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Essential work of fracture on PET films: influence of the thickness and the orientation
Polymer Testing 19 (2000) 559–568
Test Method
Essential work of fracture on PET films: influence of the thickness and the orientation M. Ll. Maspocha, V. He´naulta, D. Ferrer-Balasa,*, J.I. Velascob, O.O. Santanab a
Dept Cie`ncia dels Materials i Enginyeria Metallu´rgica, Universitat Polite`cnica de Catalunya, Av/Diagonal, 647-08028 Barcelona, Spain b Centre Catala` del Pla`stic, C/ Colom, 114-08222 Terrassa, Spain Received 1 March 1999; accepted 15 April 1999
Abstract This paper presents the fracture behaviour of films of a bioriented poly(ethylene terephthalate) (BOPET), that was studied by the Essential Work of Fracture (EWF) method. The influence of specimen thickness and molecular orientation was investigated. The results show that this method is a useful alternative for studying the plane-stress fracture of this material, finding that the specific essential work of fracture is strongly affected by the orientation [we was smaller in the direction of extrusion (MD) than in the perpendicular one (TD)], but independent of the specimen thickness in a range from 50 to 250 µm. On the other hand, the plastic work item is sensitive to variations of thickness but does not depend on orientation. 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction The Essential Work of Fracture (EWF) method seems to be the most appropriate technique to obtain fracture parameters for this kind of polymeric films. Due to their reduced thickness, and also to their ductility, it is not possible to apply the classical methods, neither the LEFM (Linear Elastic Fracture Mechanics) nor the EPFM (Elasto-Plastic Fracture Mechanics). The EWF method was originally suggested by Broberg [1] in order to characterise the fracture behaviour of ductile materials, and then developed by Mai and Cotterell [2,3] for ductile metals. It has been used * Corresponding author. Tel./fax: + 34-93-401-6706; e-mail: [email protected] 0142-9418/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 2 - 9 4 1 8 ( 9 9 ) 0 0 0 2 6 - 4
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recently to evaluate the fracture parameters of different polymers by many authors [4–15], but some aspects of this technique still remain controversial, such as the thickness influence on the fracture properties. According to Broberg, when a ductile material which contains a crack is loaded, the total work of fracture (Wf) may be divided into two terms: the essential work of fracture (We) and the nonessential (or plastic) work of fracture (Wp). The former corresponds to the instability in the crack tip—the real fracture process region—and the latter to the yielding in the surrounding region. Thus, the total work of fracture can be written in the following way: Wf = We + Wp = welt + wpβl2t
(1)
where we is the specific essential work of fracture (per ligament area unit), wp is the specific nonessential work of fracture (per volume unit), l is the ligament length, t is the specimen thickness and β is a dimensionless factor that describes the plastic zone size. The specific work of fracture, i.e. the work of fracture per unit ligament area, is: wf = Wf/lt = we + βwpl
(2)
According to Eq. (2), the plot of the specific work of fracture wf as a function of the ligament length l should be a linear relation wf = f(l), whose intercept with the y-axis gives we, and whose slope gives βwp. Indeed, the EWF method consists in testing specimens with different ligament lengths, registering Wf for each (as the area under the force–displacement curve), plotting the wf ⫺ l diagram and calculating the best fit regression line which gives we and βwp. Following the ESIS (European Structural Integrity Society) protocol of EWF [15], two restrictions on the ligament length l must be satisfied to ensure the validity of the EWF theory. The first one indicates an inferior limit for l to keep the specimen tested in plane-stress conditions. According to the ESIS, it is usually considered that this occurs when: l > max[3t, 5 mm]
(3)
Moreover, this inferior limit (l*) for which the transition of plane-stress to mixed mode conditions occurs may be verified by plotting the net maximum stress (σmax, calculated by dividing the maximum load obtained during the EWF tests by the original ligament section) against l. According to Hill [16], the σmax of a DDENT (Deeply Double Edge Notched Tension) specimen in pure plane-stress solicitation is 1.15 σy (σy being its yield stress) which rises to 2.97 σy in pure plane-strain conditions. The second restriction concerns the maximum value to give to l to preserve the specimen from edge effects, and to ensure that the ligament is fully yielded before crack propagation. Thus, the ligament length must satisfy: l* ⬍ l ⬍ l
=
min(W/3,2rp)
(4)
where W is the specimen’s width and 2rp is the crack-tip plastic zone size: 2rp = (π/8)(Ewe/σ2y) for a linear plastic zone
(5)
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2rp = (1/π)(Ewe/σ2y) for a circular plastic zone
561
(6)
where E and σy are respectively the modulus of elasticity and the yield stress obtained in a tensile test. Nowadays, these restrictions still remain uncertain, even according to the last protocol of the ESIS [15], which is a reason why more investigations are required to permit a correct application of the EWF method to polymers. Furthermore, some aspects of the EWF technique, such as its potential to characterise the fracture parameters under different material conditions (orientation, thickness, temperature, etc.) must be studied in depth. This situation, added to the great commercial importance of bioriented poly(ethylene terephthalate) (BOPET) films, explains the high interest of the present study.
