Design method of dense-phase carbon dioxide pipeline composite material crack arrestor

Abstract

The invention discloses a design method of a dense-phase carbon dioxide pipeline composite material crack stopper, which comprises the following steps: S1, selecting a sample steel pipe, and determining a steady-state expansion crack tip opening angle CTOA of a crack in the steel pipe; s2, the crack arrest critical CTOAc of the steel pipe is determined; s3, establishing a finite element model: performing grid division on the pipeline by adopting five layers of entity units, wherein a cohesion unit is adopted as a crack propagation path; s4, establishing a pressure attenuation model; s5, loading pressure by a two-step method, and simulating the pressure behind the tip of the crack; s6, determining cohesion parameters, and taking the cohesion parameters as finite element model parameters; s7, determining a crack arrestor model, setting a crack arrestor criterion, and performing finite element calculation to output CTOAa; and S8, determining a crack arrest criterion of the crack arrestor, and completing the design of the crack arrestor. According to the design method of the composite material crack arrestor for the dense-phase carbon dioxide pipeline, the problem that the crack cannot be stopped in time after the dense-phase carbon dioxide pipeline with the small caliber of OD508 or below is cracked is solved.

Description

Technical Field

[0001] This invention belongs to the field of carbon dioxide pipeline fracture control technology, specifically relating to the design method of composite material crack arresters for dense phase carbon dioxide pipelines. Background Technology

[0003] Compared to natural gas, dense-phase carbon dioxide exhibits a long decompression plateau (saturation pressure), preventing pressure release at the crack tip and allowing for long-range crack propagation, potentially causing significant loss of life and property. Once a dense-phase carbon dioxide pipeline cracks, the high-pressure gas inside cannot be immediately vented. Instead, a decompression wave is generated on each side of the fracture point and propagates to distant locations. Because the gas decompression wave velocity is lower than the crack propagation velocity, the crack tip remains under continuous high stress, and the crack continues to propagate at a high speed, leading to long-range ductile crack propagation in the gas pipeline. Long-range crack propagation in dense-phase carbon dioxide pipelines can cause enormous disasters and losses; therefore, it is crucial to ensure timely crack arrest once a pipeline cracks. Existing full-scale burst test results indicate that for CO2 pipelines with high design coefficients, it is difficult to rely on their own toughness to arrest cracks. This has become a serious bottleneck problem threatening pipeline safety and restricting the application of carbon dioxide pipelines. Summary of the Invention

[0004] The purpose of this invention is to provide a design method for a crack arrestor made of composite materials for dense phase carbon dioxide pipelines, which solves the problem that dense phase carbon dioxide pipelines with small diameters of OD508 and below cannot stop cracking in a timely manner.

[0005] The technical solution adopted in this invention is a design method for a dense-phase carbon dioxide pipeline composite material crack arrester, comprising the following steps:

[0006] S1. Select a sample steel pipe and determine the crack tip opening angle CTOA in the steel pipe through the DWTT test;

[0007] S2. The critical crack arresting CTOAc of steel pipe was determined using the dual-sample method.

[0008] S3. Establish the finite element model: Use a general program to mesh the pipeline with five layers of solid elements, and use cohesive elements for the crack propagation path.

[0009] S4. Establish a pressure attenuation model during crack propagation;

[0010] S5. Apply pressure in two steps according to the pressure decay model to simulate the pressure behind the crack tip.

[0011] S6. When the calculated CTOA matches the experimentally determined CTOA, determine the cohesive force parameter and use the cohesive force parameter as the finite element model parameter.

[0012] S7. Determine the composite material crack arrester model, set the composite material crack arrester criteria, and perform finite element calculations to output CTOAa;

[0013] S8. Determine the crack arrest criteria for the crack arrester and complete the design of the composite material crack arrester.

[0014] The invention is further characterized by:

[0015] The specific process of S1 is as follows:

[0016] S1.1 Select a steel pipe and obtain the stress-strain curve of the steel pipe by testing a transverse round bar sample;

[0017] S1.2 Conduct DWTT experiments, collect the load-displacement and load-time curves of the hammer head, and perform high-speed photography;

[0018] S1.3 Determine the linear time intervals t1 and t2 of the steel pipe. Calculate the CTOA using the opening displacement 2mm after the crack tip during the time interval t1 to t2, based on high-speed imaging and the stress-strain curve of the steel pipe.

[0019] The specific process of S2 is as follows: the drop hammer test specimens are processed according to the GB / T 8363-2018 standard. Two specimens with a width of 76.2 mm and two specimens with a width of 43 mm are processed using a herringbone notch. The drop hammer tear test is carried out. The hammering energy is collected during the drop hammer tear test. The energy S required for plastic deformation per unit volume in the area around the fracture surface is determined according to formula (1). c The critical CTOA for crack arrest of steel pipe is calculated according to formulas (2) and (3). c ;

[0020]

[0021] σ a =0.72(σ y +σ u (3);

[0022] Where Et: hammer impact energy; A: ligament area; L: ligament length; Rc: energy per unit area, representing the energy required to form a new interface; Sc: energy required for plastic deformation per unit volume in the region surrounding the fracture surface; σ y : Yield strength of steel pipe; σ u : Tensile strength of steel pipe.

[0023] The specific process of S3 is as follows: ABAQUS software is used to model the pipe section with a length five times the pipe diameter in the axial direction. 8-node solid elements are used to model the pipe. Five layers of elements are used to model the entire pipe thickness. 8-node cohesive elements with an initial thickness of zero are used to model the cohesive zone. The cohesive elements have zero thickness and a circumferential length of 0.25 mm.

