塑料压力管道破坏机理的损伤力学研究及其数值模拟
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摘要
塑料压力管道长期使用性能的研究和预测对于确定管件的检修时间和防止事故的发生具有非常重要的意义。然而，由于传统的塑料管道寿命分析方法几乎都只考虑了管道在产生宏观裂纹后的裂纹扩展过程而未涉及到管道的微观损伤演变过程，因此其预测结果与管道的实际情况相比具有一定误差。针对于此，本文利用损伤力学理论建立起塑料压力管道在真实应力下的物理模型，不仅同时考虑到了蠕变载荷和疲劳载荷对管道的作用，而且弥补了传统断裂力学理论中忽略了微观裂纹增长及损伤累积过程的缺陷，使得模型更加接近于真实情况，并利用VB语言编制了相应的预测软件，为塑料压力管道长期性能的研究和预测提供了一种新方法。
本文利用高分子材料学、损伤力学、材料力学和计算机图形学等基本理论，建立起高分子材料在蠕变和疲劳载荷长期加载过程中损伤演变的数学模型，并运用数值方法对其进行分析计算，以实现对塑料压力管道长期性能的预测和寿命分析。本方法只需通过快捷的拉伸实验得到材料的各损伤参数并代入基于损伤力学的模型中进行分析模拟，即可对材料的长期使用性能进行模拟并可对其失效寿命进行预测，从而使只通过简洁的实验即可获得材料的长期力学性能成为可能，并使对高分子材料长期性能的认识，从宏观进入微观、从定性进入定量、从静态进入动态，为预测塑料压力管道的服役寿命和检修年限提供了科学依据及分析手段。总结如下：
1．根据损伤力学原理，对高分子材料在疲劳载荷和蠕变载荷加载下的损伤演变过程进行分析，得到各情况下的本构方程，从而分别推导出相应受力状态下的损伤演变方程；
2．对疲劳和蠕变两种加载形式下的损伤过程进行深入分析，建立了相应的物理模型和数学模型，使用Visual Basic语言编写出关于各自力学参数演变的可视化程序；
3．由于高分子材料的一些物性参数具有很高的温度依赖性，因此利用DMA方法分析得到材料在各温度下的力学参数，从而可计算得到其它与温度相关的材料参数。此外，由于进行损伤力学计算还需要得到材料的损伤参数，因此利用万能实验机对试样进行拉伸实验，并通过对其实验数据的整合处理，识别得到材料在常温下的相关损伤参数；
4．对聚丙烯材料进行了基于蠕变损伤模型的数值模拟，对材料的蠕变失效破坏过程进行了模拟分析，对其服役寿命进行了预测，并将模拟结果与DMA实验结果和文献中的实验结果相验证，证明通过此预测方法得到的蠕变数据可靠性较高；
5．对聚丙烯和高密度聚乙烯材料进行了基于疲劳损伤模型的数值模拟，对材料的疲劳失效破坏过程进行了模拟分析和寿命预测，并将模拟结果与实验结果相验证，通过比较证明此预测方法得到的疲劳数据较为准确；
6．针对于塑料压力管在使用过程中所承受的真实应力状态，对疲劳和蠕变两种损伤形式进行耦合分析，建立了相应的物理模型和数学模型，使用Visual Basic语言编写出其力学参数演变的可视化程序。明确直观的模拟了塑料压力管道在实际使用过程中长期力学性能的演变过程，并可根据具体的材料、应力、温度等条件对其服役寿命进行预测；
7．对塑料压力管道的真实受力状态进行建模分析，并对管径为100mm的PE100级燃气管道在真实应力状态下的损伤过程进行了分析模拟，证明了疲劳载荷对管道寿命具有较大影响，并对本领域的未来发展方向进行了预测。
To predict the lifetime under the long-term loading of plastic pressure pipes exactly has great importance to the determination of the examination time of polymer parts and the preventing from the possibility of accidents takes place. However, traditional studies of it were nearly all based on fracture mechanics which were ignored the process before the crack engendered and the evolvement of damage in materials. This paper constructed the physical model and the mathematical model of the mechanical parameters and the evolvement of damage in the long-term creep and fatigue process of polymer material based on damage mechanics.
