Constitutive model calibration of the time and temperature-dependent behavior of high density polyethylene

HDPE is commonly used in pipelines and piping for industrial and societal infrastructure. Like most polymers, HDPE's mechanical properties are sensitive to temperature and show time dependent properties. The temperature effect on both the short and long term compressive and tensile behavior of HDPE, in a combined manner, have not been investigated thoroughly in the past. Especially the constitutive behavior of HDPE, incorporating temperature effects on its long and short term behavior, could be essential when designing such infrastructural components. Hence, the temperature effect on the short and long term response in tension and compression of HDPE is investigated in this study. The short term tensile and compressive stress-strain behavior at 23, 40, 60, and 80 °C were obtained through experiments at constant displacement rate and temperature. Tensile and compressive stress relaxation (e.g. long term) behavior at 23, 40, 50, 60, 70, and 80 °C were investigated through stress relaxation tests. The experimental results from the short term tests showed that both the tensile and compression moduli and yield strength of HDPE decrease linearly with the increase in temperature. It is also shown from the long term test that relaxation modulus in tension and compression are highly dependent on temperature. Based on the experimental results, the constitutive three network model (TNM) was calibrated and implemented in a FEA model, which was then validated through a three point bending (3 PB) relaxation test with a prescribed temperature profile. The FEA model and the calibrated model results agree markedly well with the experimental results, which indicates that the model can be used reliably to predict the temperature dependent short and long term behavior of HDPE in design and analysis of HDPE components.     

Creep behavior of in-service flexible flowline polyamide 11

The high cost (material, service, and production loss) involved to substitute a condemned flexible pipe whose pressure sheath has reached its theoretical preconized service life has motivated this study. Therefore, the main objective is to propose a constitutive equation for in-service aged polyamide 11 (PA11) describing the creep behavior as a function of temperature, stress level, and Corrected Inherent Viscosity (CIV), this latter parameter representing the level of material degradation due to hydrolysis. The constitutive equation may be employed for gap spanning analysis and also to subsidize the decision to extend the operational life of flexible pipes that have experienced more severe conditions or have been used for a longer time than designed. The current models to assess the remaining life of the sheath are based only on a single property decay based on corrected intrinsic viscosity (CIV) curves obtained from laboratory tests. To compare the result from the life-prediction model in use and the material mechanical behavior, an experimental campaign was performed using polyamide 11 (PA 11) samples retrieved from a 6″ gas production flexible flowline, which theoretically had reached a full-damaged condition after nearly 3 years operating at higher than specified temperature (80 °C). Dog-bone geometry specimens were machined from the internal, intermediate, and external layers of the flexible flowline pressure sheath. Once polymers are excellent thermal insulators, it was assumed that the material operated under different temperatures within the thickness and, therefore, presents different degradation degrees. CIV, tensile, and creep analyses were performed, confirming that the behavior is different for each region within the thickness of the pressure sheath. Differential scanning calorimetry (DSC), thermogravimetry analyses (TGA), and dynamic thermomechanical analysis (DMA) were performed to comparatively characterize the degree of crystallinity, amount of extractables and morphology of each section. A creep behavior model considering the gradient difference in the material is proposed. It is concluded that aging is different across the liner thickness, and the PA11 creep behavior may be expressed as a function of the CIV, temperature, and stress.     

A survey of methods for the detection of thermal oxidation in high-density polyethylene pipes

Seven methods for the detection of thermal oxidation of the inner wall surface of high-density polyethylene (HDPE) pipes are presented. The methods presented include infrared spectroscopy, polarized light microscopy, differential scanning calorimetry, scanning electron microscopy, gloss measurements and uniaxial creep tests. These tests have been developed on the basis of earlier reported data for a large number of PE pipes. The tests are compared with each other and with the internal pressurizing test with respect to reliability of results, the time taken to determine whether or not a pipe is oxidized, the experimental difficulties, costs, etc.     

