Method for constructing PE failure constitutive model under synergistic effect of temperature and mechanical load

Abstract

According to the construction method of the PE failure constitutive model under the synergistic effect of the temperature and the mechanical load, the engineering stress-strain data of the PE pipe at the corresponding temperature and the corresponding strain rate are obtained based on the tensile property tests of the PE pipe at the different temperatures and the different strain rates, and the true stress-strain data of the PE pipe are further obtained. Aiming at the condition that the existing polyethylene material failure criterion does not consider the service temperature, a hyperbolic constitutive model proposed by Suleiman is improved, and a polyethylene failure constitutive model based on the environment temperature-external load synergistic effect is deduced. The method can be used for predicting the mechanical properties of polyethylene at different temperatures and different strain rates, and the test and experiment cost is effectively reduced; in engineering practice, the method has important guiding significance for safe use of polyethylene buried pipelines in different service environments.

Description

Technical Field

[0001] The invention relates to the field of failure evaluation of non-metallic pipelines for gas, water and oil transmission, and in particular to a method for constructing a PE failure constitutive model with coordinated effects of temperature and mechanical load. Background Art

[0002] High-density polyethylene (HDPE) pipes are widely used in gas transmission, urban water supply, oil transportation, nuclear power cooling water transportation and other fields due to their good corrosion resistance, light weight, non-toxicity and impact resistance. However, due to the complexity of gas pipeline service (soil temperature, external load synergy), the non-standardization of pipeline production, installation and use leads to various safety hazards in its operation. Material performance analysis of polyethylene pipes in complex service environments and construction of constitutive failure models under different service temperatures and load synergy are conducive to the safe use of pipelines. At present, the performance analysis of PE pipes is mainly carried out at room temperature, and there are few reports on the failure constitutive model of PE pipes at different temperatures and strain rates. The systematic performance evolution, strength analysis and damage analysis of PE pipes at different temperatures need to be further improved. According to the service environment characteristics of polyethylene pipes, constructing a failure constitutive model of the synergy of ambient temperature and external load is the basic premise and method for exploring the safe use of polyethylene pipes.

[0003] High-density polyethylene pipes are subjected to the synergistic effects of ambient temperature and external loads during their service life. Due to the complexity of the experiment and the difficulty of theoretical derivation, there is currently no very reliable polyethylene material constitutive prediction model that takes into account the synergistic effects of the two. Summary of the invention

[0004] Purpose of the invention: The service environment (region, season) of HDPE pipelines is different, so the failure criteria of pipelines are also different. It is necessary to accurately predict the mechanical properties of pipelines and establish corresponding failure criteria to ensure the safe and stable operation of pipelines.

[0005] In order to solve the problems existing in the technical background, the present invention provides a method for constructing a failure constitutive model of polyethylene pipeline materials under the synergistic effect of ambient temperature and external load based on the analysis failure design method. The present invention intends to refer to the Von-mises stress failure criterion of steel pipelines, combine the viscoelastic material properties of HDPE pipes, carry out tensile tests at different service temperatures and different strain rates, obtain true stress-true strain data, and combine the hyperbolic constitutive model proposed by Suleiman to form a PE pipeline material constitutive model that takes into account the influence of temperature, and finally form a polyethylene failure constitutive model under the synergistic effect of ambient temperature and external load. The present invention specifically provides a method for constructing a PE (Polyethylene, PE) failure constitutive model under the synergistic effect of temperature and mechanical load, comprising the following steps:

[0006] Step 1: According to the requirements of standard GB / T8804.3-2003, polyethylene pipe tensile specimens are prepared, and uniaxial tensile tests are carried out at different temperatures and strain rates to obtain engineering stress-strain curves and yield strength;

[0007] Step 2, according to the engineering stress-strain and true stress-strain transformation formula, obtain the true stress-strain data;

[0008] Step 3, linearly fit the ratio of true strain to true stress with the true strain to obtain the values ​​of parameters a and b of the Suleiman constitutive model at different temperatures and strain rates;

[0009] Step 4, fitting the logarithmic relationship between parameters a, b and strain rate and temperature to obtain the material performance constitutive model of polyethylene pipe under the synergistic effect of ambient temperature and external load;

[0010] Step 5, combined with the Miese strength failure criterion, derive the failure criterion of buried PE pipelines under the synergistic effect of temperature and mechanical load.

