Micromechanisms of slow crack growth in polyethylene under constant tensile loading

Polymer 42 (2001) 9551±9564 www.elsevier.com/locate/polymer Micromechanisms of slow crack growth in polyethylene under constant tensile loading Christopher J.G. Plummer a,*, Anne Goldberg b, Antoine Ghanem c a Laboratoire de PolymeÁres (LP), Ecole Polytechnique FeÂdeÂrale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland b Solvay Polyole®ns Europe, 310 Rue de Ransbeek, 1120 Brussels, Belgium c Solvay Research and Technology Centre, 310 Rue de Ransbeek, 1120 Brussels, Belgium Received 26 March 2001; received in revised form 22 June 2001; accepted 29 June 2001 Abstract Circumferentially notched specimens of a ®rst generation and a third generation pipe-grade of high density polyethylene with similar weight average molar masses have been subjected to constant tensile loads at 808C. A transition from full ligament yielding to failure by stable sub-critical crack growth was observed as the applied load was decreased. The specimen lifetimes in this latter regime were dependent on the initial stress intensity factor, Ki, and failure was associated with slow crack propagation preceded by formation of a wedge-shaped cavitational deformation zone at the notch tip. The ®bril diameters in the deformation zones decreased with stress intensity factor near the transition, the limiting behaviour of a relatively slow crack growth resistant third generation grade at the lowest Ki being inferred from testing in Igepale to be the breakdown of diffuse zones of interlamellar voiding. This regime was not directly accessible to testing in air within the allotted experimental times. However, comparison with the results of accelerated testing in cyclic fatigue has indicated stable interlamellar voiding in the third generation grade not to necessitate the presence of Igepal. Moreover, in both grades, very similar modes of deformation were observed in air and in Igepal at relatively high Ki. Igepal was therefore inferred not to lead to qualitative changes in the range of mechanisms that are characteristic of slow crack growth in polyethylene. q 2001 Elsevier Science Ltd. All rights reserved. Keywords: Polyethylene; Microdeformation; Slow crack growth 1. Introduction Current interest in slow crack growth (SCG) in polyethylene (PE) is motivated by practical concerns over its long term performance in service, where it may be subject to signi®cant pressures and contact with water or other industrial ¯uids. Hydrostatic pressure testing of pipes is still widely used to assess their performance. However, for many modern PE grades, failure times may be of the order of years [1]. Pre-screening of different grades therefore generally involves accelerated testing, usually of notched specimens either taken from a pipe or moulded ad hoc. Accelerated SCG can be achieved by testing at high temperature and/or in the presence of a surfactant and/or under cyclic loading conditions. Non-ionic surfactants such as Igepale (nonyl phenol ether glycol) [2] are particularly effective for reducing the failure times of the tougher materials without affecting their ranking with respect to other grades tested under the same conditions. Indeed, according to Fleissner, ªsurfactant-assisted stress cracking is a means to markedly reduce testing time without changing the failure mechanismº [3]. This is important if such tests are to be of direct relevance to a wide range of service conditions, although the fundamental reasons for such behaviour remain unclear [4]. In the present study, we have used various microscopical techniques to examine the microdeformation mechanisms associated with SCG under tensile loading in two grades of high density PE (HDPE) at 808C in air and in Igepal. The aim was to gain insight into the micromechanisms of long-term failure in these materials and the differences in the behaviour of the different grades. The work was also motivated by our interest in the extent to which Igepal results in qualitative modi®cations in microdeformation behaviour, and hence the extent to which accelerated testing is representative of failure in air under conditions not accessible to experiment within convenient times. 2. Experimental 2.1. Materials * Corresponding author. Tel.: 141-21-693-2856; fax: 141-21-693-5868. E-mail address: christopher.plummer@ep¯.ch (C.J.G. Plummer). 0032-3861/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved. PII: S 0032-386 1(01)00476-1 The HDPE grades used in this study were two pipe-grade 9552 C.J.G. Plummer et al. / Polymer 42 (2001) 9551±9564 Table 1 Materials data for polymers PEA and PEB Resin PEA: 1st generation PEB: 3rd generation Density (kg/m 3) 956 959 Mn (kdA) 9.1 9.1 Mw (kdA) 236 215 ethylene±butene copolymers (PEA and PEB) from Solvay, with similar melt ¯ow indices and densities. Data for the two materials are given in Table 1. 2.2. Mechanical testing All the mechanical tests to be described in what follows were performed on notched specimens, under creep loading conditions and at a temperature of 808C. As discussed in the introduction, the resistance to SCG may be investigated using a range of techniques. However, since part of our aim was to compare results from the test methods that are currently most widespread in the literature, we opted for the test geometries and conditions listed below. 