Method for correcting plastic damage deformation of pipeline

Abstract

The invention belongs to the technical field of pipeline structure strength analysis and plastic energy absorption structure design, and particularly relates to a method for correcting plastic damage deformation of a pipeline. The invention provides a method for correcting plastic damage deformation of a pipeline, which comprises the following steps of: further dividing a partial region into a rigid section and a residual plastic region, and continuously correcting the size of the rigid section through comparison before and after curvature to obtain a force-displacement response curve; and finally, through a finite element verification method combining a J2 plastic deformation full-amount constitutive model considering a large deformation effect and a rigid region judgment step under a one-time unloading hypothesis, and a compilation method of a corresponding Abaqus user-defined subprogram UMAT, accurate calculation of a crushing global force-displacement response curve of the cross section of the pipeline on an upper flat plate and a lower flat plate can be realized, and the accuracy of the pipeline cross section is improved. And safety evaluation and damage evaluation of the pipeline structure are realized.

Description

A method for correcting plastic damage and deformation in pipelines Technical Field

[0001] This invention belongs to the field of pipeline structure strength analysis and plastic energy absorption structure design. Specifically, it proposes a rigid region continuous correction model and finite element verification method to solve the problem that the existing rigid-plastic model predicts a significantly smaller force value when the crushing displacement is large during the lateral crushing deformation of the pipeline cross section. This model can significantly improve the calculation accuracy of the crushing force-displacement response curve. Background Technology

[0002] During the process of plastic deformation and structural damage of a pipeline cross-section under lateral crushing, energy is dissipated through plastic deformation. The total amount of energy dissipation is approximately equal to the integral of the force value with respect to the crushing displacement during the crushing process. Obviously, the greater the total amount of energy dissipation, the stronger the pipeline's ability to resist crushing by external objects. Therefore, accurately determining the force-crushing displacement response curve during the crushing process is of great significance for correctly assessing the pipeline's ability to resist deformation damage. The existing patent "Method and Verification Method for Determining the Length of the Plastic Zone in the Crushing Process of an Elliptical Metal Ring" (CN119170172A) provides a calculation method for the force and displacement relationship of a circular or elliptical cross-section deformed under the crushing action of a pair of rigid plates, without considering the rigidification region, and in combination with a rigid-plastic pipe cross-section model. However, after comparing with the finite element analysis results (see Figures 10 and 11), it can be seen that when the crushing displacement is large, the calculation results given by the existing patent significantly underestimate the force value, and there is a large gap with the finite element calculation results of the benchmark conventional elastoplastic J2 flow incremental constitutive model. It cannot accurately obtain the force-displacement response curve in the global crushing process, which constitutes a technical limitation in related fields. Given the importance of accurate force-displacement response curves for pipeline safety assessment and design optimization, this invention proposes a continuous correction model for the stiffened region to address the problem of significantly underestimating the calculated force value when the crushing displacement is large. This model further divides a portion of the region into a stiffened region and a remaining plastic region, and continuously corrects the size of the stiffened region by comparing the curvature before and after correction to obtain the force-displacement response curve. Finally, since conventional elastoplastic finite element analysis, such as the built-in functions in Abaqus or Ansys software, generally only involves the conventional elastoplastic J2 flow incremental constitutive model, it cannot simultaneously compare, verify, and explain the differences between the force-displacement response curve obtained from the proposed continuous correction model and the force-displacement response curve calculated by the existing patent "Method and Verification Method for Determining the Length of the Plastic Region in the Crushing Process of an Elliptical Metal Ring." Therefore, this invention combines a finite element verification method that compares three models: the conventional elastoplastic J2 flow incremental constitutive model, the elastoplastic J2 deformation full-scale constitutive model without considering the stiffening assumption, and the elastoplastic J2 deformation full-scale constitutive model considering the stiffening assumption of single unloading. The invention also provides a method for compiling the corresponding Abaqus user-defined subroutine UMAT. The final results show that the method of the present invention can accurately calculate the global force-displacement response curve of the pipeline cross section under the crushing of the upper and lower flat plates, and has certain application value for pipeline structural safety assessment and damage evaluation. Summary of the Invention

[0003] The purpose of this invention is to overcome the shortcomings of the prior art and provide a method for correcting plastic damage and deformation in pipelines, which aims to solve the technical problems mentioned in the background art.

[0004] To achieve the above objectives, this invention provides a method for correcting plastic damage deformation in pipelines, specifically for circular or elliptical pipelines crushed between two parallel plates, where the major axis of the elliptical pipeline remains parallel to the crushing direction. The method includes a continuous correction model for the stiffened region and a finite element verification method. The continuous correction model for the stiffened region is shown in steps S1 and S2 below, and the finite element verification method is shown in step S3 below.

[0005] Step S1 divides the surface corresponding to the intermediate wall thickness into a top rigid elliptical region and a bottom plastic region. Set the rotation gain of the rigid elliptical region for each incremental step, conduct rigid-plastic model analysis without considering the rigid region, record the length of the plastic region at the end of each incremental step and determine whether it has reached the maximum value: if it has not reached the maximum value, iteratively repeat the above steps; if it has reached the maximum value, exit step S1 and proceed to step S2.

