Effect of specimen notch quality on the essential work of fracture of ductile polymer films

1  INFLUENCE OF THE SPECIMEN NOTCHING ON THE ESSENTIAL WORK OF FRACTURE OF DUCTILE POLYMER FILMS A.B. Martínez a, N. León a,*, A. Segovia a, J. Cailloux a, P.P. Martínez b a Centre Català del Plàstic, Departament de Ciència dels Materials i Enginyeria Metallúrgica. Universitat Politècnica de Catalunya. BARCELONATECH. C/Colom 114, 08222, Terrassa, Spain. b NUDEC SA. C/ Pintor Vila Cinca, 24-28, Pol. Ind. Can Humet de Dalt, 08213, Polinyà, Spain. * [email protected] Tlf: +34 93 783 70 22 Fax: +34 93 784 18 27 2  1. Introduction Films and thin sheets of polymers, polymer blends and polymer composites are used in a wide variety of applications like packaging, agriculture, coating, and paints market segment. Their toughness is often a basic requisite to meet some industry needs. The linear elastic fracture mechanics (LEFM) approach is used to study fractures occurring at nominal stresses well below the material yield stress. The dissipated energy is confined in a small area near the crack tip, and the fracture is brittle. The LEFM approach is not applicable when the plasticity around the crack tip becomes too large, in those cases the elastic plastic fracture mechanics (EPFM) apply. When the crack propagation occurs through a highly deformed and yielded material then the post-yield fracture mechanics (PYFM) can also be applied and the essential work of fracture (EWF) is a suitable method. The EWF characterises the plane stress toughness of ductile polymer films in mode I, basically using the double edge notched tension (DENT) configuration. The EWF method has become very popular and is increasingly used due to the apparent simple specimen preparation and the easy testing. Many works have been published on the EWF method applied to polymers with the aim of determining their fracture properties. There is an excellent review [1] of the EWF with an extensive summary of published works on polymers. The EWF experimental method was developed by Cotterell and Mai [2,3] following the Broberg's theoretical idea [4,5]. According to the theory, the value that represents the toughness, namely the specific essential work of fracture (we) is a material parameter, only if the ligament fully yields before the onset of crack propagation and is independent of the specimen geometry. There is a European Structural Integrity Society (ESIS) test protocol [6] for the EWF method, and several round-robin exercises [6-7] have been performed under the guidance of the ESIS technical committee 4 (TC4). In spite of the apparent simplicity of the test, some aspects of the validity of this technique remain controversial; there are intricate details that seem to play an important role in the repeatability and reproducibility of the EWF test.This problem has been and is still debated, and these questions indicate that the EWF procedure is not yet sufficiently defined to be considered as a standard. Some of the aspects of the test validity are related to the specimen preparation, particularly the notching technique, and they should be studied more deeply. The main aim of this work is to contribute to a better understanding and the meaning of some of the controversial factors involved in the EWF test. Specimen manufacturing and specimen alignment in the test machine grips have been studied in detail in this work. 3  Particularly, the effect of different quality notches on the shape of the experimental stress-displacement curves and how these shapes are directly related to the EWF parameters we and βwp, are analysed in detail. Furthermore, there is a limited understanding of the types of polymers in which the EWF test may be applicable.The EWF approach has been successfully applied to amorphous and semicrystalline polymers that undergo necking before crack propagation. However, there is some controversy of the applicability of the EWF test to multiphasic polymers which can have other deformation micromechanisms. This is the reason why a rubber-toughened, an ethylene-propylene block copolymer (EPBC), was selected for its application in this EWF work. 2. EWF approach 2.1. EWF concept The EWF theory is based on the hypothesis that the total energy Wf involved in the ductile fracture of a precracked specimen can be separated in two terms. WfWeWp (1) where We, the essential work of fracture, accounts for the energy necessary to generate new crack surfaces while Wp is called the plastic work or the non-essential work of fracture and includes all the other components of