Crack Propagation Behavior And Toughness Biology Essay

Published: Last Edited:

This essay has been submitted by a student. This is not an example of the work written by our professional essay writers.

The presence of cavities or voids in engineering materials influences their fracture behavior. These defects become stress concentrators, which ultimately initiates crack propagation. Such defects can be of different shapes and sizes. However, this investigation examines the effect of V-notches on the fracture behavior of neat and recycled polyethylene terephthalate injection-moldings. Notches of 0.5-4.5mm deep were introduced onto one edge of dumbbell and Izod impact samples. Tensile and Izod impact tests were conducted. The study carefully correlated the tensile properties, as well as impact properties of the materials with the role of the skin and core regions in controlling the effect of the notches. Investigation reveals that three distinct fracture behaviors existed. These include ductile, semi ductile and brittle fracture transitions. At a critical 0.6mm deep notch, there was a drastic change in the fracture pattern from ductile to semi ductile. This semi-ductile failure continued to occur even as deeper notches were introduced. When the notch depth reaches 1.5mm, however, the specimens experienced a mixed fracture behavior. These transition points were found to have corresponded well to the depths of the skin and core regions, which were measured from polarized light micrographs. The development of an anisotropic skin-core structure in injection moldings are well acknowledged, which is revealed in a constant fracture behavior between 0.6-1.0mm deep notches, considered the skin region. There is a transitional fracture pattern at 1.5mm deep notch, which marks the interface between the skin and core regions. Lastly, a constant fracture behavior is observed at notch depths ≥1.5mm, considered the core region. It is obvious that V-shaped notch provided a gradual transition in fracture behavior from the skin to the core regions, which confirms that, the fracture behavior of PET injection moldings can be dependent on the skin and core structure.


Fractures occur in materials when there are pre-existing cavities or nucleation of voids due to stressful loading. Such defects in engineering thermoplastic components are stress concentrators [1] that tend to undermine the structural stability of such components during their life span. The resultant effects of cavities, voids or defects in engineering structures so often can be catastrophic. Catastrophic failure of structures claims heavily in economic and human cost. The study of fracture mechanics therefore is meant to investigate the materials' response to fracture under a pre-determined crack condition. Understanding the fracture behavior of materials with different sizes of defects helps components designers and engineers to balance between the choice of discarding very expensive defective material and safety requirements of engineering construction. Polyethylene terephthalate is a semi-crystalline thermoplastic material known to be very notch sensitive. The notch sensitivity of PET products had led to many research investigation which reveals that both virgin (V-PET) and recycled PET (R-PET) products exhibit low fracture resistance in the presence of notch. Takano, et al [2] examined the effect of standard V-notches on polymeric materials including PET by conducting tensile test on dumbbell test bars with single and double edge notches of 1.27 and 3.175mm deep. Equations [(2) & (3)] were used to calculate the notch sensitivity factors for fracture strength (kS) and energy to fracture (kT), respectively. Results show that if a notch has no effect on the toughness of a polymeric material, the notch sensitivity factor is 1.0 otherwise; it is greater than 1.0. Their investigation shows that the values of kS for PET at 1.27 and 3.175mm notch depths were 1.02 and 1.26, respectively; while kT at the two notch depths were 7.33 and 11.21. These results therefore, prove that notches ≥1.27mm are detrimental to PET products as they fracture in a brittle manner.

In recent years, there is much effort to improve the mechanical properties of PET products as demonstrated in the work of Tanrattanakul, et al [3]. They investigated the improvement in toughness of different blends of PET by conducting tensile test on standard 2.54mm deep-notched Izod bars at a temperature range of -20 - 55oC. Their work showed that the PET samples blended with un-functionalized styrene-butadiene-styrene (SEBS) yielded at the crack root thereby fracturing in a brittle manner. On the other hand, blending PET with small amounts of functionalized SEBS elastomers was effective in increasing the ductility (toughness) of PET products. The fracture toughness of a material is known to be dependent on its morphological structure and crystallinity [4 & 5]. Therefore, Stearne, et al [5] investigated the effect of molecular weight and crystallinity on the notch sensitivity of PET injection moldings. They obtained two samples of varying degrees of crystallinity by varying the sample cooling time in the mold and the mold temperature. They conducted tensile test on the dumbbell samples cut with two notch conditions of 1.91 and 2.79mm deep. Their investigation revealed that crystallinity affects both the brittle fracture strength and yield behavior of PET injection moldings. Accordingly, the brittle fracture strength falls with increasing crystallinity, whereas the yield stress rises in the presence of notches.