This physical model was based on polymer material science, theory of damage mechanics, rheology and computer graphics, the damage condition under the long-time load was analyzed and the lifetime was predicted by the numerical simulation method use damage mechanics. The damage process of crack initiation was analyzed based on the theory of damage mechanics. The damage process before the engender of crack under the condition of long-time load can be simulated by drawing tests, the material parameters and damage parameters can be obtained from these tests which were subsequently used in the numerical simulation of damage mechanics in polymer parts. The damage processes of the polymer parts were numerically simulated by dynamical quantitative and microscopic methods, which have great importance to the determination of the examine time of polymer parts and the preventing from the possibility of accidents take place. This paper provided the scientific evidence and analytical measures to the damage process of polymer. The main work was as follows:
1. The evolvement of damage in the long-term creep and fatigue process of polymer material was analyzed by damage mechanics, One-dimensional principal damage equations were induced to analysis the damage process of polymer under the different loading situations;
2. This paper researched the damage process for the fatigue loading and creep loading, the certain physical and mathematical models were established as to each of the loadings of the polymer, the computer program for the damage process was programmed by the Visual Basic 6.0;
3. Because some material properties of polymer were nonlinearly dependent on the temperature, we used DMA method to get the dynamics properties in different temperature, from which we can get other temperature-depended material properties by calculation. The damage properties in different temperature of polymer can also be computed by the dynamic properties which were obtained from the DMA experiments;
4. The damage process of PP in long-time creep loading was obtained from the numerical simulation based on the creep damage model, the lifetime of PP was predicted which has high reliability to be compared to the data get from DMA tests;
5. The damage process of PP and HDPE in long-time fatigue loading was simulated by the VB program which based on the fatigue damage model, and the lifetime of polymer parts were predicted with the fatigue predicting program which has high reliability to be compared to the data get from DMA tests;
6. To predict the lifetime of polymer pressure pipes under the real long-life loading exactly, we use the Visual Basic 6.0 program to simulate the composed process of fatigue and creep by the mathematic model based on damage mechanics;
7. The relationship between the lifetime and the parameters in long-time loading was analyzed in this research, and the analytical results were compared with the experimental data. The relationship between temperature of environment and lifetime of polyethylene is investigated. These results demonstrate that the fatigue lifetime tend to be decreased to the increase of the stress range and the temperature under high cycle fatigue loading, and the creep lifetime will be rapidly decreased to the increase of the creep stress and the temperature under creep loading.
本文利用高分子材料学、损伤力学、材料力学和计算机图形学等基本理论，建立起高分子材料在蠕变和疲劳载荷长期加载过程中损伤演变的数学模型，并运用数值方法对其进行分析计算，以实现对塑料压力管道长期性能的预测和寿命分析。本方法只需通过快捷的拉伸实验得到材料的各损伤参数并代入基于损伤力学的模型中进行分析模拟，即可对材料的长期使用性能进行模拟并可对其失效寿命进行预测，从而使只通过简洁的实验即可获得材料的长期力学性能成为可能，并使对高分子材料长期性能的认识，从宏观进入微观、从定性进入定量、从静态进入动态，为预测塑料压力管道的服役寿命和检修年限提供了科学依据及分析手段。总结如下：
1．根据损伤力学原理，对高分子材料在疲劳载荷和蠕变载荷加载下的损伤演变过程进行分析，得到各情况下的本构方程，从而分别推导出相应受力状态下的损伤演变方程；
2．对疲劳和蠕变两种加载形式下的损伤过程进行深入分析，建立了相应的物理模型和数学模型，使用Visual Basic语言编写出关于各自力学参数演变的可视化程序；
3．由于高分子材料的一些物性参数具有很高的温度依赖性，因此利用DMA方法分析得到材料在各温度下的力学参数，从而可计算得到其它与温度相关的材料参数。此外，由于进行损伤力学计算还需要得到材料的损伤参数，因此利用万能实验机对试样进行拉伸实验，并通过对其实验数据的整合处理，识别得到材料在常温下的相关损伤参数；
4．对聚丙烯材料进行了基于蠕变损伤模型的数值模拟，对材料的蠕变失效破坏过程进行了模拟分析，对其服役寿命进行了预测，并将模拟结果与DMA实验结果和文献中的实验结果相验证，证明通过此预测方法得到的蠕变数据可靠性较高；
5．对聚丙烯和高密度聚乙烯材料进行了基于疲劳损伤模型的数值模拟，对材料的疲劳失效破坏过程进行了模拟分析和寿命预测，并将模拟结果与实验结果相验证，通过比较证明此预测方法得到的疲劳数据较为准确；
6．针对于塑料压力管在使用过程中所承受的真实应力状态，对疲劳和蠕变两种损伤形式进行耦合分析，建立了相应的物理模型和数学模型，使用Visual Basic语言编写出其力学参数演变的可视化程序。明确直观的模拟了塑料压力管道在实际使用过程中长期力学性能的演变过程，并可根据具体的材料、应力、温度等条件对其服役寿命进行预测；
7．对塑料压力管道的真实受力状态进行建模分析，并对管径为100mm的PE100级燃气管道在真实应力状态下的损伤过程进行了分析模拟，证明了疲劳载荷对管道寿命具有较大影响，并对本领域的未来发展方向进行了预测。
To predict the lifetime under the long-term loading of plastic pressure pipes exactly has great importance to the determination of the examination time of polymer parts and the preventing from the possibility of accidents takes place. However, traditional studies of it were nearly all based on fracture mechanics which were ignored the process before the crack engendered and the evolvement of damage in materials. This paper constructed the physical model and the mathematical model of the mechanical parameters and the evolvement of damage in the long-term creep and fatigue process of polymer material based on damage mechanics.