energy dissipated in the fracture process. The EWF concept establishes that the process zone can be divided into an inner process zone (IPZ) where the fracture process actually occurs and an outer process zone (OPZ) (Fig. 1). Thus, We is proportional to the IPZ area while Wp is proportional to the volume of the OPZ. Using these considerations, Eq. (1) can be rewritten in specific terms as wfW f lo. t weβwp.lo (2) where lo is the original ligament length, t is the specimen thickness and β is a factor related to the shape of the OPZ. Eq. (2) can be assessed by performing a series of tests on specimens with different original ligament lengths where load vs displacement (Fig. 2) is registered. The total energy dissipated is given by W f P.dd dr 0 (3) where dr is the displacement at complete failure. Thus, according to Eq. (2), the total energy per unit area wf can be plotted (Fig. 3) as a function of the lo. 4  From the best-fitting regression analysis, the intercept at the origin we and the slope βwp can be determined. References [1,8] reviewed the EWF approach. 2.2. Key requirements In the EWF analysis the following key assumptions are made: a) The ligament length is fully yielded prior to the onset of crack propagation. This requirement ensures that the fracture mechanism is the same irrespective of the ligament length and we is in an inherent material parameter. However, this key assumption is rarely accomplished and in most of the published articles this requirement is not satisfied and thus the we values become an apparent toughness only useful for comparison purposes.In a DENT specimen, the ligament length will be completely yielded prior the onset of crack propagation if it is less than twice the size of the plastic zone radius, rp, in plane stress conditions. For a linear plastic zone 2rpπ 8󰇧Ewe σ y 2󰇨 (4) and for a circular plastic zone 2rpEwe πσ y 2 (5) where E is the elastic modulus, σy is the uniaxial yield stress, and we is the specific essential work of fracture. Although a ligament length less than twice the plastic zone radius is a reasonable size criterion, it appears to be too restrictive considering the evidence encountered in amorphous copolyesters [1,9]. b) Fracture is under plane stress conditions. There are constraints on the ligament length to assure a pure plane stress state on the specimens. Arbitrarily based on experiences, it has been suggested a minimum ligament length between 3 and 5 times the specimen thickness [1,6]. This leads to specimens too small to be tested and handled. Then, a practical lower limit of 5 mm is accepted when preparing DENT specimens [7] of polymer blends, which have a thickness less than 1 mm. The upper limit requires the full-ligament yielding before crack initiation. Hence, lo has to be less than twice the plastic zone radius in DENT specimens.Another upper limit is given by the following relationship loW 3 (6) 5  where W is the specimen width. This last condition is necessary to prevent edge effects. c) Good quality notches. Identical and repetitive sharp notches without plastic deformation in front of the crack tip. This requirement guarantees self-similar load-displacement, stress-displacement, and ligament length-displacement curves for tested specimens with different ligament lengths. Ideally, the sharpened notches should be sharp enough to avoid that sharper notches result in a significantly lower value of we.However, the smallest reached notch tip radius was of about 1 μm. It has been experimentally demonstrated the great influence of the notches on the EWF results, Clutton [6] and Williams and Rink [7] presented results of round robin test performed within the Technical Committee 4 of the ESIS where it was clear from the results that lower values of we are obtained with the sharper notches, but βwp, the slope of the EWF plot, showed no dependence on the notch sharpness. There are several methods used in the literature for notching film specimens, and each one generates notches with different quality that may even depend on the operator. The femtosecond laser ablation technique (femtolaser) is a non-contact method for sharpening the pre-notches. Setting up properly is a complex matter in order to avoid thermal damage at the notch root.The application of this technique has allowed obtaining [9-11] repetitive notches with negligible thermal damage, without plastic deformation, and very sharp tip radius of about 1 μm. A limitation of the femtolaser technique is the availability of the equipment and the cost per notch. The most popular way used to sharpen notches