[0006] After performing the initialization step in step S2, assuming the size of the top rigid elliptical region remains unchanged, the remaining region is divided into a lower remaining plastic region and an upper rigidified region. Assuming that as the rotation angle of the elliptical region increases, the rigidified region increases, and the remaining plastic region shrinks, the remaining plastic region iterative calculation step, the step of determining the new rigidified region, and the region update step are executed sequentially until the rotation angle of the elliptical region increases. The process ends after exceeding the preset value.

[0007] Step S3: Conduct finite element verification. First, establish a finite element geometric model and set crushing boundary conditions. Then, use three different material elastoplastic constitutive models, including a conventional elastoplastic J2 flow incremental constitutive model, an elastoplastic J2 deformation full-scale constitutive model without considering the stiffening assumption, and an elastoplastic J2 deformation full-scale constitutive model considering the stiffening assumption of one unloading. Perform finite element calculations to obtain finite element force-displacement response curves, and compare them with the force-displacement response curves obtained by the continuous correction model in the stiffened region.

[0008] As a preferred approach, a rigid-plastic model analysis is performed without considering the rigidification region to solve for the crushing force with two unknown parameters. Total length of plastic region Boundary value problem: in the plastic region Inside, it satisfies the differential equation And it satisfies four boundary conditions , , , ,in, This represents the coordinates of the arc length of the plastic region on the thicker surface of the middle wall. Indicates the total arc length of the plastic region. Structural stiffness coefficient , This is the axial length of the pipe. The angle between the outer normal of the plastic region and the horizontal line. , They represent Arc length coordinates The first and second derivatives, This represents the angle between the normal vector at coordinate 's' on the intermediate wall thickness surface before crushing deformation and the horizontal line. , They represent about The first and second derivatives, Indicates the magnitude of the crushing force. Indicates wall thickness. Indicates the bending moment of the plastic hinge. , This represents the horizontal distance between the tangential contact point at the top of the crush and the boundary point of the plastic region, using the Ludwik plastic hardening relation. Indicates the material hardening index. Indicates the material hardening coefficient. Indicates the yield strength of the material. This indicates the angle of rotation within the elliptical region.

[0009] As a preferred approach, the boundary value problem is solved using the Newton-Raphson iterative method and the shooting method.

[0010] Preferably, the step of determining whether the plastic region length has reached its maximum value is to assume that the plastic region length corresponding to the default increment step number N=0 is 0; and then sequentially compare the lengths of the two regions. , , Total length of the plastic region obtained by incremental steps If the first Step Greater than the two steps before and after Then it is said that in the first The maximum plastic zone length was reached in one step.

[0011] Preferably, the method for iterative calculation steps in the remaining plastic region is to perform calculations in the remaining plastic region. Solving for unknown parameters Boundary value problem: And satisfy the boundary conditions and , ,in, , This indicates the size of the remaining plastic region in the current increment step. This represents the relative increase in the rotation angle of the elliptical region at each increment step. This indicates the horizontal distance between the tangential contact point at the top of the crush and the upper end of the remaining plastic region. Indicates the previous increment step The angle between the normal vector and the horizontal line.

[0012] As a preferred method, the method for determining the new stiffening region step and the region update step is to compare the distribution function of the absolute value of curvature in the plastic region of the current increment step and the previous increment step. Let the region where the absolute value of curvature decreases relatively be the new stiffening region. If there is no region where the absolute value of curvature decreases relatively, then the stiffening region remains unchanged. The new stiffening region and the original stiffening region are merged, the part of the remaining plastic region belonging to the new stiffening region is removed, and the next increment step calculation is carried out iteratively.

[0013] As a preferred method, the full-scale constitutive model of elastoplastic J2 deformation without considering the stiffening assumption is to use the constitutive relation under plane stress conditions: , , ,in, , Represents the normal strain component. Represents the shear strain components. , Represents the normal stress component. Represents the shear stress component. , It is von Mises stress The functions represent the modulus and Poisson's ratio after elastoplastic correction, respectively, which are determined by the uniaxial tensile curve of the material. Considering the large deformation effect of the crushing process, the strain tensor is selected as the logarithmic strain tensor, and the implementation is carried out using the ABAQUS subroutine UMAT.

[0014] Preferably, the subroutine UMAT is implemented based on the deformation gradient tensor of the current material point. Obtain the second-order logarithmic strain tensor ,in, This represents the natural logarithm operation of a second-order tensor. , Represents the deformation gradient tensor. Representing the tensor transpose operation; using a second-order tensor Positive definiteness, based on spectral decomposition Finally, the logarithmic strain tensor is obtained as ,in, , , For eigenvalues, , , It is a set of mutually orthogonal three-dimensional vectors. This represents the tensor product operation.