2. Experimental 2.1. Material The material studied was a BOPET commercialised by the Du Pont company under the name ‘Mylar A’. It was supplied in the form of DIN-A4 sheets of three different thicknesses: 50, 75, and 250 µm. These films were oriented in two directions—the direction of extrusion (machine direction, MD) and the perpendicular one (transverse direction, TD)—which determines the anisotropy in mechanical properties. The thinnest films (50–75 µm) are transparent, whereas the thickest (250 µm) are translucent. Fourier transform infra-red spectroscopy (FTIR) was carried out to study the nature of the Mylar A. It was applied to the film of thickness 50 µm—the thinnest one—to avoid too high a saturation of the peak. The spectrum obtained was then compared with two spectra found in the literature [17]: one from an amorphous PET, and one from a crystalline PET. With the Mylar A, a splitting into two of the peak at 11.5 µm was observed, which is characteristic of semicrystalline PET. 2.2. Test procedure Tensile tests were carried out following the ASTM [18] standard in order to characterise the tensile properties of this material. About 15 specimens of each set (since a set corresponds to a direction of orientation—TD or MD—for a given thickness, six sets were studied) were tested on an universal testing machine, Adamel Lhomargy (France), at constant crosshead rate of 2 mm/min at room temperature until total failure of the specimens occurred. The stress and strain values at the yield point (σy, εy) and at the breaking point (σmax, εmax), as well as the modulus of elasticity (E), were evaluated. The fracture tests were carried out following the ESIS protocol of EWF [15], in the same testing conditions as the tensile tests. DDENT specimens (Fig. 1) were prepared by cutting the sheets into rectangular coupons of total length Zt = 100 mm (length between the grips: Z = 75 mm) and of width W = 75 mm, in each direction of orientation, for each thickness. Initial notches were made perpendicularly to the traction direction with a fresh razor blade, obtaining for each
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Fig. 1. DDENT-T specimen used for the EWF approach.
set at least 24 specimens with ligament lengths varying between 1 and 25 mm. The ligament lengths were measured before the test using a travelling binocular lens. The load vs displacement curves were recorded, and the energy absorbed calculated by computer integration. 3. Results and discussion 3.1. Tensile properties A significant dispersion in the results at break (obtained with the tensile test) led the authors to test a lot more specimens than suggested by the ASTM standard (about 15 instead of five for each set). However, these tests showed that the elastic behaviour of the material does not change with the direction of orientation, since σy, εy and E remain unaffected by the orientation, as can be seen in Fig. 2. Moreover, it can be observed that the stress during plastic deformation is higher in TD than in MD, whereas the elongation at break is smaller in TD than in MD, and this independently of the thickness (in the range 50–250 µm) (Fig. 2). The results (Table 1) bring out the better resistance of the films to traction in TD than in MD, which comes from a tougher drawing in TD than in MD during the processing. It can also be seen that the influence of the orientation is higher on the rupture values than on the elastic and yielding parameters. 3.2. Fracture behaviour Six sets were tested (one in TD and one in MD for each of the three thicknesses). It was observed that the shape of the load vs displacement curves was practically identical for all the
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Fig. 2. Tensile stress vs strain curves of the films of 250 µm thickness loaded in both directions. Table 1 Mechanical properties of the BOPET films obtained with the tensile tests at 2 mm/min (standard deviation is showed in parenthesis) Set
σy (MPa)
εy (%)
E (GPa)
σmax (MPa)
εmax (%)
50 MD 50 TD 75 MD 75 TD 250 MD 250 TD
97.92 94.49 96.47 95.65 95.00 93.80
3.26 3.23 3.25 2.62 4.55 4.62
4.92 4.92 4.58 5.40 4.10 4.62
170.0 192.2 153.1 199.7 168.6 186.6
104.07 (14.41) 95.30 (4.74) 115.66 (8.26) 98.18 (3.95) 146.55 (19.14) 132.37 (6.06)
(0.65) (0.80) (1.15) (0.75) (1.90) (0.59)
(0.85) (1.05) (0.46) (0.53) (1.12) (0.67)
(0.11) (0.37) (0.21) (0.13) (0.06) (0.13)
(11.04) (5.76) (5.76) (12.59) (16.42) (5.22)
DDENT specimens: it did not change with the ligament length, which is a basic requirement of the EWF theory. Fig. 3 shows some of the load vs crosshead displacement curves for the set of the specimens with a thickness of 250 µm tested in the transverse direction. The points marked on the curves indicate the crack propagation initiation, which appears to occur before the
Fig. 3. Load vs displacement curves showing the propogation initiation in films of 250 µm thickness loaded in TD (the ligament length is given in mm in parentheses).