is the razor blade sliding technique. In this technique, the notches are sharpened by drawing a fresh razor blade across the pre-notch tip. It is advisable to do it in a single pass so that the notch follows the same track avoiding bifurcations.It has also been employed a scalpel instead of a razor blade. Unintentional introduction of residual stresses and/or the development of a plastic zone ahead of the notch tip can be easily induced by the compressive component of the sideway sliding force. The higher is the yield stress of the ductile polymer, the lesser will be the extent of the plastic deformation ahead of the notch tip. Cooling specimens below its glass transition temperature prior to sliding can be helpful. The razor blade sliding is a manual procedure which regulary results in different sharpened notches. These differences can be in the notch tip radius and/or the extent of the plastic deformation [6]. In a set of DENT specimens, it is possible to have three different specimens populations which show a distinct behaviour among them and they are responsible for the non-similarity and crossing curves in the load-displacement, stress-displacement, and ligament length-displacement plots. These include specimens with two different notches, specimens with two equal notches and negligible plastic deformation, and 6  specimens with two equal notches but both notches having noticeable plastic deformation [9]. When the specimen has two different notches, the crack initiation in both notches does not begin at the same time. Instead, when the two notches are equal, the crack initiation happens at the same time (simultaneously). Comparing specimens with and without plastic deformation at the notch root [10,12] but having the same notch tip radius it is noticed that the head of the stress-displacement curves have a different shape, which for the specimens without plastic deformation leads to a lower value for the crack tip opening displacement, that is, a lower we value too. However, the tails of these curves are independent of the notches and therefore show the same slope βwp in the EWF plots. Clearly, the EWF results are not only affected by the notch sharpness but also by the plastic deformation ahead of the notch tip. Other procedures have been tried unsuccessfully for generating notches which include scissors cut, die-punch, and scalpel cuts generated starting from the notch tip. These techniques seem to generate plastic deformation ahead of the notch tip and provide higher we values that the razor blade sliding method [6] or scalpel sliding [13]. 2.3 Other aspects and general considerations Specimen When we is an inherent material parameter, then it should be independent of the specimen geometry. Mai and Cotterell [14] verified this first by using different specimen geometries. The double edge notched tension (DENT) geometry is the most appropriate for mode I testing because the transverse stresses between the notches are tensile and buckling problems are avoided [15]. The DENT geometry is shown in Fig. 1, where W is the specimen width, t is the specimen thickness, L is the specimen length, and Z is the distance between clamps. Most work in the literature has been performed using this geometry. Two logical aspects to take into account are that the notches have to be collinear and that the specimen has to be clamped perpendicular to the collinear notches. There is experimental evidence that, when W and Z are more than twice the largest ligament value, the we value does not change [7,16-17]. On the other hand, when Z is more than twice W, the specimens can get wavy in their own plane during the test [16] and thus modify the stress distribution in the ligament zone. Values of Z smaller than W seem to be far away from the infinite plate case, being the result probably influenced by the cross-hedges proximity to the fracture region. 7  Material All polymers which fulfill the key assumptions established by the EWF approach can be successfully tested; nevertheless, they can exhibit considerable differences among them during testing. In single phase homopolymers and copolymers, full ligament yielding must show a load and stress drop (necking) in the related load-displacement and stress-displacement curves [1,9,15], but this is not the case for multiphasic polymers, as rubber toughened polymers, where other deformation micromechanisms take place, as multiple shear yielding or multiple crazing. The EWF parameters can be affected, as well as the other mechanical properties, by the microstructure, degree of crystallinity, chain