The above reviewed studies investigated only 2.54mm, and 1.91 and 2.79mm standard notch depths (ASTM D256) in each case. Since injection moldings are known to exhibit anisotropic skin-core morphological behavior, these notches are usually deep enough to penetrate through the skin region. As such, the introduction of standard notches does not provide adequate consideration for the influence of the skin region on the fracture characteristics of the bulk material. Furthermore, in slow crystallizing materials such as poly(ethylene terephthalate) (PET), the development of a distinct skin-core structure during injection molding is inevitable. PET is known also to be a very notch-sensitive material and would fracture in a very brittle manner upon introduction of notches but remains very tough if un-notched. However, the effect of notch depth on the fracture characteristics is still unclear. Therefore, it is necessary to introduce notches at various depths and examine their effects on the crack propagation behavior of injection molded PET products. If a correlation between fracture characteristics and morphology could be established, the information will be very useful to assist molders in optimizing molding conditions as well as improve the safety and reliability of the moldings.

In order to understand these effects, V-notches ranging from 0.5-4.5mm depths were introduced on single edges of dumbbell and Izod impact samples. These depths were chosen so that the notch root was positioned along the skin through the core regions of the moldings. Skin and core regions were determined through polarized optical microscopy. The fracture characteristics of the samples at various notch depths were monitored, during tensile and impact testing, by various optical devices including a CCD camera.


Material and Sample Preparation

Amorphous grade neat PET (V-PET) pellets (MA2103 LOT 601K; Mw=23000) was obtained from UNITIKA Co. Ltd. while recycled PET (R-PET) flakes were obtained from Yasuda-Sangyo Co. Ltd. V-PET pellets were used as received while R-PET flakes were extruded and pelletized prior to injection molding. The flakes were dried at 120oC for at least 5 hours prior to extrusion by a set of single screw extruder (SR-Ruder Bambi SRV-P70/62 from Nihon Yuki., Ltd. Japan). Barrel temperature was set between 255 - 290oC, and screw rotation speed was 50rpm.

Prior to injection molding, the V-PET and R-PET pellets were dried for at least four hours at 130oC, in a PICCOLO hopper-dryer from Itswa Co. Ltd. The fabrication of dumbbell samples was performed with a TOYO PSS TI-30F6 injection-molding machine at a barrel temperature range of 250 - 270oC. Mold temperature was set at 30oC while the injection and holding pressures were set at 60kgf.

Notching and Mechanical Property Characterization

V-notches of 0.5-4.5mm depths were introduced on dumbbell and Izod impact test pieces with a Type A-3 Digital Notching Machine (from Toyo Seiki Manufacturing Co., Ltd). The notching was performed in stages of 0.5mm depth in order to minimize internal deformation of the samples. The angle of the V-notches is in accordance with ASTM D256.

Tensile testing of notched and un-notched dumbbell specimens was performed with an Instron 4466 universal testing machine mounted with 10kN load cell and set at a crosshead speed of 10mm/min. At least seven sample pieces were tested for each material and notching condition. As the test progresses, CCD camera was used to monitor the notch tip during crack opening and propagation, while scanning electron microscopy was used to observe the fracture surfaces. Other sets of samples bearing the notch depths of 0.6, 1.5 and 2.0mm respectively were loaded to intermediate points on the stress-strain curves and stopped. These points include 1.2, 1.4 and 1.6kN. The samples were carefully unloaded, polished and observed in polarized optical microscopy to determine the crack behavior at these points. Izod impact testing was conducted with a TOYOSEIKIIDigital Impact Tester machine fitted with a standardized JIS K7110 Hammer bearing impact energy of 2.75J.