2.3. Cylindrical notched bar (CNB) tests in air For creep testing in air, use was made of cylindrical circumferentially notched specimens (Fig. 1(a)) machined from compression moulded plaques. The presence of a notch around the entire perimeter of a tensile test specimen promotes plane strain in the remaining ligament so that necking tends to be suppressed in favour of SCG under creep conditions. It follows that SCG tests can be performed at relatively high loads using such specimens, allowing one to reduce the overall test times. The specimen diameter was 12 mm, the total specimen length was 60 mm and the machined notch depth was generally about 2 mm. A pre-crack was introduced to the notch Fig. 2. (a) K/s as a function of a/D for D ˆ 12 mm; (b) s as a function of a/D for various values of F. tip using a fresh razor blade. The tests were carried out at 808C in force control mode using a Zwick 1400 screw driven machine equipped with an air oven. After clamping the specimen at zero load and tempering for 1 h at 808C, various ®xed loads were applied and the displacement of the lower (mobile) specimen end recorded using a mechanical extensometer. The crack length used to calculate the initial values of the stress intensity, Ki, and the ligament stress, s , was determined by inspection of the fracture surface after completion of each test. The maximum test time was limited to about two months. The stress intensity factor in a CNB specimen with a sharp notch subject to a tensile load F is given in Ref. [5] K ˆ s nom pa 1 2 2j†† 1=2  1:121 2 3:08j 1 7:344j 2 2 10:244j 2 1 5:85j 4 1 2 4j 1 4j 2 ! 1† Fig. 1. (a) Cylindrical notched bar (CNB) specimen geometry and (b) full notch creep test (FNCT) specimen geometry. where j is the reduced crack length a/D, D is the total 9553 C.J.G. Plummer et al. / Polymer 42 (2001) 9551±9564 Table 2 Summary of the test and materials parameters Resin Sample n8 Colour Geometry Environment Processing PEA PEB PEA PEB PEB PE1 PE2 PE3 PE4 PE5 Black Black Natural Black Black CNB CNB FNCT FNCT FNCT Air Air Igepal Igepal Igepal Compression Compression Compression Compression Pipe specimen diameter, s nom ˆ 4F=pD2 ; and s ˆ 4F=p D 2 2a† 2 moulding moulding moulding moulding 2.5. Summary of the test and materials parameters 2† K/s showed a maximum at a/D of about 0.18 (Fig. 2(a)) which was the reason for choosing 2 mm to be the default notch depth, that is, the approximate initial crack length. If plane strain conditions are assumed, the critical ligament stress for plastic collapse should be independent of a (for simplicity, we ignore the time dependence of the yield stress, s y). Given that s increases rapidly with a/D (Fig. 2(b)), crack propagation in this geometry is therefore expected to lead to ductile necking of the central part of the ligament, unless the ®brillar crack tip deformation zone characteristic of SCG in PE is able to propagate across its entire width ®rst [6,7]. 2.4. Full notch creep tests (FNCT) in Igepal The tests in Igepal were carried out using the FNCT geometry (Fig. 1(b)), which is now widely used in the pipe community [8±11]. In this case, the specimens take the form of a rectangular parallelepiped with dimensions 10 £ 10 £ 100 mm 3 : A notch of uniform depth was introduced by gently pushing a razor blade into the specimen at its mid-point, so that the remaining ligament was square in cross-section. The specimens were loaded using commercial creep loading apparatus (IPT, Germany) at 808C in 2% Igepal CO-630 in demineralised water, after tempering for 1 h at the test temperature. The initial loading rate was 72 MPa/min. Ki was calculated numerically using the ABAQUS w ®nite element package, there being no analytical expressions available for this geometry to our knowledge. The calculations indicated the stress intensity to be heterogeneous, increasing with distance from the centre of the ligament sides, to reach a maximum at the corners. Thus, for an initial ligament stress, s i of 3 MPa, we obtained K imin ˆ 0:12 MPam1=2 and Kimax ˆ 0:3 MPam1=2 : However, Kimin was observed to control the SCG rate under these conditions and for a given s i, K imin ˆ Ki ; where Ki is the value calculated for CNB specimens using Eq. (1) [12]. This result has been con®rmed elsewhere in the literature [8]. Ki was therefore taken to be the effective initial stress intensity factor in both geometries. The full range of materials and test parameters used in the present investigation are summarised in Tables 1 and 2. Most of the specimens were pigmented using carbon black and with the exception of PE5, which was machined from an extruded pipe, they were all prepared by compression moulding. 2.6. Microscopy After the tests, the fracture surfaces were trimmed and embedded in either an epoxy resin (Araldite D from Ciba) or distilled methyl methacrylate (MMA) containing a few wt% benzoyl peroxide. The epoxy was cured at room temperature, whereas the MMA was polymerised overnight at 408C and post-cured at 808C for a further 24 h. In general, embedding in epoxy gave better contrast owing to preferential staining of the specimen-epoxy interfaces, but MMA gave better penetration. Positive or negative staining of the HDPE was observed for both types of embedding medium, depending on the depth at which the sections were taken and the degree of penetration of internal voids by the resin and/ or the stain. An ultramicrotome (Reichert±Jung Ultracut E) and a 2.5 mm wide 35 or 458 diamond knife (Diatome) were used for sectioning. A trapezoidal surface not exceeding 1.5 mm in width