Effects of Gauge Length and Strain Rate on Fracture Toughness of Polyethylene Terephthalate Glycol (PETG) Film Using The Essential Work of Fracture Analysis.
ROBERT K.Y. LI 
YIU-WING MAI [1,2]
Essential Work of Fracture (EWF) analysis was used to study the fracture toughness of a PETG film. In the study of the gauge length (Z) effect on the specific essential work ([w.sub.e]) using Z = 50, 100, 150, 200 and 250 mm, it is observed that [w.sub.e] is independent of gauge length, except that a slightly lower [w.sub.e] value was measured for Z = 50 mm. Interestingly, for specimens with long gauge lengths (Z[greater than or equal to]150 mm in this study), brittle fracture occurred. The minimum ligament length at which ductile/brittle transition took place was observed to decrease with increasing gauge length. There is a small strain rate effect on [w.sub.e] with loading rates less than 1 mm/min. But with higher loading rates, [w.sub.e] showed no strain rate sensitivity.
The fracture characteristics for brittle polymers can be determined by using linear elastic fracture mechanics (LEFM) . For semi-brittle polymers, as manifested by small scale crack-tip plasticity, LEFM can still be applied by making adjustments to the crack length [1,2]. However, for ductile polymers, gross yielding limits the application of LEFM. Other techniques, such as J-integral and the essential work of fracture (EWF) analyses, have overcome this difficulty. Traditionally, the J-integral method has been widely applied to characterize the fracture toughness of ductile polymers [1,3-6]. More recently, the EWF approach has gained popularity because of its experimental simplicity. In the EWF method, one simply has to plot the total specific fracture work ([w.sub.f]) against the ligament length (l) curve with different values of l The y-intercept gives the specific essential work of fracture ([w.sub.e]), which is the fracture toughness of the material to be investigated. The EWE method has been applied to study the fracture behavior for metals [7-9], plastic sheets [10-18] and papers or newsprint [19, 20] in plane stress condition. It has been proven theoretically and confirmed experimentally that the specific essential work of fracture ([w.sub.e]) is equivalent to the critical J-integral value [10, 11, 21-24].
It has been found that the specific essential work of fracture ([w.sub.e]) is specimen type independent, i.e. the same [w.sub.e] values were obtained using the double-edge-notched-tension (DENT), single-edge-notched-tension (SENT) and deep-centre-notched-tension (DCNT) specimens [17, 22 and 24]. Working on a PET/PC blend, Hashemi  observed that [w.sub.e] is not affected by the specimen gauge length, however, [beta][w.sub.p] decreases with increasing gauge length. Also, specimens with short gauge lengths showed more stable load (F)-deflection ([delta]) curves than those with long lengths. No explanations were given to interpret these experimental observations and results. To do so, this will require a good understanding of the mechanics of fracture instability analysis.
The effect of loading rate on the EWF measurement has been investigated by a number of investigators and the general conclusion was that [w.sub.e] was independent of loading rate. Karger-Kocsis and Czigany (15) measured the [w.sub.e] values for biaxial-oriented filled poly(ethylene terephthalate) (BOPET) film at loading rates of v = 1 and 20 mm/min, and found that [w.sub.e] is independent of loading rate. In the work of Chan and Williams , it has been observed that We for two types of polyimide films was invariant with loading rates from 1 to 20 mm/min. Hashemi  found that for a PBT/PC blend [w.sub.e] was independent of loading rate from 2 to 50 mm/min. More recently, Karger-Kocsis, Czigany and Moskala  have determined that for an amorphous copolyester film, [w.sub.e] values at loading rates of 1, 10 and 100 mm/min are identical.
In this investigation, the fracture toughness for a polyethylene terephthalate glycol (PETG) film was characterized. Particular emphasis was placed on the gauge length and loading rate effects on the EWF measurements.
