Among the wide range of structural polymers currently available, this work deals with high-density polyethylene (HDPE). The typical viscoelastic behavior of this material is not trivial to model and has already been investigated by many authors. We employ the fractional Zener model to fit our experimental creep results of HDPE evaluated at different stress levels. This model produces fractional constitutive equations with excellent curve-fitting properties and fewer parameters to be identified in relation to traditional models. The results are compared with those ones provided by the application of the Prony series method. The first novelty of this paper is the application of the time-stress equivalence principle (TSEP), coupled to the fractional model, to estimate creep at intermediate stress levels, that in turn, were not measured experimentally but lie within the stress range used to calibrate the model. We compare the results provided by this method with those based on linear interpolation of the parameters. Although there is clear benefits requiring fewer parameters, fractional derivatives render costly computations due to their history memory. To cope with this, we propose a new algorithm, called GPE, which shows a compromise between enhanced efficiency and accuracy when compared with other proposals of the literature. These features are verified with simulations for simple functions, and a long term creep test with the fractional Zener model. The combined application of fractional derivatives, TSEP and the new GPE algorithm results in a novel efficient and effective alternative to account for the creep modeling of HDPE.

This paper presents a new approach for modeling the constitutive behavior of time-dependent materials by applying two phenomenological constitutive models to creep curves. Data obtained from short-term test are used for predicting the long-term behavior. The nonlinear viscoelastic response is modeled by using the multi-Kelvin model and the viscoplastic behavior is described by a power law. The methodology proposed herein for obtaining the constitutive formulation is based on developing master curves. Results obtained for polyethylene are discussed and compared using creep tests at different stress levels and has proved to be reliable based on the results analyzed in this work.

A new methodology for modeling the creep behavior of polymers at different temperatures, by using phenomenological constitutive models, is presented in this paper. The viscoelastic model is given by a combination of springs and dashpots and is used to describe the nonlinear response of polymers, and the viscoplastic formulation is given by a power-law equation. The approach proposed in this work is based on building master curves for different stress levels, and finding the dependency of the constitutive parameters with the temperature. After fitting the equations to the tensile creep tests at different temperatures, the final constitutive formulation is capable of modeling the behavior of polymers at any stress level and temperatures. Poly methyl metacrytale (PMMA) was used to investigate the accuracy of this proposal, and the results showed good agreement with the experimental data.

Studying the nonlinear viscoelastic behavior of high-density polyethylene (HDPE) at small strains and stresses is still a matter of interest in engineering applications such as laying submerged pipelines. Although sound modeling of such behavior requires complex phenomenological or micromechanical constitutive laws, many works have focused on the development of simplified procedures for approximating this type of nonlinear response. Usually, when these simplified methods are employed to reproduce creep behavior, they are not capable to simultaneously provide good estimates for traction tests even at constant stress or strain rates. This work describes a methodology, which has shown a good compromise to reproduce both types of responses within a given stress range. The procedure can be understood as an interpolative approach based on a master curve and the modified superposition principle to account for nonlinear effects. With this strategy, it is possible to predict the nonlinear creep behavior for an HDPE sample subjected at any constant stress level within a given experimental range. Once this predictive capability is achieved, we use an incremental algorithm based on the modified superposition principle to simulate traction tests at constant strain rates. We show that the combined application of the proposed master curve approach and the modified superposition principle results in good approximations for creep tests and simultaneously leads to remarkable agreement with experimental traction tests reported in the literature.

HDPE pipes are frequently laid in buried or submerged conditions and are often subjected to considerable internal pressure. This context requires the consideration of HDPE as a structural material and demands constitutive models to predict failure possibilities in short and long terms. This article presents an approximate procedure to simulate the viscoelastoplastic nature of HDPE's material behavior under creep conditions. While a generalized Kelvin-Voigt model based on Prony series is used to model viscoelasticity, the power law of Zapas-Crissman is adopted to account for viscoplastic effects. The associated material parameters are obtained from experimental creep-recovery tests evaluated at different stress levels and constant temperature. As this type of test allows an uncoupled procedure for identifying the viscoelastic and viscoplastic material parameters, this task is divided into two stages: (i) a constrained nonsmooth optimization problem is defined and solved for the viscoelastic parameters, and (ii) the viscoplastic parameters are determined by linear regression. Thereafter, the viscoelastic and viscoplastic parameters obtained for each experimental stress level are interpolated linearly for intermediate stress conditions. Finally, a numerical-experimental example is presented, showing that the proposed procedure is able to reproduce adequately more complex loading conditions. POLYM. ENG. SCI., 57:144-152, 2017. (C) 2016 Society of Plastics Engineers