Constitutive model and failure locus of a polypropylene grade used in offshore intake pipes

BorECO^®™ BA212E is a polypropylene block co-polymer which has become a common material in the manufacturing of large diameter non-pressurized gravity offshore intake pipelines. These lines are used for transportation of sea water for cooling of petrochemical process plants. The pipe sections are joined by butt heat fusion welding to create the pipeline. Recently a few premature failures of such pipelines have been reported in the field. Hence, there is a need to characterize the constitutive behavior of the pipe and weld material in order to properly design these pipes. The aim of this work is to determine the material constitutive behaviors of the pipe material and the welded joint material. Uniaxial tensile tests of both the pipe and weld joint material are conducted at various strain rates. Both the pipe and weld material show a rather high strain rate dependency, with the weld material having about half the yield strength than that of the pipe material. An analytical constitutive material model is developed for both the pipe and weld material, incorporating the effect of strain rate. The failure locus, expressed in terms of the equivalent plastic strain at failure vs. the stress triaxiality, for both materials is also determined as part of the constitutive model using notched dumbbell specimens. The constitutive model and failure loci for the pipe and weld material are implemented in a finite element model (FEM) and are validated by conducting a series of independent four-point bend experiments on both material types. The validation is carried out by comparing the FEM results of the four-point bend model with the experimental results, which show a rather good agreement.     

A statistical approach to characterize the viscoelastic creep compliances of a vinyl ester polymer

The objective of this study was to develop a model to predict the viscoelastic material functions of a vinyl ester (VE) polymer with variations in its experimentally obtained material properties under combined isothermal and mechanical loading. Short-term tensile creep experiments were conducted at three temperatures below the glass transition temperature of the VE polymer, with 10 replicates for each test configuration. The measured creep strain versus time responses were used to determine the creep compliances using the generalized viscoelastic constitutive equation with a Prony series representation. The variation in the creep compliances of a VE polymer was described by formulating the probability density functions (PDFs) and the corresponding cumulative distribution functions (CDFs) of the creep compliances using a two-parameter Weibull distribution. Both Weibull scale and shape parameters of the creep compliance distributions were shown to be time and temperature dependent. Two-dimensional quadratic Lagrange interpolation functions were used to characterize the Weibull parameters to obtain the PDFs and, subsequently, the CDFs of the creep compliances for the complete design temperature range during steady state creep. At each test temperature, creep compliance curves were obtained for constant CDF values and compared with the experimental data. The predicted creep compliances of the selected VE polymer in the design space are in good agreement with the experimental data for all three test temperatures.     

Viscoelastic modeling of extrusion damage in elastomer seals

ABSTRACT

The viscoelastic behavior of elastomers manifests itself in numerous ways depending on the application. In seals, the viscoelastic response of an elastomer is complex as it depends upon the specific combination of loading pressures, loading rates, chemical environment, temperature and time of loading, and ultimately long-term effects such as creep or stress relaxation can result in seal failure. One specific mechanism encountered in seals under large pressures is extrusion damage. When a seal is pressurized by a fluid, the elastomer is highly constrained; however, there is typically a very small gap between the inner and outer sealing surfaces. Over time viscoelastic creep causes the elastomer to gradually extrude into this gap until the seal ruptures. In this paper the viscoelastic creep behavior of a typical sealing elastomer, NBR, was studied. Compression creep tests were carried out over a range of strains and the measured data were used to develop a strain-dependent viscoelastic material model. The model was then implemented into a finite element analysis (FEA) simulation to study the extrusion creep behavior of an O-Ring seal. Data from the FEA model were then compared against physical test data from equivalent extrusion tests. The FEA model correlated well to the physical test data, with the strain-dependent viscoelastic material model allowing compression creep data to be used to accurately predict extrusion creep.     

