]. S. Bibliographie, O. M. Senet5, L. Friedman, R. Radder, D. Gullick et al., Une carte mondiale du stress hydrique [3] The United Nations World Water Development Report 2015 Water for a sustainable world Guide produit par l'Association des Maires de France (AMF), à l'intention des collectivités dans le cadre du décret relatif à la définition d'un descriptif détaillé des réseaux Observatoire des services publics d'eau et d'assainissement, Panorama des services et de leur performance en 2012 Verification and control of low pressure transients in distribution systems, Water Qual. Technol. Conf. Steward. Drink. Water Qual, 2003.

E. D. Patrick, D. K. O-'day, R. Weiss, S. L. Chiavri, and . Moruzzi, Modélisation statistique de la prévision des défaillances sur les conduites d'eau potable Water main evaluation for rehabilitation / remplacement Reasons for pipe damage, Guidance manual of AWWA research Fundation, pp.182-185, 1989.

M. Kremer, Vieillissement des canalisations Exemple de politique de renouvellement en France et en R.F.A, synthèse bibliographique, 1990.

, Observatoire de l'eau: État des lieux du patrimoine des réseaux d'eau potable en Seine-et- Marne, 2012.

J. Cador, Le patrimoine en canalisations d'AEP en France ; bilan des huit enquêtes départementales et estimation nationale, 2002.

, PE versus fonte : le match Available: http://www.ryb.fr/expert-blog, 2015.

, Chapter 4: PE Pipe and Fittings Manufacturing, Handbook of Polyethylene Pipe, Plastics Pipe Institute, pp.105-123

F. M. Peres and C. G. Schön, Application of the essential work of fracture method in ranking the performance in service of high-density polyethylene resins employed in pressure pipes, Journal of Materials Science, vol.15, issue.6, pp.1844-1850, 2008.
DOI : 10.1007/978-1-4899-3124-5

B. Standard and B. Iso, Plastics piping and ducting systems?Determination of the longterm hydrostatic strength of, 2003.

N. Merah, F. Saghir, Z. Khan, and A. Bazoune, Effect of temperature on tensile properties of HDPE pipe material, Plastics, Rubber and Composites, vol.64, issue.6, pp.226-230, 2006.
DOI : 10.1002/pol.1977.180150907

S. Ting, Characterization of the fracture behavior of polyethylene using measured cohesive curves. I: Effects of constraint and rate, Polymer Engineering & Science, vol.71, issue.6, 2006.
DOI : 10.1520/STP18024S

M. Fleissner, Experience with a full notch creep test in determining the stress crack performance of polyethylenes, Polymer Engineering & Science, vol.20, issue.2, 1998.
DOI : 10.1007/BF00559346

G. P. Marshall, L. E. Culver, and J. G. Williams, Craze Growth in Polymethylmethacrylate: A Fracture Mechanics Approach, Proc. R. Soc. A Math, pp.165-187, 1970.
DOI : 10.1098/rspa.1970.0173

K. Tonyali and H. Brown, On the applicability of linear elastic fracture mechanics to environmental stress cracking of low-density polyethylene, Journal of Materials Science, vol.19, issue.4, 1986.
DOI : 10.1080/00222348108246311

W. Allwood and S. Beech, The development of the 'notched pipe test'for the assessment of the slow crack growth resistance of polyethylene pipe, Constr. Build. Mater, 1993.

S. Beech, A. Channell, and L. Rose, Slow crack growth performance assessment in polyethylene pipe, Proc. 14th Int. Plast. fuel gas pipe Symp. Am. Gas Assoc, 1995.

J. Boot, Z. Guan, and I. Toropova, Structural design of thin walled polyethylene pipe linings for water mains, Plast. rubber Compos. Process. Appl, 1996.
DOI : 10.1016/0886-7798(95)00038-0

B. Cotterell and J. , The essential work of plane stress ductile fracture, Int. J. Fract, 1977.

S. C. Tjong, S. A. Xu, and R. K. Li, Work of fracture of polystyrene/high density polyethylene blends compatibilized by triblock copolymer, Journal of Applied Polymer Science, vol.68, issue.9, pp.2074-2081, 2000.
DOI : 10.1115/1.3601206

Y. Marchal, J. Walhin, and F. Delannay, Statistical procedure for improving the precision of the measurement of the essential work of fracture of thin sheets, Int. J. Fract, 1997.