2. THE ESSENTIAL WORK OF FRACTURE (EWF)
For the fracture of a pre-cracked ductile polymer, two processes can be identified and the regions at which they took place are called, respectively, the inner fracture process zone and the outer plastic zone (Fig. 1). The total fracture work ([W.sub.f]) can be written as:
[W.sub.f] = [W.sub.e] + [W.sub.p] (1)
where [W.sub.e] is the essential work of fracture and [W.sub.p] is the non-essential (plastic) work. [W.sub.e] is a pure crack resistance parameter and essentially a surface energy; it is proportional to the ligament length l (for a given specimen thickness). [W.sub.p] is a volume energy, which involves microvoiding and shear yielding and it is proportional to [l.sup.2] (also for a given specimen thickness). Thus the total fracture work [W.sub.f] in Eq 1 can be rewritten as:
[W.sub.f] = [w.sub.e]tl + [beta][w.sub.p]t[l.sup.2] (2)
where [w.sub.e] and [w.sub.p] are the specific essential work of fracture and specific plastic work, respectively. t is the specimen thickness and [beta] is the plastic zone shape factor. The specific total fracture work, [w.sub.f], is given by:
[w.sub.f] = ([w.sub.f]/tl) = [w.sub.e] + [beta][w.sub.p]l. (3)
Since both [w.sub.e] and [w.sub.p] are material constants, and [beta] is independent of l, [w.sub.f] will vary in a linear manner with l (see Eq 3). By extrapolating the curve of [w.sub.f]-l to zero ligament length. [w.sub.e] can be obtained. For different shapes of the plastic zone [beta] can be obtained from the following equations ,
[beta] = [pi]/4 for circular plastic zone
[beta] = [pi]h/4l for elliptical plastic zone
[beta] = h/2l for diamond-shaped plastic zone} (4)
where h is full height of plastic zone (by considering both halves of the DENT specimen).
3. EXPERIMENTAL WORK
Polyethylene terephthalate glycol (PETG) (Eastman Chemical Grade PETG 6763, Vinyl Plastics, Inc.) was used in this study. The films were supplied in thickness of 0.5 mm. Dumbbell-shaped tensile bars and double-edge-notched-tension (DENT) specimens were cut from the sheets with the longitudinal axis of the specimens all parallel to the long edge of the films.
A die punch with a 6 mm width in the gauge length region was used to cut dumb-bell shaped tensile bars to measure the tensile characteristics (such as yield stress and flow stress) of the PETG film. The double-edge-notched-tension (DENT) specimen geometry (Fig. 2) was used for the EWF measurement. All DENT specimens have width W equal to 50 mm.
To study the effect of gauge length on the EWF method, samples with gauge length (Z) equal to 50, 100, 150, 200 and 250 mm were prepared. The loading speed was fixed at 10 mm/min for this set of tests. For the investigation of the loading rate effect, DENT specimens with a fixed gauge length (Z) of 100 mm was used. Specimens were tested at cross-head speeds v = 0.1, 0.3, 0.6, 1.0, 10.0, 50.0 and 100.0 mm/min. All mechanical tests were conducted using an Instron 4206 testing machine and the load-deflection results were recorded with a computer data logger.
4. RESULTS AND DISCUSSION
Figure 3 shows typical force-displacement (F-[delta]) curves for DENT samples that failed in a ductile manner. All the F-[delta] curves show a very prominent load drop after reaching the maximum force. The first peak should correspond to the yielding of the PETG film based on the ligament area. After yielding the ligament necks down and is drawn out giving rise to the load drop observed after the maximum load. But this load drop is not sufficient to tear the whole ligament. To maintain tearing the load has to increase again and this is usually bigger than the minimum load after the precipitous load drop. This gave rise to the second peak appearing on the F-[delta] curves. In earlier studies by Karger-Kocsis and co-workers [16, 25, 27], infrared thermography (IT) was used to observe the plastic zone development on amorphous copolyester films, which have similar F-[delta] characteristics to the PETG film used in the current study. The IT results showed that upon reaching the maximum load, the whole ligament yi elds instantaneously, and is followed by necking up to final fracture.
It must be pointed out that under certain conditions, which will be discussed later, the DENT samples failed in a brittle manner. The corresponding F-[delta] curves will have different characteristics.