was prepared using a trimming knife and semi-thin sections (about 10 mm) removed for optical microscopy (OM) using a glass knife. The specimen was then exposed to RuO4 vapour overnight by placing it over a watch glass containing 50 mg of RuCl3´3H2O mixed with 2.5 ml of 5% aqueous NaClO. After staining, sections of between 50 and 100 nm in thickness were prepared at room temperature and picked up from distilled water onto copper TEM grids covered with a thin ®lm of carbon. Transmission electron microscopy (TEM) was carried out using a Philips EM430 (accelerating voltage 300 kV), or a Philips CM 20 (200 kV), depending on the availability of the microscopes. The fracture surfaces were also observed by scanning electron microscopy (SEM) (Philips XL-30, equipped with a ®eld emission gun) at about 2 kV. The carbon ®lled specimens generally showed little charging and could easily be observed at up to 5 kV, but beam damage in the form of coalescence of ®ne structure was more marked under these conditions. 9554 C.J.G. Plummer et al. / Polymer 42 (2001) 9551±9564 Fig. 3. Creep curves for PEA tested under different loads. 3. Results 3.1. CNB testing in air (series PE1 and PE2) Fig. 3 shows creep curves from PEA specimens loaded at different ligament stresses, illustrating the three distinct regimes typical of this type of test. The initially large deformation rate corresponded to the application of the load, the period of transient loading lasting about 30 s in this case. The subsequent evolution of the global strain was dominated by the deformation of the ligament de®ned by the notch, associated with stable necking and/or SCG at the notch tip, depending on the applied load. The onset of the ®nal stage of the deformation process corresponded to either unstable necking or crack advance through the damage zone at the crack tip. Since this was characterised by a rapid acceleration of the deformation rate, the overall failure times in the SCG regime were strongly correlated with the initiation times for crack advance. They were therefore expected to depend primarily on Ki. For notched specimens of both PEA and PEB, s y < 9 MPa at 808C at a constant loading rate of 10 mm/min, and fully ductile behaviour occurred after short times at comparable values of the initial ligament stress, s i. The lengths of the crack tip deformation zones observed at lower s i did not exceed 2 mm, becoming very much less than 2 mm at the lowest stresses investigated. Hence, residual necking in the central part of the fracture surface tended to persist over the whole range of test conditions studied, regardless of whether failure initiated by SCG. Fig. 4(a) shows s i plotted against time to failure for PEA specimens and for two different notch depths, and Fig. 4(b) shows Ki against time to failure for the same specimens. These results con®rm the specimen lifetime to be Ki controlled over most of the range of loads investigated. The high Ki plateau in Fig. 4(b) was characterised by extensive plastic necking prior to failure and the failure time was assumed to be dominated by the kinetics of the yielding process. Beyond this plateau, a sharp drop in Ki with increasing failure time marked the transition to SCG [12±15]. Fig. 4. (a) s plotted against failure time for PEA and PEB and (b) K plotted against failure time for the same specimens. The open and ®lled squares are for PEA and for notch depths of approximately 2 and 4 mm, respectively. The circles are for PEB and a notch depth of approximately 2 mm. The results for PEB specimens are also shown in Fig. 4. The high load regime of ductile behaviour was similar to that observed for PEA. However the transition to SCG behaviour was signi®cantly delayed, and neither failure nor SCG could be observed in PEB at the lowest Ki within the allotted test times. 3.2. CNB fracture surfaces in air (series PE1 and PE2) For the reasons outlined in the previous section, a neck was observed at the centre of all the fracture surfaces, its C.J.G. Plummer et al. / Polymer 42 (2001) 9551±9564 9555 Fig. 5. OM of the fracture surface of a PEA specimen tested to failure at s i ˆ 5 MPa and Ki ˆ 0:22 MPam1=2 in air: (a) image taken between crossed polarisers of part of the central necked region of the fracture surface (i) and part of the surrounding ®brillar region (ii); (b) detail from the region containing the notch tip (iii) (tensile axis as indicated by the arrows). size diminishing as Ki decreased (for a ®xed notch depth). The ®bril diameters in the regions of the fracture surfaces corresponding to SCG were also found to diminish with decreasing Ki. This was re¯ected by a decrease in the ®bril diameter at the original notch tip as the load was decreased. Moreover, there was an increase in the ®bril diameter toward the specimen centre for a given load, that is, in regions that were deformed after a certain amount of stable crack advance and hence for which K was assumed to be greater than Ki. This is shown in Figs. 5±7. Fig. 5 shows images from polarised light microscopy (OM) of a section through the fracture surface of a PEA specimen tested to failure a s i ˆ 5 MPa and Ki ˆ 0:22 MPam1=2 ; showing part of the central neck and the surrounding ®brillar region. This ®brillar region extended to the periphery of the fracture surface, although the presence of a relatively highly deformed region at the notch tip suggested some crack tip blunting in the early stages of SCG. Fig. 6(a) is a TEM image