Flexural creep of all-polypropylene composites: Model analysis

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composites depends strongly on stress, temperature, voidcontent, fiber loading, and fiber dimensions [8–11]. Oneof the greatest constraints in studying the creep behavioris the relatively long time required for performing a test.Hence, time-temperature superposition (TTS) methodsthat are able to predict the long-term data have gainedconsiderable attention [12–15]. Also many viscoelasticand empirical models have been proposed to predict thelong-term creep behavior of polymers and their composites[7, 9].In this article, the creep behavior of all-PP compositesproduced by different tape lay-ups is analyzed using simpleviscoelastic and empirical models to understand theirdeformation mechanism. Also, it has been illustratedusing the Findley equation that the applicability of themodel to predict the long-term creep depends, apart fromthe test temperature, on the material property, viz. crystallinitythat changes during the course of creep when thethermal or mechanical conditioning of the test specimensis ignored.CREEP AND CREEP MODELSCreep is a slow, progressive deformation of a materialunder constant stress. When a plastic material is subjectedto a constant load, it deforms continuously with time.This time-dependent behavior of materials, referred to asviscoelasticity, is also an important characteristic of reinforcedplastics. In general, for a constant stress, r, thecreep compliance J(t) can be written as the ratio of thestrain (e) to stress at a certain time (t) as follows:JT; ð tÞ ¼ eðT;tÞ: (1)sBesides experimental observation, highly developed creepmodeling in traditional composites can also be applied tothe polymer homocomposites to develop comprehensiveunderstanding of the creep deformation. In the past halfcentury, numerous creep models have been proposed andapplied to describe the creep behavior of viscoelasticmaterials [7, 12, 13, 16–21]. Various materials of thesame geometry may respond differently under identicalexternal effects. Such differences in response are oftenattributed to the inherent constitution of the materials.Consequently, the response behavior of a particular material,or a class of materials, is described mathematicallyby the so-called constitutive relations [22]. Thus, thecreep behavior of an isotropic linear viscoelastic systemcan be represented byZeðÞ¼s t 0 f ðÞexp t ð1t=tÞdt; (2)0where e(t) is the creep strain, t is the time, s 0 is theapplied stress, t is the retardation time, and f(t) is the distributionof the retardation time. Although it is assumedthat such an expression should represent an experimentalcreep, it is actually not so because accurate informationabout f(t) is rather elusive [23]. Several models weredeveloped using the constitutive relation to explain thecreep behavior of polymeric materials using very simpleelastic or viscous system and a complex combination ofboth. The basic constitutive equation for creep models hasthe following qualitative form:e ¼ e 0 þ e c ; (3)where e is the total strain at some time, t, after a stressapplication, e c , time-dependent creep component of strainat t, and e 0 is the instantaneous strain after stress application.The instantaneous strain component (e 0 ) is elasticand the creep component, e c , is a simple arithmetic functionof time (linear, logarithm, exponential, power law),either alone or in combination, to define the basic behaviorof this aspect. All linear viscoelastic models are madeup of linear springs and linear dashpot. Inertia effects areneglected in such models [7]. Also, there have been severalattempts to develop constitutive models to describetheir nonlinear creep behavior. The most widely usednonlinear viscoelastic models are the Schapery model andits modifications, which are based on irreversible thermodynamicsprinciples and have shown to accuratelydescribe creep performance [24, 25]. More recently, Deanand Broughton [26] modeled the nonlinear creep behaviorof polypropylene under uniaxial tension using a stretchedexponential function with four parameters. Nonlinearbehavior arises because one of the parameters, related toa mean retardation time for the relaxation process responsiblefor creep, is dependent on stress. There is no doubtthat nonlinear viscoelastic behavior predominates over amajor portion of the whole response interval of most polymericmaterials and plays the key role in most applications[16, 17]. On the other hand, if the material is testedin the linear viscoelastic range, its creep behavior can berepresented by simple rheological models. The Burgermodel, which is a combination of elastic and viscous elements,has been reported to give a satisfactory representationof the creep compliance [7, 9, 27].Burger model is a series of combinations of Maxwelland Kelvin-Voigt models [7, 9, 27]. Figure 1 shows ascheme of four-element Burger model. According to thismodel, the total strain is given by the general equatione ¼ e 1 þ e 2 þ e 3 ; (4)e ¼ s þ s ð1 expðtE 2 =ZE 1 E 2 ÞÞþ ts ; (5)2 Z 1where e 1 and e 2 are the elastic and viscous strain representedby the Maxwell model and e 3 is the viscoelasticstrain represented by Kelvin-Voigt model, E 1 and E 2 representthe moduli of the Maxwell and the Kelvin spring,Z 1 and Z 2 represent the viscosity of the Maxwell and942 POLYMER ENGINEERING AND SCIENCE—-2008 DOI 10.1002/pen
