CN115235879A - Method for predicting creep compliance of polyethylene gas pipe - Google Patents
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- 239000004698 Polyethylene Substances 0.000 title claims abstract description 73
- -1 polyethylene Polymers 0.000 title claims abstract description 72
- 229920000573 polyethylene Polymers 0.000 title claims abstract description 72
- 238000000034 method Methods 0.000 title claims abstract description 32
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- 230000006399 behavior Effects 0.000 description 9
- 230000001052 transient effect Effects 0.000 description 7
- 229920000642 polymer Polymers 0.000 description 6
- 230000008569 process Effects 0.000 description 6
- 230000004044 response Effects 0.000 description 5
- 238000013461 design Methods 0.000 description 2
- 229920001903 high density polyethylene Polymers 0.000 description 2
- 239000004700 high-density polyethylene Substances 0.000 description 2
- 230000007774 longterm Effects 0.000 description 2
- VGGSQFUCUMXWEO-UHFFFAOYSA-N Ethene Chemical compound C=C VGGSQFUCUMXWEO-UHFFFAOYSA-N 0.000 description 1
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- 230000005489 elastic deformation Effects 0.000 description 1
- 238000013401 experimental design Methods 0.000 description 1
- 238000012886 linear function Methods 0.000 description 1
- 238000003801 milling Methods 0.000 description 1
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Abstract
The invention relates to a method for predicting creep compliance of a polyethylene gas pipe, which comprises the steps of firstly obtaining a creep strain-time curve through a reasonable specific creep experiment, and then further obtaining the creep compliance-time curve, initial creep compliance, stress-related factors, J 1 And m material parameter and h 1 And (sigma) and the like, substituting the parameters into a specific formula to obtain a creep constitutive equation of the polyethylene gas pipe sample, and predicting creep strain and creep compliance of the polyethylene gas pipe under certain creep stress according to the creep constitutive equation. The method for predicting the creep compliance of the polyethylene gas pipe is high in accuracy, can accurately simulate the nonlinear creep behavior under high stress, and provides a basis for accurately analyzing the delayed failure behavior of the gas pipe. The method for predicting the creep compliance of the polyethylene gas pipe can greatly simplify the workload of the creep compliance test, save the experiment time and reduce the test and experiment costs.
Description
Technical Field
The invention relates to the technical field of creep compliance testing methods, in particular to a method for predicting creep compliance of a polyethylene gas pipe.
Background
Creep is a process or phenomenon in which strain gradually increases over time under a constant load. Creep compliance is the ratio of strain to stress at any time during creep of a material. J (t) = J 0 + Δ J (t) is the creep compliance of the material, J 0 = J (0) initial creep compliance,. DELTA.J (t) = J (t) -J 0 Transient creep compliance.
A high-density polyethylene (HDPE) gas pipeline belongs to a polymer pressure pipeline, the maximum main stress generated under the action of internal pressure is hoop normal stress which is the main factor causing creep failure of the pipeline, and the pipeline failure time is extrapolated from an empirical formula according to the hoop normal stress and the temperature according to the existing international standard ISO 9080 on the basis of summarizing a test rule. In fact, the delayed failure behavior of the polymer pressure pipeline is determined by the creep characteristic and the creep damage evolution rule of the polymer, and the service process of the polymer pressure pipeline is the process from creep deformation, damage evolution, crack propagation and breaking of the material under the long-term action of the hoop main stress. The design life of the PE buried pipeline is as long as more than 50 years, the creep property of the material plays a decisive influence on the service behavior of the pipeline, and an accurate creep constitutive model is the key of life analysis and safety design of the polymer pressure pipeline. In addition to temperature effects, the mechanical properties of polymers are dependent on stress level and load application time, and linear viscoelasticity can be exhibited under short-term application of low stress, whereas relatively strong nonlinear viscoelasticity can be exhibited under medium stress or under long-term application of low stress. Firstly, starting from a rheological model theory, constructing a differential constitutive model by connecting a spring and a kettle-sticking element in series or in parallel; and secondly, based on a basic theory of continuous medium mechanics, considering the influence of stress history on deformation based on a Boltzmann superposition principle or a modified Boltzmann superposition principle, and obtaining an integral constitutive model through Stieltjes convolution. The nonlinear effect caused by the change of the characteristic time of the material caused by the stress can be obtained by reducing the time or introducing a nonlinear function.