Determination of notch sensitivity factors

Investigations were conducted on the effects of V-notches by analyzing the notch sensitivity factors kS and kT at the successive notch depths. This gives an understanding of the effects of notches on the fracture behavior of the materials. If notches have no detrimental effects on the tensile strength and total energy absorbed upon deformation, the notch sensitivity factors for the strength (kS) and energy (kT) are equal to 1.0. Conversely, if they have detrimental effects, the notch sensitivity factors are greater than 1.0 [2]. The theoretical stress concentration factor, k, for single-edge V-notch specimens of materials is determined by equation (1):


Where r = the radius of curvature at the crack tip, a = depth of the notch.

It should be noted that equation (1) is independent of material properties. In this study, the notch sensitivity factors are determined by the following equations:



Where kS = notch sensitivity factor for yield strength, kT = notch sensitivity factor for energy. YS0 and YSi = yield stress (strength) of un-notched and notched samples respectively [subscript i is the successive notch depths], t = thickness, w = width, and a = notch depth. A0ssc and Aissc are the areas under the stress-strain curves for un-notched and notched specimens respectively.

The notch sensitivity factor for yield/fracture strength gives an understanding of how notches affect the strength of materials. On the other hand, the notch sensitivity factor for energy measures the effect of notches on the toughness of the materials.

Birefringence Observation of PET Injection-moldings

Birefringence observation was performed on the cross-section of dumbbell samples to gauge the sizes of the skin and core regions. Prior to polarized-optical-microscopy, a short section of dumbbell specimen was cut and placed in epoxy lamina. One side of the cross-section was polished with a rotational polishing wheel mounted with abrasives of different grain sizes to achieve smooth surfaces. The abrasives were used in stages from large rough grains to smooth finer grains until a smooth surface was achieved. The surface was further made as smooth and clean as possible by the use of alumina cleaner. Thereafter, the first polished side was glued to a clear and clean glass slide with araldite glue to hold it in place; and ensure that liquid does not penetrate in-between the glass and sample surface during the polishing of the opposite end of the specimen. It is left to dry. The polishing steps described above were repeated for the opposite view of the cross-section until a thin smooth and translucent view of about 30­m thickness was achieved. Polarized optical micrographs were taken from the polished specimen through a 3.34 mega pixel Nikon digital camera attached to a 10 X/0.25P magnification optical lens that is mounted on Nikon ECLIPSE E600 Polarizer. The micrographs were joined together by the use of Adobe Photoshop CS software. The resulting composite image panorama was converted to grey mode with Origin 7J [Rel v7.0265 (B265)] software by OriginLab Corporation; the contours and plots of the frequency and amplitude of their grey values over the entire cross-section were taken and analyzed.

The tensile test samples that were loaded midway to 1.2, 1.4, and 1.6kN, equally, were observed for fracture initiation. The lateral view of the area containing the notches on the test pieces were cut and placed in epoxy lamina. One side of the lateral view was polished with rotational polishing wheel as described previously in the preceding paragraph. The polished view was glued to a clean and clear glass slide and kept to dry. The polishing steps described above were repeated for the opposite lateral view of the samples until a thin smooth and translucent view of about 30­m thickness is achieved. Polarized optical micrographs were taken from the polished specimen through a 3.34 mega pixel Nikon digital camera attached to a 10 X/0.25P magnification optical lens that is mounted on Nikon ECLIPSE E600 Polarizer. The micrographs were joined together by the use of Adobe Photoshop CS software.


Cross-sectional Observation by Polarized Light Microscopy

The polarized optical micrographs of the cross-section of V-PET and R-PET specimens are shown in Figures 1(a) and (b), respectively. Distinct skin and core regions could be recognized from the birefringence and contrast of the micrographs. These figures were then converted to grayscale and subsequently contour plots defining the intensity of the grey areas were obtained by using Origin 7J [Rel v7.0265 (B265)] software by OriginLab Corporation, which are depicted in Figures 1(c) and (d). The contour plots revealed a more complex morphology where the existence of an interface between the skin and the core is clearly visible in both materials.