[0015] As a preferred method, the method for constructing a full-scale constitutive model of elastoplastic J2 deformation considering the assumption of one-time unloading stiffening is as follows: assuming that once the material undergoes one unloading, it remains linearly elastic in subsequent calculations. Calculations are first performed using a full-scale constitutive model of elastoplastic J2 deformation without considering the stiffening assumption, and the von Mises stress of each material point after convergence in each increment step is tracked and compared with the von Mises stress value after convergence in the previous increment step. If both conditions are met simultaneously—that the von Mises stress in the previous increment step is greater than the yield stress and that the von Mises stress in the current increment step is less than the von Mises stress in the previous increment step—then the material point is marked as an unloading stiffening point. In subsequent calculations, each unloading stiffening point is calculated using a linearly elastic incremental constitutive relation.

[0016] As a preferred method, the linear elastic incremental constitutive relation used for the unloading stiffening point is implemented using the UMAT subroutine of ABAQUS, and the following incremental constitutive relation is used in the UMAT subroutine:

[0017] ;

[0018] ;

[0019] ;

[0020] in, , , Indicates the increment of the stress component. , These are the elastic modulus and Poisson's ratio, respectively. , , The increments of the strain tensor components are determined by the DSTRAN array in the UMAT program.

[0021] Compared with the prior art, the beneficial effect of the pipe plastic damage deformation correction method provided by the present invention is: by setting the ratio of major axis to minor axis length... or The method of this invention is applicable to both circular and elliptical tubes, with a wide range of applications. The continuous correction model for the stiffened region proposed in this invention, compared with the finite element results corresponding to the benchmark conventional elastoplastic J2 flow incremental constitutive model, still maintains accurate crushing force-displacement response curves under large crushing displacements, solving the problem of insufficient force values ​​in existing rigid-plastic models that do not consider the stiffened region under large crushing displacements. The continuous correction model for the stiffened region proposed in this invention only involves solving ordinary differential boundary value problems, obtaining accurate force-displacement response curves without establishing a finite element model, avoiding complex steps such as mesh generation, and significantly improving the analysis efficiency of related problems. This invention proposes a systematic finite element method (FEA) to verify the superiority of the continuous correction model for the stiffened region compared to existing technologies, introducing a full-scale J2 plastic deformation constitutive model and a one-time unloading stiffening assumption, and providing an implementation method based on UMAT subroutines, making the continuous correction model for the stiffened region of this invention highly interpretable. Finally, the algorithm proposed in this invention is easily implemented using common commercial software such as Matlab and Abaqus, offering significant application convenience.

[0022] The features and advantages of the present invention will be described in detail through embodiments and in conjunction with the accompanying drawings. Attached Figure Description

[0023] Figure 1 is a schematic diagram of the cross-section of a pipe that is symmetrically compressed by a pair of parallel rigid planes above and below.

[0024] Figure 2 is a schematic diagram of the deformation mode of the 1 / 4 cross section of the rigid-plastic model without considering the rigidification region.

[0025] Figure 3 shows a schematic diagram of the deformation mode of the 1 / 4 cross section of the continuously modified model in the stiffened region.

[0026] Figure 4 shows the algorithm flowchart of the continuous correction model for the stiffened region.

[0027] Figure 5. Flowchart of the finite element verification method.

[0028] Figure 6 Length of the plastic zone The trend chart.

[0029] Figure 7 shows the deformation of the 1 / 4 section during the crushing process before the plastic region reaches its maximum size (first stage calculation).

[0030] Figure 8. Deformation diagram of 1 / 4 section as crushing deformation increases (second stage calculation).

[0031] Figure 9 shows the variation of the remaining plastic region length and the stiffened region length (calculated in the second stage).

[0032] Figure 10 Comparison of crushing force-displacement response curves obtained from different models and finite element analysis.

[0033] Figure 11 shows a magnified view of a portion of the area (the area within the box in Figure 10).

[0034] Figure 12 shows the finite element deformation results of the full-scale constitutive model {3} of the elastoplastic J2 deformation under the assumption of single-unloading stiffening. Detailed Implementation

[0035] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. However, it should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of the invention. Furthermore, descriptions of well-known structures and technologies are omitted in the following description to avoid unnecessarily obscuring the concept of the invention.

[0036] The algorithm flow of the rigid region continuous correction model proposed in this invention is shown in Figure 4; the flow of the related finite element verification method is shown in Figure 5. The rigid region continuous correction model in this invention mainly includes step 1, the first stage calculation under the assumption of no rigid region, and step 2, the second stage calculation considering the rigid region.

[0037] The steps of the pipeline plastic damage deformation correction method include: S1, dividing the middle wall thickness of the crushed pipeline into a top rigid elliptical region and a bottom plastic region, and conducting rigid-plastic model analysis under the assumption of no rigid region; setting a fixed rotation gain for each incremental step, recording the length of the plastic region at the end of each incremental step, until the length of the plastic region reaches its maximum value and then proceeding to the next step.