[0024] The specific process of S4 is as follows: a pressure attenuation model is established during crack propagation. In this model, the internal pressure is divided into the region in front of the moving crack tip and the region behind the crack tip. For the region in front of the moving crack tip, it is assumed that the pressure is equal to the crack tip pressure, that is, the attenuation from the total pressure to the steady-state crack tip pressure in front of the crack is ignored. The crack tip pressure is equal to the carbon dioxide saturation pressure. For the region behind the crack tip where the flap opening occurs, the pressure attenuation is expressed as an exponential function that varies along the circumference, as shown in formula (4):

[0025]

[0026] Wherein, when θ < 75°, C = 0.0082θ + 0.48; when θ ≥ 75°, C = 1; when θ < 80°, n = -2.6lnθ + 11; when θ ≥ 80°, n = 1.

[0027] The specific process of S5 is as follows:

[0028] The first step is to apply initial pressure in quasi-static mode using ABAQUS software without introducing cracks.

[0029] The second step involves introducing an initial crack and importing the pressurized and deformed pipe into the ABAQUS software using the Explicit solver module. Dynamic analysis is then performed to reduce the internal pressure to the steady-state crack tip pressure Ptip, and the pressure decay model in S4 is used to simulate the pressure behind the crack tip.

[0030] The specific process of S6 is as follows: After the pressure is applied in two steps, the cohesive element parameters are continuously adjusted to calculate the crack tip opening angle under the specified crack tip pressure. The CTOA is calculated using the opening displacement 2 mm behind the crack tip. The CTOA value is relatively high when the crack initially propagates, and then the CTOA value gradually decreases and stabilizes. The CTOA value after steady-state propagation is compared with the crack tip opening angle CTOA obtained from the experiment in S1 until the two are equal. The cohesive element parameters at this time are selected as the parameters of the finite element model.

[0031] The cohesive unit uses a bilinear traction force-separation curve to calculate the cohesive energy according to formula (5);

[0032]

[0033] Among them, G: cohesive energy; σ m : maximum traction force; δ c : critical separation amount; σ m = 2.8σ y ; σ y is the yield strength of the steel pipe; the initial slope of the cohesive force unit is 100 times the elastic modulus of the steel pipe, that is, K = 210×10 11 .

[0034] The specific process of S7 is as follows: The composite crack arrester adopts a hyperelastic material model based on the Marlow strain energy potential. The crack arrester and the pipeline adopt a surface-to-surface contact method. The first surface is selected as the outer surface of the pipeline, and the second surface is selected as the inner surface of the crack arrester. The tangential behavior is set to be frictionless, and the normal behavior is set to be hard contact; the failure behavior of a single fiber during the tensile process is simulated by using a hyperelastic material model based on the Marlow strain energy potential, and CTOAa is calculated and output through the finite element model.

[0035] The specific process of S8 is as follows: Compare CTOAa after the crack determined in S3 - S7 enters the crack arrester with the critical CTOAc of the steel pipe crack arrest determined in S2. When CTOAa < CTOAc, the crack arrester realizes crack arrest, and the design of the composite crack arrester is completed.

[0036] The beneficial effects of the present invention are:

[0037] The design method of the composite crack arrester for a dense-phase carbon dioxide pipeline provided by the present invention. The composite crack arrester designed by this method can realize the crack arrest function of a rapidly expanding crack through full-scale blasting test verification. Description of the Drawings

[0038] Figure 1 is the flow chart of the design method of the composite crack arrester for a dense-phase carbon dioxide pipeline of the present invention;

[0039] Figure 2 is the schematic diagram of the crack tip opening angle CTOA of the steady-state crack propagation in the steel pipe determined by experiments of the present invention;

[0040] Figure 3 is the schematic diagram of the determination of the specimen size of the double-specimen method of the present invention;

[0041] Figure 4 is the schematic diagram of the determination of Sc of the double-specimen method of the present invention;

[0042] Figure 5 is the schematic diagram of the finite element modeling of the present invention;

[0043] Figure 6 is the schematic diagram of the pressure decay model of the present invention;

[0044] Figure 7 This is a schematic diagram of the two-step crack tip pressure application method of the present invention;

[0045] Figure 8 This is a schematic diagram of the bilinear cohesive unit of the present invention;

[0046] Figure 9 This is a schematic diagram of the finite element calculation output CTOAa of the present invention. Detailed Implementation

[0047] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0048] Example 1

[0049] The dense-phase carbon dioxide pipeline composite material crack arrester design method proposed in this embodiment is as follows: Figure 1 As shown, it includes the following steps:

[0050] S1. Select a sample steel pipe and determine the crack tip opening angle CTOA in the steel pipe through the DWTT test;

[0051] S2. The critical crack arresting CTOAc of steel pipe was determined using the dual-sample method.

[0052] S3. Establish the finite element model: Use a general program to mesh the pipeline with five layers of solid elements, and use cohesive elements for the crack propagation path.

[0053] S4. Establish a pressure attenuation model during crack propagation;

[0054] S5. Apply pressure in two steps according to the pressure decay model to simulate the pressure behind the crack tip.

[0055] S6. When the calculated CTOA matches the experimentally determined CTOA, determine the cohesive force parameter and use the cohesive force parameter as the finite element model parameter.

[0056] S7. Determine the composite material crack arrester model, set the composite material crack arrester criteria, and perform finite element calculations to output CTOAa;

[0057] S8. Determine the crack arrest criteria for the crack arrester and complete the design of the composite material crack arrester.

[0058] Example 2

[0059] The dense-phase carbon dioxide pipeline composite material crack arrester design method proposed in this embodiment is as follows: Figure 1 As shown, it includes the following steps:

[0060] S1, such as Figure 2As shown, a sample steel pipe was selected, and the crack tip opening angle CTOA in the steady-state crack propagation in the steel pipe was determined by DWTT test;

[0061] The specific process is as follows:

[0062] S1.1 Select a steel pipe and obtain the stress-strain curve of the steel pipe by testing a transverse round bar sample;

[0063] S1.2 Conduct DWTT experiments, collect the load-displacement and load-time curves of the hammer head, and perform high-speed photography;

[0064] S1.3 Determine the linear time intervals t1 and t2 of the steel pipe. Calculate the CTOA using the opening displacement 2 mm after the crack tip during the time interval t1 to t2, based on high-speed imaging and the stress-strain curve of the steel pipe.