Improving the design stresses of high density polyethylene pipes and vessels used in reverse osmosis desalination plants

Nanocomposite materials have been used on a wide scale in industrial and structural applications. The present work aims at studying the mechanical properties of high density polyethylene (HDPE) grade TR-401 hexene copolymer reinforced by montmorillonite nanoparticles (MMT), used to fabricate pipes and membranes vessels for reverse osmosis desalination plants. Different volume fractions and particle sizes of the MMT clay were used to investigate the effect of this filler on the mechanical properties of the produced composite. Mechanical properties tests were carried out and good improvements of the composite properties were obtained compared to the parent polymer. The test results showed a significant enhancement of the mechanical properties at low filler proportions. Pipe fabricated from these composites had many outstanding and desirable features. For example, by adding 4.75% MMT to the HDPE produced quality pipes and fittings with the highest design stress basis of any polyethylene. A significant increase in the modulus of elasticity observed, together with an unusual increase in the design stress, approved the HDPE/MMT composite for high pressure piping and membrane vessels used in reverse osmosis desalination plants.     

Qualification of pipe-grade HDPEs: Part I,development of a suitable accelerated ageing method

Several techniques of polymer characterization and different ageing methods have been used with the aim of developing a simple, fast and reliable method to qualify commercial pipe-grade polyethylene samples, and possibly to evidence the presence of recycled PE within PE pipes. The results of the different techniques used have been compared with respect to their capability to evidence differences in the degradation rate of different HDPE samples (including virgin HDPE, HDPE pipes obtained from virgin HDPE and HDPE pipes that probably contain recycled HDPE). FT-IR, TGA and DSC were found unsuitable for this purpose but, on the contrary, MFI measurements have been found sensitive enough to evidence different degradation rates when a suitable combination of high temperature, oxygen, mechanical stresses and mixing time had been used for ageing the sample.     

Simulation of the Long Term Behaviour of Plastics Components

Summary: This paper presents a method to model the mechanical behavior of polymers over a wide time- and load-range by means of finite element analyses. The method includes a material model as well as the determination of material parameters to calibrate the material model. As a special feature of this method the model is calibrated only by using creep data that are commonly available in material data bases. So the procedure improves the simulation of the long time behavior of plastic-components without an additional experimental effort. In combination with time-temperature-superposition principle, the temperature dependency of the long term behavior is represented, too. The simulation results are validated by creep experiments on an example part.     

单向应力条件下松弛时间率相关的非线性粘弹性本构模型

基于单向拉伸实验研究和内变量理论 ,提出了一种新的简单的一维非线性粘弹性本构关系 .对两种粘弹性材料 ,即高密度聚乙烯和聚丙烯进行了不同加载速率作用下的拉伸实验研究 ,实验结果表明 ,两种材料的应力应变关系与加载速率相关 ;对材料的应力应变实验数据进行拟合发现 ,材料的松弛时间具有很强的应变率相关性 ,当应变率发生数量级变化时 ,材料的松弛时间也发生数量级的变化 .采用内变量理论 ,导出了在单轴应力条件下松弛时间率相关的非线性粘弹性本构关系的迭代形式 ,并给出其收敛条件 .当采取一次迭代形式时 ,本构关系退化为松弛时间率相关的Maxwell模型 .数值拟合的结果表明 ,一次迭代形式的本构关系就可以很好地拟合和预测实验结果 .     

Viscoelastic properties of UHMW-PE fibers in simple elongation

Stress relaxation after a simple elongational step strain, creep under a constant simple elongational stress, and stress build-up under a constant Hencky strain rate have been measured for ultrahigh-molecular-weight polyethylene (UHMW-PE) fibers. The data from the various experiments are consistent with the Boltzman superposition principle in the experimental region of small strains or short times. This leads to a simple constitutive equation in which temperature can be incorporated via time-temperature superposition. The measured power-law relaxation of the UHMW-PE fiber leads to analytical expressions for the dynamic quantities in simple elongation. The constitutive equation is the one-dimensional equivalent of the gel equation derived for cross-linking gels at the gel point. The similarity between the rheological behavior of fibers and cross-linking gels at the transition point might lead to an enhanced understanding of the molecular processes occurring during deformation.     