[0038] S2. Considering the continuous correction of the rigid region, while keeping the size of the elliptical rigid region unchanged, iteratively calculate the length of the plastic region with the maximum value in S1 and obtain the curvature; determine all new rigid regions through the curvature mentioned above; merge and correct the new rigid regions mentioned above, and update the new plastic region; end when the rotation angle of the elliptical region exceeds the preset value.

[0039] The specific implementation plan is as follows: The pipe is crushed between a pair of horizontally placed rigid plates (as shown in Figure 1). It is assumed that the pipe remains horizontally symmetrical during the crushing process, with the major axis of the elliptical pipe remaining vertical and the minor axis remaining horizontal. The crushing force applied to the plates is denoted as... The crush displacement is defined as half the decrease in distance between parallel plates during the crushing process. If the pipe is an elliptical pipe, set the outer semi-axis. and outer short half shaft Wall thickness The length of the horizontal minor axis corresponding to the thickness of the intermediate wall surface. Length of vertical semi-axis If the pipe is circular, let the outer diameter be... The wall thickness is ,but Determine the eccentricity of the ellipse. The ratio of the lengths of the major and minor axes The plastic hardening behavior of materials is determined by the Ludwik formula, i.e., uniaxial tensile stress ( - Plastic strain )curve ,in, Indicates the yield strength of the material. Indicates the hardening coefficient. This indicates the hardening index.

[0040] Step 1 (First stage calculation under the assumption of no rigidity region): Divide the surface corresponding to the intermediate wall thickness into a top rigid elliptical region (segment AC, rigid body region) and a bottom plastic region (segment CE), as shown in Figure 2. Set a fixed rotation gain for each incremental step. ,set up The number of the increment step ( ), and sequentially set the rotation angles of the rigid elliptical regions. ,...(Right now Perform the following rigid-plastic model analysis without considering the rigidification region, and record the length of the plastic region at the end of each increment step. And judge Has the maximum value been reached? If not, update the increment step number. Repeat the above steps. If the maximum value is reached, record the increment step number at this point. for After skipping step 1, the second stage calculation step 2, which considers continuous correction of the stiffened region, is carried out. The method for implementing the rigid-plastic analysis without considering the stiffened region is as shown in step 101. [The following is a separate, unrelated sentence:] Determine... The method for determining whether it is the maximum value is shown in step 102.

[0041] Step 101 (Stiff-plastic analysis method without considering the stiffened region) uses the target shooting method to solve for the following with two unknown parameters. , Boundary value problem: in the plastic region Inside, it satisfies the differential equation And it satisfies four boundary conditions , , , As shown in Figure 2, This represents the coordinates of the arc length of the plastic region on the thicker surface of the middle wall. This represents the total arc length of the unknown plastic region. , This is the axial length of the pipe. The angle between the outer normal of the plastic region and the horizontal line. express Arc length coordinates The first derivative, express Arc length coordinates The second derivative, This represents the elliptical ring (corresponding to the middle wall thickness) before crushing deformation in arc length coordinates. The original curvature at that point, This represents the original curvature of the elliptical ring at the arc length coordinate s before crushing deformation. right The derivative of , The horizontal distance between the tangent contact point B and the boundary point C of the plastic region can be represented by the corner. and the length of the plastic zone It is determined that, as a preferred approach, the target-shooting method combined with Newton-Raphson iteration is used to solve the boundary value problem.

[0042] Step 102 (Judgment) (Method to determine if it is the maximum value) By default, the plastic region length corresponding to N=0 is 0; compare the first... , , Incremental steps obtained If the first Step Greater than the two steps before and after Then it is called in The maximum plastic zone length was reached in one step.

[0043] Step 2 (Considering the second stage calculation of the rigid region): Referring to Figure 3, the size of the rigid elliptical region AC remains unchanged. After executing initialization step 201 once, steps 202, 203, and 204 are executed sequentially until the elliptical region reaches a turning point. The process ends after exceeding the preset value.

[0044] Step 201 (Initialization Step): Record the length of the plastic zone at the end of Step 1. Value The angle between the outer normal vector of the upper endpoint of the plastic region (point C in Figure 2, point D in Figure 3) and the horizontal line is... ,Right now Record the plastic region upper curvature function The absolute value is ; Arc length coordinates The corresponding remaining plastic region (see arc segment DE in Figure 3), and the stiffened region Initialize to an empty set (see arc segment CD in Figure 3), and denote the horizontal distance between the contact tangency point B and the lower endpoint D of the stiffened region (the upper endpoint of the remaining plastic region) as . ,Right now For the region Width of the horizontal projection; Set the incremental step number. The corner of the elliptical region .

[0045] Step 202 (for the remaining plastic region) (Conduct iterative calculations) ,in, In the remaining plastic region Solving for unknown parameters Boundary value problem: And satisfy the boundary conditions and , (1)

[0046] , (2)

[0047] in, The specific execution method is as follows:

[0048] (1) Introduction , Set initial conditions , The Runge-Kutta method is used to solve the system of ordinary differential equations:

[0049] ;

[0050] (3) Among them, , The unknown parameters are determined by the boundary conditions (1) and (2) using the Newton-Raphson iterative method; let the region after iteration convergence be... curvature function on The absolute value of a function .

