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The tensile force oscillation of polycarbonate at elevated temperatures.

INTRODUCTION

The use of engineering plastic materials is an important innovation in human history, and polycarbonate (PC) is one of such significant materials. PC can be manufactured into different shapes and geometric formations for specific applications. It is because PC has high tensile strength, impact strength, toughness, and optical transparency in the visible spectrum, as well as its chemical stability and good acid and alkaline resistance (1). Due to its extreme low beta transition temperature, PC is more ductile and impact resistant than poly(methyl methacrylate) (PMMA) (2).

The yielding behavior of PC has been studied extensively through the material usages, the manufacture process needs, and the academic understanding (2-6). Bauwens et al. (3-5) conducted a series of tensile and compression tests on PC over temperatures ranging from below the glass transition temperature (alpha transition) down to temperatures lower than the beta transition temperature. They suggested that two parallel thermal activation processes of molecular motion, described by the Eyring equation but with different activation energies and frequency factors, were involved in the deformation at yielding of PC. Fleck et al. (2) examined the yield and fracture response of the glassy polymers in torsion experiments under high strain rate. They claimed that the fracture was linked to the tensile cracks that formed a stepped fracture surface through microcrack nucleation and propagation, and not by the thermal instability of the material. Both the yield and fracture phenomena of PC obeyed a thermally activated rate phenomena of the Eyring type, but not in the PMMA case, because it would fracture before yielding under the condition of high strain rates. Lu and Ravi-Chandar [7] compared the deformation processes between the glassy polymer and metals, applying the intrinsic material law to numerically simulate the deformation of PC under uniaxial tension. They argued that the intrinsic material softening of PC was not necessary for shear band formation and the continuous growth of a stable neck. The above studies were focused on the effects of applied stress, strain rate, and temperature on the yielding behavior and the magnitude of the fracture stresses.

The tensile force oscillation phenomenon was observed as the Luder's band formation in metals after they were deformed plastically (8). Later, this phenomenon was also observed in polymers such as poly(ethylene terephthalate) (PET) fibers (9-12), amorphous copolyester (13), and polyimide thin films (14) as well as the syndiotactic polypropylene and its nanocomposites with montmorillonite in concentrations of less than 0.5 weight percent (15). Two characteristic instability phenomena usually occur in polymer processing and tensile testing. One is the draw resonance phenomenon, in which there is cyclic variation of the taken-up filament diameter or film thickness that occurs in melting, spinning, or film-forming processes (16). The other is the tensile force oscillation phenomenon that occurs after necking during the tensile testing. Bunn and Alock (17) proposed a mechanism that included the shearing and rebuilding of crystalline regions in the specimen and described the tensile force oscillation phenomenon. However, crystallizable polymer specimens do not necessarily exhibit force oscillation behavior, and the amorphous polymer specimens show the same unstable phenomenon as the crystallizable specimens (13). The tensile oscillation phenomenon was observed to be favored for the specimens of less oriented or smaller entanglement density (11), (13). The appearance of tensile oscillation is limited within a range of crosshead speeds and strain rates, which depends on the polymer species, sample preparation, test setup, and environment. Bazhenov (12) drew the PET films and observed the intervals of the tensile oscillation at crosshead speeds from a few mm [min.sup.-1] to several thousands mm [min.sup.-1]. However, Cao (11) and Karger-Kocsis et al. (13) found that the oscillation of PET fibers and copolyester sheets occurred in limited deformation rates ranging from 75 mm [min.sup.-1] to 200 mm [min.sup.-1] and 2 m [s.sup.-1] to 3.7 m [s.sup.-1], respectively. The amplitude of oscillations diminished rapidly to zero when the deformation rate was away from the peak value. Mouzakis (15) and Vas et al. (10) examined the yield area of the deformed polymers and found that cavities formed in parallel to the tensile direction and existed inside the specimens. In this study, the tensile force oscillation in PC was investigated in detail, with special attention paid to the effects of gamma-ray irradiation, temperature, testing environment, and strain rate on the force oscillation.

