Restricted accessResearch articleFirst published online 2026
Numerical and experimental investigation of temperature- and strain-rate-dependent double yielding in mLLDPE dumbbell specimens based on a three-network model
Double yielding is a typical tensile response of semi-crystalline polymers (SCPs), reflecting the coupled evolution of amorphous and crystalline phases. In this work, the double yielding behavior of metallocene-catalyzed linear low-density polyethylene (mLLDPE) is examined through polarized optical microscopy (POM), Fourier-transform infrared spectroscopy (FTIR), differential scanning calorimetry (DSC), X-ray diffraction (XRD), and tensile tests. Owing to its multiple short-chain branches, mLLDPE exhibits a broad lamellar thickness distribution that governs the emergence of double yielding. Combined DSC–XRD analysis further confirms lamellar fragmentation, melting, and recrystallization during deformation. DSC peak deconvolution quantitatively distinguishes high- and low-stability crystalline domains, clarifying their sequential transformation during the two yielding events. A three-network model (TNM) is adopted to describe amorphous yielding, lamellar failure, and rubber-like chain deformation. Finite-element simulations reproduce the double yielding behavior of mLLDPE specimens (NRMSE < 3%). Both yield stresses decrease linearly with temperature (R2 > 0.99) and follow the Ree–Eyring relation with strain rate (R2 > 0.94). These results deepen the understanding of structure–deformation relationships in SCPs and offer a quantitative foundation for tailoring polymer microstructures to achieve targeted mechanical performance in engineering applications.
ZhangTZengSLiL. Fabrication of polyethylene/poly (vinyl alcohol) multilayer composite film with excellent oxygen barrier properties, water resistant and high strength. J Appl Polym Sci2025; 142: e57902. https://doi.org/10.1002/app.57902
2.
KartashovDAKartsevISTolochekRV, et al.Calculation of radiation loads in a space station compartment with additional protection of high-pressure polyethylene. Cosm Res2019; 57(3): 169–175. https://doi.org/10.1134/S0010952519030055
HussanASebaibiN. Valorization of polyethylene and polypropylene fibers from waste fishing gears into cementitious material and comparison with industrial polypropylene fibers. J Build Eng2025; 104: 112281. https://doi.org/10.1016/j.jobe.2025.112281
5.
GabrielCLilgeD. Comparison of different methods for the investigation of the short-chain branching distribution of LLDPE. Polymer2001; 42(1): 297–303. https://doi.org/10.1016/S0032-3861(00)00314-1
MajumdarAKaleDD. Properties of films made from ternary blends of metallocene and conventional polyolefins. J Appl Polym Sci2001; 81(1): 53–57. https://doi.org/10.1002/app.1412
9.
KishimotoMMitaKOgawaH, et al.Effect of submicron structures on the mechanical behavior of polyethylene. Macromolecules2020; 53(20): 9097–9107. https://doi.org/10.1021/acs.macromol.0c00896
10.
WangZWangKFanZ, et al.Double yielding of polypropylene/calcium carbonate composites: influence of filler content and test conditions. J Appl Polym Sci2025; 142(25): e57046. https://doi.org/10.1002/app.57046
11.
GrosBGérardJFSottaP, et al.Double yielding in PA11: discriminating the mechanical contributions of the amorphous and crystalline fractions. Polymer2025; 335: 128844. https://doi.org/10.1016/j.polymer.2025.128844
12.
HiejimaYMisumiNIppitsuR, et al.Compressive double yielding in high-density polyethylene over a wide range of strain rates. Polymer2024; 291: 126590. https://doi.org/10.1016/j.polymer.2023.126590
13.
ManzurA. Strain rate effect on crystallinity variations in the double yield region of polyethylene. J Appl Polym Sci2008; 108(3): 1574–1581. https://doi.org/10.1002/app.27806
14.
IqbalOGuoHChenW. Structural origin of double yielding: the critical role of crystallite aggregate heterogeneity. Macromolecules2021; 54(18): 8381–8392. https://doi.org/10.1021/acs.macromol.1c01363
15.
LucasJCFaillaMDSmithFL, et al.The double yield in the tensile deformation of the polyethylenes. Polym Eng Sci1995; 35(13): 1117–1123. https://doi.org/10.1002/pen.760351308
16.