[0011] Step 1 includes: according to the requirements of standard GB / T8804.3-2003, sample is taken along the longitudinal direction of the pipeline and the joint pipe tensile specimen is made by mechanical processing; to eliminate temperature error, the specimen should be kept warm in a constant temperature box for at least 1 hour; at least 3 specimens are stretched at each temperature and each strain rate to reduce the error caused by specimen processing, tensile device and artificial surface processing.

[0012] Step 2 includes: the engineering stress-strain and true stress-strain transformation formula is:

[0013]

[0014] Where ε represents strain, dimensionless; d is the integral symbol; ε nom represents engineering strain, dimensionless; σ represents stress, unit MPa; σ nomrepresents engineering stress, unit MPa; μ represents Poisson's ratio, dimensionless; l0 and l represent the original length of the specimen and the length of the specimen after stretching, unit mm; F ​​represents the test tension, unit N; A0 and A represent the original cross-sectional area of ​​the specimen and the cross-sectional area after stretching, unit mm 2 ; Substitute the engineering stress-strain data to obtain the true stress-strain data.

[0015] Step 3 includes: Suleiman constitutive model Derivative, and transform, and let ε / σ=Y, ε=X to obtain:

[0016] Y=a+bX (1)

[0017] The ratio of true strain to true stress is linearly fitted with the true strain to obtain the values ​​of parameters a and b of the Suleiman constitutive model.

[0018] Step 4 includes:

[0019] Step 4-1, strain rate effect analysis: logarithmically fit the values ​​of Suleiman constitutive model parameters a and b at different temperatures and strain rates to obtain the relationship between Suleiman constitutive model parameters a, b and strain rate:

[0020]

[0021] Among them, A1, A2, B1, and B2 are fitting parameters; is the strain rate; Substituting formula (2) into the Suleiman constitutive model, the material constitutive model of PE pipe with respect to strain rate is obtained:

[0022]

[0023] Step 4-2, temperature effect analysis: perform exponential fitting on the A1, A2, B1, B2 values ​​at different temperatures to obtain the relationship between the fitting parameters A1, A2, B1, B2 and temperature. Among them, m1, m2, n1, n2, k1, k2, l1, l2 are fitting parameters; T is temperature, unit is °C; e is a natural constant;

[0024] Step 4-3, obtain the stress-strain constitutive model of PE pipe material with the synergistic effect of temperature and external load.

[0025] In step 4-3, the PE pipe temperature and strain rate data are substituted into the following formula to obtain the stress-strain constitutive model of the PE pipe material under the synergistic effect of temperature and external load:

[0026]

[0027] Step 5 includes: combining the Mises equivalent stress expression with the relationship between the pipe yield stress and the strain rate Where R eL is the yield stress of the pipe, unit: MPa; H and Q are fitting parameters;

[0028] Exponential fitting is performed on the H and Q values ​​at different temperatures to obtain the correlation function expression between the pipe yield stress and temperature:

[0029]

[0030] Among them, f1, f2, q1, q2 are fitting parameters;

[0031] Given the temperature and strain rate of the PE pipe, the yield stress R of the pipe at the corresponding temperature and strain rate is obtained. eL .

[0032] In step 5, the yield stress R of the pipe at the corresponding temperature and corresponding strain rate is obtained by the following formula: eL :

[0033]

[0034] The present invention also provides an electronic device, comprising a processor and a memory, wherein the memory stores program codes, and when the program codes are executed by the processor, the steps of the method are performed.

[0035] The present invention also provides a storage medium storing a computer program or instruction, and when the computer program or instruction is run on a computer, the steps in the method are executed.

[0036] Beneficial effects:

[0037] 1. The present invention is to establish a failure constitutive model and an application method for polyethylene pipes under the synergistic effect of thermal and mechanical loads.