[0065] S2. The critical crack arresting CTOAc of steel pipe was determined using the dual-sample method.

[0066] S3. Establish the finite element model: Use a general program to mesh the pipeline with five layers of solid elements, and use cohesive elements for the crack propagation path.

[0067] S4. Establish a pressure attenuation model during crack propagation;

[0068] S5. Apply pressure in two steps according to the pressure decay model to simulate the pressure behind the crack tip.

[0069] S6. When the calculated CTOA matches the experimentally determined CTOA, determine the cohesive force parameter and use the cohesive force parameter as the finite element model parameter.

[0070] S7. Determine the composite material crack arrester model, set the composite material crack arrester criteria, and perform finite element calculations to output CTOAa;

[0071] S8. Determine the crack arrest criteria for the crack arrester and complete the design of the composite material crack arrester.

[0072] Example 3

[0073] The dense-phase carbon dioxide pipeline composite material crack arrester design method proposed in this embodiment is as follows: Figure 1 As shown, it includes the following steps:

[0074] S1, such as Figure 2 As shown, a sample steel pipe was selected, and the crack tip opening angle CTOA in the steady-state crack propagation in the steel pipe was determined by DWTT test;

[0075] The specific process is as follows:

[0076] S1.1 Select a steel pipe and obtain the stress-strain curve of the steel pipe by testing a transverse round bar sample;

[0077] S1.2 Conduct DWTT experiments, collect the load-displacement and load-time curves of the hammer head, and perform high-speed photography;

[0078] S1.3 Determine the linear time intervals t1 and t2 of the steel pipe. Calculate the CTOA using the opening displacement 2 mm after the crack tip during the time interval t1 to t2, based on high-speed imaging and the stress-strain curve of the steel pipe.

[0079] S2. The critical crack arresting CTOAc of steel pipe was determined using the dual-sample method.

[0080] The specific process is as follows: Figure 3 As shown, drop hammer test specimens were processed according to GB / T 8363-2018 standard, using herringbone notch specimens. Two specimens each with a width of 76.2 mm and 43 mm were processed, and drop hammer tear tests were conducted. The impact energy was collected during the drop hammer tear test. Figure 4 As shown, the energy S required for plastic deformation per unit volume in the region surrounding the fracture surface is determined according to formula (1). c The critical CTOA for crack arrest of steel pipe is calculated according to formulas (2) and (3). c ;

[0081]

[0082] σ a =0.72(σ y +σ u (3);

[0083] Where Et: hammer impact energy; A: ligament area; L: ligament length; Rc: energy per unit area, representing the energy required to form a new interface; Sc: energy required for plastic deformation per unit volume in the region surrounding the fracture surface; σ y : Yield strength of steel pipe; σ u : Tensile strength of steel pipe;

[0084] S3. Establish the finite element model: Use a general program to mesh the pipeline with five layers of solid elements, and use cohesive elements for the crack propagation path.

[0085] S4. Establish a pressure attenuation model during crack propagation;

[0086] S5. Apply pressure in two steps according to the pressure decay model to simulate the pressure behind the crack tip.

[0087] S6. When the calculated CTOA matches the experimentally determined CTOA, determine the cohesive force parameter and use the cohesive force parameter as the finite element model parameter.

[0088] S7. Determine the composite material crack arrester model, set the composite material crack arrester criteria, and perform finite element calculations to output CTOA. a ;

[0089] S8. Determine the crack arrest criteria for the crack arrester and complete the design of the composite material crack arrester.

[0090] Example 4

[0091] The dense-phase carbon dioxide pipeline composite material crack arrester design method proposed in this embodiment is as follows: Figure 1 As shown, it includes the following steps:

[0092] S1, such as Figure 2 As shown, a sample steel pipe was selected, and the crack tip opening angle CTOA in the steady-state crack propagation in the steel pipe was determined by DWTT test;

[0093] The specific process is as follows:

[0094] S1.1 Select a steel pipe and obtain the stress-strain curve of the steel pipe by testing a transverse round bar sample;

[0095] S1.2 Conduct DWTT experiments, collect the load-displacement and load-time curves of the hammer head, and perform high-speed photography;

[0096] S1.3 Determine the linear time intervals t1 and t2 of the steel pipe. Calculate the CTOA using the opening displacement 2 mm after the crack tip during the time interval t1 to t2, based on high-speed imaging and the stress-strain curve of the steel pipe.

[0097] S2. Determining the critical CTOA for crack arrest in steel pipes using the dual-sample method. c ;

[0098] The specific process is as follows: Figure 3 As shown, drop hammer test specimens were processed according to GB / T 8363-2018 standard, using herringbone notch specimens. Two specimens each with a width of 76.2 mm and 43 mm were processed, and drop hammer tear tests were conducted. The impact energy was collected during the drop hammer tear test. Figure 4 As shown, the energy S required for plastic deformation per unit volume in the region surrounding the fracture surface is determined according to formula (1). c The critical CTOA for crack arrest of steel pipe is calculated according to formulas (2) and (3). c ;

[0099]

[0100] σ a =0.72(σ y +σ u (3);

[0101] Where Et: hammer impact energy; A: ligament area; L: ligament length; Rc: energy per unit area, representing the energy required to form a new interface; Sc: energy required for plastic deformation per unit volume in the region surrounding the fracture surface; σ y : Yield strength of steel pipe; σ u : Tensile strength of steel pipe;

[0102] S3. Establish the finite element model: Use a general program to mesh the pipeline with five layers of solid elements, and use cohesive elements for the crack propagation path.