Disclosure of Invention
Based on this, the invention aims to solve the complexity of the conventional creep type viscoelasticity constitutive model, provide a method for predicting the creep compliance of a polyethylene gas pipe, and provide a simple integral type nonlinear viscoelasticity constitutive model for predicting and analyzing the creep behavior of the polyethylene gas pipe.
The specific technical scheme is as follows:
a method for predicting creep compliance of a polyethylene gas pipe comprises the following steps:
(1) Applying a set constant load on a polyethylene gas pipe sample, and performing a plurality of groups of creep tests on the polyethylene gas pipe sample under different creep stresses to obtain a creep strain-time curve of the polyethylene gas pipe sample under each creep stress, wherein the creep stress comprises at least three groups of creep stresses below 5.4MPa and at least three groups of creep stresses greater than 5.4 MPa;
(2) Dividing creep strain under each group of creep stress levels by corresponding creep stress to obtain a creep compliance-time curve of the polyethylene gas pipe sample;
(3) Carrying out linear fitting by taking initial instantaneous elastic strain under each creep stress with the creep stress not more than 5.4MPa as a vertical coordinate and the corresponding creep stress as a horizontal coordinate to obtain initial creep compliance; the initial instantaneous elastic strain is the strain when the creep stress acting on the polyethylene gas pipe sample reaches a set value;
(4) Calculating a stress correlation factor according to an initial instantaneous elastic strain formula, wherein the initial instantaneous elastic strain formula is as follows: epsilon c (t＝0,σ)＝h 0 (σ)·J 0 ·σ；
Wherein epsilon c (t =0, σ) is initial instantaneous elastic strain, h 0 (σ) is the stress-related factor, J 0 = J (0) initial creep compliance, σ is effectCreep stress on the polyethylene gas pipe sample;
(5) Fitting a creep compliance curve of the polyethylene gas pipe sample when the creep stress does not exceed 5.4MPa according to a formula J (t) = J 0 +J 1 ·t m To obtain J 1 And m, J 1 And m are material parameters independent of stress;
(6) Fitting a creep compliance curve of the polyethylene gas pipe sample when the creep stress exceeds 5.4MPa to obtain h expressed by a sigma function 1 (σ)；
(7) The J is put into 0 、h 0 (σ)、J 1 M and h 1 (σ) substitutes the following equation: epsilon c (t,σ)＝h 0 (σ)·J 0 ·σ+h 1 (σ)·J 1 ·t m Obtaining a creep constitutive equation of the polyethylene gas pipe sample;
(8) And (5) predicting the creep strain of the polyethylene gas pipe under a certain creep stress according to the creep constitutive equation in the step (7), and dividing the obtained creep strain by the corresponding creep stress to obtain the creep compliance of the polyethylene gas pipe under the corresponding creep stress.
In some of these embodiments, the creep test is a tensile creep test.
In some of these embodiments, the tensile creep test is performed on an electronic universal tester.
In some embodiments, creep strain-time curves of the polyethylene gas pipe sample under various stresses are measured by a strain extensometer.
In some of these embodiments, the creep test has a test temperature of 20-28 ℃ and a relative humidity of 45-55%.
In some of these embodiments, the creep test has a test temperature of 22-24 ℃ and a relative humidity of 48-52%.
In some of these embodiments, the creep test has a test temperature of 23 ℃ and a relative humidity of 50%.
In some of these embodiments, the creep stress of the creep test is 2.4MPa to 9.6MPa.
In some of these embodiments, the creep stress of the creep test is 2.4MPa, 3.6MPa, 4.8MPa, 5.4MPa, 6.0MPa, 8.4MPa, and 9.6MPa.
In some embodiments, the creep stress of the creep test reaches a set value within 3.5s, and the holding time is not less than 3600s.
