Alternative accelerated and short-term methods for evaluating slow crack growth in polyethylene resins with high crack resistance

Accepted Manuscript Alternative accelerated and short-term methods for evaluating slow crack growth in polyethylene resins with high crack resistance Nuria Robledo, Carlos Domínguez, Rafael A. García-Muñoz PII:

S0142-9418(17)30793-6

DOI:

10.1016/j.polymertesting.2017.07.022

Reference:

POTE 5102

To appear in:

Polymer Testing

Received Date: 14 June 2017 Revised Date:

0142-9418 0142-9418

Accepted Date: 20 July 2017

Please cite this article as: N. Robledo, C. Domínguez, R.A. García-Muñoz, Alternative accelerated and short-term methods for evaluating slow crack growth in polyethylene resins with high crack resistance, Polymer Testing (2017), doi: 10.1016/j.polymertesting.2017.07.022. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

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Alternative accelerated and short-term methods for evaluating slow crack growth in polyethylene resins with high crack resistance

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Nuria Robledo1,2, Carlos Domínguez1,2*, and Rafael A. García-Muñoz1,2*

LATEP, Polymer Technology Laboratory, Rey Juan Carlos University, Tulipán St., 28933 Móstoles, Madrid, Spain

GIQA, Group of Environmental and Chemical Engineering, ESCET, Rey Juan Carlos

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University, Tulipán St., 28933, Móstoles, Madrid, Spain

*Corresponding author.

E-mail address: [email protected] E-mail address: [email protected]

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Abstract The current market has widely adopted the new polyethylene pipe grade PE 100 RC (resistant to cracks) for pipe applications. However, the main drawback of this material is

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the long test period (~10,000 hours) required for ranking the resins. This paper proposes a modified Pennsylvania edge-notch tensile (PENT) test with higher load and temperature conditions (2.8 MPa and 90 °C). With the modified PENT test, failure time is six times shorter but slow crack growth is maintained. Additionally, it evaluates and finds an unexpected relationship between the strain hardening modulus and specimen thickness.

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These results suggest that the 0.30-mm thickness recommended by ISO 18488 is not optimal. Therefore, thicker specimens are proposed for accurate strain hardening modulus

the new polyethylene pipe grades.

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determination. Both methods are viable alternatives for evaluating the failure resistance of

Keywords: PENT test, strain hardening modulus (SH), polyethylene, slow crack growth

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(SCG)

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1. Introduction Slow crack growth (SCG) is a key failure mode affecting polyethylene (PE) pipes. Under a relatively low stress level and after a certain amount of time, polyethylene pipes suffer a

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specific brittle failure, progressing from craze formation to subsequent propagation and ending in material failure [1, 2]. However, the introduction of bimodal and multimodal polyethylene resins, with a comonomer distribution in the high molecular weight region, has considerably improved the SCG resistance [3-5]. These new resins are more resistant to stress cracking because of recent modifications and improvements, especially with the

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introduction to the market of the high-resistance polyethylene grade PE 100 RC. However, this significant technological advancement presents challenges for conventional long-term

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SCG determination tests. SCG failure times have increased dramatically up to values of around 10,000 hours (almost one year) when using common tests such as the full notch creep test (FNCT), Pennsylvania edge-notch tensile (PENT) test, notch pipe test (NPT), and point loading test (PLT). With such a long time span, the thermal-ageing effect may seriously influence the resin failure process, preventing slow crack growth from controlling the failure mechanism. Therefore, alternative test methods that speed up the standard long-

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term methods should be sought for evaluating slow crack growth, while ensuring that brittle failure, not ductile failure or thermal ageing, controls the failure mechanism. Newly developed alternative methods reduce the long failure times in evaluating SCG

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resistance by modifying test parameters (e.g., geometry, stress, and temperature) and thus accelerating the assay [6]. The standard conditions for the PENT test are 2.4 MPa and 80 °C. We proposed modifying certain PENT test parameters to speed up the determination of

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stress-cracking resistance. Depending on the applied stress (σ), the polyethylene resins may experience brittle, ductile, or mixed failure. Brittle failure belongs to the region below the critical stress value (σc), where the material fails following slow crack growth. Slow crack growth is a thermally active process, and the failure time is generally reduced when the temperature is increased. It is necessary to find the optimal temperature conditions (above 80 °C to accelerate failure time) and degree of stress under which the failure is still brittle. We thoroughly studied all of these factors in a previous work [7], and the results suggested that a temperature increase up to 90 °C prompted the brittle failure mechanism, similar to

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that obtained for 80 °C. Additionally, a more severe loading condition of 2.8 MPa led to an SCG process under the brittle failure mode but significantly reduced the failure time. The failure surfaces were tested at different temperatures to confirm whether, under these conditions, the main failure mechanism was still slow crack growth. With modified

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parameters, failure time is six times shorter than with the standard conditions defined by the ASTM F1473 PENT test. However, at least two months are needed to ascertain the slow crack growth of some resins.