Y. Mai and P. Powell, Polym Sci Part B Polym Phys, 1991.

G. P. Cherepanov, Cracks in solids, International Journal of Solids and Structures, vol.4, issue.8, pp.811-831, 1968.
DOI : 10.1016/0020-7683(68)90059-0

J. Rice, A path independent integral and the approximate analysis of strain concentration by notches and cracks, J. Appl. Mech, 1968.

A. Griffith, The Phenomena of Rupture and Flow in Solids, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.221, issue.582-593, 1921.
DOI : 10.1098/rsta.1921.0006

G. Irwin, Analysis of stresses and strains near the end of a crack traversing a plate, SPIE MILESTONE Ser. MS, 1997.

A. S. Kobayashi, S. T. Chiu, and R. Beeuwkes, A numerical and experimental investigation on the use of J-integral, Engineering Fracture Mechanics, vol.5, issue.2, pp.293-305, 1973.
DOI : 10.1016/0013-7944(73)90024-6

R. Mcmeeking and D. Parks, On criteria for J-dominance of crack-tip fields in large-scale yielding, Elastic-plastic Fract. ASTM Int, 1979.

C. Shih and M. German, Requirements for a one parameter characterization of crack tip fields by the HRR singularity, Int. J. Fract, 1981.

, Recent finite element studies in plasticity and fracture mechanics, Comput. Methods Appl. Mech. Eng, 1979.

A. Ani and J. Hancock, J-dominance of short cracks in tension and bending, J. Mech. Phys. Solids, 1991.

V. Kumar, M. German, and C. Shih, Engineering approach for elastic-plastic fracture analysis, 1981.
DOI : 10.2172/6068291

K. B. Broberg, Critical review of some theories in fracture mechanics, International Journal of Fracture Mechanics, vol.4, issue.1, 1968.
DOI : 10.1007/BF00189139

Y. Mai and B. Cotterell, Effects of pre-strain on plane stress ductile fracture in ?-brass, Journal of Materials Science, vol.1, issue.9, 1980.
DOI : 10.1007/BF00552319

Y. Mai and B. Cotterell, On the essential work of ductile fracture in polymers, International Journal of Fracture, vol.18, issue.2, 1986.
DOI : 10.1007/BF00019787

Y. Mai and B. Cotterell, The essential work of plane stress ductile fracture of linear polyethylenes, Polymer Engineering and Science, vol.7, issue.11, 1987.
DOI : 10.1002/pen.760271106

T. Pardoen, Y. Marchal, and F. Delannay, Essential work of fracture compared to fracture mechanics???towards a thickness independent plane stress toughness, Engineering Fracture Mechanics, vol.69, issue.5, 2002.
DOI : 10.1016/S0013-7944(01)00099-6

R. Lach, K. Schneider, and R. Weidisch, Application of the essential work of fracture concept 136 to nanostructured polymer materials, Eur. Polym. J, 2005.

J. G. Williams and M. Rink, The standardisation of the EWF test, Engineering Fracture Mechanics, vol.74, issue.7, pp.1009-1017, 2007.
DOI : 10.1016/j.engfracmech.2006.12.017

E. Clutton, Fracture Mechanics Testing Methods for Polymers, Adhesives and Composites, vol.28, 2001.

S. Hashemi, Work of fracture of PBT/PC blend: Effect of specimen size, geometry, and rate of testing, Polymer Engineering & Science, vol.13, issue.5, 1997.
DOI : 10.1016/0013-7944(85)90059-1

J. Wu and Y. Mai, The essential fracture work concept for toughness measurement of ductile polymers, Polymer Engineering & Science, vol.1, issue.18, 1996.
DOI : 10.1016/0022-5096(52)90003-3

A. Arkhireyeva and S. Hashemi, Fracture behaviour of polyethylene naphthalate (PEN) Polymer (Guildf), 2002.
DOI : 10.1016/s0032-3861(01)00623-1

A. Arkhireyeva, S. Hashemi, and M. O-'brien, Factors affecting work of fracture of uPVC film, J. Mater. Sci, 1999.

D. Ferrer-balas and M. Maspoch, On the essential work of fracture method: Energy partitioning of the fracture process in iPP films, Polymer Bulletin, vol.42, issue.1, 1999.
DOI : 10.1007/s002890050440

W. Poon, E. Ching, C. Cheng, and R. Li, Measurement of plane stress essential work of fracture (EWF) for polymer films: effects of gripping and notching methodology, Polymer Testing, vol.20, issue.4, 2001.
DOI : 10.1016/S0142-9418(00)00049-0