In some embodiments, the method for predicting the creep compliance of the polyethylene gas pipe comprises the following steps:
(1) Applying a set constant load on a polyethylene gas pipe sample, and performing creep test on the polyethylene gas pipe sample under creep stresses of 2.4MPa, 3.6MPa, 4.8MPa, 5.4MPa, 6.0MPa, 8.4MPa and 9.6MPa respectively to obtain a creep strain-time curve of the polyethylene gas pipe sample under each creep stress;
(2) Dividing creep strain under each group of creep stress level by corresponding creep stress to obtain a creep compliance-time curve of the polyethylene gas pipe sample;
(3) Performing linear fitting by using initial instantaneous elastic strains with creep stresses of 2.4MPa, 3.6MPa, 4.8MPa and 5.4MPa as ordinate and corresponding creep stresses as abscissa to obtain initial creep compliance J 0 ＝7.0×10 -4 MPa -1 (ii) a The initial instantaneous elastic strain is the strain when the creep stress acting on the polyethylene gas pipe sample reaches a set value;
(4) Calculating a stress correlation factor according to an initial instantaneous elastic strain formula, wherein the initial instantaneous elastic strain formula is as follows: epsilon c (t＝0,σ)＝h 0 (σ)·J 0 ·σ；
Wherein epsilon c (t =0, σ) is initial instantaneous elastic strain, h 0 (σ) is the stress-related factor, J 0 The = J (0) is initial creep compliance, and the sigma is creep stress acting on the polyethylene gas pipe sample;
then h is obtained by calculation 0 (sigma) as ordinate and corresponding creep stress as abscissa, and obtaining correlation function of stress correlation factor and corresponding creep stress, such asThe following:
(5) Fitting a creep compliance curve of the polyethylene gas pipe sample when the creep stress does not exceed 5.4MPa according to a formula J (t) = J 0 +J 1 ·t m To obtain J 1 ＝1.52×10 -4 MPa -1 ,m＝0.23，J 1 And m are stress independent material parameters;
(6) Fitting a creep compliance curve of the polyethylene gas pipe sample when the creep stress exceeds 5.4MPa to obtain h expressed by a sigma function 1 (σ)：
(7) Subjecting said J to 0 、h 0 (σ)、J 1 M and h 1 (σ) substituting the following equation: epsilon c (t,σ)＝h 0 (σ)·J 0 ·σ+h 1 (σ)·J 1 ·t m Obtaining the creep constitutive equation of the polyethylene gas pipe sample:
(8) And (4) predicting the creep strain of the polyethylene gas pipe under a certain creep stress according to the creep constitutive equation in the step (7), and dividing the obtained creep strain by the corresponding creep stress to obtain the creep compliance of the polyethylene gas pipe under the corresponding creep stress.
Compared with the prior art, the invention has the following beneficial effects:
the invention obtains a prediction method and a prediction model capable of accurately predicting the creep compliance of the polyethylene gas pipe through reasonable experimental design and accurate model selection, and provides a simple integral nonlinear viscoelasticity constitutive model for the depolymerizationAnd predicting and analyzing the creep behavior of the ethylene gas pipe. The prediction method comprises the steps of firstly obtaining a creep strain-time curve through a reasonable specific creep experiment, and then further obtaining a creep compliance-time curve, initial creep compliance, stress correlation factors, J 1 And m material parameter and h 1 And (sigma) and the like, substituting the parameters into a specific formula to obtain a creep constitutive equation of the polyethylene gas pipe sample, and predicting creep strain and creep compliance of the polyethylene gas pipe under certain creep stress according to the creep constitutive equation. The method for predicting the creep compliance of the polyethylene gas pipe is high in accuracy, can accurately simulate the nonlinear creep behavior under high stress, and provides a basis for accurately analyzing the delayed failure behavior of the gas pipe. The method for predicting the creep compliance of the polyethylene gas pipe can greatly simplify the workload of the creep compliance test, save the experiment time and reduce the test and experiment costs.
Drawings
FIG. 1 is a schematic view of a PE100 sample and its cutting orientation on a pipe.
FIG. 2 is a drawing of a tensile creep test apparatus.
FIG. 3 is a graph of stress history (a) and creep strain versus time (b) for a tensile creep test.
FIG. 4 is a graph of creep compliance under various creep stresses.
FIG. 5 is the initial transient elastic strain under different creep stress conditions.
FIG. 6 is a stress correlation factor h of the transient elastic response 0 (σ) dependence graph of the corresponding creep stress.