4.1 EFFECT OF GAUGE LENGTH
Plots of the specific total work of fracture, [w.sub.f], against ligament length, l, for gauge lengths of 50 mm, 100 mm, 150 mm, 200 mm and 250 mm are shown in Fig. 4. The [w.sub.e] values for different gauge lengths were determined from the linear regression lines obtained from data points within the ligament range 2.5 mm [less than] l [less than] 16.6 mm. This ligament range within which data points were used for construction of the linear regression lines will be called the valid ligament length range in this work.
For valid measurement of the plane-stress [w.sub.e] value, the valid ligament length range is defined by [13, 14, 18-21]:
(3 - 5)t [less than or equal to] l [less than or equal to] min (W/3 or 2[r.sub.p]) (5)
where E is specimen thickness and 2[r.sup.p] is size of the plastic zone. 2[r.sub.p] is given by:
2[r.sub.p] = E[w.sub.e]/[pi][[[sigma].sup.2].sub.y] (6)
where E is Young's modulus and [[sigma].sub.y] is uniaxial tensile yield strength.
The conditions imposed by Eq 5 are needed for the following reasons. In the ligament range l [less than or equal to] (3-5)t, plastic constraint increases and plane-stress/plane-strain transition may occur. As the plane strain fracture toughness ([w.sub.Ie]) is lower than the plane stress value, the [w.sub.e] term in Eq 3 is no longer constant but varies with l in the plane-strain/plane-stress transition region. In the present analysis, the lower ligament limit used in the linear regression analysis was 5t ( = 2.5 mm). It can be seen from Fig. 4 that when l [less than] 5t, the [w.sub.f] values fell below the linear regression line. This supports the assumption that the plane-strain/plane-stress transition occurs in the region at l [approximately equals] (3-5)t. However, other investigators have provided evidence that the plane-strain/plane-stress transition may occur at larger l/t ratios. Wu and Mai  observed that for LLDPE film the plane-strain/planestress transition occurs at l/t = 14, while Li, Li and Tjiong  cannot observe any transition for PP/elastomer blends. Owing to the very small thickness of the presently investigated PETG film, it is difficult to obtain sensible results from samples with ligaments less than (3-5)t.
To prevent the size of the plastic zone from being disturbed by edge effects, the condition of l [less than or equal to] W/3 is set while l [less than or equal to] 2[r.sub.p] is to ensure complete yielding of the ligament before failure. In the present study, since W = 50 mm and t = 0.5 mm, these gives 5t = 2.5 mm, W/3 = 16.6 mm. For the PETG film at a testing speed of 10 mm/min, it has been measured that E = 2 GPa, [[sigma].sub.y] = 55.6 MPa, and [w.sub.e] =33 kJ/[m.sup.2]. By substituting the above values into Eq 6, 2[r.sub.p] was calculated to be 6.8 mm. The condition l [less than] 2[r.sub.p] is too restrictive for the present analysis. Therefore the condition l [less than] W/3 was employed as the upper limit for the valid ligament length range.
By taking the valid ligament length range to be
5t( = 2.5 mm) [less than or equal to] l [less than or equal to] W/3 ( = 16.6 mm) (7)
it can be seen from Fig. 4 that the data points follow a very good linear relationship for Z = 50, 100 and 150 nun. As mentioned above, and confirmed by the experimental results (see Fig. 4), the condition l [less than or equal to] 2[r.sub.p] ([approximately equals] 6.8 mm) is too restrictive. It has also been observed previously by Hashemi (12) that the condition l [less than or equal to] 2[r.sub.p] is too stringent for polycarbonate when the specimens are very thin and the plastic-zone is not circular. It can also be seen from Fig. 4 that as long as the samples failed in a ductile manner, the linear relationship between [w.sub.f] and l exists even at ligaments greater than W/3. For l [greater than] 25 mm (= W/2), the [w.sub.f] values start to fall below the linear regression lines presumably affected by the free edge effect of the specimen.
In the determination of the [w.sub.e] values, only data points within the valid ligament range were used for the regression analysis. The procedures are as listed in the EWF testing protocol (26). A least squares regression line was fitted to the data (within the valid ligament range) to provide the intercept, the 95% confidence limits on the intercept, and the standard deviation of the data with respect to the regression line. Data for specimens that lie more than 2 standard deviations from the best-fit line were eliminated from the analysis. Having rejected these points, a final least squares linear regression is applied to the remaining data to give the slope, the intercept, and the 95% confidence limits on the intercept. Results obtained from the analysis are summarized in Table 1. It can be seen that irrespective of the gauge length [w.sub.e] is equal approximately to 30 kJ/[m.sup.2], except that a slightly lower [w.sub.e] value was measured for the gauge length of 50 mm.