[0038] Based on the Von-mises failure criterion, the stress-strain data at different temperatures and strain rates were obtained by experimental method, and the failure constitutive model of polyethylene pipe with dual variables of temperature and strain was established.

[0039] 2. The method of the present invention provides a failure constitutive model for polyethylene pipelines under different service conditions, which is convenient for determining the failure constitutive model under any temperature and any external load, and analyzing the safe bearing capacity of polyethylene pipelines under corresponding service conditions.

[0040] 3. The method of the present invention is a method for establishing a failure constitutive model that is applicable to actual engineering projects. It avoids the large amount of test data required for the failure criteria of polyethylene pipelines under different service conditions, fills the gap in the research on the failure constitutive model and criteria of polyethylene pipelines under the synergistic effect of multiple factors, and has important guiding significance for the safe use of polyethylene pipelines. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments, and the above and / or other advantages of the present invention will become more clear.

[0042] Figure 1 Flowchart of the construction and application method of polyethylene failure constitutive model.

[0043] Figure 2a to Figure 2d Schematic diagram of engineering stress and strain curves of PE pipes at different strain rates at the same temperature.

[0044] Figure 3a to Figure 3d Schematic diagram of engineering stress and strain curves of PE pipe at the same strain rate and different temperatures.

[0045] Figure 4a to Figure 4d Schematic diagram of the true stress and strain curves of PE pipes at different temperatures and strain rates.

[0046] Figure 5a , Figure 5b Schematic diagram of the relationship between fitting parameters a, b and strain rate at different temperatures.

[0047] Figure 6a , Figure 6b Schematic diagram of the relationship between parameters A1, A2, B1, B2 values ​​and temperature.

[0048] Figure 7 Schematic diagram of the relationship between pipe yield stress and strain rate at different temperatures.

[0049] Figure 8 Schematic diagram of the relationship between parameters H, Q value and temperature. DETAILED DESCRIPTION

[0050] The present invention provides a method for constructing a PE failure constitutive model with synergistic effects of temperature and mechanical load, comprising the following steps:

[0051] Step 1: Prepare polyethylene pipe tensile specimens, carry out uniaxial tensile tests at different temperatures and strain rates, and obtain engineering stress-strain curves and yield strength;

[0052] Step 2, according to the engineering stress-strain and true stress-strain transformation formula, obtain the true stress-strain data;

[0053] Step 3, linearly fit the ratio of true strain to true stress with the true strain to obtain the values ​​of parameters a and b of the Suleiman constitutive model at different temperatures and strain rates;

[0054] Step 4, fitting the logarithmic relationship between parameters a, b and strain rate and temperature to obtain the material performance constitutive model of polyethylene pipe under the synergistic effect of ambient temperature and external load;

[0055] Step 5, combined with the Miese strength failure criterion, derive the failure criterion of buried PE pipelines under the synergistic effect of temperature and mechanical load.

[0056] Step 1 includes: according to the requirements of standard GB / T8804.3-2003, sample is taken along the longitudinal direction of the pipeline and the joint pipe tensile specimen is made by mechanical processing; to eliminate temperature error, the specimen should be kept warm in a constant temperature box for at least 1 hour; at least 3 specimens are stretched at each temperature and each strain rate to reduce the error caused by specimen processing, tensile device and artificial surface processing.

[0057] Step 2 includes: the engineering stress-strain and true stress-strain transformation formula is:

[0058]

[0059] Where ε represents strain; d is the integral symbol; ε nom represents engineering strain; σ represents stress; σ nom represents engineering stress; μ represents Poisson's ratio; l0 and l represent the original length of the specimen and the length of the specimen after stretching, respectively; F represents the test tension; A0 and A represent the original cross-sectional area of ​​the specimen and the cross-sectional area after stretching, respectively; substitute the engineering stress-strain data to obtain the true stress-strain data.

[0060] Step 3 includes: Suleiman constitutive model Derivative, and transform, and let ε / σ=Y, ε=X to obtain:

[0061] Y=a+bX (1)

[0062] The ratio of true strain to true stress is linearly fitted with the true strain to obtain the values ​​of parameters a and b of the Suleiman constitutive model.

