A practical approach to modeling time‐dependent nonlinear creep behavior of polyethylene for structural applications

The purpose of this work is to develop a practical method for constitutive modeling of polyethylene, based on a phenomenological approach, which can be applied for structural analysis. Polyethylene is increasingly used as a structural material, for example, in pipes installed by trenchless methods, where the relatively low stiffness of polyethylene reduces the required installation forces, chemical inertness makes it applicable for corrosive environments, and adequate strength allows its use in sewer, gas, and water lines. Polyethylene exhibits time‐dependent constitutive behavior which is also dependent on the applied stress level resulting in nonlinear stress–strain relationships. Nonlinear viscoelastic theory has been well established and a variety of modeling approaches have been derived from it. To realistically utilize the nonlinear modeling approaches in design, a simple method is needed for finding a constitutive formulation for a specific polyethylene type. This paper presents such a practical approach to nonlinear viscoelastic modeling utilizing both the multi‐Kelvin element theory and the power law functions to model creep compliance. Creep tests are used to determine material parameters and models are generated for four different polyethylene materials. The corroboration of the models is completed by comparisons with results from different tensile creep, step‐loading creep, and load‐rate tests. POLYM. ENG. SCI., 48:159–167, 2008. © 2007 Society of Plastics Engineers     

基于非线性黏弹性理论的含缺陷PE管的脆性破坏

现阶段聚乙烯管道脆性破坏失效研究,多采用线弹性断裂力学理论进行分析,鲜有考虑管材非线性黏弹性力学行为.针对这一问题,基于非线性黏弹性理论,将材料黏弹性参数用Prony级数表示,在适当假设简化下推导了变栽荷含缺陷黏弹性体能量释放率的一般表达式.结合含轴向表面裂纹PE管的脆性破坏工程案例,给出其理论模型及相应计算结果,为研究PE管道脆性断裂现象提供理论依据.     

On the long time creep and lifetime behavior in uniaxial extension of a linear low density polyethylene

This paper describes uniaxial creep measurements done on a linear low density polyethylene over a wide range of temperatures and applied stresses. It is found that the creep behavior overall is quite complex and that the one quantity which can best be used to predict useful lifetime of this material is the time at which necking is observed. The time to neck data has been used to generate a composite curve which can serve as an upper bound to lifetime prediction.     

Multi‐Relaxation Test to Characterize PE Pipe Performance

A new concept is proposed, which uses results from a multi‐relaxation test to characterize transition of deformation mechanisms in polyethylene (PE) pipes, for plastic deformation from the amorphous phase only to the involvement of the crystalline phase. The former mechanism is believed to lead to brittle fracture, while the latter to ductile fracture. This phenomenon is believed to be related to the transition from ductile to brittle (DB) fracture that has been observed in creep tests of PE pipes by reducing the applied stress below a critical level. This paper presents results from 6 PE pipes of different density and molecular weight distribution. The results suggest that high‐density PE pipes require a higher deformation level for the DB transition than the medium‐density PE pipes. The results also suggest that the trend of change in the critical stress level for the DB transition is close to the trend of change in the hydrostatic design base, but the former takes less than two weeks to complete, while the latter more than 1 year. Therefore, the multi‐relaxation test can be used as an alternative method to characterize PE pipe performance, as a means for preliminary screening or in‐service monitoring of pipe performance.     

Effects of fiber size on short‐term creep behavior of wood fiber/HDPE composites

When natural fiber‐thermoplastic composites are used in long‐term loading applications, investigating creep behavior is essential. The creep behavior of high‐density polyethylene (HDPE)‐based composites reinforced with four sizes of wood fibers (WFs) (120–80, 80–40, 40–20, and 20–10 mesh) was investigated. The instantaneous deformation and creep strain of all WF/HDPE composites increased at a fixed loading level when the temperature was increased incrementally from 25 to 85°C. At a constant loading level, composites containing the larger‐sized WFs had better creep resistance than those containing smaller‐sized fibers at all measured temperatures. The creep properties of composites with smaller‐sized WFs were more temperature‐dependent than those with larger‐sized WFs. Two creep models (Burger's model and Findley's power law model) were used to fit the measured creep data. A time–temperature superposition principle calculation was attempted for long‐term creep prediction. The Findley model fitted the composite creep curves better than the four‐element Burger's model. From the predicted creep response of the WF/HDPE composites, two groups of small fibers (120–80 and 80–40 mesh) had the lowest creep resistance over long periods of time at the reference temperature of 25°C. The largest WFs (10–20 mesh) provided the best composite creep resistance. POLYM. ENG. SCI., 55:693–700, 2015. © 2014 Society of Plastics Engineers     