[0103] The specific process is as follows: The general-purpose program uses either ABAQUS or Explicit to perform three-dimensional dynamic elastoplastic finite element analysis, simulating ductile crack propagation, such as... Figure 5 As shown, the pipe section with a length five times the pipe diameter is modeled axially. The pipe is modeled using 8-node solid elements. Five layers of elements are used to model the entire pipe thickness. The cohesive region is modeled using 8-node cohesive elements with an initial thickness of zero. The cohesive elements have zero thickness and a circumferential length of 0.25 mm.

[0104] S4. Establish a pressure attenuation model during crack propagation;

[0105] S5. Apply pressure in two steps according to the pressure decay model to simulate the pressure behind the crack tip.

[0106] S6. When the calculated CTOA matches the experimentally determined CTOA, determine the cohesive force parameter and use the cohesive force parameter as the finite element model parameter.

[0107] S7. Determine the composite material crack arrester model, set the composite material crack arrester criteria, and perform finite element calculations to output CTOAa;

[0108] S8. Determine the crack arrest criteria for the crack arrester and complete the design of the composite material crack arrester.

[0109] Example 5

[0110] The dense-phase carbon dioxide pipeline composite material crack arrester design method proposed in this embodiment is as follows: Figure 1 As shown, it includes the following steps:

[0111] S1, such as Figure 2 As shown, a sample steel pipe was selected, and the crack tip opening angle CTOA in the steady-state crack propagation in the steel pipe was determined by DWTT test;

[0112] The specific process is as follows:

[0113] S1.1 Select a steel pipe and obtain the stress-strain curve of the steel pipe by testing a transverse round bar sample;

[0114] S1.2 Conduct DWTT experiments, collect the load-displacement and load-time curves of the hammer head, and perform high-speed photography;

[0115] S1.3 Determine the linear time intervals t1 and t2 of the steel pipe. Calculate the CTOA using the opening displacement 2 mm after the crack tip during the time interval t1 to t2, based on high-speed imaging and the stress-strain curve of the steel pipe.

[0116] S2. The critical crack arresting CTOAc of steel pipe was determined using the dual-sample method.

[0117] The specific process is as follows: Figure 3 As shown, drop hammer test specimens were processed according to GB / T 8363-2018 standard, using herringbone notch specimens. Two specimens each with a width of 76.2 mm and 43 mm were processed, and drop hammer tear tests were conducted. The impact energy was collected during the drop hammer tear test. Figure 4 As shown, the energy Sc required for plastic deformation per unit volume in the area surrounding the fracture surface is determined according to formula (1), and the critical CTOAc for crack arrest of the steel pipe is calculated according to formulas (2) and (3).

[0118]

[0119] σ a =0.72(σ y +σ u (3);

[0120] Where Et: hammer impact energy; A: ligament area; L: ligament length; Rc: energy per unit area, representing the energy required to form a new interface; Sc: energy required for plastic deformation per unit volume in the region surrounding the fracture surface; σ y : Yield strength of steel pipe; σ u : Tensile strength of steel pipe;

[0121] S3. Establish the finite element model: Use a general program to mesh the pipeline with five layers of solid elements, and use cohesive elements for the crack propagation path.

[0122] The specific process is as follows: Figure 5 As shown, ABAQUS software was used to model the pipe section with a length five times the pipe diameter in the axial direction. Eight-node solid elements were used to model the pipe. Five layers of elements were used to model the entire pipe thickness. Eight-node cohesive elements with an initial thickness of zero were used to model the cohesive region. The cohesive elements had zero thickness and a circumferential length of 0.25 mm.

[0123] S4. Establish a pressure attenuation model during crack propagation;

[0124] The specific process is as follows: Figure 6As shown, a pressure attenuation model is established during crack propagation. In this model, the internal pressure is divided into the region in front of the moving crack tip and the region behind the crack tip. For the region in front of the moving crack tip, it is assumed that the pressure is equal to the crack tip pressure, that is, the attenuation from the total pressure to the steady-state crack tip pressure in front of the crack is ignored. The crack tip pressure is equal to the carbon dioxide saturation pressure. For the region behind the crack tip where the flap opening occurs, the pressure attenuation is expressed as an exponential function that varies along the circumference, as shown in formula (4):

[0125]

[0126] Where, when θ < 75°, C = 0.0082θ + 0.48; when θ ≥ 75°, C = 1; when θ < 80°, n = -2.6lnθ + 11; when θ ≥ 80°, n = 1;

[0127] S5. Apply pressure in two steps according to the pressure decay model to simulate the pressure behind the crack tip.

[0128] S6. When the calculated CTOA matches the experimentally determined CTOA, determine the cohesive force parameter and use the cohesive force parameter as the finite element model parameter.

[0129] S7. Determine the composite material crack arrester model, set the composite material crack arrester criteria, and perform finite element calculations to output CTOAa;

[0130] S8. Determine the crack arrest criteria for the crack arrester and complete the design of the composite material crack arrester.

[0131] Example 6

[0132] The dense-phase carbon dioxide pipeline composite material crack arrester design method proposed in this embodiment is as follows: Figure 1 As shown, it includes the following steps:

[0133] S1, such as Figure 2 As shown, a sample steel pipe was selected, and the crack tip opening angle CTOA in the steady-state crack propagation in the steel pipe was determined by DWTT test;

[0134] The specific process is as follows:

[0135] S1.1 Select a steel pipe and obtain the stress-strain curve of the steel pipe by testing a transverse round bar sample;

[0136] S1.2 Conduct DWTT experiments, collect the load-displacement and load-time curves of the hammer head, and perform high-speed photography;

[0137] S1.3 Determine the linear time intervals t1 and t2 of the steel pipe. Calculate the CTOA using the opening displacement 2 mm after the crack tip during the time interval t1 to t2, based on high-speed imaging and the stress-strain curve of the steel pipe.

