Flexural creep of all-polypropylene composites: Model analysis

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Isochronous strain-stress plots for CP all-PP composite speci-FIG. 2.mens.RESULTS AND DISCUSSIONDetermination of Linear Viscoelastic RegionTo ensure working in the linear viscoelastic region,isochronous experiments were conducted for the all-PPcomposites. Short-term creep experiments lasting for30 min was performed for a series of stresses increasedstepwise from 2 MPa to 10 MPa. From the series ofapplied stresses, strain–stress plots were constructed. Figure2 represents the strain–stress results for the CP all-PPcomposite specimens conducted at room temperature(23 6 1)8C. From analysis of the isochronous tests forthe CP all-PP composites (the specimens showing thelargest creep deformation), a stress of 10 MPa wasselected for testing all the samples.Experimental Creep ResultsThe experimental data for the creep strain versus timeat different temperatures ranging from 208C to808C areshown in Fig. 3 for all-PP composites with UD and CPlay-ups. As expected, variation of the test temperatureshows a remarkable effect on the creep behavior of theall-PP composites with enhanced creep tendency as thetemperature is increased. This effect can be recognized asthe effect of temperature on the mobility of the macromolecularchains. With the increase in temperature, mobilityof the macromolecules increases which leads to higherdeformation of the composites. It is also clear from theresults that the CP laminates show higher creep strainthan the UD ones at all the temperatures indicating higherresistance to creep in the case of later. This could beexplained from the difference in the composite morphology,namely crystallinity and void content as well as thereinforcement architecture [32]. In the case of UD composites,in addition to the lower amount of voids as well ashigher percentage of crystallinity, higher volume fractionof the tapes in the longitudinal direction remarkablyincreased the strength and stiffness of the all-PP compositesand thereby a reduction in creep strain. Figure 3 alsoindicates that the creep rate increases with the increase intemperature as the slope of the creep curves tends toincrease with temperature.From Fig. 3, it appears that the shapes of the variouscreep curves are amenable to the well-known reductionscheme of time–temperature superposition. Coincidenceof the data is good and the master curves obtained byTTS principle (Fig. 4) show higher creep resistance forUD all-PP composites as anticipated from the short-termcreep data. Generally, the master curves are importantsince the polymer’s behavior can be traced over muchgreater periods of time than those determined experimentally.The shift factors, a T , necessary to generate the mastercurves was obtained directly from the experimentalcreep curves plotted against time by measuring theamount of shift along the time scale necessary to superimposethe curves on the reference. The reference temperaturewas chosen as 308C for both the composite types.The log a T values thus obtained by shifting the creepcurves are listed in Table 1. It shows that log a T decreasesFIG. 3. Creep response of UD and CP all-PP composites at different temperatures (n 208C, l 308C,~ 408C, ! 508C, ^ 608C, 3 708C, " 808C); solid lines represent Burger fit.944 POLYMER ENGINEERING AND SCIENCE—-2008 DOI 10.1002/pen
TABLE 2.Parameters obtained from the Burger model.SpecimenTemperature(8C)E 1(MPa)E 2(MPa)g 1(GPa-s)g 2(GPa-s)FIG. 4. Creep strain master curves generated for all-PP compositeswith unidirectional (UD) and cross-ply (CP) lay-ups; T ref is the referencetemperature.with increasing temperature. The negative sign indicates ashift to the right of the creep curves, that is, toward thereference at lower temperature. A higher shift value thusindicates a larger shifting of the creep curve to the referencecurve. The shifting scheme indicates that as temperatureincreases, molecular relaxation accumulate at a constantrate and that the underlying mechanism of creepremains unchanged.Creep Modeling AnalysisSimulated creep curves using the Burger model arealso shown in Fig. 1 with the solid lines. It can be seenthat they show a satisfactory agreement with the experimentaldata at each temperature. The first instantaneousdeformation arises from the spring or the elastic element(E 1 ) and later time-dependent deformation comes fromthe parallel spring and dashpot (g 2 ) and from the viscousdashpot flow (g 1 ). The model parameters obtained for theall-PP composites produced by unidirectional and crossplylay-ups are shown in Table 2. According to theseresults, viscosity decreased with increase in the creep testtemperature and higher flow occurred in the dashpot andpermanent deformation increased. In the viscous part, g 2TABLE 1.Temperature (8C)Shift factor (log a T ) for the UD and CP all-PP composites.UDlog a T20 1.16 1.06730 0 040 21.215 21.14850 22.304 21.95160 23.151 22.51270 23.786 22.99880 24.426 23.501CPUD 20 1.22 6.37 12.11 0.4230 1.10 4.30 10.00 0.2540 0.94 2.67 5.00 0.1550 0.78 1.74 2.50 0.1060 0.66 1.40 2.00 0.0770 0.55 1.20 1.67 0.0780 0.48 1.09 1.11 0.06CP 20 0.49 2.39 3.33 0.1530 0.44 1.57 2.00 0.1040 0.38 0.91 1.25 0.0650 0.33 0.68 1.11 0.0360 0.29 0.63 1.10 0.0270 0.25 0.62 1.07 0.0280 0.23 0.62 1.00 0.02tends to decrease with the increase in the temperatureconfirming that the rise in temperature increases the mobilityof the polymer chains. The modulus (E 1 ) of theMaxwell spring showed a decreasing function with temperature,which can be attributed to the softening of thematerial at elevated temperature and the stiffness thusdecreased with diminished instantaneous modulus. Thisindicates that the plastic deformation becomes severe atelevated temperature. The retardant elasticity (E 2 ) and viscosity(g 2 ) showed a similar dependency on temperature,thus decreasing with increasing temperature. It could bealternatively stated that the deformation of the Kelvin-Voigt unit increased with increasing temperature. InterestinglyTable 2 also shows that the variation in the tapelay-up has a significant effect on the viscous and elasticcomponents of the Burger model as they were found tobe higher for UD than for the CP composite specimens.This arises from the difference in the microstructures andthe tape lay-up. It strongly suggests that the variationin the reinforcement architecture has a significant effect onthe viscoelastic properties. Because of the higher viscousflow and lower elastic modulus, CP composite specimensdeform more than that of the UD counterpart under thesame loading condition.The results mentioned earlier thus shows that the Burgermodel provides a constitutive representation of creepof the all-PP composites and from the modeling parameterstheir structure-to-property relationship can be betterrealized. Additionally, an empirical equation, Findleypower law, is frequently applied to simulate and predictthe long-term creep properties due to its simple expressionand satisfactory applicability [7]. In this case, themethod was adopted to provide a broad understanding ofthe all-PP composites. The simulated curves (representedby solid lines) of the all-PP composites produced by differenttape lay-ups are shown in Fig. 5. It can be seen thatthey agree well with the experimental data at each temperatureand the power law can be used as a predictivemodel for creep. The complete modeling parameters e 0 ,DOI 10.1002/pen POLYMER ENGINEERING AND SCIENCE—-2008 945
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