Creep and recovery behavior of novel organic‐inorganic polymer hybrids

A novel class of organic‐inorganic polymer hybrids were developed by meltblending up to 50 (v/v) % [about 83 (w/w) %] tin‐based polyphosphate glass (Pglass) and low‐density polyethylene (LDPE) in conventional plastics processing equipment. The creep and recovery behavior of these polymer hybrids at 30°C were studied to understand the effect of the Pglass on the creep resistance of the LDPE. The results suggest that the Pglass acts as a reinforcement and an increase in the Pglass loading leads to significantly lower creep strains. This creep resistance is further enhanced by pretreating the Pglass with coupling agents prior to incorporating them into the Pglass‐LDPE hybrids. The experimental creep compliance of these materials conformed excellently with empirical power‐law equation and a modified Burger's model, suggesting that the materials are linearly viscoelastic under the test conditions.     

HDPE蠕变行为的研究

研究HDPE的蠕变行为不仅有助于从分子运动机理上揭示聚合物的黏弹性行为,还能够预测材料使用过程中的尺寸稳定性及长期承载能力,减小工程设计误差,确保材料使用的安全性,因而具有重要的理论意义和实用价值。回顾了蠕变理论的发展,综合了近年来有关HDPE蠕变行为及形变机理的研究进展,并以HDPE单向拉伸格栅为例简要分析了此项研究的发展及应用前景。     

On the prediction of long‐term creep‐failure of GRP pipes in aqueous environment

The aim of this work was to study the long‐term failure of GRP (Glass fiber‐reinforced Polymer) pipes under the influence of moisture absorption. These pipes are used in water transportation, which has an important effect on the mechanical properties of the polymeric matrix. The GRP pipes are usually tested under ring deflection or internal pressure conditions. This study presents and analyzes experimental creep‐rupture data obtained from standard test methods under ring deflection conditions. This loading configuration simulates in laboratory the conditions verified in a subsoil installation. The creep testing was carried out under constant dead weight on unconditioned and preconditioned samples in a submerged condition. The diametrical deflection of samples was measured periodically, and the time to failure of each sample was recorded. The main purpose of this work was to determine the short and long‐term rupture energies of GRP pipes and assess the influence of moisture preconditioning on those values. The observed failure mode was always the same. It was concluded that the energy at failure decreases with time. The influence of the preconditioning on the creep‐rupture of GRP pipes was considered negligible. Different time‐dependent failure models were described and used for long‐term extrapolation of the experimental data. The maximum strain at failure decreased about 12% from 0.1 to 1,000 hr of creep testing. Furthermore, data extrapolation to 50 years predicts a reduction of strength of about 60%, founded on the most conservative time‐dependent failure criterion. POLYM. COMPOS., 2010. © 2009 Society of Plastics Engineers     

Separating stress and time dependent effects in the temperature dependent creep of polyethylene nanocomposites

The nonlinear time dependent creep of linear‐low density polyethylene (LLDPE) reinforced with montmorillonite layered silicate was investigated. A previous study related the time/stress dependence of creep compliance of the material at room temperature using the Burger and Kohlrausch‐Williams‐Watts models. Using both the creep and recovery compliance curves, we employ the Schapery formulation to study the relationship between deformation, time, stress, and temperature of LLDPE nanocomposites. Smooth mastercurves are constructed using time–temperature–stress superposition principles. The stress and temperature‐related creep constants and shift factors were determined for the material using the Schapery nonlinear viscoelastic equation. The prediction results confirm the enhanced creep resistance of nanofillers even at extended time scales and low temperatures. POLYM. ENG. SCI., 50:1646–1657, 2010. © 2010 Society of Plastics Engineers     

A procedure for modeling the nonlinear viscoelastoplastic creep of HDPE at small strains

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. © 2016 Society of Plastics Engineers     

Creep modeling of ABS pipes at variable temperature

One of the characteristic behaviors of plastic (or viscoelastic) materials is the creep phenomenon, which is defined as the continuing deformation under a constant load with time. Although research on creep of plastic pipes has been widely carried out in other plastics, little work has been reported for creep in ABS (acrylonitrile‐butadiene‐styrene) pipes at high temperatures. In this paper, the generalized Kelvin series of formulae, which consists of six Kelvin elements, a power model, as well as logarithmic regressions, are applied to the experimental data measured from creep tests under constant bending stresses at different temperatures for two ABS resins. The least‐squares method was used to adjust the Kelvin model parameters, and a Levenberg‐Marquardt non‐linear least‐squares regression procedure was used to determine the creep parameters in the power model. This led to empirical formulae for creep compliance defined as the reciprocal of the creep modulus. This creep modulus can provide a means to evaluate the long‐term structural properties for different resins used in pipe production.     