FIG. 7 is a stress correlation factor h of the transient elastic response 1 (σ) dependence graph of the corresponding creep stress.
FIG. 8 is a comparison of a predicted model and an experiment of creep behavior of PE100 material.
Detailed Description
Unless defined otherwise, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. The terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention.
The terms "comprising" and "having," and any variations thereof, are intended to cover non-exclusive inclusions. For example, a process, method, apparatus, article, or apparatus that comprises a list of steps is not limited to only those steps or modules recited, but may alternatively include other steps not recited, or may alternatively include other steps inherent to such process, method, article, or apparatus.
Example 1
1. Materials and samples
The sample is obtained from a buried polyethylene gas pipeline and is processed by numerical control milling, and the model of the pipe is PE100/SDR11/Dn315 x 28.6. The test specimen and the cutting position on the pipeline are shown in figure 1, and the size of the test specimen meets the requirements of ISO 527-2.
2. Creep test
Tensile creep testing was performed on an electronic universal tester (Zwick/Roell Z020) as shown in FIG. 2. The method comprises the following specific steps: the creep stress (2.4 MPa-9.6 MPa) reached a set value within 3.5s by applying a set constant load to the sample at room temperature (23 ℃) and 50% RH, and the load requirement of the creep test was satisfied, and the creep stress was maintained for 3600s, as shown in FIG. 3 (a). During the creep test, a creep strain-time curve at each creep stress was measured by a strain extensometer, as shown in fig. 3 (b). It can be seen that in the test process, the creep strain rapidly increases with time at the initial stage of loading, then the growth rate gradually decreases, the sample enters a steady-state creep stage after undergoing a decay creep stage, and no accelerated creep phenomenon is observed within the stress range and the test duration.
Dividing the creep strain at each stress level in fig. 3 (b) by the corresponding stress to obtain a creep compliance-time curve, as shown in fig. 4, it can be seen that when the stress does not exceed 5.4MPa, the creep compliance curves corresponding to each stress level almost coincide, which indicates that the creep compliance under the stress is independent of the stress level, and the characteristic is a linear visco-elastic creep behavior; when the stress exceeds 5.4MPa, the isochronous creep compliance under each stress increases with an increase in the stress level, and the nonlinear viscoelastic deformation characteristics are exhibited.
3. Initial transient elastic response
Instantaneous elastic deformation occurs at the moment of sudden loading due to the elastic properties of the material, and in the creep test of the present invention, the strain when the creep stress reaches a set value is taken as the initial instantaneous elastic strain, and the test result is shown in fig. 5. It can be seen that the initial instantaneous elastic strain is linearly related to the stress when the creep stress does not exceed 5.4MPa, and the initial instantaneous elastic strain and the stress satisfy a quadratic function relationship when the creep stress exceeds 5.4 MPa.
The expression for the initial transient elastic response is:
ε c (t＝0,σ)＝h 0 (σ)·J 0 ·σ
performing linear fitting on the data with the stress not exceeding 5.4MPa in the figure 5 to obtain J 0 ＝7.0×10 -4 MPa -1 。
Furthermore, a stress correlation factor h can be obtained from data of a stress exceeding 5.4MPa 0 (σ) As shown in FIG. 6, it can be seen that the stress-related factor of the transient elastic response during non-linear creep can be expressed as a linear function:
4. creep constitutive equation of PE100 pipe
Since the creep at a stress of not more than 5.4MPa is linear viscoelastic creep and the creep compliance thereof is independent of the stress, the creep compliance curves at stresses of 2.4MPa, 3.6MPa, 4.8MPa and 5.4MPa in FIG. 4 are fitted (the fitted curves are shown by solid lines in FIG. 4) as represented by J (t) = J (4) 0 +J 1 ·t m Can obtain J 1 ＝1.52×10 -4 MPa -1 ,m＝0.23。J 1 And m are material parameters independent of stress.
For nonlinear viscoelastic creep, fitting analysis is performed on the curve with the stress greater than 5.4MPa in FIG. 4, and h can be obtained 1 (σ) stress dependence, as shown in FIG. 7, can be usedThe formula is:
to sum up, according to the formula: epsilon c (t,σ)＝h 0 (σ)·J 0 ·σ+h 1 (σ)·J 1 ·t m The creep constitutive equation of the available PE100 pipe can be specifically expressed as:
5. predicting creep compliance of PE100 pipe
The creep strain of the PE100 pipe under other creep stresses can be predicted according to the creep constitutive equation,
and dividing the creep strain by the corresponding creep stress to obtain the creep compliance of the PE100 pipe under the corresponding creep stress.