For tests using gauge lengths of 50 mm and 100 mm, all specimens failed in a ductile manner (see Fig. 4a). The force-displacement curves were similar to those presented in Fig. 3. However, for tests using specimens with gauge length of 150 mm and above, some of the specimens failed in a brittle manner. Figure 5 shows force-displacement curves for some DENT specimens with gauge length of 150 mm. For small ligament lengths (i.e. l = 6.3 mm and 15.2 mm), ductile failure occurs. However, for the specimen with l = 24.8 mm, it failed in a brittle fashion. Upon reaching the maximum in the force-displacement curve, unstable crack propagation was observed, with a precipitous load drop to zero. A ductile and a brittle fractured specimen are shown in Fig. 6. The plastic zone can be clearly seen in the ductile specimen. For the brittle specimen, no ligament yielding has taken place.
In Fig. 4b, data points for ductile and brittle failures are represented by solid and open symbols, respectively. The minimum ligament length at which brittle fracture occurs can be seen to decrease with increasing gauge length in Table 2. It is thought that the brittle fracture behavior is related to the elastic energy storage in the gauge length. The longer the gauge length, the more elastic energy was stored in the gauge section of the DENT specimen. Once the crack started to propagate, the stored elastic energy would be released to aid crack propagation. An exact fracture instability analysis based on FEM is being carried out at the University of Sydney to predict these experimental results. However, an approximate analysis is given below.
Fracture becomes unstable when the applied tearing modulus [T.sub.a] is higher than the materials tearing modulus [T.sub.m]. It was shown by Mai and Powell (22) that
[T.sub.m] = 4E/[[[sigma].sup.2].sub.y] ([beta][w.sub.p]) (8a)
and from Atkins and Mai (29)
[T.sub.a] = 12 ZM/W (8b)
for the DENT geometry. For stable cracking [T.sub.m] [greater than or equal to] [T.sub.a] and vice versa. [T.sub.a] and [T.sub.m] are calculated by taking W = 50 mm, E = 2.0 GPa and [[sigma].sub.y] = 56.63 Mpa at v = 10 mm/min. Hill  proposed that the plastic constraint factor M should be equal to 1.15 for plane stress condition . However, the present investigation has indicated M should have a value of approximately 0.8 for the PETG film (see Section 4.4). Both [T.sub.a] and [T.sub.m] are calculated and shown in Table 3. It can be seen that for M = 1.15, [T.sub.m] [greater than] [T.sub.a] for Z = 50 mm only. By taking M = 0.8, which is supported from measurements on the net section stresses (Section 4.4), [T.sub.m] [greater than] [T.sub.a] for Z = 50 and 100 mm so that stable ductile tearing was predicted as observed in the experiments.
Referring to Fig. 4b, it can be seen that for specimens having gauge length of 150 mm, brittle fracture started to take place at 20 mm. For specimens with a gauge length of 200 mm, brittle fracture commenced within the valid ligament length range. For samples having a gauge length of 250 mm, brittle fracture occurred even in the plane-strain/plane-stress transition region. In fact, the majority of specimens having such a long gauge length were fractured in a brittle manner.
4.2 EFFECT OF LOADING RATE
To study the effect of loading rate on the EWF characteristics, specimens with a fixed gauge length of 100 mm were used. Plots of [w.sub.f] versus l for different loading rates are shown in Fig. 7. Linear regression lines were obtained by using data points inside the valid ligament length range (i.e. 2.5 mm [less than] l [less than] 16.6 mm) following the recommendation in the EWF testing protocol , which has already been explained in Section 4.1. It can be seen that for cases with ligaments greater than W/2 (i.e. 25 mm), the [w.sub.f] values lie below the linear regression lines.