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maximum value of the load, getting closer to it as the ligament length l decreases. In our case, these initiation points were obtained by observing the ligament area during the tests, using a binocular lens equipped with a video camera. The same apparatus was used to follow the whole propagation of the crack for each set, as illustrated by Fig. 4(b) for one of them. These pictures present the ligament: (A) before loading, (B) at propagation initiation, (C) at maximum load, and (D) after maximum load, as it has been marked in Fig. 4(a). All the DDENT specimens showed the same crack propagation behaviour, independently of their thickness, testing direction, and initial ligament length. Chan and Williams [6] observed the same phenomenon with other PET films and concluded that the crack propagation had occurred before the full yielding of the ligament. It seems logical that the decrease in load after the maximum is due to the fact that the decrease in resistance caused by the reduction of the ligament is higher than the increase of resistance attributed to a molecular orientation process. About that, it is worth noting that the yielding of the ligament could not be observed because PET films do not present any stress-whitening phenomena in their plastic deformation area. Karger-Kocsis and Czigany [7] succeeded in visualising this area for chalk-filled BOPET films by using infra-red thermography (IT): an increase in temperature in the plastic zone surrounding the ligament appears, showing its shape. Although the material that they were studying was very similar to our BOPET, they found by IT that the crack started to propagate after reaching the maximum stress. Nevertheless, in all cases the propagation started before the full ligament yielding, which in principle means that a basic requirement of the EWF theory was not met. Fig. 5(a) shows the plot of the specific work of fracture wf as a function of the ligament length l (this figure presents only one of the six wf ⫺ l diagrams plotted for the present work, one for each set). The vertical line on l* separates mixed-mode and plane-stress states, according to the stress state transitions observed in Fig. 5(b). In this figure, by plotting σmax vs l [Fig. 5(b)], one could determine the l* value at which this transition occurs. The experimental results were found to respect Hill’s criterion (in-plane-stress, σmax = 1.15σy) until a common ligament length l* of about 8–9 mm for all sets. However, if one follows strictly the ESIS protocol recommendations
Fig. 4. (a) Load vs displacement curve of a DDENT specimen of t = 75 µm, l = 16 mm, loaded in MD; (b) evolution of the crack propogation during the test (the left side corresponds to the middle of the specimen).
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Fig. 5. (a) wf as a function of l for the films of 250 µm thickness loaded in MD; (b) verification of the stress state transition with Hill’s theory for the same set.
for the minimum ligament length, a value of 5 mm should be taken as l*. Observing the wf data in the range 5–9 mm in Fig. 5(a), it can be seen that the regression line would be practically unaffected since the values lie over it. Thus, according to these results and some other works, the minimum length proposed by the ESIS in Eq. (3) seems to be an acceptable criterion. The regression lines of both stress state regions in Fig. 5(a) led to we by extrapolating to the y-axis intercept, and to βwp by calculating the slope of the lines (the results are listed in Table 2). It is worth noting that the regression coefficient R2 was always very high, which means that the results can be considered as reliable. Indeed, the conclusions that can be derived from Table 2 and Fig. 5(a) are that the specific essential work of fracture we is greater when the loading is in TD than in MD, and that we is independent of the thickness. Conversely, βwp is independent of the molecular orientation but increases clearly with the thickness. Surprisingly, our observations on an isotactic PP10 have given opposite results on the thickness dependence of we and βwp. These observations, and some of other investigators [5,11] lead us to think that both fracture parameters
Table 2 Fracture parameters obtained in plane stress state and in mixed modea, in MD and TD, for three different thickness (50, 75 and 250 µm). The coefficient of the regression lines is also shown 50 µm MD we (kJ/m2) βwp (MJ/m3) R2 wea (kJ/m2) βwpa (MJ/m3) R2a
50.78 6.34 0.96 29.21 8.83 0.98
75 µm TD 62.14 6.86 0.98 21.44 11.45 0.91
MD 46.14 7.01 0.99 25.46 9.78 0.96
250 µm TD 63.72 7.14 0.99 30.61 10.76 0.96
MD 47.16 9.24 0.99 20.45 13.23 0.97
TD 66.82 9.55 0.97 34.77 11.92 0.97
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may vary or not with the thickness depending on each material and the range studied. Fig. 6, which shows wf vs l for the six sets studied, brings out that, for each thickness, the y-axis intercept (we) is greater in TD than in MD. This is due to a greater orientation of the films in TD than in MD, which was also observed during the tensile tests and was already commented in the previous section. Moreover, the slope of the lines remains constant for the same thickness, which means that βwp is independent of the direction (MD or TD). These facts bring out that the toughness (we) can be improved by orienting the polymer molecules in the perpendicular direction to the crack path, without affecting the plastic work dissipated around it. Comparing the results with the values found in the literature, it can be seen that this semicrystalline BOPET shows we values similar to an amorphous PET [6], a filled BOPET [7], and different BOPET grades [8]. Comparing the βwp, it can be said that values between 5–10 MJ/m3 are typical of semicrystalline grades [7,8], and higher values correspond to amorphous PETs [6] that may undergo more plastic work during fracture. However, this plastic item is very sensitive to different variables such as the thickness (as demonstrated in this work) and the test speed [7,11,12]. From the mixed-mode results listed in Table 2 (denoted by the * superscript), one can see that the values obtained in this stress state do not present any reliable tendency, although the we* values are well under the we ones due to the well-known decrease in toughness when the conditions change from plane-stress to plane-strain [19]. Thus, no conclusion about the influence of the studied variables (thickness, orientation) fracture parameters in mixed mode can be brought out from the present study. The superior limit of l was compared with the theoretical prediction. The value of the cracktip plastic zone size (2rp) was calculated by the two relations [Eqs. (5) and (6)], i.e. for a circular shape and for a linear shape, for each set. The results are given in Table 3. None of these values can be considered as a reasonable superior limit for l, since the experiments showed that with
Fig. 6.