M. Light and A. Lesser, Effect of test conditions on the essential work of fracture in polyethylene terephthalate film, Journal of Materials Science, vol.20, issue.12, 2005.
DOI : 10.1007/s10853-005-2430-9

S. Hashemi, Fracture of polybutylene terephthalate (PBT) film Polymer (Guildf), 2002.
DOI : 10.1016/s0032-3861(02)00204-5

J. Karger-kocsis, T. Czigány, and E. Moskala, Thickness dependence of work of fracture parameters of an amorphous copolyester, Polymer, vol.38, issue.18, 1997.
DOI : 10.1016/S0032-3861(96)01061-0

R. Yamakawa, C. Razzino, C. Correa, and E. Hage, Influence of notching and molding conditions on determination of EWF parameters in polyamide 6, Polymer Testing, vol.23, issue.2, 2004.
DOI : 10.1016/S0142-9418(03)00080-1

M. Elmeguenni, M. Naït-abdelaziz, F. Zaïri, and J. M. Gloaguen, Fracture characterization of high-density polyethylene pipe materials using the $$J$$ J -integral and the essential work of fracture, International Journal of Fracture, vol.27, issue.2, pp.119-133, 2013.
DOI : 10.1016/j.ijplas.2010.03.007

URL : https://hal.archives-ouvertes.fr/hal-00988071

A. International, Standard Test Method for Determining J-R Curves of Plastic Materials 1, pp.1-8, 2013.

A. Benhamena, L. Aminallah, B. B. Bouiadjra, M. Benguediab, A. Amrouche et al., J integral solution for semi-elliptical surface crack in high density poly-ethylene pipe under bending, Materials & Design, vol.32, issue.5, pp.2561-2569, 2011.
DOI : 10.1016/j.matdes.2011.01.045

URL : https://hal.archives-ouvertes.fr/hal-00610338

A. Benhamena, B. Bachir-bouiadjra, A. Amrouche, G. Mesmacque, N. Benseddiq et al., Three finite element analysis of semi-elliptical crack in high density poly-ethylene pipe subjected to internal pressure, Materials & Design, vol.31, issue.6, pp.3038-3043, 2010.
DOI : 10.1016/j.matdes.2010.01.029

URL : https://hal.archives-ouvertes.fr/hal-00461519

D. Parks, The virtual crack extension method for nonlinear material behavior, Computer Methods in Applied Mechanics and Engineering, vol.12, issue.3, 1977.
DOI : 10.1016/0045-7825(77)90023-8

T. Hellen, On the method of virtual crack extensions, International Journal for Numerical Methods in Engineering, vol.85, issue.1, 1975.
DOI : 10.1115/1.3656900

H. Delorenzi, On the energy release rate and the J-integral for 3-D crack configurations, International Journal of Fracture, vol.44, issue.No. 3, 1982.
DOI : 10.1007/BF00250778

H. G. Delorenzi, Energy release rate calculations by the finite element method, Engineering Fracture Mechanics, vol.21, issue.1, pp.129-143, 1985.
DOI : 10.1016/0013-7944(85)90060-8

C. Shih, B. Moran, and T. Nakamura, Energy release rate along a three-dimensional crack front in a thermally stressed body, Int. J. Fract, 1986.

B. Moran and C. Shih, A general treatment of crack tip contour integrals, International Journal of Fracture, vol.34, issue.4, 1987.
DOI : 10.1016/0022-5096(86)90022-0

N. Trifunovic, Water transmission, p.24, 2013.

H. Darcy, Recherches expérimentales relatives au mouvement de l'eau dans les tuyaux, p.1857

DOI : 10.1680/ijoti.1939.13150

E. Wylie, V. Streeter, and L. Suo, Fluid transients in systems, 1993.

I. Shames, Mechanics of fluids, 1982.

S. Stuckenbruck, The Influence of Pipe Motion on Acoustic Wave Propagation, Journal of Fluids Engineering, vol.107, issue.4, 1985.
DOI : 10.1115/1.3242523

E. Wylie and V. Streeter, Hydraulic transients, 1983.

J. D. Ferry, Viscoelastic Properties of Polymers, 1980.

DOI : 10.1115/1.3650851

E. Meißner and G. Franke, Influence of pipe material on the dampening of water hammer, Proc. 17th Congr, 1977.

D. Williams, Waterhammer in Non-Rigid Pipes: Precursor Waves and Mechanical Damping, Journal of Mechanical Engineering Science, vol.42, issue.6, 1977.
DOI : 10.1243/PIME_PROC_1968_183_051_02

B. Sharp and K. Theng, Water hammer attenuation in uPVC pipe, Conference on Hydraulics in Civil Engineering, p.132, 1987.