This physical model was based on polymer material science, theory of damage mechanics, rheology and computer graphics, the damage condition under the long-time load was analyzed and the lifetime was predicted by the numerical simulation method use damage mechanics. The damage process of crack initiation was analyzed based on the theory of damage mechanics. The damage process before the engender of crack under the condition of long-time load can be simulated by drawing tests, the material parameters and damage parameters can be obtained from these tests which were subsequently used in the numerical simulation of damage mechanics in polymer parts. The damage processes of the polymer parts were numerically simulated by dynamical quantitative and microscopic methods, which have great importance to the determination of the examine time of polymer parts and the preventing from the possibility of accidents take place. This paper provided the scientific evidence and analytical measures to the damage process of polymer. The main work was as follows:
1. The evolvement of damage in the long-term creep and fatigue process of polymer material was analyzed by damage mechanics, One-dimensional principal damage equations were induced to analysis the damage process of polymer under the different loading situations;
2. This paper researched the damage process for the fatigue loading and creep loading, the certain physical and mathematical models were established as to each of the loadings of the polymer, the computer program for the damage process was programmed by the Visual Basic 6.0;
3. Because some material properties of polymer were nonlinearly dependent on the temperature, we used DMA method to get the dynamics properties in different temperature, from which we can get other temperature-depended material properties by calculation. The damage properties in different temperature of polymer can also be computed by the dynamic properties which were obtained from the DMA experiments;
4. The damage process of PP in long-time creep loading was obtained from the numerical simulation based on the creep damage model, the lifetime of PP was predicted which has high reliability to be compared to the data get from DMA tests;
5. The damage process of PP and HDPE in long-time fatigue loading was simulated by the VB program which based on the fatigue damage model, and the lifetime of polymer parts were predicted with the fatigue predicting program which has high reliability to be compared to the data get from DMA tests;
6. To predict the lifetime of polymer pressure pipes under the real long-life loading exactly, we use the Visual Basic 6.0 program to simulate the composed process of fatigue and creep by the mathematic model based on damage mechanics;
7. The relationship between the lifetime and the parameters in long-time loading was analyzed in this research, and the analytical results were compared with the experimental data. The relationship between temperature of environment and lifetime of polyethylene is investigated. These results demonstrate that the fatigue lifetime tend to be decreased to the increase of the stress range and the temperature under high cycle fatigue loading, and the creep lifetime will be rapidly decreased to the increase of the creep stress and the temperature under creep loading.