Creep analysis of bamboo high‐density polyethylene composites: Effect of interfacial treatment and fiber loading level

The effect of chemical treatment at fiber–plastic interface and fiber loading level on creep property of bamboo fiber high‐density polyethylene (BF/HDPE) composites was investigated. For single modifier systems, the use of maleic anhydride grafted polyethylene (PE‐g‐MA) as a coupling agent helped reduce the creep and achieved the optimum effect at the 5.7% loading level. The addition of either a semicrystalline or an amorphous MA grafted ethylene propylene rubber (sEPR‐g‐MA or aEPR‐g‐MA) as an impact modifier increased the creep. For the combined modifiers, the use of PE‐g‐MA in EPR‐g‐MA modified composites gradually improved creep performance. Four‐element Burgers model was shown to fit measured creep data well only within the specified test period. However, both partially stretched Burgers (PSB) model and fully stretched Burgers (FSB) model could be applied for characterization and prediction when the stretching exponent was fixed at certain given values. The FSB model offered a better long‐term prediction based on the short‐term creep data. Time‐temperature superposition technique produced smooth master creep curves through horizontal shifts, but it slightly over‐predicted the long‐term creep for most composite systems. POLYM. COMPOS., 2011. © 2011 Society of Plastics Engineers     

Lifetime prediction for ABS pipes subjected to combined pressure and deflection loading

As part of an investigation into the performance of acrylonitrile‐butadiene‐styrene (ABS) systems for water transportation, this paper presents a method for predicting the service lifetimes of buried pipes under in‐service loading conditions. A linear fracture mechanics approach was used to analyze brittle failure initiating from adventitious flaws located at the bore surface of pipe. Failure criteria were determined using the time‐dependent, quasistatic, plane strain fracture toughness of the ABS material, combined with empirical parameters that describe slow, steady crack growth. The expected operating conditions of a buried pipe were then separated into static loading contributions from internal pressure, diametrical deflection and residual stress. Idealized stress intensity factors associated with mode‐I crack opening under each of these components were determined using a finite element analysis and superposed to describe the general case in service. The computed nett stress intensity factor was then combined with the previously determined fracture toughness and slow crack growth data in an algorithm to simulate incremental radial crack growth from the pipe bore. Predicted failure times compared well with an experimental model of expected operating conditions, which combined hydrostatic pressure and parallel‐plate deflection loading of an internally notched pipe. The prediction method was also used to identify the factors that control the lifetime of a pipe in service. The influence of material visco‐elasticity was investigated by simulating variations in fracture toughness and slow crack growth resistance. It was proposed that, in practice, these variations are governed by opposing changes in visco‐elasticity. The effect of changing diametrical deflection and residual stress distribution were also simulated, allowing recommendations on pipe manufacture and installation conditions to be made.     

Time–temperature superposition principle applied to a kenaf‐fiber/high‐density polyethylene composite

The time–temperature superposition principle was applied to the viscoelastic properties of a kenaf‐fiber/high‐density polyethylene (HDPE) composite, and its validity was tested. With a composite of 50% kenaf fibers, 48% HDPE, and 2% compatibilizer, frequency scans from a dynamic mechanical analyzer were performed in the range of 0.1–10 Hz at five different temperatures. Twelve‐minute creep tests were also performed at the same temperatures. Creep data were modeled with a simple two‐parameter power‐law model. Frequency isotherms were shifted horizontally and vertically along the frequency axis, and master curves were constructed. The resulting master curves were compared with an extrapolated creep model and a 24‐h creep test. The results indicated that the composite material was thermorheologically complex, and a single horizontal shift was not adequate to predict the long‐term performance of the material. This information will be useful for the eventual development of an engineering methodology for creep necessary for the design of structural building products from these composites. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 1995–2004, 2005     

Fatigue behavior of medium-density polyethylene pipes for gas distribution

This paper illustrates the factors that control brittle failure under fatigue loading for test specimens cut from medium-density polyethylene pipes for gas distribution. A square bar specimen cut from a pipe with a notch was made and a fatigue test was conducted to cause a brittle failure. To obtain the correlation among stress range, frequency, temperature, and cycles to failure in this fatigue test, Coffin-Manson's frequency-modified fatigue life equation was adopted and the material constants were determined. By gradually lowering the frequency, the resistance to creep can be estimated because cycles to failure—indicating the fatigue damage—decreased, and the actual loading time—indicating the creep damage—increased.     