Derivations from the intensity of the grey areas were used to determine precisely the thickness of the skin and core regions, as shown in Figures 1(e) and (f). The plots marked with W and X represent the intensity values of the grey scale in the width and thickness directions of the samples, respectively. The horizontal and vertical cursors on the matrix (grey scale image) were adjusted along the width and thickness directions until well-defined frequency peaks were obtained. The center region in between the two maximum peak intensities (marked by arrows in Figures 1(e) and (f)) obtained from W and X plots were taken to be the core width and thickness, respectively. The remaining areas surrounding the core will be regarded as the skin. The thickness values of the skin and core were obtained from the W and X plots with data points and screen readers provided in the Origin 7J processing software. These values are presented in Table 1. Since notches were introduced in the width direction, the thickness of the skin region in this direction is noted to be 1.47mm on each side of the specimen.

Effect of V-notch depth on tensile properties of PET

Figures 2(a) and (b) show the typical stress/strain curves during tensile tests for V-PET and R-PET specimens, respectively. The curves depict the transitions in fracture behavior corresponding to various notch depths. Results indicate that the un-notched samples from both materials maintained high ductility and did not fracture below 300% strain. The introduction of a 0.6mm deep notch onto the materials, however, resulted in a drastic reduction in the ductility of both materials. This marked a change in the fracture behavior of the materials from ductile to semi-ductile where shear yielding and tearing at the notch tip was evident with increasing strain. Prior to shear yielding, there were two lines originating from the crack root at an angle of 45o as observed in Figure 3[a, b] [6]. Crack propagation eventually occurred along one of these lines through which the samples ultimately fail [Figure 3(c, d)].

V-PET and R-PET experienced a similar ductile to semi-ductile transition when notches between 0.6mm-1.5mm deep were introduced while brittle failure was imminent when deeper notches were present (2.0-4.5mm). It is important to note that the transitions from ductile to semi-ductile to brittle fracture behaviors were not gradual. A very shallow V-notch, i.e. less than 0.6mm, would not effectively cause stress concentration, thus the material remained ductile as in un-notched specimens. When the notch is deep enough to act as a stress concentration point (0.6mm≤a≤1.5mm), yielding would occur at the root of the notch. However, the onset of crack propagation would be slow since the notch root was still located within the highly amorphous skin region that is 1.48mm in thickness, as indicated in Table 1. At this notch level there would be sufficient mobility of the polymeric chain segments for plastic flow to occur at a local (molecular) level from the skin region to the crack tip [7]. With the introduction of notches deeper than 1.5mm, which would have already penetrated the more crystallized core region, brittle failure was imminent, as there was no further plastic flow from the skin region to the crack tip.

The presence of cracks in materials builds up stress concentration around the defect. It means that the stress acting on the defect is higher than any other part of the material. Increase in the stress results in increase in its intensity until a critical value where the material yields and crack initiates. Therefore, stress concentration factor gives a measure of the sensitivity of materials to cracks. Figure 4 shows the notch sensitivity factors for strength (kS) at the various notch depths determined by equation (2). The notch sensitivity factors kS for the un-notched sample is 1.0; and the notch ranges 0.5-1.0mm were slightly lower than 1.0. This indicates that the notches had no detrimental effects on the strength of the materials if the notch depths remained a≤1.5mm, which is considered the skin region. However, the slight difference between the notch sensitivity factors (kS) for un-notched sample and 0.5-1.0mm notch depths indicate that these notched samples exhibited higher yield stress than the un-notched specimens. This could be the effect of the stress field at the notch root as it changes from biaxial stress to triaxial [2] thereby increasing the materials' resistance to fracture. ASTM D 5045 provides that in the fracture toughness study of a material, the notch depth to ligament width ratio (a/w) would have to be 0.45 ≤ a/w ≤ 0.55 so that the material will have minimum resistance to crack propagation. It is obvious that the notches between 0.6-1.5mm fall short of this standard provision. Studies show that the strain rate at the crack tip is greater than the strain rate at any other region on the test piece [2]. Therefore, notches or cracks change the nature of stress field from a biaxial tensile stress to a triaxial stress in the region of the crack. This brings about the twisting of the test sample resulting in a tearing fracture [2]. In addition, results show that V-PET exhibited slightly higher yield stress than R-PET due to higher level of crystallinity, as shown in Table 2. It is evident that the yield stress of the materials was not affected by the notch depths of 0.6-1.0mm.