wf vs l in plane stress state for all sets.
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Table 3 Theoretical maximum ligament length according to the ESIS protocol for EWF, depending on the size shape of the plastic zone generated on the crack tip 75 µm
50µm MD 2rp(circular) (mm) 8.29 2rp(linear) (mm) 10.23
250 µm
TD
MD
TD
MD
TD
10.9 13.44
7.4 9.13
12.06 14.88
7.26 8.95
14.08 17.36
much higher values of l, wf(l) remains linear (with a high regression coefficient) and the curves of load vs displacement present a good similarity in the range l = 2–25 mm. Thus, the range of validity of l evaluated with 2rp also seems to fail, being too conservative in this case, and only W/3 may be considered as a reasonable superior limit for l, as has been demonstrated in other works [5,10] and is suggested in the last ESIS protocol.
4. Conclusions Although this material did not present full ligament yielding before the plastic propagation, the EWF procedure was successfully applied, showing that this requirement does not seem indispensable. It was found that we is an intrinsic property of the material, since in a plane-stress state it is independent of the sample thickness (in the range studied), and it is highly influenced by the molecular orientation. From the results obtained, one can say that the toughness of this material can be improved by orienting the molecular chains perpendicularly to the crack path. This improvement, detectable with the EWF method, is not detectable by comparison only of the elastic modulus or the yield stress. Average values of weMD = 48 kJ/m2 and weTD = 64 kJ/m2 have been obtained, independent of the thickness, which agree fairly well with those of the literature [6–8]. On the other hand, βwp was observed to be independent of the molecular orientation, but increased clearly with the thickness. However, this variation cannot be attributed to a variation in wp, since it could also be due to a variation of the shape factor β, which depends on the plastic zone size, and that could not be determined with optical methods as this material did not show any stress-whitening. Consequently, no reliable evaluation of the non-essential specific work of fracture was possible. Referring to the plastic item, βwp, a comparison was made with the results of previous works on fracture properties of PET, and it was found that this term is higher for amorphous PET than for crystalline PET, although it may be highly influenced by different testing variables. The theoretical restrictions on the ligament length proposed by the ESIS protocol on EWF were observed to be acceptable for the minimum ligament length, although not in total concordance with the procedure that we followed. Hill’s criterion as inferior limit and W/3 as superior limit should be applied.
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Acknowledgements The authors wish to thank the Teinser SA (Spain) company for supplying the Mylar A films studied here, and Dr Jordi Bou for the realisation of the IR spectrum. D. Ferrer-Balas is grateful to the CICYT for a doctoral grant. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
Broberg KB. J Mech Phys Solids 1975;23:215. Mai YW, Cotterell B. J Mater Sci 1980;15:2296. Mai YW, Cotterell B. Eng Fract Mech 1985;21:123. Mai YW, Cotterell B, Horlyck R, Vigna G. Polym Eng Sci 1987;27:804. Hashemi S. J Mater Sci 1993;28:6178. Chan WYF, Williams JG. Polymer 1994;35:1666. Karger-Kocsis J, Cziga´ny T. Polymer 1996;37:2433. Hashemi S. J Mater Sci 1997;32:1563. Wu J, Mai YW. Polym Eng Sci 1996;36:2275. Maspoch MLL, Santana OO, Grando J, Ferrer D, Martı´nez AB. Polym Bull 1997;39:249. Karger-Kocsis J, Cziga´ny T, Moskala EJ. Polymer 1997;38:4587. Karger-Kocsis J, Cziga´ny T, Moskala EJ. Polymer 1998;39:3939. Maspoch MLl, Ferrer D, Gordillo A, Santana OO, Martinez AB. J Appl Polym Sci, in press. Li WD, Li RKY, Tjong SC. Polym Testing 1997;16:563. European Structural Integrity Society, ESIS-TC4 Group, Testing Protocol for Essential Work of Fracture, 1997. Hill RH. J Mech Phys Solids 1952;4:19. Haslam J, Willis HA, Squirrell DCM. Identification and analysis of plastics, 2nd ed. London: Iliffe, 1972. ASTM Standard D882-95ª. 1995 Annual book of ASTM standards. American Society for Testing and Materials, 1995. p. 182. [19] Broek D. Elementary engineering fracture mechanics, 4th rev. ed. Dordrecht: Martinus Nijhoff Publ., 1987.