M. Güney, Contribution à l'étude du phénomène de coup de bélier en conduite viscoélastique, 1977.

M. Güney, Waterhammer in viscoelastic pipes where cross-section parameters are time- Dependent, Fourth International Conference on Pressure Surges, pp.21-33, 1983.

S. Kokoshvili, Water hammer in a viscoelastic pipe, Polymer Mechanics, vol.72, issue.5, 1970.
DOI : 10.1007/BF00856213

D. Covas, I. Stoianov, and H. Ramos, The dynamic effect of pipe-wall viscoelasticity in hydraulic transients. Part I???experimental analysis and creep characterization, Journal of Hydraulic Research, vol.19, issue.5, 2004.
DOI : 10.1002/pen.11683

D. Covas, I. Stoianov, and J. Mano, The dynamic effect of pipe-wall viscoelasticity in hydraulic transients. Part II???model development, calibration and verification, Journal of Hydraulic Research, vol.90, issue.1, 2005.
DOI : 10.1080/00221689309498876

, Water hammer in pressurized polyethylene pipes: conceptual model and experimental analysis, Urban Water J, 2004.

B. Brunone and B. Karney, Velocity Profiles and Unsteady Pipe Friction in Transient Flow, Journal of Water Resources Planning and Management, vol.126, issue.4, 2000.
DOI : 10.1061/(ASCE)0733-9496(2000)126:4(236)

B. Brunone and A. Berni, Wall Shear Stress in Transient Turbulent Pipe Flow by Local Velocity Measurement, Journal of Hydraulic Engineering, vol.136, issue.10, 2010.
DOI : 10.1061/(ASCE)HY.1943-7900.0000234

A. Soares, D. Covas, and L. Reis, Analysis of PVC Pipe-Wall Viscoelasticity during Water Hammer, Journal of Hydraulic Engineering, vol.134, issue.9, 2008.
DOI : 10.1061/(ASCE)0733-9429(2008)134:9(1389)

H. Duan and M. Ghidaoui, Unsteady friction and visco-elasticity in pipe fluid transients, Journal of Hydraulic Research, vol.90, issue.3, 2010.
DOI : 10.1080/00221686.2006.9521717

A. Soares and D. Covas, Unsteady Flow with Cavitation in Viscoelastic Pipes, International Journal of Fluid Machinery and Systems, vol.2, issue.4, 2009.
DOI : 10.5293/IJFMS.2009.2.4.269

L. Hadj-ta?eb and E. Hadj-ta?eb, Numerical Simulation of Transient Flows in Viscoelastic Pipes with Vapour Cavitation, International Journal of Modelling and Simulation, vol.29, issue.2, 2009.
DOI : 10.1080/02286203.2009.11442526

A. , K. Conf, and . Ser, Investigation of transient cavitating flow in viscoelastic pipes, Earth Environ. Sci, 2010.

A. Keramat, A. Tijsseling, Q. Hou, and A. Ahmadi, Fluid???structure interaction with pipe-wall viscoelasticity during water hammer, Journal of Fluids and Structures, vol.28, 2012.
DOI : 10.1016/j.jfluidstructs.2011.11.001

E. Achouyab and B. Bahrar, Numerical modeling of phenomena of waterhammer using a model of fluid???structure interaction, Comptes Rendus Mécanique, 2011.
DOI : 10.1016/j.crme.2011.02.003

A. Colombo, P. Lee, and B. Karney, A selective literature review of transient-based leak detection methods, Journal of Hydro-environment Research, vol.2, issue.4, 2009.
DOI : 10.1016/j.jher.2009.02.003

A. Soares, D. Covas, and L. Reis, Inverse Transient Analysis for leak detection in a PVC pipe network, Water Manag. challenges Glob. Chang, 2007.

A. Lazhar, L. Hadj-taïeb, and E. Hadj-taïeb, Two leaks detection in viscoelastic pipeline systems by means of transient, Journal of Loss Prevention in the Process Industries, vol.26, issue.6, pp.1341-1351, 2013.
DOI : 10.1016/j.jlp.2013.08.007

R. Théodor and P. Lascaux, Initiation à l'analyse numérique: CNAM cours A, 1982.

E. Fischer, H. Sterzel, and G. Wegner, Investigation of the structure of solution grown crystals of lactide copolymers by means of chemical reactions, 1973.