orientation, molecular weight, additives such as plasticisers, among others. Maximum stress Hill [18-19] has shown, for rigid perfectly plastic materials in the DENT geometry under plane stress conditions, that no stress can exceed the value of 1.15 σy. This value rises until 2.97 σy for pure plane strain state condition. Where σy is the uniaxial tensile stress. Thus, the maximum stress registered during the DENT tests, σmax, has to be comprised between σy and 1.15 σy and its value is equal for all ligaments, when there is pure plane stress conditions. Theoretically, at lower values of lo, the specimen can be in a mixed state of stress which increases σmax, and so the Hill criterion could be employed to determine the lower limit of the ligament length. Nevertheless, in practice, the experimental scatter in the σmax values difficulties the application of this criterion. Clutton [6] suggested another criterion which does not use the yield stress but uses the mean of the maximum stresses (σmax) as follows 0.9σmaxσmax1.1σmax (7) The Clutton criterion only removes data where errors in dimensional measurements or loads exist though these load errors can be undetected if the same load cell is used for all tests [7,20]. Based on our experience, the limits of the Clutton criterion might be reduced to be comprised between ± 5% of σmax. Specimen thickness It seems that in non-oriented amorphous polymers of thicknesses lower than 1 mm, the we and βwp values remained unchanged. The small differences encountered in [21-22] are within the statistical error. In the case of semicrystalline thermoplastics, differences in the EWF parameters can be found [16] but are attributed to variations in the crystallinity of the samples. 8  Test speed and temperature The selected test speed is, in principle, somewhat arbitrary. Although, the magnitude of the mechanical properties varies not only with the temperature but also with the test speed as a consequence of the viscoelastic nature of the polymers. As can be expected, Increasing test speed causes an increase in σmax and a decrease in dr, which together contribute to a drop in we and βwp values [16-17,22] but it is slightly at the conventional test speeds. Raising the temperature has the same effect as decreasing the test speed. Thus, while σmax decreases and dr increases, both values of we and βwp increase [17,21,23-24]. Displacement measurements The displacement has been usually measured from the cross-head, but it has been also measured using video extensometers [25] or digital image correlation systems [9,11]. There is experimental evidence that the we value is insensitive to changes of the gauge length chosen for displacement measurements. Nonetheless, the slope βwp of the EWF plots increases slightly with incrementing the gauge length [10,25]. This slight increase in the βwp value has been attributed [10] to a higher contribution of the viscoelastic energy when the distance between the OPZ zone and the gauge marks is larger. 3. Experimental details 3.1 Material Polypropylene requires improved toughness at both room and low temperatures to fulfill some industry requirements . This study has been conducted on an ethylenepropylene block copolymer (EPBC). This copolymer has been synthesised through the spheripol process using a Ziegler- Natta catalyst of the fourth generation in two steps. The microstructure consists [26] of elastomeric ethylene-propylene particles embedded in the polypropylene matrix. The presence of different phases leads to different glass transition temperatures, one associated with the elastomeric particles (Tg,EPR), and the other one with the polypropylene matrix (Tg,PP). The mechanism responsible for the toughness reinforcement is the formation of shear bands around the elastomeric particles which absorbs most of the deformation energy. This mechanism is always accompanied by the cavitation (void formation) of the elastomeric particles. Table 1 summarises the main characteristics of this EPBC grade. The ethylene content and the isotacticity index were measured via Nuclear Magnetic Resonance (NMR), the average molecular mass in number (Mn) and weight (Mw) were determined by Gel 9  Permeation Chromatography (GPC). The Tg’s were revealed by dynamic mechanical thermal analysis (DMTA). The raw material in form of pellets was kindly supplied by Repsol. Films with thickness of 0.5 mm were cast-extruded from the pellets. The melt flow index (MFI) of both the pellets and the films were determined following the ISO standard 1133 at 230°C/2.1 kg. The results showed in table 1 indicate almost no polymer degradation during the extrusion process. 