Creep strain-time curves at stress levels (2.4 MPa, 3.6MPa, 4.8MPa, 5.4MPa, 6.0MPa, 8.4MPa, and 9.6 MPa) predicted using the above-described creep constitutive equation prediction model are plotted in FIG. 8, as indicated by solid lines. Compared with the test results shown in fig. 3, the prediction model can well describe the linear and nonlinear creep behaviors of the PE100, can accurately predict the creep strain of the PE100 pipe under each stress level, and can further accurately predict the creep compliance of the PE100 pipe under the corresponding creep stress. Therefore, when more creep compliance under different stresses needs to be obtained, the creep strain under each creep stress does not need to be tested, and the corresponding creep strain and creep compliance can be obtained by substituting the corresponding creep stress into the creep constitutive equation, so that the workload of creep compliance testing is greatly simplified, the experimental time is saved, and the testing cost is reduced.
The technical features of the embodiments described above may be arbitrarily combined, and for the sake of brevity, all possible combinations of the technical features in the embodiments described above are not described, but should be considered as being within the scope of the present specification as long as there is no contradiction between the combinations of the technical features.
The above-mentioned embodiments only express several embodiments of the present invention, and the description thereof is more specific and detailed, but not construed as limiting the scope of the invention. It should be noted that, for a person skilled in the art, several variations and modifications can be made without departing from the inventive concept, which falls within the scope of the present invention. Therefore, the protection scope of the present patent shall be subject to the appended claims.
Claims (10)
1. The method for predicting the creep compliance of the polyethylene gas pipe is characterized by comprising the following steps of:
(1) Applying a set constant load on a polyethylene gas pipe sample, and performing a plurality of groups of creep tests on the polyethylene gas pipe sample under different creep stresses to obtain a creep strain-time curve of the polyethylene gas pipe sample under each creep stress, wherein the creep stress comprises at least three groups of creep stresses below 5.4MPa and at least three groups of creep stresses greater than 5.4 MPa;
(2) Dividing creep strain under each group of creep stress levels by corresponding creep stress to obtain a creep compliance-time curve of the polyethylene gas pipe sample;
(3) Carrying out linear fitting by taking the initial instantaneous elastic strain under each creep stress with the creep stress not more than 5.4MPa as a vertical coordinate and the corresponding creep stress as a horizontal coordinate to obtain initial creep compliance; the initial instantaneous elastic strain is the strain when the creep stress acting on the polyethylene gas pipe sample reaches a set value;
(4) Calculating a stress correlation factor according to an initial instantaneous elastic strain formula, wherein the initial instantaneous elastic strain formula is as follows: epsilon c (t＝0,σ)＝h 0 (σ)·J 0 ·σ；
Wherein，ε c (t =0, σ) is initial instantaneous elastic strain, h 0 (σ) is the stress-related factor, J 0 = J (0) is initial creep compliance, and sigma is creep stress acting on the polyethylene gas pipe sample;
(5) Fitting a creep compliance curve of the polyethylene gas pipe sample when the creep stress does not exceed 5.4MPa according to a formula J (t) = J 0 +J 1 ·t m To obtain J 1 And m, J 1 And m are material parameters independent of stress;
(6) Fitting a creep compliance curve of the polyethylene gas pipe sample when the creep stress exceeds 5.4MPa to obtain h expressed by a sigma function 1 (σ)；
(7) Subjecting said J to 0 、h 0 (σ)、J 1 M and h 1 (σ) substitutes the following equation: epsilon c (t,σ)＝h 0 (σ)·J 0 ·σ+h 1 (σ)·J 1 ·t m Obtaining a creep constitutive equation of the polyethylene gas pipe sample;
(8) And (5) predicting the creep strain of the polyethylene gas pipe under a certain creep stress according to the creep constitutive equation in the step (7), and dividing the obtained creep strain by the corresponding creep stress to obtain the creep compliance of the polyethylene gas pipe under the corresponding creep stress.