IqbalOHabumugishaJCFengS, et al.Microstructural origin of the double yield points of the metallocene linear low-density polyethylene (mLLDPE) precursor film under uniaxial tensile deformation. Polymers2020; 13(1): 126. https://doi.org/10.3390/polym13010126
17.
FotheringhamDGCherryBW. The role of recovery forces in the deformation of linear polyethylene. J Mater Sci1978; 13: 951–964. https://doi.org/10.1007/BF00544690
Gaucher-MiriVSéguélaR. Tensile yield of polyethylene and related copolymers: mechanical and structural evidences of two thermally activated processes. Macromolecules1997; 30(4): 1158–1167. https://doi.org/10.1021/ma9601878
21.
SeguelaRRietschF. Double yield point in polyethylene under tensile loading. J Mater Sci Lett1990; 9(1): 46–47. https://doi.org/10.1007/BF00722865
22.
HawardRNThackrayG. The use of a mathematical model to describe isothermal stress-strain curves in glassy thermoplastics. Proc R Soc Lond Ser A Math Phys Sci1968; 302(1471): 453–472. https://doi.org/10.1098/rspa.1968.0029
23.
EyringH. Viscosity, plasticity, and diffusion as examples of absolute reaction rates. J Chem Phys1936; 4(4): 283–291. https://doi.org/10.1063/1.1749836
24.
TreloarLRG. Physics of rubber elasticity (Oxford classic texts in the physical sciences)[M]. Oxford University Press, 2005.
25.
BoyceMCParksDMArgonAS. Large inelastic deformation of glassy polymers. Part I: rate dependent constitutive model. Mech Mater1988; 7(1): 15–33. https://doi.org/10.1016/0167-6636(88)90003-8
ZhangYChiRWangS, et al.A novel phenomenological constitutive model for semi-crystalline polymers across a wide strain-rate range. Polymers2025; 17(6): 762. https://doi.org/10.3390/polym17060762
28.
IadarolaACiardielloRPaolinoDS. A new effective phenomenological constitutive model for semi‐crystalline and amorphous polymers. Polym Eng Sci2024; 64(8): 3730–3750. https://doi.org/10.1002/pen.26808
LiJZhuZLiT, et al.Quantification of the Young's modulus for polypropylene: influence of initial crystallinity and service temperature. J Appl Polym Sci2020; 137(16): 48581. https://doi.org/10.1002/app.48581
31.
DetrezFCantournetSSeguelaR. A constitutive model for semi-crystalline polymer deformation involving lamellar fragmentation. C R Mec2010; 338(12): 681–687. https://doi.org/10.1016/j.crme.2010.10.008
32.
UchidaMTadaN. Micro-meso-to macroscopic modeling of deformation behavior of semi-crystalline polymer. Int J Plast2013; 49: 164–184. https://doi.org/10.1016/j.ijplas.2013.03.007
33.
HaoPLaheriVDaiZ, et al.A rate-dependent constitutive model predicting the double yield phenomenon, self-heating and thermal softening in semi-crystalline polymers. Int J Plast2022; 153: 103233. https://doi.org/10.1016/j.ijplas.2022.103233
34.
HaoPDaiZLaheriV, et al.A unified amorphous–crystalline viscoplastic hardening law for non-isothermal modelling of thermoplastics and thermosets. Int J Plast2022; 159: 103469. https://doi.org/10.1016/j.ijplas.2022.103469
35.
SedighiamiriAGovaertLEVan DommelenJAW. Micromechanical modeling of the deformation kinetics of semicrystalline polymers. J Polym Sci B Polym Phys2011; 49(18): 1297–1310. https://doi.org/10.1002/polb.22297
36.
AyoubGZaïriFNaït-AbdelazizM, et al.Modelling large deformation behaviour under loading–unloading of semicrystalline polymers: application to a high density polyethylene. Int J Plast2010; 26(3): 329–347. https://doi.org/10.1016/j.ijplas.2009.07.005
37.
AyoubGZaïriFFréderixC, et al.Effects of crystal content on the mechanical behaviour of polyethylene under finite strains: experiments and constitutive modelling. Int J Plast2011; 27(4): 492–511. https://doi.org/10.1016/j.ijplas.2010.07.005
38.
