the bottom layer, R 2 Is the radius of a curved surface in the pipeline at the defect of the top layer, R 3 Is the radius of the curved surface in the intact part of the pipeline.
For thin-wall pipelines, buckling occurs in the elastic stage of pipeline materials, and for pipelines with thicker wall thickness, the pipeline enters the elastoplastic stage when buckling occurs, so that the buckling stress-strain curve is expressed by adopting a Ramberg-Osgood equation:
wherein epsilon is strain, sigma is stress, E is elastic modulus, epsilon y For strain, sigma y Is the yield stress and β is the strain hardening exponent.
From equations (2) (3) and (4), the tangential modulus of each segment of the ring can be deduced as:
E t1 ，E t2 ，E t3 the tangential moduli of the bottom layer, top layer and intact tubing, respectively.
According to fig. 1, the resultant moment M of the mesogenic surface can be obtained by equilibrium analysis:
M ＝ M 0 + pR(w-w 0 ) (8)
meaning of parameters in the formula, w 0 And M 0 Is a small radial displacement and bending moment caused by a small initial displacement.
Then, by combining equations (2) - (9) with the classical theory of Timoshenko (1961), it is possible to obtain the critical buckling pressures (p) of the pipeline with irregular defects in symmetric and antisymmetric buckling modes b ) Is defined by the differential equation:
1) Symmetric buckling mode
2) Anti-symmetric buckling mode
Boundary conditions of the two buckling modes are respectively as follows: 1) Symmetric buckling mode
2) Anti-symmetric buckling mode:
by solving the characteristic equations (10) - (12), the following solutions can be obtained
Combining equations (16) - (18) with the boundary conditions for the symmetric buckling modes yields the following equation:
wherein:
I 11 ＝-sin(k 2 θ 1 )；I 12 ＝0；I 13 ＝cos(k 1 θ 1 )；I 14 ＝-cos(k 2 θ 1 )； I 21 ＝sin[k 2 θ 2 ]；I 22 ＝-sec(k 3 π)cos[k 3 (π-θ 2 )]；I 23 ＝0；I 24 ＝cos[k 2 θ 2 ]；/>I 31 ＝-k 2 cos(k 2 θ 1 )；I 32 ＝0；I 33 ＝-k 1 sin(k 1 θ 1 )；I 34 ＝k 2 sin(k 2 θ 1 )；I 35 ＝0；I 36 ＝0；I 41 ＝cos[k 2 θ 2 ]；I 42 ＝-k 3 sec(k 3 π)sin[k 3 (π-θ 2 )]；I 43 ＝0；I 44 ＝-k 2 sin[k 2 θ 2 ]；I 45 ＝0；I 46 ＝0；/> I 61 ＝I 62 ＝0；I 63 ＝1；I 64 ＝0；
[I]is a matrix containing critical buckling pressures. Obviously A 12 、A 21 、A 22 、A 32 、w 0 And M 0 Are non-zero parameters. Thus, matrix [ I ]]The determinant value of (2) is zero. I.e.
The critical buckling pressure of the irregularly corroded defective pipe in the symmetric buckling mode of i=0 (20) can be obtained by solving equation (20).
For the anti-symmetric buckling mode, we can obtain by solving equations (13) - (15)
w 2 ＝C 21 sink 2 θ+C 22 cosk 2 θ,forθ 1 ≤θ≤θ 2 (22)
w 3 ＝C 31 sink 3 θ+C 32 cosk 3 θ,forθ 2 ≤θ≤π (23)
Combining equations (21) - (23) with the boundary conditions for the anti-symmetric buckling mode, the following equation can be derived:
wherein the elements in [ J ] are:
J 11 ＝sin(k 1 θ 1 )；J 12 ＝-sin(k 2 θ 1 )；J 13 ＝-cos(k 2 θ 1 )；J 14 ＝0；J 21 ＝0；J 22 ＝sin[k 2 (θ 1 +θ 2 )]；J 23 ＝cos[k 2 θ 2 ]；
J 24 ＝(cos[k 3 θ 2 ]-sin[k 3 (π-θ 2 )]/sink 3 π；J 31 ＝k 1 cos(k 1 θ 1 )；
J 32 ＝-k 2 cos(k 2 θ 1 )；J 33 ＝k 2 sin(k 2 θ 1 )；J 34 ＝0；J 41 ＝0；J 42 ＝k 2 cos[k 2 θ 2 ]；
J 43 ＝-k 2 sin[k 2 θ 2 ]；J 44 ＝-Sin[k 3 θ 2 ]+k 3 cos[k 3 (π+θ 2 )]/sink 3 π.