2. The method for predicting the creep compliance of the polyethylene gas pipe according to claim 1, wherein the creep stress of the creep test is 2.4MPa to 9.6MPa.
3. The method of claim 2, wherein the creep stress of the creep test is 2.4MPa, 3.6MPa, 4.8MPa, 5.4MPa, 6.0MPa, 8.4MPa, and 9.6MPa.
4. The method for predicting the creep compliance of the polyethylene gas pipe according to claim 1, wherein the creep stress corresponding to the creep test reaches a set value within 3.5s, and the holding time is not less than 3600s.
5. The method for predicting the creep compliance of the polyethylene gas pipe according to any one of claims 1 to 4, wherein the testing temperature of the creep test is 20 to 28 ℃ and the relative humidity is 45 to 55%.
6. The method for predicting the creep compliance of the polyethylene gas pipe material as claimed in claim 5, wherein the testing temperature of the creep test is 22-24 ℃, and the relative humidity is 48-52%.
7. The method for predicting creep compliance of a polyethylene gas pipe according to any one of claims 1 to 4, wherein the creep test is a tensile creep test.
8. The method of claim 7, wherein the tensile creep test is performed in an electronic universal tester.
9. The method for predicting creep compliance of a polyethylene gas pipe according to any one of claims 1 to 4, wherein a creep strain-time curve of the polyethylene gas pipe sample under each stress is measured by a strain extensometer.
10. The method for predicting the creep compliance of the polyethylene gas pipe according to claim 1, comprising the steps of:
(1) Applying a set constant load on a polyethylene gas pipe sample, performing creep test on the polyethylene gas pipe sample under creep stress of 2.4MPa, 3.6MPa, 4.8MPa, 5.4MPa, 6.0MPa, 8.4MPa and 9.6MPa respectively, and measuring a creep strain-time curve of the polyethylene gas pipe sample under each creep stress;
(2) Dividing creep strain under each group of creep stress level by corresponding creep stress to obtain a creep compliance-time curve of the polyethylene gas pipe sample;
(3) Performing linear fitting by using initial instantaneous elastic strains with creep stresses of 2.4MPa, 3.6MPa, 4.8MPa and 5.4MPa as ordinate and corresponding creep stresses as abscissa to obtain initial creep compliance J 0 ＝7.0×10 -4 MPa -1 (ii) a The initial instantaneous elastic strain is the strain when the creep stress acting on the polyethylene gas pipe sample reaches a set value;
(4) Calculating a stress correlation factor according to an initial instantaneous elastic strain formula, wherein the initial instantaneous elastic strain formula is as follows: epsilon c (t＝0,σ)＝h 0 (σ)·J 0 ·σ；
Wherein epsilon c (t =0, σ) is initial instantaneous elastic strain, h 0 (σ) is the stress-related factor, J 0 = J (0) is initial creep compliance, and sigma is creep stress acting on the polyethylene gas pipe sample;
then h is obtained by calculation 0 (σ) fitting with the corresponding creep stress as abscissa, with the ordinate as ordinate, to obtain a correlation function of the stress correlation factor with the corresponding creep stress as follows:
(5) Fitting a creep compliance curve of the polyethylene gas pipe sample when the creep stress does not exceed 5.4MPa according to a formula J (t) = J 0 +J 1 ·t m To obtain J 1 ＝1.52×10 -4 MPa -1 ,m＝0.23，J 1 And m are stress independent material parameters;
(6) Fitting a creep compliance curve of the polyethylene gas pipe sample when the creep stress exceeds 5.4MPa to obtain h expressed by a sigma function 1 (σ)：
(7) Subjecting said J to 0 、h 0 (σ)、J 1 M and h 1 (σ) substituting the following equation: epsilon c (t,σ)＝h 0 (σ)·J 0 ·σ+h 1 (σ)·J 1 ·t m Obtaining the creep constitutive equation of the polyethylene gas pipe sample:
(8) And (5) predicting the creep strain of the polyethylene gas pipe under a certain creep stress according to the creep constitutive equation in the step (7), and dividing the obtained creep strain by the corresponding creep stress to obtain the creep compliance of the polyethylene gas pipe under the corresponding creep stress.
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