[0138] S2. The critical crack arresting CTOAc of steel pipe was determined using the dual-sample method.

[0139] The specific process is as follows: Figure 3 As shown, drop hammer test specimens were processed according to GB / T 8363-2018 standard, using herringbone notch specimens. Two specimens each with a width of 76.2 mm and 43 mm were processed, and drop hammer tear tests were conducted. The impact energy was collected during the drop hammer tear test. Figure 4 As shown, the energy Sc required for plastic deformation per unit volume in the area surrounding the fracture surface is determined according to formula (1), and the critical CTOAc for crack arrest of the steel pipe is calculated according to formulas (2) and (3).

[0140]

[0141]

[0142] σ a =0.72(σ y +σ u (3);

[0143] Where Et: hammer impact energy; A: ligament area; L: ligament length; Rc: energy per unit area, representing the energy required to form a new interface; Sc: energy required for plastic deformation per unit volume in the region surrounding the fracture surface; σ y : Yield strength of steel pipe; σ u : Tensile strength of steel pipe;

[0144] S3. Establish the finite element model: Use a general program to mesh the pipeline with five layers of solid elements, and use cohesive elements for the crack propagation path.

[0145] The specific process is as follows: Figure 5 As shown, ABAQUS software was used to model the pipe section with a length five times the pipe diameter in the axial direction. Eight-node solid elements were used to model the pipe. Five layers of elements were used to model the entire pipe thickness. Eight-node cohesive elements with an initial thickness of zero were used to model the cohesive region. The cohesive elements had zero thickness and a circumferential length of 0.25 mm.

[0146] S4. Establish a pressure attenuation model during crack propagation;

[0147] The specific process is as follows: Figure 6As shown, a pressure attenuation model is established during crack propagation. In this model, the internal pressure is divided into the region in front of the moving crack tip and the region behind the crack tip. For the region in front of the moving crack tip, it is assumed that the pressure is equal to the crack tip pressure, that is, the attenuation from the total pressure to the steady-state crack tip pressure in front of the crack is ignored. The crack tip pressure is equal to the carbon dioxide saturation pressure. For the region behind the crack tip where the flap opening occurs, the pressure attenuation is expressed as an exponential function that varies along the circumference, as shown in formula (4):

[0148]

[0149] Where, when θ < 75°, C = 0.0082θ + 0.48; when θ ≥ 75°, C = 1; when θ < 80°, n = -2.6lnθ + 11; when θ ≥ 80°, n = 1;

[0150] S5. Apply pressure in two steps according to the pressure decay model to simulate the pressure behind the crack tip, such as... Figure 7 As shown,;

[0151] The specific process is as follows:

[0152] The first step is to apply initial pressure in quasi-static mode using ABAQUS software without introducing cracks.

[0153] The second step involves introducing an initial crack and importing the pressurized and deformed pipe into the ABAQUS software's Explicit solver module for dynamic analysis. The internal pressure is reduced to the steady-state crack tip pressure Ptip, and the pressure decay model in S4 is used to simulate the pressure behind the crack tip.

[0154] S6. When the calculated CTOA matches the experimentally determined CTOA, determine the cohesive force parameter and use the cohesive force parameter as the finite element model parameter.

[0155] The specific process is as follows: After the two-step loading pressure is completed, the cohesive element parameters are continuously adjusted, the crack tip opening angle under the specified crack tip pressure is calculated, and the CTOA is calculated using the opening displacement 2mm behind the crack tip. The CTOA value is relatively high when the crack initially propagates, and then the CTOA value gradually decreases and stabilizes. The CTOA value after steady-state propagation is compared with the crack tip opening angle CTOA obtained from the experiment in S1 until the two are equal. The cohesive element parameters at this time are selected as the finite element model parameters.

[0156] like Figure 8 As shown, the cohesive unit adopts a bilinear traction force-separation curve, and the cohesive energy is calculated according to formula (5);

[0157]

[0158] Where G: cohesive energy; σ m : Maximum traction force; δ c : Critical separation quantity; σ m =2.8σ y ;σ y The yield strength of the steel pipe is given by K; the initial slope of the cohesive element is 100 times the elastic modulus of the steel pipe, i.e., K = 210 × 10⁻⁶. 11 ;

[0159] S7. Determine the composite material crack arrester model, set the composite material crack arrester criteria, and perform finite element calculations to output CTOAa;

[0160] S8. Determine the crack arrest criteria for the crack arrester and complete the design of the composite material crack arrester.

[0161] Example 7

[0162] The dense-phase carbon dioxide pipeline composite material crack arrester design method proposed in this embodiment is as follows: Figure 1 As shown, it includes the following steps:

[0163] S1, such as Figure 2 As shown, a sample steel pipe was selected, and the crack tip opening angle CTOA in the steady-state crack propagation in the steel pipe was determined by DWTT test;

[0164] The specific process is as follows:

[0165] S1.1 Select a steel pipe and obtain the stress-strain curve of the steel pipe by testing a transverse round bar sample;

[0166] S1.2 Conduct DWTT experiments, collect the load-displacement and load-time curves of the hammer head, and perform high-speed photography;

[0167] S1.3 Determine the linear time intervals t1 and t2 of the steel pipe. Calculate the CTOA using the opening displacement 2 mm after the crack tip during the time interval t1 to t2, based on high-speed imaging and the stress-strain curve of the steel pipe.

[0168] S2. The critical crack arresting CTOAc of steel pipe was determined using the dual-sample method.