V. Gaucher and ?. Miri, Reversible strain-induced order in the amorphous phase of a low-density ethylene/butene copolymer, Journal of Polymer Science Part B: Polymer Physics, vol.35, issue.13, 1997.
DOI : 10.1002/(SICI)1099-0488(19970930)35:13<2151::AID-POLB15>3.0.CO;2-3

S. Hillmansen and S. Hobeika, The effect of strain rate, temperature, and molecular mass on the tensile deformation of polyethylene, Polymer Engineering & Science, vol.38, issue.8, 2000.
DOI : 10.1021/ie50436a023

S. Hobeika, Y. Men, and G. Strobl, -vinyl acetate), Macromolecules, vol.33, issue.5, 2000.
DOI : 10.1021/ma9910484

C. G. Sell and J. Haudin, Lois de comportement mécanique des polymères solides, JM Introd. à la mécanique des polymères. Inst. Natl. Polytech. Lorraine, 1995.

Q. Fang, T. Wang, H. Beom, and H. Zhao, Rate-dependent large deformation behavior of PC/ABS, Polymer, vol.50, issue.1, 2009.
DOI : 10.1016/j.polymer.2008.10.042

J. Richeton, S. Ahzi, K. S. Vecchio, F. C. Jiang, and R. R. Adharapurapu, Influence of temperature and strain rate on the mechanical behavior of three amorphous polymers: Characterization and modeling of the compressive yield stress, International Journal of Solids and Structures, vol.43, issue.7-8, pp.2318-2335, 2006.
DOI : 10.1016/j.ijsolstr.2005.06.040

URL : https://hal.archives-ouvertes.fr/hal-00096988

G. Boisot, Mécanismes et modélisation mécanique de la déformation, de l'endommagement et de la rupture du PolyAmide 11 pur et renforcé choc, 2009.

C. G. 'sell, J. Hiver, and A. Dahoun, Experimental characterization of deformation damage in solid polymers under tension, and its interrelation with necking, Int. J. Solids Struct, 2002.

T. Yannick, Identification Par Analyse Inverse Du Comportement Mecanique Des Polymers Solides; Applications Aux Sollicitations Multiaxiales Et Rapides, 1998.

F. Rabah, Etude Expérimentale et Modélisation Numérique du comportement mécanique du PEHD à l'état vierge et après vieillissement thermique, 2012.

A. Lustiger and N. Ishikawa, An analytical technique for measuring relative tie-molecule concentration in polyethylene, Journal of Polymer Science Part B: Polymer Physics, vol.29, issue.9, 1991.
DOI : 10.1002/polb.1991.090290902

H. Kausch, Polymer Fracture, 2012.

R. Lang, A. Stern, and G. Doerner, Applicability and limitations of current lifetime prediction models for thermoplastics pipes under internal pressure, Die Angew. Makromol. Chemie, 1997.

A. Frank, W. Freimann, G. Pinter, and R. Lang, A fracture mechanics concept for the accelerated characterization of creep crack growth in PE-HD pipe grades, Engineering Fracture Mechanics, vol.76, issue.18, 2009.
DOI : 10.1016/j.engfracmech.2009.06.009

R. Krishnaswamy, Analysis of ductile and brittle failures from creep rupture testing of highdensity polyethylene (HDPE) pipes Polymer (Guildf), 2005.
DOI : 10.1016/j.polymer.2005.09.084

M. Barker, J. Bowman, and M. Bevis, The performance and causes of failure of polyethylene pipes subjected to constant and fluctuating internal pressure loadings, Journal of Materials Science, vol.23, issue.4, 1983.
DOI : 10.1007/BF00551979

B. Choi, A. Chudnovsky, and R. Paradkar, Experimental and theoretical investigation of stress corrosion crack (SCC) growth of polyethylene pipes, Polymer Degradation and Stability, vol.94, issue.5, 2009.
DOI : 10.1016/j.polymdegradstab.2009.01.016

V. Brosa, C. Bernal, and P. Frontini, Calibration of fracture mechanics parameters and J?R curve determination in polyethylene side-grooved arc-shaped specimens, Eng. Fract. Mech, 1999.