EXPERIMENTAL

PC sheets of 2 mm thickness (Lexan 9030-113) were obtained from the General Electric Company (Fairfield, CT). Specimens of 80 mm by 10 mm by 2 mm were cut from these sheets and machined to the tensile specimen size. A gauge width of 6 mm and gauge length of 40 mm, with a 10 mm radius arc, connected the grip areas. The arc diameter of the dumbbell-shaped specimen was required to be large enough to prevent stress concentration in the corners. All specimens were ground, finely polished, annealed at 100[degrees]C for 24 h and furnace cooled to ambient temperature for stabilization. Some specimens were irradiated by gamma rays with a dose from 30 kGy to 200 kGy. The tensile tests were performed at temperatures from 30 to 98[degrees]C using a universal testing machine (Hung-Ta Instrument, Taichung, Taiwan) with a built-in furnace. The effect of the crosshead speed on the force self-oscillation was found using an Instron universal tensile test machine, with the crosshead speed varied from 0.084 mm min -I to 1008 mm [min.sup.-1]. The tensile tests were conducted in air, water, and oil baths. The glass transition temperature ([T.sub.g]) of PC was determined using a differential scanning calorimeter (DSC).

RESULTS AND DISCUSSION

Tensile Teas Performed in Air

Tensile testing was performed in air at temperature 70[degrees]C and crosshead speed of 0.84 mm [min.sup.-1]. A fender was placed between the specimen and an electric fan inside the furnace. The test results are illustrated in Fig. 1. A clear upper yield point follows the elastic deformation at the beginning of the test. The force oscillation regions are present immediately after the upper yield, in resemblance to amorphous copolyesters (13). The test conditions in the high oscillation frequency region (elongation ranged from 5 mm to 15 mm) and the low oscillation frequency region (15-34 mm elongation) occurred when the electric fan was turned off and on, respectively. The high and low frequencies were measured to be 0.02 [s.sup.-1] and 0.01 [s.sup.-1]. The force oscillation can be explained in the following. After the necking starts, the applied tensile load provides the mechanical energy to form the plastic deformation in the transition region between the neck and non-oriented polymer with the spontaneous emission of heat. If the heat is large enough to increase the temperature in the transition zone to the maximum value such that the elastic modulus of this zone decreases significantly and the stress is reduced. However, due to the heat conduction, the temperature in this zone will decrease to its original one and so does the stress (the original high value). Here we assume that heat conduction takes place in the transition zone and that in the rest part of the specimen is neglected. The high and low stresses will be alternative to appear until the necking propagation is complete. The critical temperature for force oscillation may be the crystallization temperature or the glass transition temperature, because the crystalline material and rubber material have low elastic modulus than the amorphous material. Note that when the maximum temperature in the transition zone is lower than the critical value for force oscillation, the necking would propagate without the force oscillation. The transition zone is then filled with the shear band or craze markings. As the electric fan is on and off, the air circulation is responsibly fast and slow. The high air circulation yields the fast heat dissipation, which means a low maximum temperature and long oscillation period. Therefore, the use of the electric fan would Lower the oscillation frequency. Figure 2 demonstrates the tensile tests conducted in air at 80[degrees]C without the fender and at a crosshead speed of 0.84 mm [min.sup.-1]. An upper yield is present after the elastic deformation. When the fan was allowed to blow on the specimen directly, no oscillation was observed in the necking region because the maximum temperature was lower than the critical temperature for force oscillation. The oscillation was observed again when the fan was turned off. The frequency was estimated to be 0.02 [s.sup.-1].

Tensile tests were conducted in air with a crosshead speed of 0.84 mm min-1 at various temperatures. The curves of load versus elongation are shown in Fig. 3. The upper yield points follow the elastic deformation. The plastic deformations occur immediately after yielding. The upper yield point decreases and the plastic elongation increases with increasing temperature. The corresponding fracture strain increases with increasing temperature, and the fracture load changes in the opposite trend.