[0051] Step 203 (Determine the new stiffening region) In the region Above, comparison and Determine if the conditions are met. The smallest , recorded as ,Right now , Denotes the infimum of a set; if all points within this region... All satisfy When the above set is an empty set, let be... ;remember For the region .

[0052] Step 204 (Update Parameters and Regions) merges the stiffened regions and corrects the update. Assuming that the rigidified region only exhibits rigid body motion and no deformation, the portion of the remaining plastic region belonging to the rigidified region is removed and updated to... , obtain area New endpoint D, and update ,in," " represents the union of sets, " "" indicates set difference operation; updates the normal angle of endpoint D of the plastic region. Update settings incremental steps Update the rotation angle of the elliptical region .

[0053] As a preferred method, the rotation angle is recorded in each incremental step. Downward Collapse Displacement and crushing force The corresponding curves of crushing force and crushing displacement are obtained, namely the crushing force-displacement response curve. If step 101 is only executed repeatedly until the end, this method corresponds to the prior art in the existing patent "Method and verification method for determining the length of the plastic zone in the crushing process of an elliptical metal ring" (CN119170172A) (denoted as model {4}); the continuous correction model of the stiffened region proposed in this invention (denoted as model {5}) includes the additional judgment of the maximum plastic zone length (step 102) and the continuous correction of the stiffened region (step 2).

[0054] Another objective of this invention is to propose a finite element verification method that can explain the difference between the continuous correction model for the stiffened region proposed in this invention (denoted as model {5}) and the existing rigid-plastic model that does not consider the stiffened region (denoted as model {4}): (1) First, establish a finite element geometric model and set crushing boundary conditions; (2) Then, use three different material constitutive models, including the conventional elastoplastic J2 flow incremental constitutive model (denoted as model {1}), the elastoplastic J2 deformation full-scale constitutive model without considering the stiffening assumption (denoted as model {2}), and the elastoplastic J2 deformation full-scale model considering the stiffening assumption of one-time unloading. The constitutive model (denoted as model {3}) was subjected to finite element calculations to obtain the finite element force-displacement response curves, which were then compared with the crushing force-displacement response curves of models {4} and {5}. Among them, a conventional elastoplastic J2 flow incremental constitutive model (model {1}) was added using the built-in function of the ABAQUS commercial finite element software, which will not be described in detail here. Model {2} was implemented by programming the ABAQUS material user subroutine UMAT. The specific implementation method is shown in the following steps [3]. Model {3} was implemented by programming the ABAQUS subroutine UMAT. The specific implementation method is shown in the following steps [4].

[0055] Step 3 (Implementation method of model {2} based on UMAT subroutine): The J2 plastic deformation full constitutive model under the assumption of 2D plane stress is determined by the following three formulas:

[0056] ; (4)

[0057] ; (5)

[0058] ; (6)

[0059] in, , Represents the normal strain component. Represents the shear strain components. , Represents the normal stress component. Represents the shear stress component. , It is von Mises stress The functions represent the modulus and Poisson's ratio after elastic-plastic correction, respectively, which are determined by the uniaxial tensile curve of the material. The specific method is as follows: step 301. As a preferred option, in order to consider the large deformation effect of the crushing process, the strain tensor is selected as the logarithmic strain tensor. The definition of the logarithmic strain tensor and the calculation method based on UMAT are shown in step 302. The stress tensor is determined by the strain tensor through equations (4), (5), and (6), and then the writing of the UMAT subroutine is completed.

[0060] Step 301 (Confirm) , (Method) Let the uniaxial tensile stress-strain curve of the material be... ,in, Indicates uniaxial stress. To represent uniaxial strain, then , ,in, The linear elastic modulus of the material. is the Poisson's ratio of the material's linear elasticity.

[0061] Step 302: The UMAT subroutine in the ABAQUS software provides the deformation gradient tensor at each material point. The second-order logarithmic strain tensor ,in, This represents the natural logarithm operation of a second-order tensor. , Represents the deformation gradient tensor. This represents the tensor transpose operation; preferably, it uses tensors. The positive definiteness of spectral decomposition ,in, , , For eigenvalues, , , Given a set of mutually orthogonal three-dimensional unit vectors, the logarithmic strain tensor is ultimately obtained as... .

[0062] Step 4 (Implementation method of model {3} based on UMAT subroutine) Assuming that the material remains linearly elastic in subsequent calculations after unloading, the calculation is carried out according to the method in Step 3, and the von Mises stress of each material point (i.e. the integration point of the finite element) after convergence in each increment step is tracked and compared with the von Mises stress value after convergence in the previous increment step. If two conditions are met at the same time (1) the von Mises stress of the previous increment step is greater than the yield stress and (2) the von Mises stress of the current increment step is less than the von Mises stress of the previous increment step, then the material point is marked as the unloading stiffening point. In subsequent calculations, each unloading stiffening point is calculated using a linearly elastic incremental constitutive relation. The specific UMAT subroutine execution method is shown in Step 401.