obviously, the determinant of [ J ] is also zero:
|J| ＝ 0 (25)
the critical buckling pressure of the irregular corrosion defective pipe in the anti-symmetric buckling mode can be obtained by solving equation (25).
A two-dimensional finite element model of the pipeline with external irregular defects is established, and the buckling response of the pipeline is calculated by using AB AQUS software. Meshing is performed using eight-node linear brick units (CPS 8R) with reduced integration, as shown in FIG. 2. The radial directions of the complete area and the defective area are divided into 6 and 2 units, respectively, each of which is disposed 5 ° and 2 ° in the circumferential direction, respectively. A Ramberg-Osgood material model (equation (4)) was used for buckling simulation to approximate the stress-strain relationship of 304 steel. A uniform external pressure was applied to the outside of the ring and the nonlinear buckling problem was load analyzed using the Riks method. And finally, extracting the maximum LPF value in the whole loading process, and calculating the critical buckling pressure of the pipeline. Here, it should be noted that the two-dimensional finite element model established for verifying the present method does not take into account the effect of the relative position between the initial ovality and the defect on the consistency.
The prior theoretical method is verified by utilizing a finite element model with an internal and an external defect pipeline. The results of the finite element model are very consistent with the results of the proposed method and most of the differences are within 8%, indicating the accuracy with which the present method is used to determine critical buckling pressures. The accuracy of the study was demonstrated.

Claims (1)

1. The method for calculating the critical elastoplastic buckling pressure of the steel pipeline containing the irregular corrosion defect is characterized by comprising the following steps of:
s1, assuming a long irregular defect pipeline, wherein the average radius of the irregular defect pipeline is R and the wall thickness t, and the irregular defect pipeline is influenced by external pressure p; when the pipe and the defect are long enough, any point displacement on each section along the axis of the pipe is the same, and the buckling of the pipe is simplified into a two-dimensional plane problem; therefore, the deformation problem of the corrosion defect pipeline is analyzed based on the plane strain assumption, the displacement is only related to the polar angle theta, and the radial displacement of any point of the pipeline section is w; and ignoring the circumferential displacement v caused by the centerline extension;
the irregular defect of the pipeline consists of a bottom layer defect and a top layer defect; according to symmetry, take half of pipeline cross-section ring, the ring of half section divide into three parts, polar angle scope is:
theta is the angle, theta 1 Angle theta is the included angle of the defect of the half bottom layer 2 The sum of the angles of the corrosion defects of the half bottom layer and the half top layer;
the wall thickness and average radius of the underlying defect, the top defect, and the intact zone are different, expressed as:
wherein t is the thickness of the pipeline, t 1 Is the wall thickness of the pipeline at the defect of the bottom layer, t 2 Is the wall thickness of the pipeline at the defect of the top layer, t 3 The thickness of the wall of the intact part of the pipeline is calculated;
r is the radius of a curved surface in a pipeline, R 1 Is the radius of a curved surface in a pipeline at the defect of the bottom layer, R 2 Is the radius of a curved surface in the pipeline at the defect of the top layer, R 3 A radius of a curved surface in the intact part of the pipeline;
s2, adopting a Ramberg-Osgood equation for a stress-strain curve:
wherein epsilon is strain, sigma is stress, E is elastic modulus, epsilon y For yielding strain, sigma y Is the yield stress, beta is the strain hardening exponent;
the tangential modulus of each segment of the ring is:
E t1 ，E t2 ，E t3 the tangent modulus of the intact pipeline is respectively the bottom layer defect position, the top layer defect position;
s3, obtaining the resultant moment M of the middle curved surface through balance analysis:
M＝M 0 +pR(w-w 0 ) (8)
wherein w is 0 And M 0 Is a small radial displacement and bending moment caused by a small initial displacement;
then, by combining equations (2) - (9) with the classical theory of Timoshenko, the critical buckling pressure p of the pipeline with irregular defects in the symmetrical and antisymmetric buckling modes is obtained b Is defined by the differential equation:
1) Symmetric buckling mode
2) Anti-symmetric buckling mode
S4, boundary conditions of the two buckling modes are respectively as follows:
1) Symmetric buckling mode
w 1 (0)＝w 0 .