G. Clarke and J. Landes, Evaluation of the J Integral for the Compact Specimen, J. Test. Eval, 1979.

J. Tancrez, J. Pabiot, and F. Rietsch, Damage and fracture mechanisms in thermoplastic-matrix composites in relation to processing and structural parameters, Composites Science and Technology, vol.56, issue.7, 1996.
DOI : 10.1016/0266-3538(96)00013-9

D. Huang, The application of fracture mechanics to materials selection, Polymer Engineering & Science, vol.29, issue.18, 1996.
DOI : 10.1007/BF00351402

A. Saleemi and J. Nairn, The plane-strain essential work of fracture as a measure of the fracture toughness of ductile polymers, Polymer Engineering and Science, vol.16, issue.4, 1990.
DOI : 10.1002/pen.760300404

R. Varadarajan, E. K. Dapp, and C. M. Rimnac, Static fracture resistance of ultra high molecular weight polyethylene using the single specimen normalization method, Polymer Testing, vol.27, issue.2, pp.260-268, 2008.
DOI : 10.1016/j.polymertesting.2007.11.010

URL : http://europepmc.org/articles/pmc3563271?pdf=render

P. Lam and Y. Chao, Determination of constraint-modified JR curves for carbon steel storage tanks, Am. Soc. Mech. Eng, pp.133-142, 2002.
DOI : 10.1115/pvp2002-1116

URL : https://digital.library.unt.edu/ark:/67531/metadc742994/m2/1/high_res_d/799687.pdf

S. Marie, Approche énergétique de la déchirure ductile, 1999.

A. A. Rassis, Contribution à l'étude de la déchirure ductile à chaud dans les joints soudés et modélisation numérique en approche globale et en approche locale, 1995.

E. Roos, U. Eisele, and H. Silcher, Effect of stress state on the ductile fracture behavior of largescale specimens, Constraint Eff. Fract. ASTM Int, 1993.

T. Luu and G. Perrin, Plastic and damage behaviour of a high strength X100 pipeline steel: Experiments and modellingTanguy Plastic and damage behaviour of a high strength X100 pipeline steel: Experiments and modelling, Int. J, 2008.

X. Zhu, J. A. Joyceg, K. , J. , and C. , Review of fracture toughness (G, K, J, CTOD, CTOA) testing and standardization, CTOA) testing and standardization, pp.1-46, 2012.
DOI : 10.1016/j.engfracmech.2012.02.001

URL : http://digitalcommons.unl.edu/cgi/viewcontent.cgi?article=1048&context=usnavyresearch

R. Hiss, S. Hobeika, C. Lynn, and G. Strobl, Network Stretching, Slip Processes, and Fragmentation of Crystallites during Uniaxial Drawing of Polyethylene and Related Copolymers. A Comparative Study, Macromolecules, vol.32, issue.13, 1999.
DOI : 10.1021/ma981776b

C. G. Sell, J. Hiver, A. Dahoun, and A. Souahi, Video-controlled tensile testing of polymers and metals beyond the necking point, J. Mater. Sci, 1992.

E. C. Ching, W. K. Poon, R. K. Li, and Y. Mai, Effect of strain rate on the fracture toughness of some ductile polymers using the essential work of fracture (EWF) approach, Polymer Engineering & Science, vol.60, issue.12, pp.2558-2568, 2000.
DOI : 10.1016/S0013-7944(98)00024-1

G. C. Jacob, J. M. Starbuck, J. F. Fellers, S. Simunovic, and R. G. Boeman, Strain rate effects on the mechanical properties of polymer composite materials, Journal of Applied Polymer Science, vol.46, issue.1, pp.296-301, 2004.
DOI : 10.1051/jphys:01985004604055100

H. S. Costa, J. M. Reis, L. M. Paim, M. L. Silva, R. L. Junior et al., Failure analysis of corroded pipelines reinforced with composite repair systems, Engineering Failure Analysis, vol.59, pp.223-236, 2016.
DOI : 10.1016/j.engfailanal.2015.10.007

H. S. Da-costa-mattos, L. M. Paim, and J. M. Reis, Analysis of burst tests and long-term hydrostatic tests in produced water pipelines, Engineering Failure Analysis, vol.22, pp.128-140, 2012.
DOI : 10.1016/j.engfailanal.2012.01.011

M. Allouti, Étude de la nocivité de défauts dans les canalisations de transport de gaz tels les éraflures, 2010.

H. Adib-ramezani, J. Jeong, and G. Pluvinage, Structural integrity evaluation of X52 gas pipes subjected to external corrosion defects using the SINTAP procedure, International Journal of Pressure Vessels and Piping, vol.83, issue.6, pp.420-432, 2006.
DOI : 10.1016/j.ijpvp.2006.02.023

S. Zike and L. Mikkelsen, Correction of Gauge Factor for Strain Gauges Used in Polymer Composite Testing, Experimental Mechanics, vol.2, issue.3, 2014.
DOI : 10.1016/0749-6419(86)90005-7