[0063] Step 401 (Implementation method of UMAT subroutine for unloading stiffened point constitutive relation) The following incremental constitutive relation is used in the UMAT subroutine:

[0064] ;

[0065] ;

[0066] ;

[0067] in, , , Indicates the increment of the stress component. , For elastic modulus and Poisson's ratio, , , The increments of the strain tensor components are determined by the DSTRAN array in the UMAT program.

[0068] The programming models {4} and {5} are implemented using Matlab, while the models {1}, {2}, and {3} are modeled and calculated using ABAQUS software combined with the UMAT subroutine method. Since the circular pipe is only... In special cases, the implementation process and effects of the present invention will be explained using a general elliptical pipe as an example.

[0069] The geometric parameters are as follows: length of the horizontal minor axis of the ellipse. The length of the vertical semi-axis is The wall thickness is Length of the horizontal external minor axis of the ellipse The vertical outer semi-major axis of the ellipse eccentricity , Pipe length The material parameters are as follows: hardening coefficient Hardening index Yield strength elastic modulus Poisson's ratio ; The crushing force is denoted as Reference crushing force ; .

[0070] Let the dimensionless crushing force be... ; Proceed to the first stage of calculation under the assumption of no rigid region in step 1. As shown in Figure 2, the cross-section is divided into a top rigid elliptical region (segment AC) and a bottom plastic region (segment CE), and the elliptical region rotation gain is set for each incremental step. Set the elliptical rotation angles sequentially. ,in, Number the increment steps; for each increment step, use a shooting method combining Newton-Raphson iteration to solve for the following problem with two unknown parameters. , Boundary value problem: in the plastic region Inside, it satisfies the differential equation And it satisfies four boundary conditions , , , , where angular coordinates Indicated , The analytical expression is determined by the following equations (7) and (8):

[0071] , (7) , (8)

[0072] , (9)

[0073] Arc length coordinates and angular coordinates Satisfying the relation And similarly, Where EllipticE represents the elliptic integral of the second kind (defined by the equation...). Sure); The horizontal distance between the tangent contact point B and the boundary point C of the plastic region is determined by the following formula:

[0074] ;

[0075] It should be noted that, due to the requirements of the Newton-Raphson iteration, the initial value of P must be set to be greater than and close to... .

[0076] Figure 6 shows the length of the plastic zone at different increment steps in the first stage of calculation. The change diagram shows how the elliptical region rotates. As the value increases, the length of the plastic region initially increases rapidly, then the rate of increase slows down, reaching its maximum value in the 131st increment step, thus ending the first stage of calculation; Figure 7 shows the dimensions of the plastic region in the first stage of calculation. The deformation diagram of the 1 / 4 section before reaching the maximum value (middle wall thickness surface), numbered 1, 2, 3, 4, 5, 6, 7 only represents the order of the deformation diagrams. Among them, the thin solid line represents the rigid elliptical region, while the thick solid line at the bottom represents the plastic region. It can be seen that when the crushing deformation is small, the plastic region is short. As the crushing deformation increases, the plastic region becomes longer. The result is consistent with that shown in Figure 6, which illustrates the rationality of the first stage calculation.

[0077] After incremental step 131, the plastic region has reached its maximum length, so step 1 is skipped, and step 2 is entered (considering the second stage calculation of the rigid region); as shown in Figure 3, the size of the rigid elliptical region AC remains unchanged in subsequent calculations. The plastic region is then assumed to split into a rigid region (region CD) and a remaining plastic region (region DE). Initialization step 201 is executed, and steps 202, 203, and 204 are executed sequentially until the elliptical region reaches a turning point. The process ends after exceeding a preset value. In this embodiment, when... Step 2 will exit at that time.

[0078] Figure 8 shows the deformation of the 1 / 4 section (middle wall thickness) as the crushing deformation increases during the second stage calculation; it should be noted that, since it is assumed that the rigid segment of the ellipse does not deform, at the corner... When the force is large, the entire cross-section may self-intersect vertically. During actual crushing, the area before the contact tangency point (i.e., segment AB in Figure 3) will deform into a horizontal segment, as shown in Figure 12. However, this only relates to the visualization of the deformation and does not affect the accuracy of the crushing force-displacement response curve discussed in this invention. In Figure 8, curve numbers 8, 9, 10, 11, 12, and 13 only indicate the sequence in the second stage. The rigid elliptical region is represented by a thin dashed line, the stiffened region by a thick solid line (region Z), and the remaining plastic region by a thin solid line (region Z). As shown in the figure, as the crushing displacement further increases, the stiffened region becomes significantly longer, while the remaining plastic region becomes significantly smaller.

[0079] Figure 9 shows the changes in the length of the remaining plastic region and the length of the stiffened region in the second stage of calculation (after increment step 131). Clearly, the length of the remaining plastic region increases with the increment step number. The length of the remaining plastic region decreases almost linearly with increasing increment step number; for example, the length of the remaining plastic region shrinks from its maximum value (close to 0.012 m) to 0.002 m at the end. Similarly, the length of the stiffened region decreases with increasing increment step number. The increase is almost linear (from 0 to close to 0.01m).