[0169] The specific process is as follows: Figure 3 As shown, drop hammer test specimens were processed according to GB / T 8363-2018 standard, using herringbone notch specimens. Two specimens each with a width of 76.2 mm and 43 mm were processed, and drop hammer tear tests were conducted. The impact energy was collected during the drop hammer tear test. Figure 4 As shown, the energy S required for plastic deformation per unit volume in the region surrounding the fracture surface is determined according to formula (1). c The critical CTOA for crack arrest of steel pipe is calculated according to formulas (2) and (3).c ;

[0170]

[0171] σ a =0.72(σ y +σ u (3);

[0172] Where Et: hammer impact energy; A: ligament area; L: ligament length; Rc: energy per unit area, representing the energy required to form a new interface; Sc: energy required for plastic deformation per unit volume in the region surrounding the fracture surface; σ y : Yield strength of steel pipe; σ u : Tensile strength of steel pipe;

[0173] S3. Establish the finite element model: Use a general program to mesh the pipeline with five layers of solid elements, and use cohesive elements for the crack propagation path.

[0174] The specific process is as follows: Figure 5 As shown, ABAQUS software was used to model the pipe section with a length five times the pipe diameter in the axial direction. Eight-node solid elements were used to model the pipe. Five layers of elements were used to model the entire pipe thickness. Eight-node cohesive elements with an initial thickness of zero were used to model the cohesive region. The cohesive elements had zero thickness and a circumferential length of 0.25 mm.

[0175] S4. Establish a pressure attenuation model during crack propagation;

[0176] The specific process is as follows: Figure 6 As shown, a pressure attenuation model is established during crack propagation. In this model, the internal pressure is divided into the region in front of the moving crack tip and the region behind the crack tip. For the region in front of the moving crack tip, it is assumed that the pressure is equal to the crack tip pressure, that is, the attenuation from the total pressure to the steady-state crack tip pressure in front of the crack is ignored. The crack tip pressure is equal to the carbon dioxide saturation pressure. For the region behind the crack tip where the flap opening occurs, the pressure attenuation is expressed as an exponential function that varies along the circumference, as shown in formula (4):

[0177]

[0178] Where, when θ < 75°, C = 0.0082θ + 0.48; when θ ≥ 75°, C = 1; when θ < 80°, n = -2.6lnθ + 11; when θ ≥ 80°, n = 1;

[0179] S5. Apply pressure in two steps according to the pressure decay model to simulate the pressure behind the crack tip, such as... Figure 7 As shown,;

[0180] The specific process is as follows:

[0181] The first step is to apply initial pressure in quasi-static mode using ABAQUS software without introducing cracks.

[0182] The second step involves introducing an initial crack and importing the pressurized and deformed pipe into the ABAQUS software's Explicit solver module for dynamic analysis. The internal pressure is reduced to the steady-state crack tip pressure Ptip, and the pressure decay model in S4 is used to simulate the pressure behind the crack tip.

[0183] S6. When the calculated CTOA matches the experimentally determined CTOA, determine the cohesive force parameter and use the cohesive force parameter as the finite element model parameter.

[0184] The specific process is as follows: After the two-step loading pressure is completed, the cohesive element parameters are continuously adjusted, the crack tip opening angle under the specified crack tip pressure is calculated, and the CTOA is calculated using the opening displacement 2mm behind the crack tip. The CTOA value is relatively high when the crack initially propagates, and then the CTOA value gradually decreases and stabilizes. The CTOA value after steady-state propagation is compared with the crack tip opening angle CTOA obtained from the experiment in S1 until the two are equal. The cohesive element parameters at this time are selected as the finite element model parameters.

[0185] like Figure 8 As shown, the cohesive unit adopts a bilinear traction force-separation curve, and the cohesive energy is calculated according to formula (5);

[0186]

[0187] Where G: cohesive energy; σ m : Maximum traction force; δ c : Critical separation quantity; σ m =2.8σ y ;σ y The yield strength of the steel pipe is given by K; the initial slope of the cohesive element is 100 times the elastic modulus of the steel pipe, i.e., K = 210 × 10⁻⁶. 11 ;

[0188] S7. Determine the composite material crack arrester model, set the composite material crack arrester criteria, and perform finite element calculations to output CTOAa;

[0189] The specific process is as follows: Figure 9As shown, the composite material crack arrester adopts a hyperelastic material model based on Marlow strain potential. The crack arrester and the pipeline adopt a surface-to-surface contact method. The first surface is selected as the outer surface of the pipeline, and the second surface is selected as the inner surface of the crack arrester. The tangential behavior is set to frictionless, and the normal behavior is set to hard contact. The failure behavior of a single fiber during the tensile process is simulated by a hyperelastic material model based on Marlow strain potential, and the CTOAa is calculated and output through the finite element model.

[0190] S8. Determine the crack arrest criteria for the crack arrester and complete the design of the composite material crack arrester.

[0191] Example 8

[0192] The dense-phase carbon dioxide pipeline composite material crack arrester design method proposed in this embodiment is as follows: Figure 1 As shown, it includes the following steps:

[0193] S1, such as Figure 2 As shown, a sample steel pipe was selected, and the crack tip opening angle CTOA in the steady-state crack propagation in the steel pipe was determined by DWTT test;

[0194] The specific process is as follows:

[0195] S1.1 Select a steel pipe and obtain the stress-strain curve of the steel pipe by testing a transverse round bar sample;

[0196] S1.2 Conduct DWTT experiments, collect the load-displacement and load-time curves of the hammer head, and perform high-speed photography;

[0197] S1.3 Determine the linear time intervals t1 and t2 of the steel pipe. Calculate the CTOA using the opening displacement 2 mm after the crack tip during the time interval t1 to t2, based on high-speed imaging and the stress-strain curve of the steel pipe.