The force oscillation phenomenon shown in the load-elongation curves becomes apparent at temperatures higher than 40[degrees]C, and the oscillation frequency increases with increasing temperature. That is, the plastic deformation in the transition zone accompanied with certain amount of heat takes place during the tensile test at temperature below 40[degrees]C in air, but no force oscillation appears. The heat conduction would raise the medium temperature to be greater than the critical temperature for the force oscillation. The force self-oscillation is a thermal activation process. For the same environmental condition, the applied load provides the mechanical energy to form plastic deformation in the transition region with the same amount of heat at different temperatures. According to heat conduction theory, the time to reach the maximum temperature (above the critical value for force oscillation) decreases with increase of testing temperature and so does the time to go back the original temperature. That is, the oscillation frequency decreases with increasing temperature. This can be seen from Fig. 4 showing the relationship between the logarithm of the oscillation frequency and the reciprocal of the absolute temperature with the crosshead speed at 0.84 mm [min.sup.-1].

Two slopes of the bended line are shown in Fig. 4. This confirms that the relation obeys the Arrhenius equation as described by

[upsilon] = [[upsilon].sub.0] exp(--Q/RT) (1)

where [upsilon] is the force oscillation frequency, Do is the preexponential factor, Q is the activation energy, R is the gas constant, and T is the absolute temperature. It indicates that there are two deformation mechanisms, the shear deformation and the craze formation, which are involved in the deformation of polymeric materials under tensile loading. Bucknall et al. (18), (19) studied the dead load tensile creep experiment on acrylonitrile-butadiene-styrene (ABS) polymers with and without the addition of glass beads at ambient temperature. They found that the shear deformation was predominated at the early stage of tensile creep test and the contribution of crazing to creep deformation increases with increasing time and stress. In this study, both the shear deformation and the crazing, which usually take place in the plastic deformation of PC, could be expected. The plastic deformation active in the low temperature range (less than ca. 60[degrees]C) is observed as the slip band deformation, whereas in the high temperature range (greater than ca. 70[degrees]C) the craze formation dominates. The activation energies responsible for slip band deformation and craze formation were determined to be 5.3 kJ [mol.sup.-1] and 0.45 kJ [mol.sup.-1], respectively. The slip bands shown in Fig. 5 were clearly observed on the surface of the tensile specimen, which was deformed in air at temperatures less than 60[degrees]C. The slip bands are inclined by approximately 45[degrees] with respect to the necking direction. The crazes were found over the entire tensile specimen at temperatures above 70[degrees]C. The craze morphologies were examined by a scanning electron microscope. It can be seen from Fig. 6 that the cavities containing cleavage fibers are exposed on the surface and that they penetrate vertically into the specimen.

The Tensile Tests Performed in Water and Oil Baths

The specimens were immersed in a thermostatic oil bath during tensile testing, with a 0.84 mm [min.sup.-1]crosshead speed at various temperatures. The curves of load versus elongation are shown in Fig. 7. The upper yield point appears after the elastic elongation and the plastic deformation occurs after the yielding. No force oscillation is present in the plastic deformation region. The reason can be explained qualitatively in the following. The oil carries heat away faster than the air. That is, the thermal conductivity is greater in silicon oil (0.14 [W.m.sup.-1][K.sup.-1]at 50[degrees]C) than in air (0.024 [W.m.sup.-1][K.sup.-1] at 25[degrees]C). The maximum temperature in the transition zone, when exposed to the oil, is lower than the critical value for the force oscillation. The fracture strain increases with increasing temperature until the temperature approaches 80[degrees]C. The fracture mechanism is changed from shear deformation to craze formation around 70-80[degrees]C. The fracture elongation increases with increasing temperature at temperature greater than 80[degrees]C. The tensile tests performed in the thermostatic water bath demonstrated a similar phenomenon to that in the thermostatic oil bath, i.e., no force oscillation was detected in the water bath. The thermal conductivity of water at 25[degrees]C is 0.58 [W.m.sup.-1][K.sup.-1], which is greater than the thermal conductivity of silicon oil.