The notch sensitivity factors for energy (kT) at the various notch depths calculated from equation (3) are shown in Figure 5. It is clearly seen that when the notch is ≤0.5mm deep, the kT value remains at 1.0, which indicate that these notches had no detrimental effect on the materials. However, when the notch depth extends further into the skin region at 0.6-1.00mm, the kT value increased to 6.0. This marks a transition from ductile to semi-ductile fracture behavior. This shows that while kS remained stable at ≤1.5mm deep notches, kT experienced mild detrimental effects [2]. It is clear that both materials (VPET and RPET) experienced similar transition in fracture behavior from ductile to semi-ductile at notch depths of between 0.6-1.5mm. However, brittle failure was imminent when deeper notches of 2.0 mm and above were introduced. This is evident in the successively higher kT recorded between 2.0-4.5mm notch depths. As mentioned earlier, three distinct transitions in fracture behavior exist, namely ductile, semi-ductile, and brittle fracture behaviors. KS has shown that the materials will remain tough and maintain their structural stability if the notch depth is ≤0.5mm. On the other hand, notches between 0.6-1.0mm deep will be structurally unstable, while deeper notches ≥1.5mm will cause catastrophic failure in materials.

Fracture modes at intermediate loading points during tensile test

Further investigations were conducted on the three distinct fracture transitions that were identified earlier in Figure 2[a, b] for samples tested at various notch conditions. This was to investigate if crack opening occurred prior to the necking or failure of specimens introduced with 0.6, 1.5, and 2.0mm deep notches. Figure 6(a) shows the three loading points 1, 2, and 3 [1.2, 1.4, and 1.6kN, respectively], on the load-displacement curve for 0.6mm deep notch samples. The birefringence observation of samples that were loaded up to points 1, 2 and 3 are shown in Figures 6[b-d]. It is seen from Figure 6(b) that two shear lines at angle of 45⁰ had already appeared at the crack root when a 1.2kN load was applied as indicated by point 1. The loading of a new sample to 1.4kN, at point 2, resulted in the extension of the two lines towards the opposite end of the sample width. The lines continued to extend with higher load (1.6kN - point 3) until they reach the width end of the samples where shear yielding occurred. Figures 6[b-d] show that there was no crack opening in the 0.6mm notch deep samples prior to shear yielding; this means that crack opening did not occur in the materials until after shear banding. It is worthy to note that the sample was able to shear band because the 0.6mm deep notch was still located in the amorphous skin region.

However, the load-displacement curve of 1.5mm deep notch specimens shown in Figure 7(a) shows that the material could sustain only 1.2kN load before necking and subsequent failure. This means that the material failed below 1.4kN load when a 1.5mm deep notch was introduced. Figures 7(b) shows the birefringence of the materials. In the figure, what would have been the two lines originating from the crack root at angle of 45⁰ became straight lines in the direction of the pre-crack. It is evident that the material yielded at this notch depth, nonetheless brittle failure was imminent. Figure 7[a, b] clearly shows that the notch was already at the interface between the skin and the core; hence, there was no further plastic flow of the skin towards the crack tip resulting in brittle failure as the crack penetrates the more crystallized core region. This fracture transition marks the onset of brittle failure in the materials when deeper notches were introduced, i.e. the 2.0mm notch deep samples did not attain 1.2kN load before brittle fracture.

Tensile Fracture Surfaces

Figures 8(a) and (b) depict the fracture surfaces of tensile test V-PET and R-PET samples, respectively. It is evident that high plastic deformation occurred in V-PET and R-PET at a notch depth of 6.0mm. This is indicative of ductile failure. It is observed that during crack propagation there was micro voids nucleation around the crack tip (indicated by arrows), which eventually coalesced along the crack path thereby leaving lobe-like fibrils. The micro void is clearly seen from the images of high magnification camera monitored movie recorded during tensile testing [refer to Figure 3(c)]. It is evident also that there was tapering in thickness towards the notch direction as the materials fractured in a semi-ductile manner from the notch end of the specimen's width to the opposite side [Figure 8(a-b)]. This tapering in thickness is caused by a continuous plastic flow [8] from the amorphous skin layer with lower stress concentration towards areas of high stress concentration, such as the notch root, which can only occur when the notch does not penetrate through the skin, i.e. notch depth is less than 1.5mm.