Test Method
Essential work of fracture on PET films: influence of the thickness and the orientation M. Ll. Maspocha, V. He´naulta, D. Ferrer-Balasa,*, J.I. Velascob, O.O. Santanab a
Dept Cie`ncia dels Materials i Enginyeria Metallu´rgica, Universitat Polite`cnica de Catalunya, Av/Diagonal, 647-08028 Barcelona, Spain b Centre Catala` del Pla`stic, C/ Colom, 114-08222 Terrassa, Spain Received 1 March 1999; accepted 15 April 1999
Abstract This paper presents the fracture behaviour of films of a bioriented poly(ethylene terephthalate) (BOPET), that was studied by the Essential Work of Fracture (EWF) method. The influence of specimen thickness and molecular orientation was investigated. The results show that this method is a useful alternative for studying the plane-stress fracture of this material, finding that the specific essential work of fracture is strongly affected by the orientation [we was smaller in the direction of extrusion (MD) than in the perpendicular one (TD)], but independent of the specimen thickness in a range from 50 to 250 µm. On the other hand, the plastic work item is sensitive to variations of thickness but does not depend on orientation. 2000 Elsevier Science Ltd. All rights reserved.
1. Introduction The Essential Work of Fracture (EWF) method seems to be the most appropriate technique to obtain fracture parameters for this kind of polymeric films. Due to their reduced thickness, and also to their ductility, it is not possible to apply the classical methods, neither the LEFM (Linear Elastic Fracture Mechanics) nor the EPFM (Elasto-Plastic Fracture Mechanics). The EWF method was originally suggested by Broberg [1] in order to characterise the fracture behaviour of ductile materials, and then developed by Mai and Cotterell [2,3] for ductile metals. It has been used * Corresponding author. Tel./fax: + 34-93-401-6706; e-mail: [email protected] 0142-9418/00/$ - see front matter 2000 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 2 - 9 4 1 8 ( 9 9 ) 0 0 0 2 6 - 4
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recently to evaluate the fracture parameters of different polymers by many authors [4–15], but some aspects of this technique still remain controversial, such as the thickness influence on the fracture properties. According to Broberg, when a ductile material which contains a crack is loaded, the total work of fracture (Wf) may be divided into two terms: the essential work of fracture (We) and the nonessential (or plastic) work of fracture (Wp). The former corresponds to the instability in the crack tip—the real fracture process region—and the latter to the yielding in the surrounding region. Thus, the total work of fracture can be written in the following way: Wf = We + Wp = welt + wpβl2t
(1)
where we is the specific essential work of fracture (per ligament area unit), wp is the specific nonessential work of fracture (per volume unit), l is the ligament length, t is the specimen thickness and β is a dimensionless factor that describes the plastic zone size. The specific work of fracture, i.e. the work of fracture per unit ligament area, is: wf = Wf/lt = we + βwpl
(2)
According to Eq. (2), the plot of the specific work of fracture wf as a function of the ligament length l should be a linear relation wf = f(l), whose intercept with the y-axis gives we, and whose slope gives βwp. Indeed, the EWF method consists in testing specimens with different ligament lengths, registering Wf for each (as the area under the force–displacement curve), plotting the wf ⫺ l diagram and calculating the best fit regression line which gives we and βwp. Following the ESIS (European Structural Integrity Society) protocol of EWF [15], two restrictions on the ligament length l must be satisfied to ensure the validity of the EWF theory. The first one indicates an inferior limit for l to keep the specimen tested in plane-stress conditions. According to the ESIS, it is usually considered that this occurs when: l > max[3t, 5 mm]
(3)
Moreover, this inferior limit (l*) for which the transition of plane-stress to mixed mode conditions occurs may be verified by plotting the net maximum stress (σmax, calculated by dividing the maximum load obtained during the EWF tests by the original ligament section) against l. According to Hill [16], the σmax of a DDENT (Deeply Double Edge Notched Tension) specimen in pure plane-stress solicitation is 1.15 σy (σy being its yield stress) which rises to 2.97 σy in pure plane-strain conditions. The second restriction concerns the maximum value to give to l to preserve the specimen from edge effects, and to ensure that the ligament is fully yielded before crack propagation. Thus, the ligament length must satisfy: l* ⬍ l ⬍ l
=
min(W/3,2rp)
(4)
where W is the specimen’s width and 2rp is the crack-tip plastic zone size: 2rp = (π/8)(Ewe/σ2y) for a linear plastic zone
(5)
M.L. Maspoch et al. / Polymer Testing 19 (2000) 559–568
2rp = (1/π)(Ewe/σ2y) for a circular plastic zone
561
(6)
where E and σy are respectively the modulus of elasticity and the yield stress obtained in a tensile test. Nowadays, these restrictions still remain uncertain, even according to the last protocol of the ESIS [15], which is a reason why more investigations are required to permit a correct application of the EWF method to polymers. Furthermore, some aspects of the EWF technique, such as its potential to characterise the fracture parameters under different material conditions (orientation, thickness, temperature, etc.) must be studied in depth. This situation, added to the great commercial importance of bioriented poly(ethylene terephthalate) (BOPET) films, explains the high interest of the present study.