The Effect of Gamma Ray Irradiation on Tensile Tests

The PC tensile specimens were irradiated by gamma rays with doses of 30 and 200 kGy. The tensile tests were conducted in different environments, including air, water, and oil baths. The crosshead speed under the three environments was fixed at 0.84 mm [min.sup.-1], and the interval between two near temperatures was 10[degrees]C. The experimental observations were consistent and the results of 30 kGy dose used were reported. The curves of load versus elongation are illustrated in Fig. 8a-c for the tests in air, water, and oil, respectively. As shown in Fig. 8a, the oscillations are present at all temperatures from 30[degrees]C to 100[degrees]C for the tensile load tests conducted in air. The gamma-ray irradiation makes the chain scission in PC so that the glass transition temperature decreases with increasing dosage. The polymeric chain is more easily to flow in the rubber state than in glassy state. Thus the glass transition temperature of the polymeric material is closely related to the critical temperature for force oscillation. The glass transition temperatures are 148.7[degrees]C and 144.6[degrees]C for non-irradiated PC and irradiated PC of 200 kGy, respectively. Therefore, the force oscillation was observed in the irradiated PC at 30[degrees]C in air, but it did not appear in the non-irradiated PC under the same condition (see Fig. 3). Fracture load in general decreases with increasing temperature when the temperature is greater than 60[degrees]C. The elongations at break are almost the same when the temperatures are lower than 50[degrees]C, but increased at higher temperatures. The elongations of the specimens at the break with the gamma irradiation treatment are slightly shorter than those without the radiation, as compared with the curves shown in Fig. 3.

The primary difference of the load-elongation curves conducted in air and in water (or in oil) is that no oscillations are observed in tests in water (or oil) bath. The load-elongation curves obtained in water and oil are shown in Fig. 8b and c, respectively. The reason is that the heat in the transition zone generated by the applied tensile load dissipated so fast in water and oil baths that the maximum temperature in the transition zone is lower than the critical value for force oscillation. The elongation at the break of the specimen with gamma ray dose of 30 kGy tested in a water bath increases with increasing temperature, then drops rapidly to a minimum at 70[degrees]C, and finally increases with increasing temperature in the range from 70[degrees]C to 90[degrees]C. There is a transition temperature at 70[degrees]C, at which the deformation mechanism of the PC changes. Figure 8c shows the results of the tensile tests on the irradiated specimens conducted in oil bath at various temperatures under crosshead speed 0.84 mm [min.sup.-1]. The load--elongation results conducted in the oil bath are different from those conducted in the water bath, as the fracture loads and elongations at the break monotonically decrease with increasing temperature. The elongations are shorter for the irradiated specimens than for the non-irradiated ones (see Fig. 7) because the former has a lower glass transition temperature than the latter.

The glass transition temperatures [T.sub.g], as determined by DSC, are 148.7[degrees]C, 149.3[degrees]C, and 144.6[degrees]C for the non-irradiated specimen before tensile test, the non-irradiated specimen tested in air at 90[degrees]C, and the specimen irradiated with 200 kGy before tensile test, respectively. There is a 0.6[degrees]C increase from the non-irradiated specimens before test to after test in air at 90[degrees]C due to the molecular chain elongation or orientation alignment in hot air relative to the non-irradiated specimen before test. It can be seen in Fig. 3 that the upper yield stress is greater at 30[degrees]C than at 90[degrees]C but that the corresponding elongation at the break is shorter. A significant temperature drop of 4.1[degrees]C was found for the irradiated specimens. The molecular chains are scission during the irradiation process so that the [T.sub.g] of irradiated PC decreases. A comparison of the load versus elongation curves for tests at temperature 30[degrees]C. provided in Figs. 3 and 8a, indicates that the upper yield stress is greater for the non-irradiated specimen than for the irradiated one. This implies that the molecular weight is reduced due to the gamma-ray irradiation and enhanced by the tensile stress.