[0198] S2. Determining the critical CTOA for crack arrest in steel pipes using the dual-sample method. c ;

[0199] The specific process is as follows: Figure 3 As shown, drop hammer test specimens were processed according to GB / T 8363-2018 standard, using herringbone notch specimens. Two specimens each with a width of 76.2 mm and 43 mm were processed, and drop hammer tear tests were conducted. The impact energy was collected during the drop hammer tear test. Figure 4 As shown, the energy S required for plastic deformation per unit volume in the region surrounding the fracture surface is determined according to formula (1). c The critical CTOA for crack arrest of steel pipe is calculated according to formulas (2) and (3). c ;

[0200]

[0201] σ a =0.72(σ y +σ u (3);

[0202] Where Et: hammer impact energy; A: ligament area; L: ligament length; Rc: energy per unit area, representing the energy required to form a new interface; Sc: energy required for plastic deformation per unit volume in the region surrounding the fracture surface; σ y : Yield strength of steel pipe; σ u : Tensile strength of steel pipe;

[0203] S3. Establish the finite element model: Use a general program to mesh the pipeline with five layers of solid elements, and use cohesive elements for the crack propagation path.

[0204] The specific process is as follows: Figure 5 As shown, ABAQUS software was used to model the pipe section with a length five times the pipe diameter in the axial direction. Eight-node solid elements were used to model the pipe. Five layers of elements were used to model the entire pipe thickness. Eight-node cohesive elements with an initial thickness of zero were used to model the cohesive region. The cohesive elements had zero thickness and a circumferential length of 0.25 mm.

[0205] S4. Establish a pressure attenuation model during crack propagation;

[0206] The specific process is as follows: Figure 6 As shown, a pressure attenuation model is established during crack propagation. In this model, the internal pressure is divided into the region in front of the moving crack tip and the region behind the crack tip. For the region in front of the moving crack tip, it is assumed that the pressure is equal to the crack tip pressure, that is, the attenuation from the total pressure to the steady-state crack tip pressure in front of the crack is ignored. The crack tip pressure is equal to the carbon dioxide saturation pressure. For the region behind the crack tip where the flap opening occurs, the pressure attenuation is expressed as an exponential function that varies along the circumference, as shown in formula (4):

[0207]

[0208] Where, when θ < 75°, C = 0.0082θ + 0.48; when θ ≥ 75°, C = 1; when θ < 80°, n = -2.6lnθ + 11; when θ ≥ 80°, n = 1;

[0209] S5. Apply pressure in two steps according to the pressure decay model to simulate the pressure behind the crack tip, such as... Figure 7 As shown,;

[0210] The specific process is as follows:

[0211] The first step is to apply initial pressure in quasi-static mode using ABAQUS software without introducing cracks.

[0212] The second step involves introducing an initial crack and importing the pressurized and deformed pipe into the ABAQUS software's Explicit solver module for dynamic analysis. The internal pressure is reduced to the steady-state crack tip pressure Ptip, and the pressure decay model in S4 is used to simulate the pressure behind the crack tip.

[0213] S6. When the calculated CTOA matches the experimentally determined CTOA, determine the cohesive force parameter and use the cohesive force parameter as the finite element model parameter.

[0214] The specific process is as follows: After the two-step loading pressure is completed, the cohesive element parameters are continuously adjusted, the crack tip opening angle under the specified crack tip pressure is calculated, and the CTOA is calculated using the opening displacement 2mm behind the crack tip. The CTOA value is relatively high when the crack initially propagates, and then the CTOA value gradually decreases and stabilizes. The CTOA value after steady-state propagation is compared with the crack tip opening angle CTOA obtained from the experiment in S1 until the two are equal. The cohesive element parameters at this time are selected as the finite element model parameters.

[0215] like Figure 8 As shown, the cohesive unit adopts a bilinear traction force-separation curve, and the cohesive energy is calculated according to formula (5);

[0216]

[0217] Where G: cohesive energy; σ m : Maximum traction force; δ c : Critical separation quantity; σ m =2.8σ y ;σ y The yield strength of the steel pipe is given by K; the initial slope of the cohesive element is 100 times the elastic modulus of the steel pipe, i.e., K = 210 × 10⁻⁶. 11 ;

[0218] S7. Determine the composite material crack arrester model, set the composite material crack arrester criteria, and perform finite element calculations to output CTOAa;

[0219] The specific process is as follows: Figure 9 As shown, the composite material crack arrester adopts a hyperelastic material model based on Marlow strain potential. The crack arrester and the pipeline adopt a surface-to-surface contact method. The first surface is selected as the outer surface of the pipeline, and the second surface is selected as the inner surface of the crack arrester. The tangential behavior is set to frictionless, and the normal behavior is set to hard contact. The failure behavior of a single fiber during the tensile process is simulated by a hyperelastic material model based on Marlow strain potential, and the CTOAa is calculated and output through the finite element model.

[0220] S8. Determine the crack arrest criteria for the crack arrester and complete the design of the composite material crack arrester;

[0221] The specific process is as follows: The CTOAa after the crack enters the crack arrester, as determined by S3-S7, is compared with the critical crack arrest value CTOAc of the steel pipe, as determined by S2. When CTOAa...

Claims

1. A design method for a crack arrester made of composite materials for dense-phase carbon dioxide pipelines, characterized in that, Includes the following steps: S1. Select a sample steel pipe and determine the crack tip opening angle CTOA in the steel pipe through the DWTT test; S2. The critical crack arresting CTOAc of steel pipe was determined using the dual-sample method. S3. Establish the finite element model: Use a general program to mesh the pipeline with five layers of solid elements, and use cohesive elements for the crack propagation path. S4. Establish a pressure attenuation model during crack propagation; S5. Apply pressure in two steps according to the pressure decay model to simulate the pressure behind the crack tip. S6. When the calculated CTOA matches the experimentally determined CTOA, determine the cohesive force parameter and use the cohesive force parameter as the finite element model parameter. S7. Determine the composite material crack arrester model, set the composite material crack arrester criteria, and perform finite element calculations to output CTOAa; S8. Determine the crack arrest criteria for the crack arrester and complete the design of the composite material crack arrester.