[0063] Step 4 includes:

[0064] Step 4-1, strain rate effect analysis: logarithmically fit the values ​​of Suleiman constitutive model parameters a and b at different temperatures and strain rates to obtain the relationship between Suleiman constitutive model parameters a, b and strain rate:

[0065]

[0066] Among them, A1, A2, B1, and B2 are fitting parameters; is the strain rate; Substituting formula (2) into the Suleiman constitutive model, the material constitutive model of PE pipe with respect to strain rate is obtained:

[0067]

[0068] Step 4-2, temperature effect analysis: perform exponential fitting on the A1, A2, B1, B2 values ​​at different temperatures to obtain the relationship between the fitting parameters A1, A2, B1, B2 and temperature. Among them, m1, m2, n1, n2, k1, k2, l1, l2 are fitting parameters; T is temperature, unit is °C; e is a natural constant;

[0069] Step 4-3, obtain the stress-strain constitutive model of PE pipe material with the synergistic effect of temperature and external load.

[0070] In step 4-3, the PE pipe temperature and strain rate data are substituted into the following formula to obtain the stress-strain constitutive model of the PE pipe material under the synergistic effect of temperature and external load:

[0071]

[0072] Step 5 includes: combining the Mises equivalent stress expression with the relationship between the pipe yield stress and the strain rate Where R eL is the yield stress of the pipe, unit: MPa; H and Q are fitting parameters;

[0073] Exponential fitting is performed on the H and Q values ​​at different temperatures to obtain the correlation function expression between the pipe yield stress and temperature:

[0074]

[0075]

[0076] Among them, f1, f2, q1, q2 are fitting parameters;

[0077] Given the temperature and strain rate of the PE pipe, the yield stress R of the pipe at the corresponding temperature and strain rate is obtained. eL .

[0078] In step 5, the yield stress R of the pipe at the corresponding temperature and corresponding strain rate is obtained by the following formula: eL :

[0079]

[0080] like Figure 1As shown, in a specific embodiment of the present invention, a method for constructing a PE failure constitutive model with synergistic effects of temperature and mechanical load is provided, comprising the following steps:

[0081] Step 1, determine the mechanical properties of polyethylene materials, make joint pipe tensile specimens according to GB / T8804 standard, conduct uniaxial tensile tests at different temperatures and different strain rates, and obtain engineering stress-strain curves and yield strength;

[0082] Step 2, according to the engineering stress-strain and true stress-strain transformation formula, obtain the true stress-strain data;

[0083] Step 3: Linearly fit the ratio of true strain to true stress with the true strain to obtain the values ​​of constitutive model parameters a and b at different temperatures and strain rates.

[0084] Step 4, fitting the logarithmic relationship between parameters a, b and strain rate and temperature to obtain the constitutive model of PE pipe material performance under the synergistic effect of ambient temperature and external load.

[0085] Step 5, combined with the Von-mises strength failure criterion, derive the failure criterion of the buried PE pipeline under the synergistic effect of ambient temperature and external load.

[0086] Step 1 includes: according to the requirements of GB / T8804, take samples along the axial direction of the pipe and process them into tensile specimens, and polish the surface of the specimens with sandpaper of no less than 400#. In order to eliminate the influence of temperature factors on the mechanical properties of PE pipes, the specimens should be kept in an incubator for at least 1 hour after clamping before the tensile test can be carried out. The engineering stress-strain curves of PE pipes at the same temperature and different strain rates are shown in Figure 1. Figure 2a , Figure 2b , Figure 2c , Figure 2d As shown in the figure, the engineering stress-strain curves of PE pipes at different temperatures at the same strain rate are as follows: Figure 3a , Figure 3b , Figure 3c , Figure 3d shown.