The Effect of the Strain Rate on the Tensile Test

Crosshead speeds of 0.084, 0.84, 25.2, 252, and 1008 mm min' were used in this study. The load oscillation phenomenon was observed only when the tests were conducted in air without external disturbances and with crosshead speeds less than 0.84 mm [min.sup.-1]. Figure 9a and b shows the tensile curves for tests conducted in air at three temperatures. The crosshead speeds for Fig. 9a and b were 0.084 mm [min.sup.-1] and 25.2 mm [min.sup.-1], respectively. The Young's moduli of PC at 50[degrees]C, 70[degrees]C, and 80[degrees]C can be obtained from the initial slopes of Fig. 9a is 2.5 [+ or -] 0.3 GPa. The oscillations are observed in Fig. 9a, but not in Fig. 9b. Table 1 gives an overall summary of the experimental observations of force oscillation.

TABLE 1. Summary of the observation of force oscillations.

Medium                   Experimental
                         environment

                         Air

Crosshead speed          Fan turned    Fan turned   Oil/water
                         off           on           bath

Crosshead speed          Yes           No           No
[less than or equal to]
0.084 mm [min.sup.-1]

Crosshead speed >        No            No            No
0.84 mm [min.sup.-1]


It was mentioned in the previous section that the force oscillation occurs when the applied tensile load provides the mechanical energy to form plastic deformation with sufficient heat in the transition zone of the specimen. Assume the same experimental conditions but only varying the crosshead speed, then the amount of heat generated and its conduction would depend on the magnitude of crosshead speed. Three levels of the crosshead speed related with force oscillation are discussed. Firstly, the crosshead speed is so fast that the tensile test may be considered as an adiabatic process. The heat is linearly proportional to the temperature increment in the transition zone. When the temperature in the transition zone is greater than the critical value for force oscillation, the force will decrease. Because of the adiabatic process, the temperature in the transition region keeps constant (does not change with time). Thus the force remains constant, and no oscillation is observed. On the other hand, if the temperature in the transition zone is lower than the critical value for force oscillation, the force would not drop. That is. the force is maintained constant during the necking propagation and no force oscillation is observed. Secondly, when the crosshead speed is very slow, the heat in the transition zone is dissipated as soon as it is generated. The temperature increment in the transition zone is insignificant and the force maintains the same value. Thus no force oscillation will be observed. Thirdly, the crosshead speed is set in the certain range such that the temperature in the transition zone is greater than the critical value for force oscillation. The force oscillation is observed. Because of the limitation of the test machine used in this work, the effect of the crosshead speed less than 0.084 mm [min.sup.-1] is not studied. However, it may be concluded that no force oscillation will occur at the crosshead speed lower than 0.084 mm [min.sup.-1].

Bazhenov (12) studied the oscillated neck propagation during the cold drawing of amorphous PET. He proposed two mechanisms for the oscillations during the necking. Firstly, the heat instability is related to the rise of temperature in a narrow transitional region between the neck and the non-oriented polymer. The heat in the narrow transitional region is being converted from the mechanical work done by the applied tensile load. He modified the Barenblatt-Toda's equation to include the effect of the draw ratio on the heating of a polymer. The author concluded that (1) the appearance of oscillations in any polymer is in some interval of the crosshead speeds, where the draw stress decreases with an increase in crosshead speed, and (2) oscillations are observed at high crosshead speeds when the draw stress increases with an increase in the speed. The result of oscillation at high crosshead speed in PET was obtained by mathematical formation, and the reasons were not clearly stated. According to the author's numerical analysis and the PET experiment, the amplitude of the oscillation decreases significantly with increasing crosshead speed. It seems that force oscillations would not be observed if the crosshead speed is very high. From the experimental point of view, the test machine cannot detect stress oscillation at high crosshead speeds. This implied that the condition of the appearance of oscillation in any polymer would exist only in some interval of the crosshead speeds. Thus it is consistent with the present experiment. In Bazhenov's analysis of the transition mechanism in PET, from glassy to rubber-like state and to crystallization, the role of heat was not considered.