Abdul-HameedHMessagerTAyoubG, et al.A two-phase hyperelastic-viscoplastic constitutive model for semi-crystalline polymers: application to polyethylene materials with a variable range of crystal fractions. J Mech Behav Biomed Mater2014; 37: 323–332. https://doi.org/10.1016/j.jmbbm.2014.04.016
39.
AhziSMakradiAGregoryRV, et al.Modeling of deformation behavior and strain-induced crystallization in poly (ethylene terephthalate) above the glass transition temperature. Mech Mater2003; 35(12): 1139–1148. https://doi.org/10.1016/S0167-6636(03)00004-8
40.
MakradiAAhziSGregoryRV, et al.A two-phase self-consistent model for the deformation and phase transformation behavior of polymers above the glass transition temperature: application to PET. Int J Plast2005; 21(4): 741–758. https://doi.org/10.1016/j.ijplas.2004.04.012
41.
KumarMRaviKSinghSS. Predicting the double-yield phenomenon in low-density polyethylene film using three-network viscoplastic model. Mech Mater2023; 184: 104736. https://doi.org/10.1016/j.mechmat.2023.104736
42.
WangZWangK. Double yielding of mLLDPE: effects of temperature and strain-rate and insights into dumbbell specimen deformation and self-heating. J Appl Polym Sci2025; 143: e70128. https://doi.org/10.1002/app.70128
43.
WangYJYanWD. Investigation on chain structure of LLDPE obtained by ethylene in-situ copolymerization with DSC and XRD. Chin Sci Bull2007; 52(6): 736–742. https://doi.org/10.1007/s11434-007-0093-4
44.
SilvestreCCimminoSRaimoM, et al.Structure and morphology development in films of mLLDPE/LDPE blends during blowing. Macromol Mater Eng2006; 291(12): 1477–1485. https://doi.org/10.1002/mame.200600239
45.
BergstromJSBischoffJE. An advanced thermomechanical constitutive model for UHMWPE. Int J Struct Changes Solids2010; 2(1): 31–39.
46.
LiCXiaZWuL, et al.Strain-dependent evolution of the rigid amorphous fraction of low-density polyethylene under deformation. Macromolecules2025; 58(5): 2320–2335. https://doi.org/10.1021/acs.macromol.4c02773
MhlabeniTRamjeeSLópezJ, et al.Thermal and rheological properties of fischer–tropsch Wax/High‐Flow LLDPE blends. Macromol Mater Eng2024; 309(8): 2300125. https://doi.org/10.1002/mame.202300125
49.
PopliRGlotinMMandelkernL, et al.Dynamic mechanical studies of α and β relaxations of polyethylenes. J Polym Sci Polym Phys Ed1984; 22(3): 407–448. https://doi.org/10.1002/pol.1984.180220306
50.
KakueMSekiyaMToguD, et al.Elucidation of the isothermal crystallization behavior of polyethylene/polystyrene block copolymers by peak separation of differential scanning calorimetry curves. Kobunshi Ronbunshu2019; 76(2): 150–156. (in Japanese). https://doi.org/10.1295/koron.2018-0047
51.
HynčíkLKochováPŠpičkaJ, et al.Identification of the lldpe constitutive material model for energy absorption in impact applications. Polymers2021; 13(10): 1537. https://doi.org/10.3390/polym13101537
52.
ChenHSongPComminsT, et al.Characterization and modelling of bisphenol-a type epoxy polymer over a wide range of rates and temperatures. Polymer2022; 249: 124860. https://doi.org/10.1016/j.polymer.2022.124860
53.
ReeTEyringH. The relaxation theory of transport phenomena[M]//Rheology. Academic Press, 1958, pp. 83–144.
FarahaniMFBagheriR. A new look at tensile yielding in isotactic polypropylene: role of strain rate and thermal softening. Polym Bull2022; 79: 11157–11176. https://doi.org/10.1007/s00289-021-03997-z
56.
JohnsenJClausenAHGryttenF, et al.A thermo-elasto-viscoplastic constitutive model for polymers. J Mech Phys Solid2019; 124: 681–701. https://doi.org/10.1016/j.jmps.2018.11.018