For EWF measurements carried out at loading rates v = 0.1, 0.3, 0.6. 1.0 and 10.0 mm/min, all samples failed in a ductile manner. When the loading rate v was increased to 50.0 and 100 mm/min, brittle fracture took place. Tensile stress-strain curves measured on dumb-bell shaped tensile bars, Fig. 8, also confirm that ductile failure (i.e. yielding followed by subsequent drawing of the necked section) prevails with strain rates less than 10 mm/min. For v = 20 mm/min and above, all dumb-bell shaped tensile bars failed in a brittle manner. Values of the yield ([[sigma].sub.y]) and flow ([[sigma].sub.f]) stresses are summarized in Table 4. It can be observed that yield stress [[sigma].sub.y] at maximum load increases with increasing loading rate. However, the strain rate sensitivity for the flow stress [[sigma].sub.f] at drawing of the neck is weak.
Summaries of the EWF characteristics for the PETG measured at different loading rates are summarized in Table 5. There appears to be a definitive but small strain rate effect for [w.sub.e] when the loading rates v [less than or equal to] 1 mm/min. For v [greater than or equal to] 1 mm/min, no strain rate effect on [w.sub.e] can be observed. Previous investigations by Chan and Williams , Karger-Kocsis and Czigany [15, Hashemi , and Karger-Kocsis et al.  have indicated no strain rate effect on the [w.sub.e] values for the respective polymer systems used in those studies. It is interesting to observe that the lowest loading rates used were either equal to or above 1 mm/min [14, 15, 17, 25]. Whether by lowering the loading rates to below 1 mm/min will see a strain rate effect would be an interesting exercise. Ultimately, rate-dependent [w.sub.e] values must be associated with viscoelastic processes that occur in the inner fracture processes zone. However, there has not been much work, either theoreti cal or experimental, on the strain rate effect [w.sub.e] of ductile polymers.
From Table 5, it can be seen that [beta][w.sub.p], which is the slope of the [w.sub.f] versus l plot, remains constant in the loading rate range 0.1 to 1.0 mm/mm where [w.sub.e] shows strain rate sensitivity. However, when v is in the range [greater than] 1.0 mm/min where [w.sub.e] shows strain rate insensitivity, [beta][w.sub.p] decreases slightly with increases in loading rate ([beta][w.sub.p] decreases from 8.76 to 8.11 MJ/[m.sup.3] when v increases from 0.6 to 10 mm/min), even though the change is very mild. This is in contradiction to the observations by Karger-Kocsis and Czigany , Hasheini , and Karger-Kocsis et al . In those studies it has been observed that a significant increase in [beta][w.sub.p] with increasing loading rate (although [w.sub.e] is unaffected by the change in loading rate in those studies).
4.3 The Shape Factor [beta]
Measurement for the shape factor can be obtained from the height of the plastic zone (h) vs. ligament length (l) plots (Fig. 9). From Eq 4, it can be seen that:
For diamond shaped plastic zone
h = 2[beta]l (9)
For elliptical plastic zone
h = 4[beta]/[pi]l (10)
Therefore, the slope of the h vs. l plot is equal to 2[[beta].sub.diamond] if the plastic zone is diamond shaped, and is equal to (4/[pi])[[beta].sub.elliptical] if the plastic zone is elliptical in shape. The slopes of the h vs. l plots, and the calculated [[beta].sub.diamond] and [[beta].sub.elliptical] values are all listed in Table 3. As can be seen, both [[beta].sub.diamond] and [[beta].sub.elliptical] fluctuate with gauge length, which are consequences of the large scatter in the measured h vs. l plots (Fig. 9). The major difficulties in measuring the height of the plastic zone h are due to the irregularities and the diffused boundaries between the elastic and plastic zones (Fig. 10). Therefore, in the present investigation, meaningful shape factor values cannot be obtained from the h vs. l plots.
4.4 Validity of Test Results
One of the prerequisites for EWF analysis is that a cracked specimen should undergo full ligament yielding prior to the onset of crack growth. In this study, visual inspections have supported the assumption of full ligament yielding before the onset of crack growth for the PETG DENT specimens. Working on amorphous copolyester films, which have very similar force-displacement characteristics to the PETG film studied in this work, Karger-Kocsis et al. (16, 25) have employed the technique of infrared imaging and observed that full ligament yielding indeed has taken place before crack growth. Therefore, it is with certainty that the above prerequisite has been satisfied. However, it would be of interest to look at the prerequisite from another perspective.
