A method for predicting bursting pressure of thin-walled steel pipe
Through thin-wall shell theory and iterative calculation model, the stress concentration effect is considered, and the blasting pressure when the blasting point of the steel pipe is approached is accurately predicted, which solves the problem that the prediction results of the traditional model are inconsistent with the test results, and improves the evaluation of the internal pressure resistance of the steel pipe accuracy.
Patent Information
- Application Number
- CN202011431394.8
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2020-12-10
- Publication Date
- 2024-12-13
- Estimated Expiration
- 2040-12-10
AI Technical Summary
When the blasting point of the steel pipe is close to the pipe joint, it is difficult for traditional mechanical models to accurately predict the blasting pressure. The reason is that the stress concentration effect caused by the joint affects the overall deformation state of the pipeline, resulting in a far difference between the prediction results and the test results.
Using a calculation model based on thin-wall shell theory, considering the inconsistency between the stiffness of the joint material and the stiffness of the pipe material, by determining the radial deformation equation of the pipe wall under the internal ballast load, the maximum radial deformation and circumferential stress are calculated to determine whether the resistance is achieved. Tensile strength, iteratively calculate until the pipeline is damaged.
This method takes into account the stress concentration effect, and the resulting blasting pressure value is closer to the test results, which improves the accuracy of evaluating the internal pressure resistance of steel pipes.
Smart Images
Figure CN112561147B_ABST
Abstract
Description
Technical Field
[0001] The invention relates to the technical field of thin-wall steel pipe bursting pressure prediction, and in particular to a method for predicting the bursting pressure of a thin-wall steel pipe when a bursting point is close to a joint. Background Art
[0002] Pipeline joints are one of the most important components of the entire pipeline network, but they are also one of the weakest links in the entire pipeline network system. At present, the research on pipeline joints in industry and academia mainly focuses on analyzing the mechanical properties of joints under external loads and improving the joint structure to meet specific working conditions. The internal pressure burst test of steel pipes shows that in most cases, the location of the burst point is located in the middle of the pipeline. In this case, the pipeline burst pressure solved by the traditional mechanical model is consistent with the test value. In other cases, the burst point is located near the joint. In this case, the pipeline burst pressure solved by the traditional mechanical model is far different from the test result. The reason is that the stress concentration effect caused by the joint affects the overall deformation state of the pipeline, and the radial deformation of the pipeline when it is compressed and expanded is discontinuous in the axial direction. Therefore, when the burst point is close to the joint, the prediction of the pipeline burst pressure needs to consider the stress concentration effect. Summary of the invention
[0003] The purpose of the invention is to provide a method for predicting the bursting pressure of a thin-walled steel pipe when the bursting point is close to a pipe joint.
[0004] In order to achieve the above object, the present invention is implemented by the following technical solutions:
[0005] The theoretical basis of the "traditional mechanics model" is the classical elastic-plastic mechanics theory. During the calculation process, it is assumed that the deformation of the pipeline is uniform when subjected to internal pressure load. In the steel pipe bursting test, when the bursting point is close to the middle of the pipeline, the pipeline bursting pressure calculated by this model is consistent with the test value.
[0006] The present invention proposes a method for predicting the bursting pressure of a thin-walled steel pipe when the bursting point is close to a pipe joint. The parameters that need to be determined before the prediction calculation include the geometric dimensions of the steel pipe (pipeline inner diameter, outer diameter, wall thickness), the distance between the bursting point and the joint, and the elastic modulus and tensile strength of the pipe. In the prediction calculation, it is assumed that the length of the pipe is infinite, that the deformation of the pipe wall at an infinite distance (far away from the joint position) under the internal pressure load is not constrained by the joint, and that the pipe joint is a rigid structure, and the deformation of the joint caused by the internal pressure is not considered. Based on the thin-walled shell theory, the difference between the stiffness of the joint material and the stiffness of the pipe material is taken into account in the calculation. When the pipe is subjected to the internal pressure load, the radial deformation of the pipe wall close to the joint is discontinuous along the axial direction.