[0080] Figure 10 compares the force-displacement response curves obtained from five different calculation models during the crushing process: the conventional elastoplastic J2 flow incremental constitutive model (model {1}) based on ABAQUS (version 6.13); the elastoplastic J2 deformation full-scale constitutive model (implemented by the UMAT subroutine of ABAQUS, model {2}) proposed in this invention without considering the stiffening assumption; the elastoplastic J2 deformation full-scale constitutive model (implemented by the UMAT subroutine of ABAQUS, model {3}) proposed in this invention considering the stiffening assumption of one-time unloading; the rigid-plastic model (model {4}) algorithm (without considering the stiffening region) in the aforementioned patent "Method and Verification Method for Determining the Length of the Plastic Zone in the Crushing Process of an Elliptical Metal Ring"; and the rigid-plastic model algorithm (model {5}) proposed in this invention with the stiffening region continuous correction model algorithm. The results are analyzed as follows:

[0081] (1) When The dimensionless crush displacement calculated by all models ( ) - Dimensionless crushing force ( The curves all meet the requirements well;

[0082] (2) When When the value exceeds 1.3, the crushing displacement is large (see the boxed area in Figure 10, and Figure 11 shows a local magnified view of the boxed area). The crushing force predicted by the rigid-plastic model {4}, which does not consider the rigidified region, is significantly smaller than the force value corresponding to the reference finite element model {1}. The results of the continuous correction model {5} for the rigidified region proposed in this invention and the reference model {1} ​​are in good agreement, which shows that the model {5} proposed in this invention significantly improves the prediction accuracy of the force-displacement response curve and maintains high accuracy over a wider range.

[0083] (3) The prediction curves of the full-scale constitutive model {3} of elastic-plastic J2 deformation under the assumption of stiffening after one unloading proposed in this invention are in good agreement with the prediction curves of models {1} and {5}. The prediction results of the full-scale constitutive model {2} of elastic-plastic J2 deformation without the assumption of stiffening proposed in this aspect are in good agreement with the rigid-plastic model {4} without the stiffening region. Because after the material in model {3} undergoes one unloading, the linear elastic incremental constitutive equation is adopted, and the stiffness of the linear elastic material is much greater than the stiffness of the material in plastic deformation. Therefore, the material after one unloading in model {3} is approximately subject to stiffening effect, while the full-scale constitutive model {2} of elastic-plastic J2 deformation without the assumption of stiffening does not have a stiffening effect. This explains why the continuous correction model {5} of the stiffening region and the benchmark model {1} ​​are in good agreement, while the rigid-plastic model {4} without the stiffening region and the benchmark model {1} ​​are not in good agreement. The above comparison fully demonstrates the superiority and interpretability of the continuous correction model {5} of the stiffening region proposed in this invention.

[0084] (4) Figure 12 shows the finite element deformation results considering the model {3} proposed in this invention, where the dark area represents the area that has undergone one unloading; the finite element model is modeled with a 1 / 4 symmetrical section, and the crushing plane is the top rigid plane, which does not deform; initially, the rigid plane contacts the outer major semi-axis of the elliptical section (length is At the top, the length of the extrinsic semi-axis is... (See configuration) 1 ); as the rigid plane moves parallel downward (see configuration) 2 The top section exhibits a continuously increasing unloading zone (dark color), while the middle section shows an unloading stiffening zone. Material points in this zone are located on both the inner and outer walls, while no unloading stiffening occurs in the thicker middle wall area. As the rigid plane further crushes the cross-section, the horizontal section significantly increases in size. Simultaneously, the size of the middle unloading stiffening zone also significantly increases, leading to a significant reduction in the size of the remaining plastic region at the bottom (see configuration). 3 , 4 , 5 Therefore, the full-scale constitutive model of elastoplastic J2 deformation under the assumption of one-time unloading stiffening proposed in this invention {3} directly shows the existence of the intermediate stiffening region, further confirming the rationality of the continuous correction model {5} of the stiffening region proposed in this invention.

[0085] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions or improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for correcting plastic damage deformation in pipelines, characterized in that, For the process of a circular or elliptical pipe being crushed between two parallel plates, with the major axis of the elliptical pipe remaining parallel to the crushing direction, the continuous correction model for the stiffened region includes the following steps: S1, dividing the middle wall thickness of the crushed pipe into a top rigid elliptical region and a bottom plastic region, and conducting a rigid-plastic model analysis under the assumption of no stiffened region; setting a fixed rotation angle gain for each increment step, recording the length of the plastic region at the end of each increment step, until the length of the plastic region reaches its maximum value, and then proceeding to the next step; S2, considering the continuous correction of the stiffened region, keeping the size of the elliptical rigid region unchanged, iteratively calculating the final maximum plastic region length in S1 and obtaining the curvature distribution; determining the new stiffened region by comparing the curvature distribution in the previous and subsequent increment steps; merging and correcting the new stiffened regions mentioned above, and updating the new plastic region; ending when the rotation angle of the elliptical region exceeds a preset value.