Characterization of tension set behavior of a silicone rubber at different loads and temperatures via digital image correlation

This work aims to determine the tensile set behavior of a silicone rubber under different stress magnitudes and temperatures through digital image correlation implemented in an improved creep experimental set-up. Creep-recovery strains were measured with time at 20, 40 and 60 °C under tensile strengths of 98.1, 196.2 and 394.3 kPa, respectively. The behavior of creep and recovery strain with time at the different stress magnitudes and temperatures was successfully obtained by the experiments. The corresponding elastic and viscous components of the material for each condition were determined from the results. Overall, all obtained creep behaviors matched with the behavior of a four-element model of creep-recovery. The increase of temperature generated an increase of creep compliance at the three loads, but the increase of tensile load produced a decrease of creep compliance for the three temperatures. The strain was not recovered entirely in any case for the test time stated.     

Ageing effects and internal stresses in quenched unfilled and clay-filled high density polyethylene

The stress relaxation and creep behaviour of high density polyethylene (HDPE), unfilled or filled with clay particles, were measured after different ageing times after quenching from 120 °C. The measurements were performed at room temperature in the uniaxial extension mode. Ageing time had a pronounced influence on the viscoelastic properties, e.g. the creep curves shifted to longer times with increasing ageing time. The internal stresses, as evaluated from stress relaxation data, were found to increase markedly when the ageing period was extended, and it was suggested that this behaviour may be associated with relaxation of thermal residual stresses. It was furthermore suggested that the change in residual stresses, in addition to the physical ageing process, could also affect the ageing behaviour of HDPE, i.e. the change in viscoelastic properties with ageing time. Clay addition changes the ageing behaviour of HDPE, which could be attributed to a change in the internal stress dependence of the ageing time and/or to a difference in the physical ageing process. The effects of a surface treatment on the ageing of HDPE-clay composites are also evaluated and discussed.     

Micromechanical modeling of the deformation kinetics of semicrystalline polymers

The mechanical behavior of semicrystalline polymers is strongly dependent on their crystallinity level, the initial underlying microstructure, and the evolution of this structure during deformation. A previously developed micromechanical constitutive model is used to capture the elasto‐viscoplastic deformation and texture evolution in semicrystalline polymers. The model represents the material as an aggregate of two‐phase layered composite inclusions, consisting of crystalline lamellae and amorphous layers. This work focuses on adding quantitative abilities to the multiscale constitutive model, in particular for the stress‐dependence of the rate of plastic deformation, referred to as the slip kinetics. To do that, the previously used viscoplastic power law relation is replaced with an Eyring flow rule. The slip kinetics are then re‐evaluated and characterized using a hybrid numerical/experimental procedure, and the results are validated for uniaxial compression data of HDPE, at various strain rates. A double yield phenomenon is observed in the model prediction. Texture analysis shows that the double yield point in the model is due to morphological changes during deformation, that induce a change of deformation mechanism. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1297–1310, 2011     

The influence of short-chain branching on the creep behavior of oriented polyethylene,and its effect on the efficiency of crosslinking by electron irradiation

Studies have been made of the creep behavior of oriented (15:1) polyethylenes containing 0.4 and 1.3 butyl branches per 1000 C atoms. Increasing the branch concentration reduces significantly the creep strain and the equilibrium strain rate. The data have been fitted to an established model comprising two thermally activated processes in parallel, relating to the amorphous network at low stress, and the crystal phase at high stress. Analysis based on this model indicates the similarity between branching, entanglements, and crosslinks on the creep response. The creep behavior of electron-beam-irradiated materials shows that increasing the branch concentration makes the polyethylene more susceptible to mainchain scission, indicated by increased creep flow rates at higher stress, consistent with previous rubber elasticity studies. Irradiation in an acetylene atmosphere with low (< 1 Mrad) doses is shown to reduce the creep rates at all accessible stresses, and this attributed to an increase in crosslinking compared with scission. © 1994 John Wiley & Sons, Inc.     

Creep behavior and lifetime prediction of PMMA immersed in liquid scintillator

The creep behavior of PMMA immersed in liquid scintillator at room temperature was experimentally studied with a new type of creep test machine. Both short-term and creep-rupture tensile tests at eight stress levels were performed. A master curve of creep compliance at a reference stress was obtained according to the Time-Stress Superposition Principle. The master curve was compared with the actual long-term creep curve. It demonstrates that the two curves coincide well at short times. However, the actual creep data shows a higher creep rate as time goes on. The actual lifetime is much shorter than that predicted by the master curve. Furthermore, the relationship between long-term creep limited strength and service life was determined. The results can be used to guide the safety design of PMMA vessels for application in a neutrino observatory.     