In addition, the force oscillation in metals is worthy to mention. The heat conductivity of polymers is lower than that of metals by a factor of three orders of magnitude. As a result, the temperature increment in metals is negligible under tensile test if the neck appears. However, the force serration (or force oscillation) in metals under tensile testing is observed in the certain temperature range (20), (21). The force serration in metals is termed as dynamic strain aging observed in metals containing interstitial solutes. This phenomenon can be explained in the following. The high tensile load produces plastic flow due to movement of edge dislocation with Cottrell atmosphere such that the edge dislocation separates from the enclosed interstitial solutes. The Cottrell atmosphere is formed as the interstitial solutes are being enclosed by edge dislocations. The low tensile load produces plastic flow by the motion of isolated dislocations. When the testing temperature exceeds a critical value, the interstitial solutes will diffuse into the hydrostatic stress contour induced by the edge dislocation and move to its neighborhood to form the Cottrell atmosphere. The edge dislocation escaping away from Cottrell atmosphere and interstitial solutes catching it back to form Cottrell atmosphere occur alternatively. And the tensile load will correspondingly be high and low. Thus the process is repeated, and the force serrations are observed in metals. However, when the temperature increases to a certain value such that the interstitial solutes move so fast and the edge dislocation no longer can attract to these solutes, the Cottrell atmosphere cannot form. As a result, the force serrations will not be observed. Because the solute movement follows the Fick's law of diffusion and the diffusivity obeys the Arrhenius equation, the solutes catching dislocations occurs only in certain temperature range.

The general plastic deformation of PC in the tensile test can be divided into two stages. A similar trend has been observed in previously published documents (7), (11). The plastic stress remained constant with increasing the draw ratio in the first stage, when the draw ratio is less than 0.63. Necking began to propagate during this stage at a constant rate, as the cross-section was reduced uniformly in the gauge length. After the necking propagation finished, the stress or force was increased in order to overcome the work hardening, with a further increase in the draw ratio. The second stage was located at the draw ratios greater than 0.7.

At a given temperature, the upper yield points, plastic deformation stresses, and fracture stresses increase with increasing strain rate. The present experimental observations on the relationship between the yield stress (or fracture stress) and the strain rate agree with documented reports for non-irradiated specimens tested in air (2-5). The upper yielding point increasing with strain rate is because plastic deformation required time to form shear band (or craze). Note that heat generated in the non-oriented polymer is neglected before upper yielding. Most of the mechanical energy is then stored as elastic energy before the upper yielding point.

CONCLUSIONS

The tensile testing of PC at elevated temperatures was investigated in air, water, and oil environments. Force oscillations were observed for PC tested in air, but not in water or oil. The occurrence of force oscillation is determined by the heat dissipation rate of the PC during the necking propagation. The oscillation phenomenon is attributed to the local variation in elastic modulus resulting from the temperature change. Two mechanisms, the shear band deformation and the craze formation, were based on the deformation at both low and high temperatures. The corresponding activation energies of force oscillation for the tensile tests in air were determined to be 5.3 kJ [mol.sup.-1] for the shear band formation and 0.45 kJ [mol.sup.-1] for the craze formation. The transition temperature from shear bands to crazing deformation was determined to be about 70[degrees]C. However, for the tensile tests in water and oil, the transition temperature occurred when elongation at fracture on the load-elongation curve dropped significantly. The force oscillation phenomenon would occur preferably under low strain rates within the testing range and in irradiated specimens.

Correspondence lo: Sanboh Lee; e-mail: sblee@mse.nthu.edu.tw

Contract grant sponsor National Science Council of Taiwan.

DOI 10.1002/pen.23286

Published online in Wiley Online Library (wileyonlinelibrary.com).

[c] 2012 Society of Plastics Engineers

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Donyau Chiang, (1) Meng-Leung Tsai, (2) Sanboh Lee (2)

(1.) Instrument Technology Research Centre, National Applied Research Laboratories, Hsinchu, Taiwan

(2.) Department of Materials Science and Engineering, National Tsing Hua University, Hsinchu, Taiwan
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Publication:Polymer Engineering and Science
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Date:Mar 1, 2013
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