Nonlinear viscoelastic model for the prediction of double yielding in a linear low‐density polyethylene film

Tensile testing and tensile creep experiments for linear low‐density polyethylene in a thin‐film form were examined and analyzed in terms of a nonlinear viscoelastic model. The proposed model, based on two distinct thermally activated rate processes (Eyring models), was proved to describe the double‐yield‐point tensile behavior of the material tested. The required model parameters were evaluated from the corresponding creep‐strain curves, and this revealed the relationship between the main aspects of the inelastic behavior of polymers, that is, the monotonic loading and creep response. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 91: 3519–3527, 2004     

Micromechanical modeling of roll‐to‐roll processing of oriented polyethylene terephthalate films

In this article, the thermo‐mechanical time‐dependent behavior of oriented polyethylene terephthalate (PET) films, which are used as a substrate material for flexible Organic Light‐Emitting Diode (OLED)s, is analyzed. These films are subjected to conditions that are representative for the industrial manufacturing process. Effects of creep and thermal shrinkage are experimentally observed simultaneously. The aim of the article is to demonstrate the ability of the micromechanically‐based model, which was previously used to separately describe both creep and thermal shrinkage of the polyethylene terephthalate film, to simulate experimentally observed anisotropic behavior of the film under complex loading conditions. This anisotropic behavior results from the microstructure, the internal stress state, and differences in constitutive behavior of the phases. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2016 , 133, 43384.     

Plastic deformation of low‐density polyethylene reinforced with biodegradable polylactide,Part 2: Creep characterization and modeling

The behavior of low‐density polyethylene (LDPE) and two blends prepared with polylactide (PLA) was determined by means of a novel video‐controlled testing method under stretching at constant true strain rate, under creep at constant true stress, and under creep at constant nominal stress. Most tests were performed at 23°C and 50°C. In this second part, the experimental data are modeled with the G'Sell‐Jonas phenomenological law expressing the axial true stress versus axial true strain and axial true strain rate. This model describes correctly the various deformation stages: (i) initial viscoelasticity, (ii) plastic yielding, and (iii) strain hardening up to rupture. It shows clearly the reinforcing effect of the PLA particles that increases the yield stress in stretching experiments and slows down the deformation kinetics under creep. It is shown how the local stress/strain behavior is related to the standard force/extension curves. Consequently, it is proposed that tensile tests at constant true strain rates should be systematically preferred to creep tests for the characterization of constitutive relations because they take much less time to be performed. POLYM. ENG. SCI., 2011. © 2010 Society of Plastics Engineers.     

Effect of molecular weight and branch content on the creep behavior of oriented polyethylene

Creep studies were carried out on a range of homopolymers and copolymers of polyethylene with well‐defined molecular weight and branch content. The creep data were analyzed in terms of two thermally activated processes acting in parallel and the effects of molecular weight and branch content are discussed. It is shown that increasing either the number‐average molecular weight or the weight‐average molecular weight gives improved creep behavior at all stress levels. The introduction of butyl branches leads to lower creep at low‐stress levels but can give rise to higher creep at high stress. Plots of the equilibrium log₁₀(strain rate) versus stress at fixed draw ratio (strain) can be used to define sections through a unique true stress/true strain/strain rate surface for each material. These creep results have an additional value in terms of the link between slow crack propagation (SCG) in polyethylene and fibril creep, confirming the proposal made elsewhere that SCG can be quantified in terms of creep to failure across the true stress/true strain/strain rate surface. © 2003 Wiley Periodicals, J Appl Polym Sci 89: 1663–1670, 2003     

Blends of maleic‐anhydride‐grafted polyethylene with polyethylene for improved cathodic disbondment performance

Buried metal structures such as pipes are usually protected by a coating, often in conjunction with cathodic protection (CP). Whilst this minimizes corrosion, it can also lead to the loss of adhesion between the protective coating and metal structure by a phenomenon called cathodic disbondment (CD). In this study, various medium‐density polyethylene (MDPE) compositions with maleic‐anhydride‐grafted‐polyethylene (MAH‐ g ‐PE) have been formulated to investigate the effect on CD performance, as well as both wet and dry bond strength. The results indicate an improvement in both CD performance and bond strength for all compositions. Differential scanning calorimetry (DSC) and pressure‐volume‐temperature (PVT) experiments are used to characterize the polymer formulations developed and to aid in the understanding of the reasons for such improvement. Energy dispersive X‐ray spectroscopy (EDXS) has been used to obtain surface analysis data on disbonded materials in order to evaluate the failure mode during the CD process. It is found that there may be an optimum loading of the polar functional groups in MDPE necessary for the best CD performance, and that wet adhesion strength (rather than dry) is an important parameter to assess and understand the CD performance of coatings. © 2001 Society of Chemical Industry