[0087] Step 2 includes: according to the conversion formula between engineering stress-strain and true stress-strain, the true stress-strain curve of PE pipe at different temperatures and different strain rates is obtained, such as Figure 4a , Figure 4b , Figure 4c , Figure 4d As shown:

[0088]

[0089] Step 3 includes: Suleiman formula Take the derivative and transform to get Let ε / σ=Y, ε=X to get Y=a+bx. Linearly fit the ratio of true strain to true stress with true strain to obtain the values ​​of constitutive model parameters a and b. The values ​​of a and b at different temperatures and strain rates are shown in Table 1.

[0090] Table 1

[0091]

[0092] Step 4 includes: to determine the relationship between the parameters a, b and the strain rate, logarithmic fitting is performed on the values ​​of a and b at different temperatures and strain rates, such as Figure 5a , Figure 5b As shown, the logarithmic relationship between parameters a, b and strain rate is shown in the above formula (2):

[0093]

[0094] In the formula, A1, A2, B1, B2 are fitting parameters; is the strain rate. The values ​​of A1, A2, B1, and B2 at different temperatures are shown in Table 2.

[0095] Table 2

[0096]

[0097]

[0098] Substituting the expressions of a and b into the formula Y=a+bX, the constitutive model of PE pipe with respect to strain rate is obtained, as shown in the above formula (3):

[0099]

[0100] In order to reflect the temperature effect of PE pipes, the relationship between parameters A1, A2, B1, B2 and temperature is determined. Therefore, exponential fitting is performed on the A1, A2, B1, B2 values ​​at different temperatures, such as Figure 6a , Figure 6b The exponential relationships between parameters A1, A2, B1, B2 and temperature are as follows: shown.

[0101] Wherein, m1, m2, n1, n2, k1, k2, l1, l2 are fitting parameters; T is temperature, unit is °C. The values ​​of fitting parameters m1, m2, n1, n2, k1, k2, l1, l2 are shown in Table 3.

[0102] Table 3

[0103]

[0104] By integrating the above equations, we can obtain the constitutive model of PE pipe based on Suleiman hyperbolic model considering the influence of temperature and the change of strain rate, as shown in equation (4) above:

[0105]

[0106] The temperature and strain rate of the PE pipe under different loads are known, and the constitutive model of the pipe at the corresponding temperature and strain rate under the load is obtained by substituting them into the above formula.

[0107] Step 5 includes: by processing the tensile data of PE samples at different temperatures and strain rates, it is found that the yield stress of the pipe at different temperatures has a logarithmic relationship with the strain rate, such as Figure 7 Therefore, the relationship between the pipe yield stress and the strain rate is described by the Eyring flow theory model. Where R eL is the yield stress of the pipe, unit: MPa; is the pipe strain rate; H and Q are fitting parameters. For the H and Q values ​​at different temperatures listed in Table 4, exponential fitting is performed, as shown in Figure 8 As shown, the relevant function expression of pipe yield stress and temperature is obtained. Where f1, f2, q1, q2 are fitting parameters, and their values ​​are shown in Table 5; T is temperature, unit: °C.

[0108] Table 4

[0109] Temperature / ℃ -15 0 15 30 H 51.738 43.233 37.334 29.275 Q 2.5159 2.1565 1.8937 1.5448

[0110] Table 5

[0111] <![CDATA[f1]]> <![CDATA[f2]]> <![CDATA[q1]]> <![CDATA[q2]]> 43.3849 -0.0124 2.1615 -0.0106

[0112] Given the temperature and strain rate of the PE pipe, substituting them into formula (5) can obtain the yield stress R of the pipe at the corresponding temperature and strain rate: eL :

[0113]

[0114] The present invention provides a method for constructing a PE failure constitutive model with synergistic effects of temperature and mechanical load. There are many methods and ways to implement the technical solution. The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the protection scope of the present invention. All components not specified in this embodiment can be implemented using existing technologies.