K. Hoffmann, An introduction to measurements using strain gages, 1989.

C. Perry, The resistance strain gage revisited, Exp. Mech, 1984.
DOI : 10.1007/bf02323989

P. Stehlin, Strain distribution in and around strain gauges, Journal of Strain Analysis, vol.7, issue.3, 1972.
DOI : 10.1243/03093247V073228

M. Beatty and S. Chewning, Numerical analysis of the reinforcement effect of a strain gage applied to a soft material, International Journal of Engineering Science, vol.17, issue.7, 1979.
DOI : 10.1016/0020-7225(79)90019-3

R. Watson, Bonded Electrical Resistance Strain Gages, Exp. solid Mech, 2008.
DOI : 10.1007/978-0-387-30877-7_12

. Micro-measurements, VISHY precision group), " Strain Gages and Instruments Application Note TT-609

S. Courtin and C. Gardin, Advantages of the J-integral approach for calculating stress intensity factors when using the commercial finite element software ABAQUS, Engineering Fracture Mechanics, vol.72, issue.14, 2005.
DOI : 10.1016/j.engfracmech.2005.02.003

K. Hibbitt, ABAQUS: User's Manual, 1997.

A. Chehab and I. Moore, Constitutive model for high density polyethylene to capture strain reversal, Pipeline Div. Spec. Conf, 2006.

A. D. Drozdov and J. D. Christiansen, Thermo-viscoelastic and viscoplastic behavior of highdensity polyethylene, Int. J. Solids Struct, vol.45, pp.14-15, 2008.
DOI : 10.1016/j.ijsolstr.2008.03.008

URL : https://doi.org/10.1016/j.ijsolstr.2008.03.008

O. U. Colak and N. Dusunceli, Modeling Viscoelastic and Viscoplastic Behavior of High Density Polyethylene (HDPE), Journal of Engineering Materials and Technology, vol.41, issue.4, p.572, 2006.
DOI : 10.1007/s00707-002-0966-1

, Recent Developments in Durability Analysis of Composite Systems, 2000.

B. Aour, F. Zaïri, M. Naït-abdelaziz, J. M. Gloaguen, O. Rahmani et al., A computational study of die geometry and processing conditions effects on equal channel angular extrusion of a polymer, International Journal of Mechanical Sciences, vol.50, issue.3, pp.589-602, 2008.
DOI : 10.1016/j.ijmecsci.2007.07.012

URL : https://hal.archives-ouvertes.fr/hal-00264507

F. Zaïri, B. Aour, J. M. Gloaguen, M. Naït-abdelaziz, and J. M. Lefebvre, Numerical modelling of elastic???viscoplastic equal channel angular extrusion process of a polymer, Computational Materials Science, vol.38, issue.1, pp.202-216, 2006.
DOI : 10.1016/j.commatsci.2006.02.008

C. Zhang and I. Moore, Nonlinear mechanical response of high density polyethylene. Part I: Experimental investigation and model evaluation, Polymer Engineering & Science, vol.27, issue.2, 1997.
DOI : 10.1007/BF00542902

C. Zhang and I. Moore, Nonlinear mechanical response of high density polyethylene. Part II: Uniaxial constitutive modeling, Polymer Engineering & Science, vol.32, issue.2, 1997.
DOI : 10.1002/pen.760321606

N. Brown and I. M. Ward, The influence of morphology and molecular weight on ductile-brittle transitions in linear polyethylene, Journal of Materials Science, vol.17, issue.5, pp.1405-1420, 1983.
DOI : 10.1007/BF01111960

E. Roos and U. Eisele, Determination of material characteristic values in elastic-plastic fracture mechanics by means of J-integral crack resistance curves, J. Test. Eval, 1988.

U. Eisele and E. Roos, Evaluation of different fracture-mechanical J-integral initiation values with regard to their usability in the safety assessment of components, Nuclear Engineering and Design, vol.130, issue.3, 1991.
DOI : 10.1016/0029-5493(91)90216-5

P. Krawczak, Techniques de l ' Ingénieur Essais mécaniques des plastiques Caractéristiques à long terme et ténacité, pp.0-29, 2013.

A. N. Institute, Manual for Determining the Remaining Strength of Corroded Pipelines: A Supplement to ASME B31 Code for Pressure Piping, 1991.