2. Experimental 2.1. Material The material studied was a BOPET commercialised by the Du Pont company under the name ‘Mylar A’. It was supplied in the form of DIN-A4 sheets of three different thicknesses: 50, 75, and 250 µm. These films were oriented in two directions—the direction of extrusion (machine direction, MD) and the perpendicular one (transverse direction, TD)—which determines the anisotropy in mechanical properties. The thinnest films (50–75 µm) are transparent, whereas the thickest (250 µm) are translucent. Fourier transform infra-red spectroscopy (FTIR) was carried out to study the nature of the Mylar A. It was applied to the film of thickness 50 µm—the thinnest one—to avoid too high a saturation of the peak. The spectrum obtained was then compared with two spectra found in the literature [17]: one from an amorphous PET, and one from a crystalline PET. With the Mylar A, a splitting into two of the peak at 11.5 µm was observed, which is characteristic of semicrystalline PET. 2.2. Test procedure Tensile tests were carried out following the ASTM [18] standard in order to characterise the tensile properties of this material. About 15 specimens of each set (since a set corresponds to a direction of orientation—TD or MD—for a given thickness, six sets were studied) were tested on an universal testing machine, Adamel Lhomargy (France), at constant crosshead rate of 2 mm/min at room temperature until total failure of the specimens occurred. The stress and strain values at the yield point (σy, εy) and at the breaking point (σmax, εmax), as well as the modulus of elasticity (E), were evaluated. The fracture tests were carried out following the ESIS protocol of EWF [15], in the same testing conditions as the tensile tests. DDENT specimens (Fig. 1) were prepared by cutting the sheets into rectangular coupons of total length Zt = 100 mm (length between the grips: Z = 75 mm) and of width W = 75 mm, in each direction of orientation, for each thickness. Initial notches were made perpendicularly to the traction direction with a fresh razor blade, obtaining for each
562
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Fig. 1. DDENT-T specimen used for the EWF approach.
set at least 24 specimens with ligament lengths varying between 1 and 25 mm. The ligament lengths were measured before the test using a travelling binocular lens. The load vs displacement curves were recorded, and the energy absorbed calculated by computer integration. 3. Results and discussion 3.1. Tensile properties A significant dispersion in the results at break (obtained with the tensile test) led the authors to test a lot more specimens than suggested by the ASTM standard (about 15 instead of five for each set). However, these tests showed that the elastic behaviour of the material does not change with the direction of orientation, since σy, εy and E remain unaffected by the orientation, as can be seen in Fig. 2. Moreover, it can be observed that the stress during plastic deformation is higher in TD than in MD, whereas the elongation at break is smaller in TD than in MD, and this independently of the thickness (in the range 50–250 µm) (Fig. 2). The results (Table 1) bring out the better resistance of the films to traction in TD than in MD, which comes from a tougher drawing in TD than in MD during the processing. It can also be seen that the influence of the orientation is higher on the rupture values than on the elastic and yielding parameters. 3.2. Fracture behaviour Six sets were tested (one in TD and one in MD for each of the three thicknesses). It was observed that the shape of the load vs displacement curves was practically identical for all the
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Fig. 2. Tensile stress vs strain curves of the films of 250 µm thickness loaded in both directions. Table 1 Mechanical properties of the BOPET films obtained with the tensile tests at 2 mm/min (standard deviation is showed in parenthesis) Set
σy (MPa)
εy (%)
E (GPa)
σmax (MPa)
εmax (%)
50 MD 50 TD 75 MD 75 TD 250 MD 250 TD
97.92 94.49 96.47 95.65 95.00 93.80
3.26 3.23 3.25 2.62 4.55 4.62
4.92 4.92 4.58 5.40 4.10 4.62
170.0 192.2 153.1 199.7 168.6 186.6
104.07 (14.41) 95.30 (4.74) 115.66 (8.26) 98.18 (3.95) 146.55 (19.14) 132.37 (6.06)
(0.65) (0.80) (1.15) (0.75) (1.90) (0.59)
(0.85) (1.05) (0.46) (0.53) (1.12) (0.67)
(0.11) (0.37) (0.21) (0.13) (0.06) (0.13)
(11.04) (5.76) (5.76) (12.59) (16.42) (5.22)
DDENT specimens: it did not change with the ligament length, which is a basic requirement of the EWF theory. Fig. 3 shows some of the load vs crosshead displacement curves for the set of the specimens with a thickness of 250 µm tested in the transverse direction. The points marked on the curves indicate the crack propagation initiation, which appears to occur before the
Fig. 3. Load vs displacement curves showing the propogation initiation in films of 250 µm thickness loaded in TD (the ligament length is given in mm in parentheses).