引文
1．董孝理．塑料压力管道快速开裂危险性和制止措施．新型建筑材料，1997，5：29—32
2．潘红斌．塑料压力管道的应用及其焊接技术．太原科技．2002(4)：15—17
3．孙彤彤．HDPE管材的开发与应用概况．塑料，2001，27(6)：42—45
4．黄家文，金谦．国内外塑料管道技术发展动态．上海建材．2002(3)：9—12
5．张玉川．塑料埋地排水管及其在我国的发展前景．中国塑料，2001，15(3)：5—15
6．李亚峰，陈加豪．塑料管在给排水管道工程中的应用．沈阳建筑工程学院学报，2000，16(3)：207—209
7．徐佩弦．塑料件的失效．北京：国防工业出版社，1998．第一版
8．王茂忠，王文广．塑料给水管材的开发现状．塑料科技，2000(1)：17—20
9．胡永民，王建民．给水系统中塑料管材的应用现状及分析．工程塑料应用，2001，29(2)：44—47
10．刘伯元，徐凌秀．中国塑料管技术进展．现代塑料加工应用，1999，11(3)：60—64
11．中国工业管道网：www．pipes．net．cn
12．陈祖敏．影响聚乙烯管材耐环境应力开裂的因素及对策．塑料科技，2000，6：27—29
13．董孝理．从应用角度考虑塑料压力管的力学破坏问题．新型建筑材料，1999，10：11—13
14．周维祥．塑料测试技术．北京：化学工业出版社，1997：135—142
15．林明宝等译．塑料测试方法手册．上海：上海科学技术文献出版社．1994，6．第一版
16. R.K. Krishnaswamy, M.J. Lamborn, A.M. Sukhadia, D.F. Register, P.L. Maeger, P.S. Leer ers. Rapid crack propagation failures in HDPE pipes:Polymer Engineering & Science, 2006,46(10):1358-1362
17. S. Hillmansen, S. Hobeika, R.N. Haward, P.S. Leevers. The effect of strain rate, temperature, and molecular mass on the tensile deformation of polyethylene. Polymer Engineering & Science, 2000,40(2):481-489
18．刘秀国，刘厚俊等．聚乙烯压力管道抗快速裂纹扩展性能的实验研究．工程塑料应用，2003，31(1)：49—51
19. Zhuo Zhuang, Yongjin Guo. Analysis of dynamic fracture mechanisms in gas pipelines. Engineering Fracture Mechanics, 1999,64:271-289
20. Leevers PS. The extension force for rapid crack propagation along a gas pressurised pipeline. Imperial College of Science Technology and Medicine, 1992,12:45-55.
21．庄茁，O’Donoghue P．E．天然气管道裂纹稳定扩展问题的分析模型和最小二乘法解答．固体力学学报，1997，18(3)：229-239
22. Kanninen M F, Leung C P, O'Donoghue, Morrow T B. Joint final report on the development of a ductile pipe fracture model. Virginia:Pipeline Research Committee, 1992:15-18
23. P.E.O'Donoghue, S.T. Green, M.F. Kanninen, P.K. Bowles, The development of a fluid/structure interaction model for flawed fluid containment boundaries with applications to gas transmission and distribution piping. Computers & Structures, 1991,38(5-6): 501-513
24．庄茁．断裂动力学有限元程序的开发及在天然气管道裂纹扩展问题上的应用．工程力学，1999，16(1)：105-113
25. A. Ivankovic, G.P. Venizelos. Rapid Crack. Propagation in Plastic Pipe:Predicting Full-Scale Critical Pressure from S4 Test Results. Engineering Fracture Mechanics, 1998,59(5):607-622
26. C.J. Greenshields, G.P. Venizelos, A. Ivankovic. A Fluid-Structure Model for Fast Brittle Fracture in Plastic Pipes. Journal of Fluids and Structures, 2000,14:221-234
27. Hyungyil LEE, David M. Parks. Line-Spring Finite Element for Fully Plastic Crack Growth-Ⅱ. Surface Cracked Plates and Pipes. Solids Structures, 1998, 35(36):5139-5158
28. G. Huysmans, I. Verpoest, G. De Roeck. Structural Analysis of GRP Pipe Couplers by Using a Fracture Mechanical Approach. Elsevier Science, 1998,29B:477-487
29．冯耀荣，庄茁等．裂纹尖端张开角及在输气管线止裂预测中的应用．石油学报，2003，24(4)：100-107