2) Anti-symmetric buckling mode:
by solving the characteristic equations (10) - (12), the following solutions are obtained
Combining equations (16) - (18) with the boundary conditions for the symmetric buckling modes yields the following equation:
wherein:
I 11 ＝-sin(k 2 θ 1 )；
I 12 ＝0；
I 13 ＝cos(k 1 θ 1 )；
I 14 ＝-cos(k 2 θ 1 )；
I 21 ＝sin[k 2 θ 2 ]；
I 22 ＝-sec(k 3 π)cos[k 3 (π-θ 2 )]；
I 23 ＝0；
I 24 ＝cos[k 2 θ 2 ]；
I 31 ＝-k 2 cos(k 2 θ 1 )；
I 32 ＝0；I 33 ＝-k 1 sin(k 1 θ 1 )；
I 34 ＝k 2 sin(k 2 θ 1 )；
I 35 ＝0；I 36 ＝0；
I 41 ＝cos[k 2 θ 2 ]；
I 42 ＝-k 3 sec(k 3 π)sin[k 3 (π-θ 2 )]；
I 43 ＝0；I 44 ＝-k 2 sin[k 2 θ 2 ]；
I 45 ＝0；
I 46 ＝0；
I 61 ＝I 62 ＝0；
I 63 ＝1；
I 64 ＝0；
[I]is a matrix containing critical buckling pressures; a is that 12 、A 21 、A 22 、A 32 、w 0 And M 0 All non-zero parameters; thus, matrix [ I ]]The determinant value of (2) is zero; i.e.
|I|＝0 (20)
The critical buckling pressure of the irregular corrosion defect pipeline in the symmetrical buckling mode is obtained by solving an equation (20);
s5, for the anti-symmetrical buckling mode, obtaining by solving equations (13) - (15):
w 2 ＝C 21 sink 2 θ+C 22 cosk 2 θ,for θ 1 ≤θ≤θ 2 (22)
w 3 ＝C 31 sink 3 θ+C 32 cosk 3 θ,for θ 2 ≤θ≤π (23)
combining equations (21) - (23) with the boundary conditions for the anti-symmetric buckling mode yields the following equation:
wherein the elements in [ J ] are:
J 11 ＝sin(k 1 θ 1 )；
J 12 ＝-sin(k 2 θ 1 )；
J 13 ＝-cos9k 2 θ 1 )；
J 14 ＝0；
J 21 ＝0；
J 22 ＝sin[k 2 (θ 1 +θ 2 )]；
J 23 ＝cos[k 2 θ 2 ]；
J 24 ＝(cos[k 3 θ 2 ]-sin[k 3 (π-θ 2 )]/sink 3 π；
J 31 ＝k 1 cos(k 1 θ 1 )；
J 32 ＝-k 2 cos(k 2 θ 1 )；
J 33 ＝k 2 sin(k 2 θ 1 )；
J 34 ＝0；
J 41 ＝0；
J 42 ＝k 2 cos[k 2 θ 2 ]；
J 43 ＝-k 2 sin[k 2 θ 2 ]；
J 44 ＝-Sin[k 3 θ 2 ]+k 3 cos[k 3 (π+θ 2 )]/sink 3 π.
obviously, the determinant of [ J ] is also zero:
the critical buckling pressure of the irregular corrosion defective pipe in the anti-symmetric buckling mode is obtained by solving equation (25).
CN202310782697.1A 2023-06-29 2023-06-29 Method for calculating critical elastoplastic buckling pressure of steel pipeline containing irregular corrosion defects Pending CN116822294A (en)

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