3.2 Specimen preparation Two kinds of specimens were prepared; dumbbell shaped specimens for uniaxial tensile tests and DENT specimens for EWF tests. All specimens were prepared and tested in the machine direction (MD) of the cast-extruded EPBC film. Dumbbell shaped specimens were obtained in a cutting press with the shape and dimensions of Type IV specimen as defined in ASTM standard D 638. The DENT specimens used to perform the EWF tests were obtained by cutting rectangular coupons 60 mm wide x 90 mm long (Fig. 1). To minimise the plastic deformation at the pre-notch root, the pre-notching on the specimens coupons were obtained by applying a saw over a sandwich formed by the EPBC specimen coupon compressed between two skin layers of a 1 mm thick coupons of polymethyl methacrylate (PMMA). 3.3 Notch sharpening Table 2 presents a summary of the ten sets of specimens that were prepared. Two sets of specimens were pre-notched to obtain samples with ligaments separated 1 mm comprised between 5 and 20 mm. The pre-notches in the first set of specimens were sharpened by the femtolaser ablation technique (reference SF) using optimised operation conditions [10] to avoid thermal damage. In the second set of specimens, the pre-notches were sharpened by the traditional method of sliding a fresh razor blade (reference SG) across the pre-notch tip in only one pass to follow the same track and thus avoid bifurcations. It was intended to apply the minimum compressive force during the sideway sliding, in order to minimise both the plastic deformation and the volume material accumulation at the notch tip. The EWF approach was applied on these two sets of specimens. Other eight sets of specimens were also prepared. In each set, all specimens had the same ligament length, lo = 11 mm. Six sets were prepared with different notches, as follows: Set 3 -S: Only pre-notched specimens Set 4 -SD: Pre-notched + additional deformation of the notch root 16  In Fig. 19 are represented the mean stress-displacement curve DR for the noncollinear notches and the mean stress-displacement curve SG which accounts for collinear notches obtained with the same notch sharpening procedure as the noncollinear notches. These curves show equal σmax and σi values for both the collinear and non-collinear specimens, but, in this last one, the curve is slightly shifted to the right which implies larger di and thus higher we values than the curve DR. 4.5 Tilted specimens The last set of specimens was notched by sliding a razor blade across the pre-notch tip as in set 2. The specimens had a ligament length of 11 mm, but the tests were performed with the specimens tilted 5 degrees on the grips. Fig. 20 shows the stress-displacement curve and some registered frames of the tilted specimens. The arrows on these frames stand out the initiation points of notch propagation and are directly related to circles traced on the average stressdisplacement curve. It is noticed in this figure that the notches do not begin its propagation at the same time, that is, the notches do not propagate simultaneously. The non-simultaneous crack propagation was also observed [9] in non-tilted specimens and was attributed to differences in the quality of the two notches in the same specimen. In Fig. 19 the average stress-displacement curve AT is represented to be compared with the stress-displacement curves SG and DR corresponding to collinear non-tilted and non-collinear non-tilted sets of specimens, respectively. The tilted specimens and the non-collinear specimens have the stress-displacement curve slightly shifted to the right when both are compared to the SG specimens, but the shape of the curve in the propagation zone is different. 5. Conclusions The specimens sharpened by femtolaser contain sharpened notches with a radius of curvature of 1 μm and negligible plastic deformation in front of the crack tip. All these specimens have equal repetitive notches that result in equal values for the displacement di at the onset of crack initiation. The di value coincides with the crack tip opening displacement CTODc at crack initiation. All this leads to self-similar loaddisplacement and stress-displacement curves where the heads (from d = 0 to di) overlap. Integration of the stress-displacement curve between d = 0 and di gives the specific essential work of fracture we. The razor blade sharpened specimens generated the same radius of curvature that the femtolaser sharpened specimens, but, in the first case, the specimens