from a thin section taken from just in front of the notch tip in the specimen shown in Fig. 5, where the ®brils were relatively ®ne. There was a sharp interface between the damage zone and the surrounding undeformed material. Moreover, the internal structure of this part of the deformation zone was relatively uniform through its thickness, indicating most of the deformation to have occurred at the interface. The ®brillar texture here was on about the same scale as the dominant lamellae [16], and indeed there was some continuity between the ®brils and lamellae adjacent to the interface, as is apparent from Fig. 6(a). Fig. 6(b) is from about 2 mm from the notch tip, showing a somewhat greater ®bril spacing than in Fig. 6(a). Fig. 6. TEM of a section through the fracture surface shown in Fig. 5: (a) section from just in front of the notch tip; (b) section from about 2 mm from the notch tip; (c) section from just outside the central neck; (d) section from behind the neck (tensile axis as indicated by the arrows). 9556 C.J.G. Plummer et al. / Polymer 42 (2001) 9551±9564 Fig. 7. The crack tip deformation zone in a PEA specimen tested at s i ˆ 7 MPa and Ki ˆ 0:3 MPam1=2 in air: (a) overview of the deformation zone; (b) OM of the deformation zone tip; (c) low magni®cation TEM image of the deformation zone tip; (d) detail of the internal structure of the region marked (i) in (c) (tensile axis as indicated by the arrows). Texture was also visible within the ®brils, certain of which appeared to consist of a bundle of `sub-®brils' associated with individual lamellae, drawn together in a ®nely voided, branched structure at the ®bril base. However, the bulk of the deformation at the origin of the ®brillar texture in the interior of the deformation zone again appeared to have taken place at or close to the interface with the undeformed material. Closer to the central neck the main ®brils were considerably coarser, although ®ner `cross-tie' ®brils were still visible between them, as shown in Fig. 6(c). The existence of these cross-tie ®brils is signi®cant in that they permit stress transfer perpendicular to the main ®bril direction and hence promote stress concentration at the craze tip [17]. However, in the present case, the essentially twodimensional images provided by the thin sections were potentially misleading, since high magni®cation SEM of the fracture surfaces indicated the matrix ligaments to be sheet-like. Thus the structure of the deformation zone was closer to that of a closed cell foam than to a truly ®brillar structure. This trend was even more marked at the specimen centre, the internal structure of the macroscopic neck being characterised by large isolated voids, which became extended along the deformation direction. Fig. 6(d) shows the early stages of voiding in the outer part of the neck, where the void density was relatively high. In addition to the intact cross-tie ®brils visible in Fig. 6(d), ®brillar debris was present at the void surfaces, indicating breakdown of crazes or craze-like structures during void formation. The internal structure of the deformed ligaments in Fig. 6(c) and (d) re¯ected a gradual drawing down of the bulk lamellar texture throughout the thickness of the deformation zone. The interface between the deformed and the undeformed material was consequently relatively poorly de®ned. In the more highly deformed regions of the macroscopic neck, continued drawing of the voided regions resulted in a pronounced layered texture. The central part of the neck, however, showed relatively limited voiding. At s i ˆ 7 MPa and Ki ˆ 0:3 MPam1=2 ; deformation in PEA was globally more ductile and the ®nal stages of deformation involved more extensive necking than in the specimen described previously. The initial stages of failure were nevertheless still characterised by the formation of a crack tip deformation zone. Fig. 7 shows the structure of the tip of this deformation zone at various magni®cations in a specimen which had been unloaded after a limited amount of SCG and the crack faces wedged open during embedding. The deformation zone extended a few 100 mm into the specimen, and consisted entirely of unconnected voids with necking of the intervening ligaments, which incorporated many individual lamellae. Relatively large, isolated voids were present at the deformation zone tip, visible optically in Fig. 7(b) and again as the heavily stained regions in Fig. 7(c) and (d) shows a detail of a partly deformed ligament between two such voids, in which the evolution of the lamellar texture suggests a relatively weak deformation gradient (cf. Fig. 6(c) and (d)). Owing to the highly interconnected nature of the matrix ligaments in this case, crack advance through the deformation zone tended to draw the material behind the crack tip towards the specimen centre. Hence, in spite of the highly inhomogeneous voided structure of the damage zone ahead of the crack tip, the peripheral regions of the fracture surfaces corresponding to SCG in specimens such as that in Fig. 7 appeared relatively smooth when observed by SEM or OM, and contiguous with the central neck. For PEB tested in air, very similar behaviour was observed in the SCG regime to that in PEA for comparable Ki, although the failure times were much longer. Representative TEM micrographs from a specimen tested with s i ˆ 6 MPa and Ki ˆ 0:26 MPam1=2 are given in Fig. 8, showing ®brillar structure from the periphery of the fracture surface (Fig. 8(a) and (b)) and coarser voiding from closer to the specimen centre (Fig. 8(c)). There is some suggestion of an C.J.G. Plummer et al. / Polymer 42 (2001) 9551±9564 9557 Fig. 8. The crack tip deformation zone in a PEB specimen tested at s i ˆ 6 MPa and Ki ˆ 0:26 MPam1=2 in air: (a) ®brillar deformation at the periphery of the fracture surface; (b) detail of the edge of the deformation zone in (a); (c) voiding behind the central neck (tensile axis as indicated by the arrows). Fig. 9. Fracture surface of a PEB specimen tested at s i ˆ 3 MPa and Ki ˆ 0:13 MPam1=2 in Igepal: (a) SEM of the fracture surface; (b) re¯ected light micrograph of the fracture surface; (c) detail of the fracture surface (the region indicated in (a)). 