2. The design method for a dense-phase carbon dioxide pipeline composite material crack arrester according to claim 1, characterized in that, The specific process of S1 is as follows: S1.1 Select a steel pipe and obtain the stress-strain curve of the steel pipe by testing a transverse round bar sample; S1.2 Conduct DWTT experiments, collect the load-displacement and load-time curves of the hammer head, and perform high-speed photography; S1.3 Determine the linear time intervals t1 and t2 of the steel pipe. Calculate the CTOA using the opening displacement 2mm after the crack tip during the time interval t1 to t2, based on high-speed imaging and the stress-strain curve of the steel pipe.

3. The design method for a dense-phase carbon dioxide pipeline composite material crack arrester according to claim 1, characterized in that, The specific process of S2 is as follows: Drop hammer test specimens are processed according to GB / T 8363-2018 standard. Two specimens with a chevron notch and two with a width of 76.2 mm and two with a width of 43 mm are processed respectively. A drop hammer tearing test is then conducted. During the drop hammer tearing test, the hammering energy is collected, and the energy S required for plastic deformation per unit volume in the area surrounding the fracture surface is determined according to formula (1). c The critical CTOA for crack arrest of steel pipe is calculated according to formulas (2) and (3). c ; s a =0.72(σ y +s u ) (3); Where Et: hammer impact energy; A: ligament area; L: ligament length; Rc: energy per unit area, representing the energy required to form a new interface; Sc: energy required for plastic deformation per unit volume in the region surrounding the fracture surface; σ y : Yield strength of steel pipe; σ u : Tensile strength of steel pipe.

4. The design method for a dense-phase carbon dioxide pipeline composite material crack arrester according to claim 1, characterized in that, The specific process of S3 is as follows: ABAQUS software is used to model the pipe section with a length five times the pipe diameter in the axial direction. 8-node solid elements are used to model the pipe. Five layers of elements are used to model the entire pipe thickness. 8-node cohesive elements with an initial thickness of zero are used to model the cohesive zone. The cohesive elements have zero thickness and a circumferential length of 0.25 mm.

5. The design method for a dense-phase carbon dioxide pipeline composite material crack arrester according to claim 1, characterized in that, The specific process of S4 is as follows: a pressure attenuation model is established during crack propagation. In this model, the internal pressure is divided into the region in front of the moving crack tip and the region behind the crack tip. For the region in front of the moving crack tip, it is assumed that the pressure is equal to the crack tip pressure, that is, the attenuation from the total pressure to the steady-state crack tip pressure in front of the crack is ignored. The crack tip pressure is equal to the carbon dioxide saturation pressure. For the region behind the crack tip where the flap opening occurs, the pressure attenuation is expressed as an exponential function that varies along the circumference, as shown in formula (4): Wherein, when θ < 75°, C = 0.0082θ + 0.48; when θ ≥ 75°, C = 1; when θ < 80°, n = -2.6lnθ + 11; when θ ≥ 80°, n = 1.

6. The design method for a dense-phase carbon dioxide pipeline composite material crack arrester according to claim 1, characterized in that, The specific process of S5 is as follows: The first step is to apply initial pressure in quasi-static mode using ABAQUS software without introducing cracks. The second step involves introducing an initial crack and importing the pressurized and deformed pipe into the ABAQUS software using the Explicit solver module. Dynamic analysis is then performed to reduce the internal pressure to the steady-state crack tip pressure Ptip, and the pressure decay model in S4 is used to simulate the pressure behind the crack tip.

7. The design method for a dense-phase carbon dioxide pipeline composite material crack arrester according to claim 1, characterized in that, The specific process of S6 is as follows: After the pressure is loaded by the two-step method, the cohesive unit parameters are continuously adjusted, the crack tip opening angle under the specified crack tip pressure is calculated, and the CTOA is calculated using the opening displacement 2 mm behind the crack tip. The CTOA value is relatively high at the initial crack propagation, and then gradually decreases and stabilizes. The CTOA value after steady-state propagation is compared with the crack tip opening angle CTOA of the crack steady-state propagation obtained in the test in S1 until the two are equal. The cohesive unit parameters at this time are selected as the finite element model parameters; The cohesive unit adopts a bilinear traction-separation curve, and the cohesive energy is calculated according to formula (5); Where G: cohesive energy; σ m : Maximum traction force; δ c : Critical separation quantity; σ m =2.8σ y ;σ y The yield strength of the steel pipe is given by K; the initial slope of the cohesive element is 100 times the elastic modulus of the steel pipe, i.e., K = 210 × 10⁻⁶. 11 .

8. The design method for a dense-phase carbon dioxide pipeline composite material crack arrester according to claim 1, characterized in that, The specific process of S7 is as follows: The composite crack arrester adopts a hyperelastic material model based on the Marlow strain energy potential. The crack arrester and the pipeline adopt a surface-to-surface contact method. The first surface is selected as the outer surface of the pipeline, and the second surface is selected as the inner surface of the crack arrester. The tangential behavior is set to be frictionless, and the normal behavior is set to be hard contact; The failure behavior of a single fiber during the tensile process is simulated by using a hyperelastic material model based on the Marlow strain energy potential, and the CTOAa is calculated and output through the finite element model.

9. The design method for a dense-phase carbon dioxide pipeline composite material crack arrester according to claim 1, characterized in that, The specific process of S8 is as follows: The CTOAa after the crack enters the crack arrester determined in S3 - S7 is compared with the critical crack arrest CTOAc of the steel pipe determined in S2. When CTOAa < CTOAc, the crack arrester achieves crack arrest, and the design of the composite crack arrester is completed.

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