had some plastic deformation in front of the notch root. When testing selected razor blade sharpened specimens, with the same level of deformation in front of the crack tip, it has been obtained stress-displacement curves which follow the same trends than that the 17  obtained with the femtolaser sharpened specimens. The main difference is the larger di value (equal to CTODc) for the razor blade sharpened specimens. It results in a higher we value for the razor blade that as compared to the femtolaser sharpened specimens. When there are represented all normalized curves of the tails of the stressdisplacement plots (values comprised between di and dr) overlap, independently of both the original ligament length and the sharpening method, indicating the same propagation behaviour and equal βwp values. For specimens with different notches but equal ligament lengths, the shape of the stress-displacement curves is different although the crack initiation stress σi values are the same. The shape of the curves from the beginning (d = 0) until reaching σmax is identical, and the σmax values are equal, as well as the displacement value corresponding to σmax. The crack initiation stress σi values are also independent of the notch, but it is not the case for the corresponding displacements di which increase with the radius of curvature at the notch root and with the plastic deformation in front of the notch tip. The area under the stress-displacement curve from d = 0 until di is greater when di is larger and, consequently, resulting higher we values. The range between the displacements, which correspond to σmax and σi, increase when the radius of curvature of the notch root and/or the plastic deformation in front of the notch tip are larger. The tails of the stress-displacement curves lying between the displacement value at the onset of crack initiation di and the displacement at rupture dr overlap, indicating that the propagation follows the same behaviour, i.e., it is independent of the notch, which results in equal values of the slope of the regression line βwp in the EWF plots for sets of specimens with different notches. In sets of specimens containing notches of different quality, the load-displacement curves will not be self-similar and can cross each other. The stress-displacement curves will have different di's and do not overlap, between d = 0 and the different di's. One millimeter non-collinear notches do not modify the σmax and σi values obtained with the collinear specimens. The shape of the stress-displacement curve changes slightly, and the small increase in di gives a slight increase in the we value, too. The specimen manufacture has crucial importance and plays a very important role on the accuracy, repeatability, and reproducibility of the results. The incorrect alignment of the specimens on the grips (when the specimens are tilted) causes changes in the shape of the stress-displacement curve and the nonsimultaneous initiation (at the same displacement and time) of the two notches of the same specimen. The classical way to sharpen specimens by sliding a razor blade across the pre-notch can yield various types of notches that may depend on the operator and the ductility of the polymer, and then specimens with notches of different quality can be produced. The femtolaser ablation technique allows obtaining equal repetitive notches with a radius of curvature at the notch root of 1 μm and without plastic deformation in front of the notch tip, and therefore it is a very suitable technique for the notch sharpening of ductile polymer films. 18  It is confirmed that a key requirement to obtain meaningful results is to have repetitive notches without plastic deformation in front of the notch root. It is also confirmed that the specimens should have collinear notches, and that the correct alignment (without tilting) of the specimen on the grips of the testing machine is likewise required. The EWF has been successfully applied on a rubber-toughened semicrystalline polymer (EPBC). This multiphase polymer has multiple shear yielding as a deformation mechanism which is different of polymers that undergo necking before the onset of crack propagation and where there is a consensus on the validity of the EWF test. Acknowledgements Authors acknowledge the Spanish Ministry of Economy and Competitiveness for their financial support through the research project MAT2012-37762-C02-01. N. León expresses his gratitude to the National Council for Science and Technology (CONACYT) based in Mexico for the doctoral fellowship. References [1] Bárány T, Czigány T, Karger-Kocsis J. Application of the essential work of fracture (EWF) concept for polymers, related blends and composites: A review. Prog Polym Sci 2010; 35: 1257-87. [2] Mai YW, Cotterell B. On the essential work of ductile fracture in polymers. Int J Fract 1986; 32: 105-25. [3] Cotterell B, Reddel JK. The essential work of plane stress ductile fracture. Int J Fract 1977; 13: 267-77. [4] Broberg KB. Critical review of some theories in fracture mechanics. Int J Fract 1968; 4: 11-9. [5] Broberg KB. On stable crack growth. J Mech Phys Solids 1975; 23: 215-37. [6] Clutton E. Essential work of fracture. In: Moore DR, Pavan A, Williams JG, editors. 