The net section stress ([[sigma].sub.n], defined as [F.sub.max]/lt, where [F.sub.max] is the maximum load in the force-displacement curve for a DENT specimen) is plotted against the ligament for different gauge lengths and cross-head speeds (Figs. 11 and 12, respectively). It can be seen that at small ligaments, [[sigma].sub.n] decreased with increasing l until a critical ligament value (1 [approximately equals] 10 mm) is reached and thereafter the steady state net section stress [[[sigma].sub.n].sup.*] remained constant.
Hill  suggested that owing to plastic constraint imposed by the notches, the yield stress for DENT sample geometry will be raised to 1.15 times the uniaxial yield stress. In the present investigation, it is seen that the steady state [[[sigma].sub.n].sup.*] values measured at the different loading rates all lied between 1.l5[[sigma].sub.y] and [[sigma].sub.f] ([approximately equals]0.64[[sigma].sub.y]). Referring to Fig. 11, for v = 10 mm/min, [[[sigma].sub.n].sup.*]/[[sigma].sub.y] [approximately equals] 0.8 for the different gauge lengths (Z) used. This gives the plastic constraint factor M = 0.8 that was used in calculating the applied tearing modulus [T.sub.a] (Eq 8b and Table 3).
Results from other investigators also suggested that the steady state [[[sigma].sub.n].sup.*] values may not necessary be equal to 1.15[[sigma].sub.y] for the DENT specimen geometry. Hashemi  has observed that for a PBT/PC blend, 0.91[[sigma].sub.y] [less than] [[[sigma].sub.n].sup.*] [less than] 1.19 [[sigma].sub.f]. The results of Karger-Kocsis et al. [16, 25] on amorphous copolyester films with different thickness (which have very similar DENT force-displacement curve characteristics to the PETG film studied in this work) have shown that [[[sigma].sub.n].sup.*] [less than] 1.15 [[sigma].sub.y]. On the other hand, Wu and Mai  have observed that for LLDPE film, [[[sigma].sub.n].sup.*] [less than] 1.15 [[sigma].sub.y]. Therefore, the requirement that [[[sigma].sub.n].sup.*] = 1.15 [[sigma].sub.y] for the DENT specimen geometry may not be a necessary pre-requisite for the EWE to apply so long as [[[sigma].sub.n].sup.*] exceeds the flow stress (and in this case [[[sigma].sub.n].sup.*] [approximately equals] 1.3 [[sigma].sub.f]) .
The effects of gauge length and loading rate on the EWE characterization of a PETG film (nominal thickness = 0.5 mm) have been investigated in this study using the DENT specimen geometry. Increasing the gauge length will cause unstable brittle fracture to take place. The longer the gauge length, the shorter the ligament length value at which unstable fast fracture begins. The ligament length requirement of l [less than] min(W/3, 2[r.sub.p]) is too restrictive for the present polymer film. In this study, W/3 [approximately equals] 16.6 mm, and 2[r.sub.p] [approximately equals] 7.6 mm. The requirement of l [less than] W/3 is an acceptable upper bound for the valid ligament length range. As long as the DENT samples failed in a ductile manner, [w.sub.e] is independent of specimen gauge length for Z [greater than or equal to] 100 mm. However, a slightly lower [w.sub.e] value was measured for Z = 50 mm.
There is a small strain rate effect on [w.sub.e] when the loading rate v is below 1 mm/min. For v above 1 mm/mm, no strain rate sensitivity on [w.sub.e] can be observed. In the regime where [w.sub.e] shows a strain rate sensitivity (i.e. v [less than] 1 mm/min), [beta][w.sub.p] is insensitive to strain rate. However, in the regime where [w.sub.e] shows no strain rate sensitivity (i.e. v [greater than] 1 mm/min), [beta][w.sub.p] decreases slightly with increasing loading rate.