A. Miller, Review of limit loads of structures containing defects, International Journal of Pressure Vessels and Piping, vol.32, issue.1-4, 1988.
DOI : 10.1016/0308-0161(88)90073-7

M. Staat, Plastic collapse analysis of longitudinally flawed pipes and vessels, Nucl. Eng. Des, 2004.

M. Staat, Local and global collapse pressure of longitudinally flawed pipes and cylindrical vessels, International Journal of Pressure Vessels and Piping, vol.82, issue.3, 2005.
DOI : 10.1016/j.ijpvp.2004.07.022

J. Kiefner, W. Maxey, R. Eiber, and A. Duffy, Failure Stress Levels of Flaws in Pressurized Cylinders, ASTM Spec. Tech, 1973.
DOI : 10.1520/STP49657S

M. Bouaziz, M. Guidara, C. Schmitt, J. Capelle, E. H. Taïeb et al., Failure Analysis of HDPE Pipe for Drinking Water Distribution and Transmission, Des. Model. Mech. Syst, 2015.
DOI : 10.1007/978-3-319-17527-0_41

M. B. Amara, G. Pluvinage, J. Capelle, and Z. Azari, Crack Tip Opening Angle as a Fracture Resistance Parameter to Describe Ductile Crack Extension and Arrest in Steel Pipes under Service Pressure, Physical Mesomechanics, vol.94, issue.95, pp.355-369, 2015.
DOI : 10.1016/j.compstruc.2012.01.004

H. Westergaard, Theory of elasticity and plasticity, 1952.
DOI : 10.4159/harvard.9780674436923

A. Eringen, Mechanics of continuaJohn Wiley and Sons, 1967.

S. Timoshenko and J. Goodier, Theory of Elasticity, 1970.

, Dossier technique: Tubes PE100, GLYNWED Alaxias Company

M. A. Guidara, M. A. Bouaziz, C. Schmitt, J. Capelle, E. Haj-taïeb et al., Structural integrity assessment of defected high density poly-ethylene pipe: Burst test and finite element analysis based on J-integral criterion, Engineering Failure Analysis, vol.57, pp.282-295, 2015.
DOI : 10.1016/j.engfailanal.2015.07.042

A. Jlali, E. Hadj-taïeb, and C. Thirriot, Algorithme simplifi?? de calcul de ph??nom??nes de propagation d???ondes dans un syst??me de conduites avec embranchement, La Houille Blanche, issue.1, pp.81-89, 2005.
DOI : 10.1051/lhb:200501011

C. Schmitt, G. Pluvinage, E. Hadj-taieb, and R. Akid, Water pipeline failure due to water hammer effects, Fatigue & Fracture of Engineering Materials and Structures, vol.107, issue.12, pp.1075-1082, 2006.
DOI : 10.1061/(ASCE)0733-9429(2001)127:2(134)

A. Fouzi and F. Ali, Comparative Study of the Phenomenon of Propagation of Elastic Waves in Conduits, 2011.


N. Syahruddin, LNG Loading Lines Surge Analysis for ESD System Application, 2011.

J. Emadi and A. Solemani, Maximum water hammer sensitivity analysis, World Acad. Sci. Eng. Technol, vol.5, issue.1, pp.353-356, 2011.

B. Rajani and S. Mcdonald, Water Mains Break Data on Different Pipe Materials for, Natl. Res. Counc. Canada, 1992.

B. Rajani, C. Zhan, and S. Kuraoka, Pipe??soil interaction analysis of jointed water mains, Canadian Geotechnical Journal, vol.33, issue.3, 1996.
DOI : 10.1139/t96-061

R. Morris, Principal Causes and Remedies of Water Main Breaks, Journal - American Water Works Association, vol.56, issue.6, 1967.
DOI : 10.1002/j.1551-8833.1964.tb01263.x

, Numerical Methods for Reliability and Safety Assessment, 2015.

M. H. Meliani, Z. Azari, G. Pluvinage, and J. Capelle, Gouge assessment for pipes and associated transferability problem, Engineering Failure Analysis, vol.17, issue.5, pp.1117-1126, 2010.
DOI : 10.1016/j.engfailanal.2010.01.007

A. K. Soares, D. I. Covas, and N. J. Carriço, Transient vaporous cavitation in viscoelastic pipes, Journal of Hydraulic Research, vol.109, issue.5, 2012.
DOI : 10.1115/1.3243120

C. Apollonio, D. I. Covas, G. De-marinis, A. Leopardi, H. M. Ramos et al., Creep functions for transients in HDPE pipes, Urban Water Journal, vol.17, issue.5, 2016.
DOI : 10.1061/(ASCE)0733-9429(2008)134:9(1389)