6 Mechanical Characterization and Numerical Modeling of High Density Polyethylene Pipes 65 y1=yy1/e1 y2=yy2/e2 y0 = s/(y1+y2) y = y0 DO WHILE ( dly < 4. ) y0 = y x1 = EXP((h1+P*g1)/(KK*T))/e1 x2 = EXP((h2+P*g2)/(KK*T))/e2 sinh1 = log(y0*x1+sqrt((y0*x1)**2.+1.)) sinh2 = log(y0*x2+sqrt((y0*x2)**2.+1.)) f = K*T*(sinh1/v1+sinh2/v2)-s ff=K*T*(x1/SQRT((y0*x1)**2.+1.)/v1+x2/SQRT((y0*x2)**2.+1.)/v2) y = y0-f/ff dly = log10(y0)-log10(abs(f/ff)) END DO DECRA(1) = y*DTIME C RETURN END References 1. Hu, J., Li, Y., Chen, W., Zhao, B., Yang, D.: Effects of temperature and stress on creep properties of ethylene tetrafluoroethylene (ETFE) foils for transparent buildings. Polym. Test. 59, 268–276 (2017) 2. Zhou, F., Hou, S., Qian, X., Chen, Z., Zheng, C., Xu, F.: Creep behavior and lifetime prediction of PMMA immersed in liquid scintillator. Polym. Test. 53, 323–328 (2016) 3. Takahashi, Y., Tateiwa, T., Shishido, T., Masaoka, T., Kubo, K., Yamamoto, K.: Size and thickness effect on creep behavior in conventional and vitamin E-diffused highly crosslinked polyethylene for total hip arthroplasty. J. Mech. Behav. Biomed. Mater. 62, 399–406 (2016) 4. Fatima, M., Mohamed, S., Mohamed, E.: Burst behavior of CPVC compared to HDPE thermoplastic polymer under a controlled internal pressure. Proc. Struct. Integrity. 3, 380–386 (2017) 5. Moon, J., Bae, H., Song, J., Choi, S.: Algorithmic methods of reference-line construction for estimating long-term strength of plastic pipe system. Polym. Test. 56, 58–64 (2016) 6. Zhang, Y., Jar, P.-Y.B.: Time-strain rate superposition for relaxation behavior of polyethylene pressure pipes. Polym. Test. 50, 292–296 (2016) 7. Vakili-Tahami, F., Adibeig, M.R.: Using developed creep constitutive model for optimum design of HDPE pipes. Polym. Test. 63, 392–397 (2017) 8. Taherzadehboroujeni, M., Kalhor, R., Fahs, G., Moore, R., Case, S.: Accelerated testing method to estimate the long-term hydrostatic strength of semi-crystalline plastic pipes. Polym. Eng. Sci. 60, (2019) 9. Kühl, A., Muñoz-Rojas, P.A., Barbieri, R., Benvenutti, I.J.: A procedure for modeling the nonlinear viscoelastoplastic creep of HDPE at small strains. Polym. Eng. Sci. 57, 144–152 (2017) 10. Cheng, C., Widera, G.O.: Development of maximum secondary creep strain method for lifetime of HDPE pipes. J. Press. Vessel. Technol. 131, 021208 (2009) 11. Guedes, R.M.: A viscoelastic model for a biomedical ultra-high molecular weight polyethylene using the time-temperature superposition principle. Polym. Test. 30, 294–302 (2011) 12. Colak, O.U., Dusunceli, N.: Modeling viscoelastic and viscoplastic behavior of high density polyethylene (HDPE). J. Eng. Mater. Technol. 128, 572–578 (2006) 13. Reis, J.M.L., Pacheco, L.J., da Costa Mattos, H.S.: Tensile behavior of post-consumer recycled high-density polyethylene at different strain rates. Polym. Test. 32, 338–342 (2013) 14. Bilgin, O.: Modeling viscoelastic behavior of polyethylene pipe stresses. J. Mater. Civ. Eng. 26, 676–683 (2014) 15. Taherzadeh, M., Baghani, M., Baniassadi, M., Abrinia, K., Safdari, M.: Modeling and homogenization of shape memory polymer nanocomposites. J. Compos. Part B Eng. 91, 36–43 (2016) 16. Yang, F., Mousavie, A., Oh, T., Yang, T., Lu, Y., Farley, C., Bodnar, R., Niu, L., Qiao, R., Li, Z.: Sodium–sulfur flow battery for low-cost electrical storage. J. Adv Energy Mater. 8, 1701991 (2018) 17. Piavis, W., Turn, S., Mousavi, A.: Non-thermal gliding-arc plasma reforming of dodecane and hydroprocessed renewable diesel. Int J Hydrogen Energy. 40, 13295–13305 (2015) 18. Eyring, H.: Viscosity, plasticity, and diffusion as examples of absolute reaction rates. J. Chem. Phys. 4, 283–291 (1936) 19. Bauwens, J.: Yield condition and propagation of Lüders’ lines in tension–torsion experiments on poly (vinyl chloride). J. Polym. Sci. B Polym. Phys. 8, 893–901 (1970) 20. Bauwens-Crowet, C., Bauwens, J.-C., Homès, G.: The temperature dependence of yield of polycarbonate in uniaxial compression and tensile tests. J. Mater. Sci. 7, 176–183 (1972) 21. Bauwens-Crowet, C.: The compression yield behaviour of polymethyl methacrylate over a wide range of temperatures and strain-rates. J. Mater. Sci. 8, 968–979 (1973)
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