9558 C.J.G. Plummer et al. / Polymer 42 (2001) 9551±9564 Fig. 10. OM of deformation in transverse sections through the fracture surface of a PEB specimen tested at s i ˆ 3 MPa and Ki ˆ 0:12 MPam1=2 in Igepal: (a) phase contrast image from the notch tip; (b) the same region observed between crossed polarisers; (c) phase contrast image from in front of the notch tip (tensile axis as indicated by the arrows). increased density of ®ne ®brils in the interior of the coarse voids in Fig. 8(c) compared with those in Fig. 6(d), but this was dif®cult to quantify. 3.3. FNCT fracture surfaces in Igepal (series PE3, PE4 and PE5) Figs. 9±11 show the fracture surface of a PEB specimen tested in Igepal at s i ˆ 3 MPa and Ki ˆ 0:12 MPam1=2 ; which failed after 2523 h. The fracture surface appeared relatively smooth at low magni®cations and macroscopic necking was restricted. (The neck was displaced to one side of the fracture surface in this specimen owing to slightly asymmetric loading conditions during crack propagation.) Deformation below the fracture surface in the peripheral regions took the form of ®ne crack-like deformation zones at and immediately below the fracture surface, growing roughly parallel to this latter (Fig. 10). The images in Fig. 10(a) and (b) indicate little apparent blunting at the notch tip, the layer of oriented material visible on the lefthand side of Fig. 10(b) being due to the notching procedure. The TEM micrographs shown in Fig. 11 were taken from sections through the fracture surface in Figs. 8 and 9 at about 2 mm from the notch tip, and were typical of the whole of the fracture surface with the exception of the central neck. The more heavily stained regions of the thin sections contained small, roughly equiaxed voids, and intervening undeformed or relatively undeformed lamellae are visible as light bands within these regions (Fig. 11(a)). The deformation zones were relatively diffuse, and their internal structure was closely correlated with that of the matrix. Where the dominant lamellae were locally at a high angle to the loading direction, they remained intact during the initial stages of deformation, so that we might loosely refer to this as `interlamellar cavitation'. On the other hand, lamellae parallel to the loading direction were cleaved where they intersected the deformation zones. A detail from a region that had undergone interlamellar cavitation is shown in Fig. 11(b). Fibrillar texture is visible between the dominant lamellae in this micrograph, this presumably having resulted from drawing of the interlamellar material (including any secondary lamellae present). The lamellae perpendicular to the stress axis also showed some fragmentation within the deformed regions. This was thought to be at least partly due to the development of localised shear stresses within the lamellae in the presence of the voids, leading to what is sometimes referred to as `block slip' [18,19]. However, as will be seen later, close examination of the base of micro-necks in the relatively coarse ®brillar deformation zones observed at higher K indicated block slip not to be contingent on interlamellar voiding. Fig. 11(c) is less typical of the deformation in this specimen, but of interest in that the cavitation was relatively coarse (region (i), for example) owing to the local agglomeration of carbon black particles visible in the micrograph. The ®ne interlamellar ®brillation seen in Fig. 11(b) is present elsewhere in this micrograph (region (ii)). At the fracture surface, shown in Fig. 11(d), extensive fragmentation of lamellae by block slip or cleavage was visible, the lamellae being almost entirely reduced to small, roughly equiaxed fragments. This is often assumed to be a precursor to craze formation in semicrystalline polymers [20]. However, in Fig. 11(d) fracture intervened locally before the network of lamellar fragments and interlamellar ®brils was able to develop into the drawn ®brillar structure implicit in most de®nitions of crazing. Fig. 12 shows deformation in a PEB specimen taken from an extruded pipe and tested under the same conditions as the specimen in Figs. 9±11. In this case, the specimen failed after 1175 h, indicating a somewhat reduced resistance to SCG compared with that of the compression moulded sheets. Fig. 12(a) shows a detail from a deformation zone in which both lamellar block slip (region (i) for example) and lamellar cleavage (region (ii)) were particularly apparent. Fig. 12(b) shows a section through the fracture surface itself from about 1 mm ahead of the notch, showing somewhat more extensive deformation than in Fig. 11(d). C.J.G. Plummer et al. / Polymer 42 (2001) 9551±9564 9559 Fig. 11. TEM of a section through part of the fracture surface of a PEB specimen tested at s i ˆ 3 MPa and Ki ˆ 0:12 MPam1=2 in Igepal: (a) overview; (b) localised interlamellar cavitation behind the fracture surface; (c) region of relatively diffuse deformation behind the fracture surface, showing both relatively coarse cavitation (i) and ®ner interlamellar cavitation (ii); (d) detail of deformation at the fracture surface (tensile axis as indicated by the arrows). Fig. 12. TEM of a section through part of the fracture surface of an extruded PEB specimen tested at s i ˆ 3 MPa and Ki ˆ 0:12 MPam1=2 in Igepal: (a) detail of deformation in behind the fracture surface; (b) detail of deformation at the fracture surface (tensile axis as indicated by the arrows). 