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Effect of the specimen dimensions and the test speed on the fracture toughness of iPP by the essential work of fracture (EWF) method. J Appl Polym Sci 1999; 73: 177-87. [17] Arkhireyeva A, Hashemi S, O’Brien M. Factors affecting work of fracture of uPVC film. J Mater Sci 1999; 34: 5961-74. [18] Hill R. On discontinuous plastic states, with special reference to localized necking in thin sheets. J Mech Phys Solids 1952; 1: 19-30. [19] Hill R. The mathematical theory of plasticity. New York: Oxford University Press; 1998. [20] Tuba F, Oláh L, Nagy P. On the valid ligament range of specimens for the essential work of fracture method: The inconsequence of stress criteria. Eng Fract Mech 2013; 99: 349-55. [21] Arkhireyeva A, Hashemi S. Combined effect of temperature and thickness on work of fracture parameters of unplasticized PVC film. Polym Eng Sci 2002; 42: 504-18. [22] Maspoch ML, Gamez-Perez J, Karger-Kocsis J. Effects of thickness, deformation rate and energy partitioning on the work of fracture parameters of uPVC films. Polym Bull 2003; 50: 279-86. [23] Arkhireyeva A, Hashemi S. Influence of temperature on plane stress ductile fracture of poly (ethylene terephthalate) film. Plast Rubber Compos 2001; 30: 125-31. 20  [24] Hashemi S, Arkhireyeva A. Influence of temperature on work of fracture parameters in semi-crystalline polyester films. J Macromol Sci B 2002; 41: 863-80. [25] Gamez-Perez J, Santana OO, Martínez AB, Maspoch ML. Use of extensometers on essential work of fracture (EWF) tests. Polym Test 2008; 27: 491-7. [26] Martínez AB, Arencón D, Rodríguez J, Salazar A. Influence of the notch sharpening on the impact fracture toughness of ethylene-propylene block copolymers. Polym Test 2014; 36: 75-81. [27] Hashemi S, O’Brien D. The essential work of plane-stress ductile fracture of poly (ether – ether ketone) thermoplastic. J Mater Sci 1993; 28: 3977-82. 21  FIGURE CAPTIONS Figure 1. DENT specimen geometry. Figure 2. Load-displacement curves for the femtolaser sharpened specimens. Specimen set 1. Figure 3. EWF plots for the (▲) femtolaser and (●) razor blade sharpened specimens. Figure 4. Summary of the femtolaser sharpened specimens (lo = 11 mm). Specimen set 8. Figure 5. Summary of the razor blade sharpened specimens (lo = 11 mm). Specimen set 5. Figure 6. Stress-displacement curves for the femtolaser sharpened specimens. Specimen set 1. Figure 7. Stress-displacement curves for the razor blade sharpened specimens. Specimen set 2. Figure 8. CTODc determination for (▲) femtolaser and (●) razor blade sharpened specimens. Figure 9. Stress-displacement curve for femtolaser and razor blade sharpened specimens (lo = 17 mm). Figure 10. Stress-displacement curves for the femtolaser and razor blade sharpened specimens shifted along the axis of displacement (lo = 17 mm). Figure 11. Normalized tails of the stress-displacement curves for femtolaser sharpened specimens. Specimen set 1. Figure 12. Normalized tails of the stress-displacement curves for razor blade sharpened specimens. Specimen set 2. Figure 13. Summary of pre-notched specimens (lo = 11 mm). Specimen set 3. Figure 14. Stress-displacement curves of specimens from set 3 until set 8 (lo = 11 mm). Figure 15. Summary of the deformed pre-notched specimens (lo = 11 mm). Specimen set 4. Figure 16. Summary of the liquid N2 razor blade sharpened specimens (lo = 11 mm). Specimen set 6. Figure 17. Summary of the specimens pre-notched with a scalpel and sharpened by a razor blade (lo = 11 mm). Specimen set 7. Figure 18. Stress-displacement curve for specimens with non-collinear notches (lo = 11 mm). Specimen set 9. 22  Figure 19. Stress-displacement curves for well-aligned collinear specimens (SG), wellaligned non-collinear specimens (DR), and collinear tilted specimens (AT). Figure 20. Stress-displacement curve for tilted specimens (lo = 11 mm). Specimen set 10.