In Figure 8(c), there was a mixed failure (semi ductile to brittle fracture behavior) [8]. Similar tapering of specimen as seen in Figure 8[a, b] also occurred in 1.5mm deep notched samples. Nevertheless, it is easy to observe two fracture phases as the notch approaches the interface between the skin and core regions. At the notch root, which contains the residual part of the skin, there is significant degree of plasticity. However, as the crack progresses through this interface into the core region, crazing was observed within the core region, as indicated by arrows in Figure 8(c), which lead to semi brittle failure.

Figure 8[d, e] shows the brittle fracture surface of V-PET and R-PET, respectively, when notch depths ≥2.0mm were introduced. Cavities or voids were seen as circular voids at the roots of the notches but these were unable to coalesce and resist fracture thereby forming craze that leads to eventual brittle fracture. It is obvious from Figure 8[d, e] that there was no tapering of thickness in the specimens when notches have already penetrated the core region. When the notch was core-deep the plastic flow of the amorphous skin region towards the notch tip was not possible, hence brittle fracture was imminent.

Effect of V-notches on Izod impact properties of PET

Figure 9 shows that V-PET and R-PET had a gradual loss of strength when impacted upon as the notches deepen. The un-notched and 0.5mm-notched samples did not fracture upon impact. However, both V-PET and R-PET experienced brittle fracture and recorded impact strengths of about 25kJ/m2 when a critical notch depth of 0.6mm was introduced. When subsequent deeper notches of between 0.6-1.0mm were introduced, the specimens experienced a gradual but consistent decline in impact resistance. This could be due to the gradual thinning of the amorphous skin region with increasing notch depth, which reduces the effectiveness of the skin in suppressing crack propagation during impact loading. When the notch approaches the boundary between the skin and the core, i.e. the interface 1.5±0.2mm, there was a transitional change in the loss of impact strength. Minimum impact resistance in the material was observed when a 2.0mm deep notch was introduced. Further increments in notch depth resulted in a consistently low impact strength.

The fracture behavior of the materials under impact testing is seen to be different from their behavior under tensile loading. Under impact testing, the impact is very sudden that plastic flow from the skin to the crack tip was not possible; hence, they exhibited brittle failure, which was characterized with a gradual and consistent loss of impact strength. However, under tensile loading three distinct fracture behaviors were revealed at different notch depths. This is because while the notches remain at the amorphous skin regions, the molecular chains can slide past one another and realign thereby causing plastic flow [9] towards the crack tip.

Izod Impact Fracture Surfaces

Figures 10[a, b] represent the impact fracture surfaces of VPET and RPET at the various notch depts. The micrographs show similar brittle fracture even as the notches extend deeper into the core region. The circular-shaped craze at the crack root indicates sudden disruption of voids nucleation and coalescence due to impact. It can be concluded that due to sudden impact on the materials no plastic flow from the skin region towards the stress concentration region was possible.


This investigation has revealed that the fracture behavior of PET injection moldings responded in transitional phases from the skin through the interphase to the core regions of the samples. Thus, three distinct fracture transitions were clearly observed from the results indicating that the skin and core morphology plays significant role in the fracture behavior of PET injection molded components. The notch sensitivity factor for strength (kS) for V-PET is seen to be lower than the kS for R-PET because of higher crystallinity in V-PET. Howbeit, V-PET and R-PET had similar notch sensitivity factors for energy kT. Tensile loading provided a transitional fracture behavior from ductile, semi-ductile to brittle failure of the materials; on the other hand, impact testing resulted in their brittle failure and gradual loss of impact strength. By loading the specimens to intermediate points on the load-displacement curves, it has been shown that crack opening did not occur in the specimens prior to yielding. Therefore, it could be concluded that crack opening, in the materials that failed in a semi-ductile manner, was a post-necking phenomenon.