9560 C.J.G. Plummer et al. / Polymer 42 (2001) 9551±9564 Fig. 13. TEM of a sections through the fracture surface of a PEB specimen tested at s i ˆ 5:4 MPa and Ki ˆ 0:23 MPam1=2 in Igepal: (a) deformation behind the fracture surface close to the notch; (b) detail from close to the notch showing interlamellar cavitation; (c) coarse ®brillation close to the centre of the fracture surface; (d) detail of deformation at the base of one of the ®brils shown in (c) (tensile axis as indicated by the arrows). A relatively mature ®brillar structure (albeit buckled) is visible in the bottom right hand corner of this ®gure, thought to re¯ect the craze formation mechanism referred to above. Fig. 13 shows deformation in a compression moulded PEB specimen tested in Igepal at s i ˆ 5:4 MPa and Ki ˆ 0:22 MPam1=2 ; which failed after 210 h. In this case, the ®brillar deformation was globally much coarser than in the same grade tested in Igepal at Ki ˆ 0:12 MPam1=2 : Fibrillation on the scale of the lamellar texture and occasional stable zones of interlamellar cavitation were visible close to the notch tip, as shown in Fig. 13(a) and (b). However, towards the centre of the fracture surface for Ki ˆ 0:22 MPam1=2 the texture was more reminiscent of that seen in PEA and PEB tested in air. This is shown in Fig. 13(c); although the ®brillar structure had collapsed after unloading in this case, ®brillation was clearly on a scale much greater than that of the initial lamellar texture. The early stages of lamellar deformation were particularly evident at the base of the larger ®brils in this specimen. Fig. 13(d), for example, shows the block slip of the dominant lamellae in the absence of local interlamellar cavitation referred to in the context of Fig. 11. The behaviour of PEA tested in Igepal at s i ˆ 3:1 MPa and Ki ˆ 0:13 MPam1=2 was again similar to that of PEA and PEB tested in air. There was substantial necking prior to ultimate failure, which occurred after 10 h, and, as shown in Fig. 14, severe cavitation behind the neck at the centre of the fracture surface. The peripheral region of ®brillar deformation was very similar to that in Fig. 5, for example, with progressively ®ner ®brillation towards the notch tip. TEM nevertheless con®rmed the stable interlamellar cavitation characteristic of PEB deformed under these conditions to be absent. It should be mentioned for completeness that the specimen shown in Fig. 14 was not carbon black ®lled. However, with the exception of isolated regions of localised damage such as that shown in Fig. 11(c), the nature and C.J.G. Plummer et al. / Polymer 42 (2001) 9551±9564 9561 Fig. 14. Overview of the fracture surface of a PEA specimen tested at s i ˆ 3:1 MPa and Ki ˆ 0:13 MPam1=2 in Igepal: (a) transmitted light OM of a section through the ®brillar region; to save space, two contiguous parts of the section are shown side by side; the top left-hand corner of the ®gure corresponds to the interior of the fracture surface and the bottom left-hand corner includes the notch tip, indicated by the arrow; (b) SEM of the fracture surface, with the notch tip indicated by the arrow. extent of microdeformation were not observed to be correlated with the presence of the ®ller particles. 4. Discussion The deformation induced structures at the crack tip described in the previous section varied considerably in scale, ranging from diffuse zones of interlamellar deformation with ®bril dimensions roughly commensurate with the lamellar spacing (or thickness) of about 10 nm, to craze-like deformation zones with ®bril diameters of 0.1 mm or more. Indeed the central macroscopic necks observed in all the specimens may be considered to represent the limiting 9562 C.J.G. Plummer et al. / Polymer 42 (2001) 9551±9564 case of the trend towards coarser ®brillation at higher stresses. The applied stress is also known to in¯uence the craze ®bril spacing in glassy polymers, this having been interpreted in terms of a unique surface instability mechanism for ®bril formation [21,22]. However, the extended range of ®bril diameters and spacings observed during SCG in HDPE suggests that it may be more realistic to consider ®brillation in this case to involve two or more distinct damage mechanisms, as will be described in what follows. Moreover, the smallest ®bril diameters were associated with relatively low K in the present tests, whereas the opposite is generally true of craze ®brils in glassy polymers [22]. The characteristics of the different regimes of SCG described in the previous section may be summarised in more detail as follows: 1. In the peripheral regions of the fracture surfaces of compression moulded PEB tested at Ki ˆ 0:12 MPam1=2 in Igepal, SCG occurred via breakdown of interlamellar ®brils, after widespread interlamellar voiding. 