[0007] Specifically, a method for predicting the bursting pressure of a thin-walled steel pipe considering the stress concentration effect comprises the following steps:
[0008] S1) According to the thin-wall shell theory, the radial deformation equation of the tube wall under internal pressure load is determined:
[0009] Where w is the radial deformation of the pipe wall, x is the axial distance from the point to the joint, k is a dimensionless value, and q (x) is the axially distributed pressure load on the pipe wall;
[0010] S2) Determine the point position with the maximum radial deformation
[0011] Taking the derivative of equation (1) and setting it equal to zero, we can obtain the x value at the maximum radial deformation:
[0012] d(u r ) / dx=dw / dx=-2βe -βx cosβx=0(2); where is a constant to be determined, E is the elastic modulus of the pipe, t is the pipe wall thickness, r is the average radius of the pipe, D is the bending stiffness of the pipe and
[0013] Available
[0014] S3) Determine the radial deformation of the pipe wall under internal pressure load:
[0015] Where p is the internal pressure, w is the 0 is the radial deformation of the tube wall at x=0, and v is the Poisson’s ratio of the tube;
[0016] S4) Obtain the maximum radial deformation of the pipeline
[0017] Substituting equation (3) into equation (4) we can get the maximum radial deformation u of the pipeline: r,max ;
[0018] S5) Obtain the maximum circumferential strain inside the pipe wall under internal pressure load:
[0019]
[0020] S6) Obtain the maximum hoop stress inside the pipe wall under internal pressure load:
[0021] σ θ =Eε θ (6);
[0022] S7) Whether the annular stress in the pipe wall reaches the tensile strength is used as the criterion for pipeline failure to determine σ θ Is it greater than the tensile strength of the pipe?
[0023] If σ θ <σ s, then continue to iterate, increase the pressure p by a certain step size (such as 0.1) to take p = 1.1, and repeat steps S1) to S7) until σ θ ≥σ s ; Among them, σ s is the tensile limit of the pipe;
[0024] If σ θ ≥σ s , the pipeline is considered broken and the iteration ends.
[0025] Compared with the prior art, the present invention has the following advantages:
[0026] The present invention provides a method for predicting the bursting pressure of a thin-walled steel pipe taking into account the stress concentration effect when the bursting point is close to the pipe joint. The method is applicable to the case where the bursting point is close to the joint in the internal pressure bursting test of a thin-walled steel pipe. Based on the thin-walled shell theory, the calculation model proposed by the present invention takes into account the discontinuity of deformation at various locations of the pipe when subjected to internal pressure loads caused by the inconsistency between the joint stiffness and the pipe stiffness. The pipe near the joint will produce stress concentration due to the discontinuity of radial deformation. By comparing the bursting pressure of the pipe calculated with the conventional elastic theory, the bursting pressure value obtained by this method is closer to the test result, which has important reference value for evaluating the internal pressure resistance of the steel pipe. BRIEF DESCRIPTION OF THE DRAWINGS
[0027] Figure 1 It is a schematic diagram of the radial deformation of the pipe wall near the joint obtained in the present invention.
[0028] Figure 2 It is a schematic diagram of the actual radial deformation of the tube wall of the steel tube after being subjected to internal pressure in the present invention. DETAILED DESCRIPTION
[0029] The embodiments of the present invention are described in further detail below in conjunction with the accompanying drawings.