30．由小川，庄茁，冯耀荣，霍春勇，庄传晶．西气东输管道裂纹的韧性减速机理研究．工程力学，2004，21(4)：57-65
31．邓增杰，周敬恩．工程材料的断裂与疲劳．北京：机械工业出版社，1995
32．J．勒麦特．损伤力学教程．北京：科学出版社，1996
33．王中光．材料的疲劳．北京：国防工业出版社，1993
34．李兆霞．损伤力学及其应用．北京：科学出版社，2002
35．黄克智．材料的损伤断裂机理和宏微观力学理论．北京：清华大学出版社，1999
36．余寿文，冯西桥．损伤力学．北京：清华大学出版社，1997
37．张行．断裂与损伤力学．北京：北京航空航天大学出版社，2006
38．韩哲文．高分子科学实验．上海：华东理工大学出版社，2005
39．周克印，徐行健等．基于损伤测试的构件疲劳剩余寿命估算方法研究．中国安全科学学报，2004，14(5)：110-113
40．朱锡雄，朱国瑞．高分子材料强度学．杭州：浙江大学出版社，1992
41．徐灏．疲劳强度．北京：高等教育出版社，1988
42．李春葆，刘圣才，张植民．Visual Basic程序设计．北京：清华大学出版社，2005
43．何曼君．高分子物理．上海：复旦大学出版社，1998
44．周光泉，刘孝敏．粘弹性理论．合肥：中国科学技术大学出版社，1996
45. Dixon—Stubb PJ. Journal Mater Sci, 1981, 64: 233
46．卢少忠，卢晓晔等．塑料管道工程的性能生产应用．北京：中国建材工业出版社，2004
47．李国辉．埋地输气管道疲劳强度分析．管道技术与设备．2006，2：45-46
48. W. Balika, G. Pinter, R. W. Lang. Systematic Investigations of Fatigue Crack Growth Behavior of a PE-HD Pipe Grade in Through-Thickness Direction. Journal of Applied Polymer Science, Vol. 103, 1745-1758 (2007)
49. Hertzberg R W, Manson J A. Fatigue of Engineeering Plastics. New York: Academic Press, 1980
50. Kinloch A J, Young R J. Fracture Behaviour of Polymers. London: Appl Sci Pub, 1982
51．桂祖桐．聚乙烯树脂及其应用．北京：化学工业出版社，2002
52．张小文．塑料管道及管件加工与应用．北京：中国石化出版社，2003
53．汪大林．输气管道的储气与调峰，www．GB50028．com
54．董峰，徐苓安．脉动流条件下煤气计量的误差估计．煤气与热力，1998，18(1)：27-31
55．益小苏．高分子材料的制备与加工．杭州：浙江大学出版社，1997
56．王玉梅，郭书平．国外天然气管道事故分析．油气储运，2000，19(7)：5-10
2．潘红斌．塑料压力管道的应用及其焊接技术．太原科技．2002(4)：15—17
3．孙彤彤．HDPE管材的开发与应用概况．塑料，2001，27(6)：42—45
4．黄家文，金谦．国内外塑料管道技术发展动态．上海建材．2002(3)：9—12
5．张玉川．塑料埋地排水管及其在我国的发展前景．中国塑料，2001，15(3)：5—15
6．李亚峰，陈加豪．塑料管在给排水管道工程中的应用．沈阳建筑工程学院学报，2000，16(3)：207—209
7．徐佩弦．塑料件的失效．北京：国防工业出版社，1998．第一版
8．王茂忠，王文广．塑料给水管材的开发现状．塑料科技，2000(1)：17—20
9．胡永民，王建民．给水系统中塑料管材的应用现状及分析．工程塑料应用，2001，29(2)：44—47
10．刘伯元，徐凌秀．中国塑料管技术进展．现代塑料加工应用，1999，11(3)：60—64
11．中国工业管道网：www．pipes．net．cn
12．陈祖敏．影响聚乙烯管材耐环境应力开裂的因素及对策．塑料科技，2000，6：27—29
13．董孝理．从应用角度考虑塑料压力管的力学破坏问题．新型建筑材料，1999，10：11—13
14．周维祥．塑料测试技术．北京：化学工业出版社，1997：135—142
15．林明宝等译．塑料测试方法手册．上海：上海科学技术文献出版社．1994，6．第一版
16. R.K. Krishnaswamy, M.J. Lamborn, A.M. Sukhadia, D.F. Register, P.L. Maeger, P.S. Leer ers. Rapid crack propagation failures in HDPE pipes:Polymer Engineering & Science, 2006,46(10):1358-1362
17. S. Hillmansen, S. Hobeika, R.N. Haward, P.S. Leevers. The effect of strain rate, temperature, and molecular mass on the tensile deformation of polyethylene. Polymer Engineering & Science, 2000,40(2):481-489
18．刘秀国，刘厚俊等．聚乙烯压力管道抗快速裂纹扩展性能的实验研究．工程塑料应用，2003，31(1)：49—51
19. Zhuo Zhuang, Yongjin Guo. Analysis of dynamic fracture mechanisms in gas pipelines. Engineering Fracture Mechanics, 1999,64:271-289
20. Leevers PS. The extension force for rapid crack propagation along a gas pressurised pipeline. Imperial College of Science Technology and Medicine, 1992,12:45-55.