For the EWF analysis with DENT specimens, the condition that the steady state net section stress [[[sigma].sub.n].sup.*] = 1.15[[sigma].sub.y] is not necessary for the present PETG film. This conclusion is also supported by other studies in that [[[sigma].sub.n].sup.*] [not equal to] 1.15[[sigma].sub.y].
Emma C. Y. Ching is the recipient of a Postgraduate Studentship from the City University of Hong Kong and she would like to thank M. K. Fung for his comments. Y-W Mai also wishes to thank the Australian Research Council for supporting his work in ductile fracture mechanics of tough polymers.
(1.) Department of Physics and Materials Science City University of Hong Kong Tot Chee Avenue, Kowloon, Hong Kong
(2.) Centre for Advanced Materials Technology (CAMT) Department of Mechanical and Mechatronic Engineering J07 University of Sydney Sydney, New South Wales 2006, Australia
(1.) J. G. Williams, Fracture Mechanics of Polymers, Ellis Horwood, Chichester, England (1984).
(2.) W. Y. Tam, T. Cheung, and R. K. Y. Li, Polymer Testing, 15, 363 (1996).
(3.) S. Hashemi and J. G. Williams, Polymer, 27, 384 (1986).
(4.) D. D. Huang and J. G. Williams, J. Mater. Sci., 22, 2503 (1987).
(5.) I. Narisawa and M. T. Takemori, Polym. Eng. Sci., 29, 671 (1989).
(6.) H. Swei, B. Crist, and S. H. Carr, Polymer, 32, 1440 (1989).
(7.) B. Cotterell and J. K. Reddel, Int. J. Fract., 13, 267 (1977).
(8.) Y-W. Mai and B. Cotterell, J. Mater. Sci., 15, 2296 (1980).
(9.) Y-W. Mai and B. Cotterell, Eng. Fract. Mech., 21, 123 (1985).
(10.) Y. W. Mai, B. Cotterell, R. Horlyck, and G. Vigna, Polym. Eng. Sci., 27, 804 (1987).
(11.) C. A. Paton and S. Hashemi, J. Mater. Sci., 27, 2279 (1992).
(12.) S. Hashemi, J. Mater. Sci., 28, 6178 (1993).
(13.) S. Hashemi and D. O'Brien, J. Mater. Sci., 28, 3977 (1993).
(14.) W. Y. F. Chan and J. G. Williams, Polymer, 35, 1666 (1994).
(15.) J. Karger-Kocsis and T. Czigany, Polymer, 12, 2433 (1996).
(16.) J. Karger-Kocsis, T. Czigany, and E. J. Moskala, Polymer, 38, 4587 (1997).
(17.) S. Hashemi, Polym. Eng. Sci., 37, 912 (1997).
(18.) A. Pegoretti, A. Marchi, and T. Ricco, Polym. Eng. Sci., 37, 1045 (1997).
(19.) R. S. Seth, A. G. Robertson, J. D. Hoffman, and Y-W. Mai, Tappi J., 76, 109 (1993).
(20.) Y-W. Mai, H. He, R. Leung, and R. S. Seth, In Fracture Mechanics: 26th Volume, STP 1256, pp. 587-99, W G Reuter, et al. eds, ASTM, Philadelphia (1995).
(21.) Y-W. Mai and B. Cotterell, Int. J. Fract., 32, 105 (1986).
(22.) Y-W. Mai and P. Powell, J. Polym. Sci., Part B., Polym. Phys., 29, 785 (1991).
(23.) J. S. Wu, Y-W. Mai, and B. Cotterell, J. Mater. Sci., 28, 3373 (1993).
(24.) J. S. Wu and Y-W. Mai, Polym. Eng. Sci., 36, 2275 (1996).
(25.) J. Karger-Kocsis, T. Czigany, and E. J. Moskala, Polymer, 39, 3939 (1998).
(26.) Testing Protocol for Essential Work of Fracture, ESIS TC-4 Group (October 1997).
(27.) J. Karger-Kocsis, Polymer Bulletin, 37, 119 (1996).
(28.) W. D. Li, R. K. Y. Li, and S. C. Tjong, Polymer Testing, 16, 563 (1997).