Claims

1. A method for constructing a PE failure constitutive model with synergistic effects of temperature and mechanical load, characterized in that: The following steps are involved: Step 1: Prepare polyethylene pipe tensile specimens, carry out uniaxial tensile tests at different temperatures and strain rates, and obtain engineering stress-strain curves and yield strength; Step 2, according to the engineering stress-strain and true stress-strain transformation formula, obtain the true stress-strain data; Step 3, linearly fit the ratio of true strain to true stress with the true strain to obtain the values ​​of parameters a and b of the Suleiman constitutive model at different temperatures and strain rates; Step 4, fitting the logarithmic relationship between parameters a, b and strain rate and temperature to obtain the material performance constitutive model of polyethylene pipe under the synergistic effect of ambient temperature and external load; Step 5, combined with the Miese strength failure criterion, derive the failure criterion of buried PE pipelines under the synergistic effect of temperature and mechanical load.

2. The method according to claim 1, characterized in that Step 1 includes: according to the requirements of standard GB / T8804.3-2003, sample is taken along the longitudinal direction of the pipeline and the joint pipe tensile specimen is made by mechanical processing; to eliminate temperature error, the specimen should be kept warm in a constant temperature box for at least 1 hour; at least 3 specimens are stretched at each temperature and each strain rate to reduce the error caused by specimen processing, tensile device and artificial surface processing.

3. The method according to claim 2, characterized in that Step 2 includes: the engineering stress-strain and true stress-strain transformation formula is: Where ε represents strain; d is the integral symbol; ε nom represents engineering strain; σ represents stress; σ nom represents engineering stress; μ represents Poisson's ratio; l0 and l represent the original length of the specimen and the length of the specimen after stretching, respectively; F represents the test tension; A0 and A represent the original cross-sectional area of ​​the specimen and the cross-sectional area after stretching, respectively; substitute the engineering stress-strain data to obtain the true stress-strain data.

4. The method according to claim 3, characterized in that Step 3 includes: Suleiman constitutive model Derivative, and transform, and let ε / σ=Y, ε=X to obtain: Y=a+bX (1) The ratio of true strain to true stress is linearly fitted with the true strain to obtain the values ​​of parameters a and b of the Suleiman constitutive model.

5. The method according to claim 4, characterized in that Step 4 includes: Step 4-1, strain rate effect analysis: logarithmically fit the values ​​of Suleiman constitutive model parameters a and b at different temperatures and strain rates to obtain the relationship between Suleiman constitutive model parameters a, b and strain rate: Among them, A1, A2, B1, and B2 are fitting parameters; is the strain rate; Substituting formula (2) into the Suleiman constitutive model, the material constitutive model of PE pipe with respect to strain rate is obtained: Step 4-2, temperature effect analysis: perform exponential fitting on the A1, A2, B1, B2 values ​​at different temperatures to obtain the relationship between the fitting parameters A1, A2, B1, B2 and temperature Among them, m1, m2, n1, n2, k1, k2, l1, l2 are fitting parameters; T is temperature, unit is °C; e is a natural constant; Step 4-3, obtain the stress-strain constitutive model of PE pipe material with the synergistic effect of temperature and external load.

6. The method according to claim 5, characterized in that In step 4-3, the temperature and strain rate data of the PE pipe are substituted into the following formula to obtain the stress-strain constitutive model of the PE pipe material under the synergistic effect of temperature and external load:

7. The method according to claim 6, characterized in that Step 5 includes: combining the Mises equivalent stress expression with the relationship between the pipe yield stress and the strain rate Where R eL is the yield stress of the pipe, unit: MPa; H and Q are fitting parameters; Exponential fitting is performed on the H and Q values ​​at different temperatures to obtain the correlation function expression between the pipe yield stress and temperature: Among them, f1, f2, q1, q2 are fitting parameters; Given the temperature and strain rate of the PE pipe, the yield stress R of the pipe at the corresponding temperature and strain rate is obtained. eL .

8. The method according to claim 7, characterized in that In step 5, the yield stress R of the pipe at the corresponding temperature and corresponding strain rate is obtained by the following formula: eL :

9. An electronic device, comprising a processor and a memory, wherein the memory stores program codes, and when the program codes are executed by the processor, the processor executes the steps of the method according to any one of claims 1 to 8.

10. A storage medium, characterized in that: A computer program or instruction is stored, and when the computer program or instruction is run on a computer, the steps of the method according to any one of claims 1 to 8 are executed.

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