[0030] A method for predicting bursting pressure of thin-walled steel pipes considering stress concentration effect comprises the following steps:
[0031] S1) According to the thin-wall shell theory, the radial deformation equation of the tube wall under internal pressure load is determined:
[0032] Where w is the radial deformation of the pipe wall, x is the axial distance from the point to the joint, k is a dimensionless value, and q (x) is the axially distributed pressure load on the pipe wall;
[0033] S2) Determine the point position with the maximum radial deformation
[0034] Taking the derivative of equation (1) and setting it equal to zero, we can obtain the x value at the maximum radial deformation:
[0035] d(ur ) / dx=dw / dx=-2βe -βx cosβx=0(2); where is a constant to be determined, E is the elastic modulus of the pipe, t is the pipe wall thickness, r is the average radius of the pipe, D is the bending stiffness of the pipe and
[0036] Available
[0037] S3) Determine the radial deformation of the pipe wall under internal pressure load:
[0038] Where p is the internal pressure, w is the 0 is the radial deformation of the tube wall at x=0, and v is the Poisson’s ratio of the tube;
[0039] S4) Obtain the maximum radial deformation of the pipeline
[0040] Substituting equation (3) into equation (4) we can get the maximum radial deformation u of the pipeline: r,max ;
[0041] S5) Obtain the maximum circumferential strain inside the pipe wall under internal pressure load:
[0042]
[0043] S6) Obtain the maximum hoop stress inside the pipe wall under internal pressure load:
[0044] σ θ =Eε θ (6);
[0045] S7) Whether the annular stress in the pipe wall reaches the tensile strength is used as the criterion for pipeline failure to determine σ θ Is it greater than the tensile strength of the pipe?
[0046] If σ θ <σ s , then continue to iterate, increase the pressure p by a certain step size (such as 0.1) to take p = 1.1, and repeat steps S1) to S7) until σ θ ≥σ s ; Among them, σ s is the tensile limit of the pipe;
[0047] If σ θ ≥σ s , the pipeline is considered broken and the iteration ends.
[0048] The above iterative process can be performed through MATLAB program.
[0049] like Figure 1As shown, a schematic diagram of the theoretical radial deformation of the pipe wall near the joint obtained based on the prediction model of the present invention. In the figure, x=0 represents the junction of the pipe and the joint. Since the rigid joint limits the radial deformation of the pipe wall, the radial deformation of the pipe here is y=0. The radial deformation of the pipe wall near the joint has a maximum value, which is the burst point obtained based on the prediction model of the present invention.
[0050] like Figure 2 As shown in FIG. 1 , it is a schematic diagram of the actual radial deformation of the pipe wall near the joint. The rigid joint constrains the radial deformation of the pipe wall. Affected by the stress concentration effect, the radial deformation of the pipe wall near the joint is approximately arc-shaped.
[0051] The above description is only a preferred embodiment of the present invention. It should be pointed out that ordinary technicians in this technical field can make several improvements and modifications without departing from the concept of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.
Claims
1. A method for predicting the bursting pressure of thin-walled steel pipes. Features The steps include: S1) According to the thin-wall shell theory, the radial deformation equation of the tube wall under internal pressure load is determined: Where w is the radial deformation of the pipe wall, x is the axial distance from the point to the joint, k is a dimensionless value, and q (x) is the axially distributed pressure load on the pipe wall; S2) Determine the point position with the maximum radial deformation Taking the derivative of equation (1) and setting it equal to zero, we can obtain the x value at the maximum radial deformation: in, is a constant to be determined, E is the elastic modulus of the pipe, t is the pipe wall thickness, r is the average radius of the pipe, D is the bending stiffness of the pipe and Available S3) Determine the radial deformation of the pipe wall under internal pressure load: Where p is the internal pressure, w is the 0 is the radial deformation of the tube wall at x=0, and v is the Poisson’s ratio of the tube; S4) Obtain the maximum radial deformation of the pipe wall Substituting equation (3) into equation (4) we can get the maximum radial deformation u of the pipeline: r,max ; S5) Obtain the maximum circumferential strain inside the pipe wall under internal pressure load: S6) Obtain the maximum hoop stress inside the pipe wall under internal pressure load: s θ =Ee θ (6); S7) Whether the annular stress in the pipe wall reaches the tensile strength is used as the criterion for pipeline failure to determine σ θ Is it greater than the tensile strength of the pipe? If σ θ <σ s , then continue to iterate, increase the pressure p with a certain step length, and repeat steps S1) to S7) until σ θ ≥σ s ; Among them, σ s is the tensile strength of the pipe; If σ θ ≥σ s , the pipeline is considered broken and the iteration ends.