(29.) A. G. Atkins and Y-W Mai, Elastic and Plastic Fracture: Metals, Polymers, Ceramics, Composites, Biological Materials, pp. 699-701, Ellis Horwood, Chichester, England (1985).
(30.) R. H. Hill, J. Mech. Phys. Solids, 4, 19 (1952).
Effect of Specimen Gauge Lenght on the EWF Analysis of DENT PETG Film. The Crosshead Speed is 10 mm/min. Gauge Length Z [w.sub.e] [plus or minus] 2[sigma] R (mm) (kJ/[m.sup.2]) (kJ/[m.sup.2]) 50 25.66 [plus or minus]9 0.9888 100 29.84 [plus or minus]9 0.9964 150 34.13 [plus or minus]5 0.9984 200 33.98 [plus or minus]8 0.9930 250 Brittle fracture Gauge Length Z [w.sub.f] vs. I (mm) 50 [w.sub.f] = 25.66 + 8.54I 100 [w.sub.f] = 29.84 + 8.11I 150 [w.sub.f] = 34.13 + 8.17I 200 [w.sub.f] = 33.98 + 7.53I 250 Effect of Specimen Gauge Length on the Ductile/Brittle Transition. Crosshead Speed Specimen Gauge Length Ligament Length at Which (mm/min) (mm) Ductile/Brittle Transition Occurs 10 50 All ductile fracture 10 100 All ductile fracture 10 150 20 mm 10 200 11 mm 10 250 All brittle fracture Effect of Specimen Gauge Length on the EWF Characteristics of DENT PETG Film. The Crosshead Speed is 10 mm/min. Gauge Length Z [w.sub.e] [beta][w.sub.p] [T.sub.a] [T.sub.m] (mm) (kJ/[m.sup.2]) (MJ/[m.sup.3]) M = 0.8 M = 1.15 50 25.66 8.54 9.6 13.8 21.30 100 29.84 8.11 19.2 27.6 20.23 150 34.13 8.17 28.8 41.4 20.38 200 33.98 7.53 38.4 55.2 18.78 250 Brittle fracture Gauge Slope of h [[beta].sub.diamond] [[beta].sub.elliptical] Length Z vs. I (mm) plot 50 0.173 0.087 0.136 100 0.149 0.075 0.117 150 0.226 0.113 0.178 200 0.106 0.053 0.083 250 Effect of Loading Rate on the Yield ([[sigma].sub.y]) and Flow ([[sigma].sub.f]) Stress for PETG Film. Loading Rate Yield Stress [[sigma].sub.y] Flow stress [[sigma].sub.f] (mm/min) (MPa) (MPa) 0.1 46.89 31.64 0.3 48.51 31.56 0.6 49.55 31.89 1 53.73 33.65 10 56.63 34.43 20 57.58 [*] Brittle failure 30 57.26 [*] Brittle failure 50 58.85 [*] Brittle failure 100 60.68 [*] Brittle failure (*.)These values are the tensile strengths as the samples failed in brittle manner. Effect of Loading Rate on the EWF Analysis of DENT PETG Film. The Gauge Length is 100 mm. Loading rate v [w.sub.e] [plus or minus][sigma] R (mm/min) (kJ/[m.sup.2]) (kJ/[m.sup.2]) 0.1 22.14 [plus or minus]8 0.9966 0.3 24.31 [plus or minus]4 0.9981 0.6 28.28 [plus or minus]5 0.9986 1.0 31.85 [plus or minus]5 0.9970 10.0 29.84 [plus or minus]9 0.9964 50.0 Brittle fracture 100.0 Brittle fracture Loading rate v [w.sub.f] vs. I (mm/min) 0.1 [w.sub.f] = 22.14 + 8.66I 0.3 [w.sub.f] = 24.31 + 8.90I 0.6 [w.sub.f] = 28.28 + 8.76I 1.0 [w.sub.f] = 31.85 + 8.18I 10.0 [w.sub.f] = 29.84 + 8.11I 50.0 100.0
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|Author:||CHING, EMMA C.Y.; LI, ROBERT K.Y.; MAI, YIU-WING|
|Publication:||Polymer Engineering and Science|
|Article Type:||Brief Article|
|Date:||Feb 1, 2000|
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