Numerical Results (Macro-mechanical Approach)

Five creep tests on the MDPE pipe material were used to develop the model, as in Table 4. The parameters of the nonlinear viscoelastic model (Eq. 11) are given in Table 4. Figures 8 and 9 compare experimental and simulated data. It is shown that the simulated strain data fit well. At stress levels other than those used for model development, the simulations match the experimental results as well, except when close to the highest stress (9.32 MPa) where the strain curve changes drastically and digresses from the main group strain (see Figure 9). Similar results have been found for HDPE materials at stresses higher than 10 MPa, as shown by Liu and Polak (2005).

Table 4. Nonlinear viscoelastic model for MDPE. Kelvin elements = 3.

H= 500

x2 = 10000

із = 200000

Stress (MPa)

E0 (MPa)

E1

E2

E3

3.12

640

1137.4169

1067.2127

1168.6089

5.10

470

804.3798

718.0750

588.7810

6.23

420

813.3631

668.5170

422.0754

8.40

410

690.8382

572.2448

224.6822

Figure 8. Creep tests vs. model simulations at modelling stresses.

Figure 9. Creep tests vs. model simulations at verification stresses.

4. Conclusions

Two different approaches to study the mechanical behaviour of medium – and high-density polyethylene subjected to uniaxial tension are presented. From the results, the following conclusions can be drawn: 1) The described theories offer practical avenues of obtaining accurate representations of the behaviour of polyethylene from both the micro – and macro-scopic viewpoints; 2) For the microscopic approach, it is possible to couple the various deformation mechanisms and degradation processes taking place at the crystal level; 3) Material parameters are easily defined from experimental tensile tests; 4) The numerical stress-strain responses agree, up to certain deformations, with the experimental ones obtained by Hillmansen et al. (2000) and G’Sell et al. (2002); 5) For the macroscopic approach, the model simulates well the creep behaviour of medium – and high-density polyethylene; 6) The material parameters are obtained from creep tests directly on pipe material; 7) The model represents well the strong nonlinear viscoelasticity observed experimentally at intermediate stress levels; and 8) Both approaches could be applied to model other polymeric materials.

References

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Asaro, R. J. and Rice, J. R. 1977. Strain localization in ductile single crystals. Journal of the Mechanics and Physics of Solids, 25: 309-338.

G’Sell, C., Dahoun, A., Hiver, J. M., and Addiego, F. 2002. Competition des mecanismes de cisaillement plastique et d’endommagement dans les polymers solides en traction uniaxiale, Materiaux, 1-5.

Hillmansen, S., Hobeika, S., Haward, R. N., and Leevers, P. S. 2000. The effect of strain rate, temperature, and molecular mass on the tensile deformation of polyethylene. Polymer Engineering and Science, 40: 481-489.

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Parks, D. M. and Ahzi, S. 1990. Polycrystalline plastic deformation and texture evolution for crystals lacking five independent slip systems. Journal of the Mechanics and Physic of Solids, 38: 701-724.