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maximum value of the load, getting closer to it as the ligament length l decreases. In our case, these initiation points were obtained by observing the ligament area during the tests, using a binocular lens equipped with a video camera. The same apparatus was used to follow the whole propagation of the crack for each set, as illustrated by Fig. 4(b) for one of them. These pictures present the ligament: (A) before loading, (B) at propagation initiation, (C) at maximum load, and (D) after maximum load, as it has been marked in Fig. 4(a). All the DDENT specimens showed the same crack propagation behaviour, independently of their thickness, testing direction, and initial ligament length. Chan and Williams [6] observed the same phenomenon with other PET films and concluded that the crack propagation had occurred before the full yielding of the ligament. It seems logical that the decrease in load after the maximum is due to the fact that the decrease in resistance caused by the reduction of the ligament is higher than the increase of resistance attributed to a molecular orientation process. About that, it is worth noting that the yielding of the ligament could not be observed because PET films do not present any stress-whitening phenomena in their plastic deformation area. Karger-Kocsis and Czigany [7] succeeded in visualising this area for chalk-filled BOPET films by using infra-red thermography (IT): an increase in temperature in the plastic zone surrounding the ligament appears, showing its shape. Although the material that they were studying was very similar to our BOPET, they found by IT that the crack started to propagate after reaching the maximum stress. Nevertheless, in all cases the propagation started before the full ligament yielding, which in principle means that a basic requirement of the EWF theory was not met. Fig. 5(a) shows the plot of the specific work of fracture wf as a function of the ligament length l (this figure presents only one of the six wf ⫺ l diagrams plotted for the present work, one for each set). The vertical line on l* separates mixed-mode and plane-stress states, according to the stress state transitions observed in Fig. 5(b). In this figure, by plotting σmax vs l [Fig. 5(b)], one could determine the l* value at which this transition occurs. The experimental results were found to respect Hill’s criterion (in-plane-stress, σmax = 1.15σy) until a common ligament length l* of about 8–9 mm for all sets. However, if one follows strictly the ESIS protocol recommendations
Fig. 4. (a) Load vs displacement curve of a DDENT specimen of t = 75 µm, l = 16 mm, loaded in MD; (b) evolution of the crack propogation during the test (the left side corresponds to the middle of the specimen).
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Fig. 5. (a) wf as a function of l for the films of 250 µm thickness loaded in MD; (b) verification of the stress state transition with Hill’s theory for the same set.