2. The method for correcting plastic damage deformation in a pipeline as described in claim 1, characterized in that, A rigid-plastic model analysis was conducted without considering the rigidification region, and the crushing force was solved by a target-shooting method combining Newton-Raphson iteration. Total length of plastic region Boundary value problem with two unknown parameters: in the plastic region Within, it satisfies the second-order ordinary differential equation And it satisfies four boundary conditions ， ， ， ,in, This represents the coordinates of the arc length of the plastic region on the thicker surface of the middle wall. Indicates the total arc length of the plastic region. The structural stiffness coefficient, This is the axial length of the pipe. The angle between the outer normal of the plastic region and the horizontal line. They represent Arc length coordinates The first and second derivatives, This represents the angle between the normal vector at coordinate 's' on the intermediate wall thickness surface before crushing deformation and the horizontal line. 、 They represent The first and second derivatives of s Indicates wall thickness. ， This represents the horizontal distance between the tangential contact point at the top of the crush and the boundary point of the plastic region, using the Ludwik plastic hardening relation. Indicates the material hardening index. Indicates the material hardening coefficient. Indicates the yield strength of the material. This indicates the angle of rotation within the elliptical region.

3. The method for correcting plastic damage deformation in a pipeline as described in claim 2, characterized in that, Solving for unknown parameters using a shooting method combining Newton-Raphson iteration The boundary value problem defined by a second-order ordinary differential equation is used to determine the size of the remaining plastic region: And satisfy the boundary conditions and and in, ， This indicates the size of the remaining plastic region in the current increment step. This represents the relative increase in the rotation angle of the elliptical region at each increment step. This indicates the horizontal distance between the tangential contact point at the top of the crush and the upper end of the remaining plastic region. Indicates the previous increment step The angle between the normal vector and the horizontal line.

4. The method for correcting plastic damage deformation in a pipeline as described in claim 3, characterized in that, The method for determining the new stiffening region is to compare the distribution function of the absolute value of curvature in the plastic region of the current increment step with that of the previous increment step. Let the region where the absolute value of curvature decreases relatively be the new stiffening region. If there is no region where the absolute value of curvature decreases relatively, then the stiffening region remains unchanged. The new stiffening region and the original stiffening region are merged, the part of the remaining plastic region that belongs to the new stiffening region is removed, and the calculation of the next increment step is carried out iteratively.

5. The method for correcting plastic damage deformation in a pipeline as described in claim 4, characterized in that, It also includes finite element verification. The finite element verification method includes establishing a finite element geometric model, setting boundary conditions, and performing finite element calculations using a conventional elastoplastic J2 flow incremental constitutive model, an elastoplastic J2 deformation full constitutive model without considering the stiffening assumption, and an elastoplastic J2 deformation full constitutive model considering the stiffening assumption of one unloading. The finite element force-displacement response curves are obtained and compared with the force-displacement response curves obtained by the continuous correction model in the stiffening region.

6. The method for correcting plastic damage deformation in a pipeline as described in claim 5, characterized in that, The constitutive model of the full-scale elastoplastic J2 deformation without considering the stiffening assumption adopts the constitutive relation under plane stress conditions. Considering the large deformation effect of the crushing process, the strain tensor is selected as the logarithmic strain tensor and implemented by ABAQUS subroutine UMAT programming.

7. The method for correcting plastic damage deformation in a pipeline as described in claim 6, characterized in that, The subroutine UMAT is implemented to calculate the logarithmic strain tensor considering large deformation effects, based on the deformation gradient tensor of the current material point. Obtain the second-order logarithmic strain tensor Where ln denotes the natural logarithm operation of the second-order tensor. ， Represents the deformation gradient tensor. Representing the tensor transpose operation; using a second-order tensor Positive definiteness, based on spectral decomposition Finally, the logarithmic strain tensor is obtained as ,in, ， ， For eigenvalues, ， ， A set of mutually orthogonal three-dimensional vectors. This represents the tensor product operation.

8. The method for correcting plastic damage deformation in a pipeline as described in claim 7, characterized in that, In the full-scale constitutive model of elastoplastic J2 deformation under the assumption of single-unloading stiffening, it is assumed that the material remains linearly elastic in subsequent calculations after a single unloading. Calculations are first performed using the full-scale constitutive model of elastoplastic J2 deformation without considering stiffening, and the von Mises stress of each material point after convergence in each increment step is tracked and compared with the von Mises stress value after convergence in the previous increment step. If both conditions are met—that the von Mises stress in the previous increment step is greater than the yield stress and the von Mises stress in the current increment step is less than the von Mises stress in the previous increment step—then the material point is marked as an unloading stiffening point. In subsequent calculations, the linear elastic incremental constitutive relation used for the unloading stiffening point is implemented using the UMAT subroutine of ABAQUS, with strain imported from the DSTRAN array in the UMAT program.

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