Time dependence of piezoresistance for the conductor‐filled polymer composites

The piezoresistance and its time dependence of conductor‐filled polymer composites have been investigated. To reveal the origin of the time dependence of piezoresistance, the creep of the polymer matrix is also studied. Based on the interparticle separation change under the applied stress, a model has been developed to predict the piezoresistance and its time dependence. By analyzing this model, the influences of applied stress, filler particle diameter, filler volume fraction, matrix compressive modulus, potential barrier height, and the matrix creep behavior on the piezoresistance and its time dependence are interpreted quantitatively. These predicted results are compared with the experimental data obtained on the polymer composites filled with conductor fillers, and good agreements were obtained. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 2739–2749, 2000     

Functional evaluation of a liquid-molding two component combination resin

Functional parameters contributing to the recognizable good performance of a highly crosslinked olefinic polymer based on cyclopentadiene have been evaluated by a limited range of stress decay and creep recovery from a fixed deformation over constant time periods. The experimental design for these involved a calculated stress (load) at the initial sample deformation (displacement) for determination of changes in stress in bending mode and flex creep under applied load at three constant temperature segments of 6 h each with 20 min recovery time between segments. The results have identified a behavior which is typical of interfacial orientational effect in a two-component system. Thermal conductivity, heat capacity and density at the same temperatures were measured for determination of variations in thermal diffusivity as an indication of the competing effects of densification and thermal expansion for such a system.Static charging and polarization experiments were performed for evaluation of other desired uses of this material, in moving parts and in direct or induced voltage applications. The latter allows measurement of dynamic charge transport through the resin matrix. Calculations indicate generation of charge carriers from weak secondary bonding typical of polymer interlaces. The polarization itself consists of dipole orientation characterized by relatively high activation energy.The intrinsic mechanical properties for this material had been determined by the manufacturer, but the performance parameters reported in this study have been determined for the first time for exploration of further uses for this material.The author wishes to acknowledge the assistance provided by Ralph Pitman in the preparation of the samples for this work.     

Load-displacement behavior for double-edge cracked plate of polytetrafluoroethylene

Polytetrafluoroethylene (PTFE) has been employed in many engineering applications, mainly due to its special properties such as high electrical resistivity, high melting temperature, chemical inertness, corrosion resistance and very low friction. Although there are many works on PTFE, very few attempts have been made to understand the fracture behavior of this material. For this reason, the load-displacement behavior of double-edge cracked specimens of PTFE was examined and modeled and is reported in this paper. Specimens were tested under monotonic tensile load in quasi-static conditions at constant temperature. Images of the region around the crack were captured with a high-resolution camera and then processed by digital image correlation to obtain the displacement fields. Using these data, values of crack tip opening displacement and crack extension were estimated. To model the behavior of PTFE, a constitutive phenomenological model based on saturation and power law expressions combined with a damage evolution equation is proposed. The predictions are in good agreement with the experimental data.     

Cyclic viscoplasticity of high-density polyethylene/montmorillonite clay nanocomposite

Observations are reported on high-density polyethylene (HDPE) and nanocomposite, where HDPE matrix is reinforced with montmorillonite (MMT) nanoclay, in uniaxial cyclic tensile tests with various cross-head speeds ranging from 1 to 50 mm/min. Each cycle of deformation involves tension up to the maximal strain ?_max = 0.1 and retraction down to the zero stress. The study focuses on low-cycle deformation programs with N = 5 cycles in each test.A constitutive model is derived for the viscoplastic response of polymers at three-dimensional cyclic deformations with small strains. Given a strain rate and a maximum strain, the stress-strain relations involve eight material constants that are found by fitting the experimental data. Good agreement is demonstrated between the observations and the results of numerical simulation. It is shown that the rate of cyclic deformation affects the adjustable parameters in a physically plausible way.