for the minimum ligament length, a value of 5 mm should be taken as l*. Observing the wf data in the range 5–9 mm in Fig. 5(a), it can be seen that the regression line would be practically unaffected since the values lie over it. Thus, according to these results and some other works, the minimum length proposed by the ESIS in Eq. (3) seems to be an acceptable criterion. The regression lines of both stress state regions in Fig. 5(a) led to we by extrapolating to the y-axis intercept, and to βwp by calculating the slope of the lines (the results are listed in Table 2). It is worth noting that the regression coefficient R2 was always very high, which means that the results can be considered as reliable. Indeed, the conclusions that can be derived from Table 2 and Fig. 5(a) are that the specific essential work of fracture we is greater when the loading is in TD than in MD, and that we is independent of the thickness. Conversely, βwp is independent of the molecular orientation but increases clearly with the thickness. Surprisingly, our observations on an isotactic PP10 have given opposite results on the thickness dependence of we and βwp. These observations, and some of other investigators [5,11] lead us to think that both fracture parameters
Table 2 Fracture parameters obtained in plane stress state and in mixed modea, in MD and TD, for three different thickness (50, 75 and 250 µm). The coefficient of the regression lines is also shown 50 µm MD we (kJ/m2) βwp (MJ/m3) R2 wea (kJ/m2) βwpa (MJ/m3) R2a
50.78 6.34 0.96 29.21 8.83 0.98
75 µm TD 62.14 6.86 0.98 21.44 11.45 0.91
MD 46.14 7.01 0.99 25.46 9.78 0.96
250 µm TD 63.72 7.14 0.99 30.61 10.76 0.96
MD 47.16 9.24 0.99 20.45 13.23 0.97
TD 66.82 9.55 0.97 34.77 11.92 0.97
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may vary or not with the thickness depending on each material and the range studied. Fig. 6, which shows wf vs l for the six sets studied, brings out that, for each thickness, the y-axis intercept (we) is greater in TD than in MD. This is due to a greater orientation of the films in TD than in MD, which was also observed during the tensile tests and was already commented in the previous section. Moreover, the slope of the lines remains constant for the same thickness, which means that βwp is independent of the direction (MD or TD). These facts bring out that the toughness (we) can be improved by orienting the polymer molecules in the perpendicular direction to the crack path, without affecting the plastic work dissipated around it. Comparing the results with the values found in the literature, it can be seen that this semicrystalline BOPET shows we values similar to an amorphous PET [6], a filled BOPET [7], and different BOPET grades [8]. Comparing the βwp, it can be said that values between 5–10 MJ/m3 are typical of semicrystalline grades [7,8], and higher values correspond to amorphous PETs [6] that may undergo more plastic work during fracture. However, this plastic item is very sensitive to different variables such as the thickness (as demonstrated in this work) and the test speed [7,11,12]. From the mixed-mode results listed in Table 2 (denoted by the * superscript), one can see that the values obtained in this stress state do not present any reliable tendency, although the we* values are well under the we ones due to the well-known decrease in toughness when the conditions change from plane-stress to plane-strain [19]. Thus, no conclusion about the influence of the studied variables (thickness, orientation) fracture parameters in mixed mode can be brought out from the present study. The superior limit of l was compared with the theoretical prediction. The value of the cracktip plastic zone size (2rp) was calculated by the two relations [Eqs. (5) and (6)], i.e. for a circular shape and for a linear shape, for each set. The results are given in Table 3. None of these values can be considered as a reasonable superior limit for l, since the experiments showed that with
Fig. 6.
wf vs l in plane stress state for all sets.
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Table 3 Theoretical maximum ligament length according to the ESIS protocol for EWF, depending on the size shape of the plastic zone generated on the crack tip 75 µm
50µm MD 2rp(circular) (mm) 8.29 2rp(linear) (mm) 10.23
250 µm
TD
MD
TD
MD
TD
10.9 13.44
7.4 9.13
12.06 14.88
7.26 8.95
14.08 17.36
much higher values of l, wf(l) remains linear (with a high regression coefficient) and the curves of load vs displacement present a good similarity in the range l = 2–25 mm. Thus, the range of validity of l evaluated with 2rp also seems to fail, being too conservative in this case, and only W/3 may be considered as a reasonable superior limit for l, as has been demonstrated in other works [5,10] and is suggested in the last ESIS protocol.
4. Conclusions Although this material did not present full ligament yielding before the plastic propagation, the EWF procedure was successfully applied, showing that this requirement does not seem indispensable. It was found that we is an intrinsic property of the material, since in a plane-stress state it is independent of the sample thickness (in the range studied), and it is highly influenced by the molecular orientation. From the results obtained, one can say that the toughness of this material can be improved by orienting the molecular chains perpendicularly to the crack path. This improvement, detectable with the EWF method, is not detectable by comparison only of the elastic modulus or the yield stress. Average values of weMD = 48 kJ/m2 and weTD = 64 kJ/m2 have been obtained, independent of the thickness, which agree fairly well with those of the literature [6–8]. On the other hand, βwp was observed to be independent of the molecular orientation, but increased clearly with the thickness. However, this variation cannot be attributed to a variation in wp, since it could also be due to a variation of the shape factor β, which depends on the plastic zone size, and that could not be determined with optical methods as this material did not show any stress-whitening. Consequently, no reliable evaluation of the non-essential specific work of fracture was possible. Referring to the plastic item, βwp, a comparison was made with the results of previous works on fracture properties of PET, and it was found that this term is higher for amorphous PET than for crystalline PET, although it may be highly influenced by different testing variables. The theoretical restrictions on the ligament length proposed by the ESIS protocol on EWF were observed to be acceptable for the minimum ligament length, although not in total concordance with the procedure that we followed. Hill’s criterion as inferior limit and W/3 as superior limit should be applied.
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Acknowledgements The authors wish to thank the Teinser SA (Spain) company for supplying the Mylar A films studied here, and Dr Jordi Bou for the realisation of the IR spectrum. D. Ferrer-Balas is grateful to the CICYT for a doctoral grant. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18]
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