The long-term creep behavior may be predicted fromshort-term creep data by applying the time-temperaturesuperposition (TTS) principle. The premise of TTS is thattemperature accelerates the creep deformation kinetics.Hence creep curves at different temperatures may beshifted along the logarithmic time axis until they superimposeto form creep master curve extending to much longertimes than the short term data. The validity of TTSmust be established by long-term tests but is nonethelessuseful for obtaining a general description of the material’slong-term behavior [29, 30].FIG. 1.Schematic representation of the four-element Burger model.Kelvin dashpot respectively, s is the applied stress andt is the creep time.Besides the constitutive models, empirical or mathematicaldescriptions have also been widely studied [7]due to their simple expression and satisfactory simulationor prediction capability. Among these, the Findley powerlaw model is commonly accepted. The constitutive equationproposed by Findley is simplified in the followingform [7, 28]:e F ¼ e 0 þ e c t n : (6)Here n is a dimensionless material parameter, e 0 is the instantaneousor time-independent strain (functions of stressand environment variables including temperature, moisture,etc.), and e c is the time-dependent term. The symbolt may be taken to represent a dimensionless time ratiot/t 0 , where t 0 is the unit time. e 0 , e c , and n are creepparameters and each can be assigned a numerical valueby experimentally measuring the instantaneous and timedependentcompliance of a viscoelastic material and thencalculating the values from Eq. 6. Because of the oversimplificationof this model (it does not take into considerationthe changes in the shape of the material), thevalues calculated from the above equation cannot beuniversally applied. The shape of a material depends onmolecular mobility and is a function of the microstructureand molecular alignments during the processing of materialsand the shape from sample to sample can be influencedby other external factors such as moisture content,humidity, and temperature. Since all-PP composites likeother viscoelastic materials are very much influenced bythe factors as detailed above, the parameters obtainableby the power law model can only give an approximationof the real behavior. Nevertheless, it is expected that thismodel can be used as a first hand tool to predict the longtermdeformation behavior of all-PP composites.EXPERIMENTALIn this study, commercially available all-PP (PURE 1 )coextruded tapes, obtained from Lankhorst-Indutech B.V.(Sneek, The Netherlands), was used to make the unidirectional(UD) and cross-ply (CP) laminates. The PP tapeshave a skin-core-skin (A-B-A) morphology with PPhomopolymer as the core and a random PP copolymer asthe skin layer. The other characteristics of these coextrudedtapes are available in the literatures published earlier[31, 32].The manufacture of all-PP composites involved a twostageprocess—winding of the PP tapes, [both unidirectional(08) and cross-ply (08/908)], and consolidation ofthe fabric plies at a suitable temperature and pressure inan autoclave. For winding the tapes, a filament windingtechnique was adopted. A detailed description of the compositemanufacture is available in the references [31, 32].Flexural creep tests were performed using three-pointbending mode at temperatures ranging from 208C to808C, in the same DMA Q800 apparatus. Isothermal testswere run on the specimens by increasing the temperaturestepwise by 108C. Before the creep measurement, thespecimens were equilibrated for 5 min at each temperatureand then the flexural creep behavior was tested for30 min. All the tests were performed under a constantload of 10 MPa. Test specimens of dimensions 60 3 153 1.8 mm 3 (length 3 width 3 thickness) were employedfor creep studies and the average of three statisticallyrelevant creep data has been reported for each kind ofspecimen.To determine the crystallinity of the all-PP composites,differential scanning calorimetric (DSC) investigationswere performed before and after the creep tests using aMettler-Toledo DSC 821 instrument (Greifensee, Switzerland).The crystallinity contents of the composites werecharacterized from the enthalpy of fusion associated inthe first heating run. Heating scans were performed from258C to 2008C at a heating rate of 108C/min with nitrogenblanketing inside the sample chamber. An average ofthree specimens was taken for each of the specimens.The crystallinity was then determined by taking the ratioof the enthalpy of fusion of the all-PP composite to theenthalpy of fusion of 100% crystalline PP taken as207.1 J/g [33].DOI 10.1002/pen POLYMER ENGINEERING AND SCIENCE—-2008 943
Page 1: Flexural Creep of All-Polypropylene
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Flexural creep of all-polypropylene composites: Model analysis

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