2. In the central regions of the fracture surface of PEB (where K . Ki) tested at Ki ˆ 0:12 MPam1=2 in Igepal and the outer regions of the fracture surface of the same grade tested at Ki ˆ 0:22 MPam1=2 in Igepal, widespread interlamellar voiding occurred, but the interlamellar ®brils initially remained relatively stable with respect to crack formation. Continued drawing of material containing fragmented lamellae and interlamellar voids led to craze-like structures prior to fracture. This type of deformation has also been observed in the periphery of the fracture surfaces of specimens of a medium density PE (MDPE) tested at Ki ˆ 0:12 MPam1=2 in Igepal, and whose resistance to SCG was intermediate between that of PEA and PEB [23]. 3. Coarse ®brillation was seen at the centre of the fracture surfaces of PEB tested at Ki ˆ 0:22 MPam1=2 in Igepal, in the periphery of the fracture surfaces of PEA tested at Ki ˆ 0:12 MPam1=2 in Igepal and in the periphery of the fracture surfaces of PEA and PEB tested in air at Ki ˆ 0:2 and 0.25 MPam 1/2. It was assumed to result from ®brillation by breakdown of the interlamellar material without prior interlamellar voiding. This was inferred from both the lack of lamellar fragmentation and the lack of interlamellar voiding beyond the interface between the main damage zones and the surrounding material. The voids became coarser as K increased, leading to morphologies in which the deformed matrix ligaments formed continuous sheets rather than ®brils, and eventually to macroscopic necking. The sequence of mechanisms, sketched in Fig. 15, or the preponderance of a given mechanism, will be governed by the K dependence of the various processes involved. Fig. 16 provides a qualitative representation of the competition Fig. 15. Schematic of the proposed damage mechanisms as a function of K. between these different mechanisms as a function of Ki, based on the above observations. The time to yield increases rapidly as the global stress falls below the short-term yield stress, which is represented by an equivalent K value, Ky. The appearance of interlamellar cavitation in the PEB grade at relatively low K after long times is assumed to re¯ect a relatively strong strain rate dependence of the local stress required for cavitation. The effective stress for interlamellar ®brillar breakdown is therefore taken to be greater than that for interlamellar cavitation at long times, although the curves for the respective mechanisms presumably cross over at some intermediate time, as suggested in Fig. 16. The crossover of the curves for cavitation and interlamellar ®brillar breakdown corresponds to the onset of the regime of coarse ®brillation. In this regime, breakdown of the interlamellar regions prior to macroscopic necking is not thought to lead to immediate macroscopic failure for two reasons. First, the onset of the instability depends on the local lamellar orientation and second, the accompanying changes in the local stress state may promote plastic deformation rather than further rupture. A synergy between local drawing and decohesion (by chain scission or by disentanglement) is also implicit in some current models for crazing in amorphous polymers [22,24]. Hence if breakdown of interlamellar material in HDPE under the present conditions results from disentanglement, as has often been suggested in the past [7,25], there is a strong analogy between this mode of deformation and disentanglement crazing in glassy polymers [24,26,27]. Both modes of deformation are favoured over bulk necking by high temperatures and long times (or low strain rates). Indeed, at temperatures just below Tg, modes of diffuse local cavitation have also been identi®ed in certain glassy polymers, these sometimes being referred to as `intrinsic crazing' [28]. At higher stresses, however, where HDPE becomes very unstable with respect to the formation of large voids, a better analogy might be with a rubber toughened system in which the second phase undergoes extensive cavitation. In the case of an unmodi®ed semicrystalline polymer, microstructural features such as C.J.G. Plummer et al. / Polymer 42 (2001) 9551±9564 Fig. 16. Schematic of the proposed relative load-time dependence of the basic damage mechanisms of SCG in HDPE. A sample loaded relatively rapidly (loading line (i)) will reach its macroscopic yield stress ®rst and undergo macroscopic necking, with ultimate failure occurring by ductile tearing. Loading line (ii) ®rst intercepts the load-time curve for breakdown of interlamellar ®brils, but this process can only initiate after formation of interlamellar voids at a somewhat higher load, leading to an instability and coarse ®brillation as described in the text, as will any load line within the hatched region. Loading line (iii), on the other hand, intercepts the loadtime curve for interlamellar cavitation ®rst and stable zones of interlamellar cavitation are therefore expected to be present behind the fracture surface. Also, if the load at which breakdown of interlamellar ®brils occurs is well below the yield stress, there will be little further drawing down of these zones prior to ultimate failure. the spherulite diameter or local ¯uctuations in the lamellar orientation presumably determine the void distribution. In SCG in polyoxymethylene (POM), for example, in which similar mechanisms have been evoked to account for the formation of ®brillar damage zones, ®bril diameters at intermediate K are thought to be linked to local correlations in the lamellar trajectories on a scale of about 10 lamellar thicknesses, giving a stacked lamellar morphology [25]. Stable interlamellar cavitation was not seen in specimens of the PEA grade under any of the conditions investigated here. To explain this, it is reasonable to invoke the absence of the long, branched chains thought to be characteristic of the high molar mass fraction of the PEB grade. This is expected to reduce the resistance of the interlamellar material to breakdown by disentanglement, so that the corresponding curves should be displaced as shown in Fig. 16. (It is unclear whether zones of stable interlamellar ®brillation are totally suppressed in PEA, since data are still lacking for the behaviour in the low Ki limit for this material in Igepal.) There is less reason to suppose a priori the molecular weight distribution to have a dominant in¯uence on interlamellar cavitation, which occurs at more local length scales and is hence expected to be primarily dependent on factors such as the effective cohesive energy density, for example [29]. The resistance to SCG itself is not necessarily directly linked to interlamellar cavitation, but the ultimate breakdown of all types of ®brillar or necked 9563 structure will also re¯ect the instability of the interlamellar material. The above discussion is based on the assumption that the specimens tested in Igepal did indeed re¯ect the limiting behaviour at low K in air. Up to now we have not been able to provoke the formation of stable regions of interlamellar cavitation in PEB in air under creep conditions. However, in studies of microdeformation during accelerated testing by fatigue loading [30], very similar structures to those in Fig. 11 have been observed close to the notch tips of PEB tested at low Ki. They are therefore not uniquely a consequence of Igepal. G'Sell et al. have also reported similar changes to be associated with a transition to continuous SCG in fatigue experiments on PEA with Kmax < 0:2 MPam1=2 ; the continuous regime again being characterised by relatively smooth fracture surface [31]. The transition from interlamellar cavitation to coarse cavitation observed in the PE4 specimen tested in Igepal at high Ki, also shows that both mechanisms may occur in the same specimen under suitable conditions. Igepal therefore does not necessarily lead to stable interlamellar ®brillation in PEB, depending on the effective value of K. 5. Conclusions In notched HDPE specimens subject to static loading, high stress, short-term failure is initiated by yielding across the whole of the load-bearing ligament, accompanied by coarse cavitation in the specimen interior. As K decreased, there was a transition to SCG, characterised by the formation of a ®brillar crack tip damage zone. The ®brils became progressively ®ner as K decreased further, and in notched specimens of a relatively tough, 3rd generation pipe grade tested for about a month at 808C in Igepal at low Ki, the fracture surfaces appeared smooth, crack propagation being associated with localised interlamellar cavitation. The existence of zones of stable interlamellar cavitation behind the main crack front was assumed to re¯ect the relative stability of the interlamellar ®brils in this grade under these conditions. (It may prove to be more appropriate to refer to cavitation or ®brillation between dominant lamellae here, but this point has not yet been explored fully.) Direct interlamellar breakdown without prior cavitation has been argued to be at the origin of coarser cavitational mechanisms observed in a less resistant 1st generation pipe grade under the same conditions, and in both the 1st and the 3rd generation pipe grades tested in air at higher loads. The difference in behaviour of the two grades was attributed to the relative ease of disentanglement in the 1st generation pipe grade. The present work is nevertheless based on a relatively limited number of specimens tested under a limited range of conditions, and certain of the above hypotheses require con®rmation by more extensive testing. In particular it would be interesting to look at the long-term behaviour in 9564 C.J.G. Plummer et al. / Polymer 42 (2001) 9551±9564 Igepal of the 1st generation pipe grade at relatively low Ki, in order to investigate the eventual presence of stable interlamellar cavitation. It would also be interesting to examine in more detail any eventual microstructural differences between the different grades in the light of their different microdeformation behaviour (segregation of different molar mass fractions and the dominant-secondary lamellar structure). Moreover, the question of the fundamental reasons for accelerated crack growth in the presence of Igepal has not been addressed. This would clearly be necessary in any attempt to establish a ®rm link between accelerated and unaccelerated crack growth behaviour. Nevertheless, identi®cation of the relevant damage mechanisms and their dependence on K represents an important step in this direction. Acknowledgements We acknowledge the ®nancial support of Solvay Polyole®ns Europe, Belgium throughout this work and the technical support of the Interdepartmental Centre of Electron Microscopy of the EPFL. References [1] Scheirs J, BoÈhm LL, Boot JC, Leevers PS. Trends Polym Sci 1996;4:408. 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