Viscoplastic behaviour of a medium density polyethylene (MDPE): Constitutive equations based on double nonlinear deformation model

Abstract The viscoplastic behaviour of a medium density ethylene–butene copolymer (MDPE) is investigated by using samples cut out from thick-walled MDPE pipe. Extensive experimental work has been performed to characterise the nonlinear time-dependent response of such semi-crystalline thermoplastic material. Tests were carried out at 60 °C, on smooth tensile, full axisymmetrically notched creep tensile (FNCT) and double edge notched tensile (DENT) specimens. Tests were conducted under constant strain rate, creep, stress relaxation and dip-test conditions. The experimental data on smooth uniaxial specimens indicate two regimes of creep deformation as well as the existence of a back stress effect. The notched geometries allowed to investigate the creep behaviour of a structure with a local multiaxial stress states near to the crack tip. In order to model the observed material behaviour, a double inelastic deformation model, DID, containing two additive inelastic mechanisms is suggested. Both DID model and its parameters’ optimiser are already implemented in the F.E.M. Zset code at Ecole des Mines de Paris. It is shown that this model is able to reproduce the creep strain history on homogeneous uniaxial tensile tests in a large range of strain rate including the back stress effects, as well as on cracked specimens. Moreover, the time dependent multiaxial stress–strain fields computed (under finite strain formulation) in the vicinity of the crack tip are in good accordance with the Riedel and Rice (RR) analytical singularities. Thus, this fully predictive model clearly shows its superiority and effectiveness over models that take into account only one inelastic viscoplastic deformation under uniaxial conditions.

[1]  Thomas J. R. Hughes,et al.  Unconditionally stable algorithms for quasi-static elasto/visco-plastic finite element analysis , 1978 .

[2]  D. Vokoun,et al.  On backstresses, overstresses, and internal stresses represented on the mesoscale , 2005 .

[3]  J. Ganghoffer,et al.  Continuous symmetries and constitutive laws of dissipative materials within a thermodynamic framework of relaxation: Part I: Formal aspects , 2007 .

[4]  Jacques Besson,et al.  Large scale object-oriented finite element code design , 1997 .

[5]  Erhard Krempl,et al.  Rate (time)-dependent deformation behavior: an overview of some properties of metals and solid polymers , 2003 .

[6]  Georges Cailletaud,et al.  Study of plastic/viscoplastic models with various inelastic mechanisms , 1995 .

[7]  P. B. Bowden,et al.  The plastic flow of isotropic polymers , 1972 .

[8]  Noëlle Billon,et al.  Creep damage mechanisms in polyethylene gas pipes , 2001 .

[9]  I. Ward.  Review: The yield behaviour of polymers , 1971 .

[11]  H. Eyring.  Viscosity, Plasticity, and Diffusion as Examples of Absolute Reaction Rates , 1936 .

[12]  S. Bodner,et al.  A Large Deformation Elastic-Viscoplastic Analysis of a Thick-Walled Spherical Shell , 1972 .

[13]  M. Boyce,et al.  Large inelastic deformation of glassy polymers. part I: rate dependent constitutive model , 1988 .

[14]  A. Argon.  A theory for the low-temperature plastic deformation of glassy polymers , 1973 .

[15]  H. Ben Hadj Hamouda,et al.  Fracture mechanics global approach concepts applied to creep slow crack growth in a medium density polyethylene (MDPE) , 2007 .

[16]  J. Z. Zhu,et al.  The finite element method , 1977 .

[17]  S. R. Bodner,et al.  Constitutive Equations for Elastic-Viscoplastic Strain-Hardening Materials , 1975 .

[18]  Oscar Lopez-Pamies,et al.  Thermo-mechanical large deformation response and constitutive modeling of viscoelastic polymers over a wide range of strain rates and temperatures , 2006 .

[19]  C. Popelar,et al.  Viscoelastic material characterization and modeling for polyethylene , 1990 .

[20]  W. T. Koiter,et al.  Asymptotic approximations to crack problems , 1973 .

[21]  M. Kitagawa,et al.  Nonlinear constitutive equation for polyethylene under combined tension and torsion , 1990 .

[22]  J. Jonas,et al.  Yield and transient effects during the plastic deformation of solid polymers , 1981 .

[23]  Erhard Krempl,et al.  Extension of the viscoplasticity theory based on overstress (VBO) to capture non-standard rate dependence in solids , 2002 .

[24]  O. Colak,et al.  Modeling of the monotonic and cyclic Swift effects using an isotropic, finite viscoplasticity theory based on overstress (FVBO) , 2004 .

[25]  Ozgen U. Colak,et al.  Modeling deformation behavior of polymers with viscoplasticity theory based on overstress , 2005 .

[26]  Hermann Riedel,et al.  Creep deformation at crack tips in elastic-viscoplastic solids , 1981 .