21．庄茁，O’Donoghue P．E．天然气管道裂纹稳定扩展问题的分析模型和最小二乘法解答．固体力学学报，1997，18(3)：229-239
22. Kanninen M F, Leung C P, O'Donoghue, Morrow T B. Joint final report on the development of a ductile pipe fracture model. Virginia:Pipeline Research Committee, 1992:15-18
23. P.E.O'Donoghue, S.T. Green, M.F. Kanninen, P.K. Bowles, The development of a fluid/structure interaction model for flawed fluid containment boundaries with applications to gas transmission and distribution piping. Computers & Structures, 1991,38(5-6): 501-513
24．庄茁．断裂动力学有限元程序的开发及在天然气管道裂纹扩展问题上的应用．工程力学，1999，16(1)：105-113
25. A. Ivankovic, G.P. Venizelos. Rapid Crack. Propagation in Plastic Pipe:Predicting Full-Scale Critical Pressure from S4 Test Results. Engineering Fracture Mechanics, 1998,59(5):607-622
26. C.J. Greenshields, G.P. Venizelos, A. Ivankovic. A Fluid-Structure Model for Fast Brittle Fracture in Plastic Pipes. Journal of Fluids and Structures, 2000,14:221-234
27. Hyungyil LEE, David M. Parks. Line-Spring Finite Element for Fully Plastic Crack Growth-Ⅱ. Surface Cracked Plates and Pipes. Solids Structures, 1998, 35(36):5139-5158
28. G. Huysmans, I. Verpoest, G. De Roeck. Structural Analysis of GRP Pipe Couplers by Using a Fracture Mechanical Approach. Elsevier Science, 1998,29B:477-487
29．冯耀荣，庄茁等．裂纹尖端张开角及在输气管线止裂预测中的应用．石油学报，2003，24(4)：100-107
30．由小川，庄茁，冯耀荣，霍春勇，庄传晶．西气东输管道裂纹的韧性减速机理研究．工程力学，2004，21(4)：57-65
31．邓增杰，周敬恩．工程材料的断裂与疲劳．北京：机械工业出版社，1995
32．J．勒麦特．损伤力学教程．北京：科学出版社，1996
33．王中光．材料的疲劳．北京：国防工业出版社，1993
34．李兆霞．损伤力学及其应用．北京：科学出版社，2002
35．黄克智．材料的损伤断裂机理和宏微观力学理论．北京：清华大学出版社，1999
36．余寿文，冯西桥．损伤力学．北京：清华大学出版社，1997
37．张行．断裂与损伤力学．北京：北京航空航天大学出版社，2006
38．韩哲文．高分子科学实验．上海：华东理工大学出版社，2005
39．周克印，徐行健等．基于损伤测试的构件疲劳剩余寿命估算方法研究．中国安全科学学报，2004，14(5)：110-113
40．朱锡雄，朱国瑞．高分子材料强度学．杭州：浙江大学出版社，1992
41．徐灏．疲劳强度．北京：高等教育出版社，1988
42．李春葆，刘圣才，张植民．Visual Basic程序设计．北京：清华大学出版社，2005
43．何曼君．高分子物理．上海：复旦大学出版社，1998
44．周光泉，刘孝敏．粘弹性理论．合肥：中国科学技术大学出版社，1996
45. Dixon—Stubb PJ. Journal Mater Sci, 1981, 64: 233
46．卢少忠，卢晓晔等．塑料管道工程的性能生产应用．北京：中国建材工业出版社，2004
47．李国辉．埋地输气管道疲劳强度分析．管道技术与设备．2006，2：45-46
48. W. Balika, G. Pinter, R. W. Lang. Systematic Investigations of Fatigue Crack Growth Behavior of a PE-HD Pipe Grade in Through-Thickness Direction. Journal of Applied Polymer Science, Vol. 103, 1745-1758 (2007)
49. Hertzberg R W, Manson J A. Fatigue of Engineeering Plastics. New York: Academic Press, 1980
50. Kinloch A J, Young R J. Fracture Behaviour of Polymers. London: Appl Sci Pub, 1982
51．桂祖桐．聚乙烯树脂及其应用．北京：化学工业出版社，2002
52．张小文．塑料管道及管件加工与应用．北京：中国石化出版社，2003
53．汪大林．输气管道的储气与调峰，www．GB50028．com
54．董峰，徐苓安．脉动流条件下煤气计量的误差估计．煤气与热力，1998，18(1)：27-31
55．益小苏．高分子材料的制备与加工．杭州：浙江大学出版社，1997
56．王玉梅，郭书平．国外天然气管道事故分析．油气储运，2000，19(7)：5-10
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