In recent years, methods such as the natural draw ratio (NDR) [8-10] and the strain

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hardening (SH) modulus () have been developed based on short-term mechanical properties. The main advantage of both methods is that they significantly reduce the stress

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crack resistance evaluation time to a few hours. Both methods were correlated with the failure time according to standard SCG tests, such as PENT, FNCT and environmental stress crack resistance (ESCR). However, several works reported that the strain hardening modulus correlates better with the PENT test than with the NDR [11].The strain hardening modulus methodology (ISO 18488) analyses the last part of the stress–strain curve further above the natural draw ratio region [12] to simulate the fibrillar condition developed in

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craze formation [13-15]. This procedure correlates well with SCG tests (e.g., FNCT or PENT), and is thus a feasible method for ranking materials according to their short-term SCG performance, while using a small amount of material [16]. The strain hardening modulus method has gained acceptance by the scientific community and companies, with

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many research groups studying the approach [17-20] and extending its use to other pipe materials, such as polypropylene [19].

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This study evaluates slow crack growth using the PENT test, a standard SCG test reported in ASTM F1473. However, this is a modified PENT test: the influential parameters of applied stress and temperature were changed in order to quickly evaluate stress-cracking resistance but without altering the brittle failure mechanism characteristic of slow crack growth. The SCG evaluation time was six times shorter with the modified PENT test. In addition, the strain hardening modulus was evaluated as an alternative to conventional long-term methods, but again we modified several physical variables to determine the best experimental conditions and correlations with conventional SCG tests. Thus, the strain rate

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and specimen thickness were compared with the standard parameters adopted by ISO 18488. Both variables were proved to significantly influence the strain hardening modulus value determination; therefore, the specimen thickness recommended by ISO 18488 is not

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the optimal value.

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2. Experimental 2.1.Materials This work studied 14 commercial PE 80, PE 100, and PE 100+ polyethylene grades, all of

bimodal molecular weight distribution. 2.2.Pennsylvania edge-notch tensile (PENT) tests

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which were ethylene-1-butene copolymers based on a Ziegler–Natta catalyst and with

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To perform the PENT tests, 10-mm-thick plaques were compression-moulded in a hydraulic press at 180 °C with a nominal pressure of 200 bars. Afterwards, they were cooled slowly for 5 hours at a rate of approximately 0.5 °C/min until reaching room

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temperature. During the cooling stage, the pressure was decreased naturally in accordance with ASTM F1473. Specimens of 50 × 25 × 10 mm were machined from the plaques, followed by notches slowly pressed into the specimen by a razor blade at a speed of about 200 µm/min. Side notches of 1.0 mm and a front notch of 3.5 mm were made according to ASTM F1473.

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This study evaluated the standard PENT test and a modified PENT test. The standard PENT test was developed by Norman Brown et al. [21] and later standardised in ASTM F1473 and ISO 16241; its established conditions are 2.4 MPa and 80 °C. For the modified

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PENT test proposed by our group [7], the conditions were 2.8 MPa and 90 °C. 2.3.Strain hardening modulus determination

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The strain hardening modulus is easily determined from a simple uniaxial tensile test at 80 °C and was performed according to ISO 18488. The test was performed in a universal testing machine (INSTRON 5565) with a 500 N load cell, and the elongation was determined using a video extensometer (INSTRON 2663-822). The samples were compression-moulded to a sheet with a hydraulic press at 180 °C and a nominal pressure of 200 bars, and the cooling rate was 15 °C/min, as per ISO 1872-2. After pressing, the samples were annealed for 1 hour at 120 °C and then slowly cooled to room temperature. Dumbbell-shaped specimens were punched from the pressed sheets, and the initial distance between the gauge marks on the centre of the test specimen was approximately 12.5 ± 0.1

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mm. Two sheets were pressed, one 0.30 + 0.05/-0.03 mm thick (ISO 18488) and the other 2.0 ± 0.1 mm thick. The laboratory device used to measure the thickness had the required accuracy (0.005 mm). This device is usually controlled using certified calibration standards in the range of the thicknesses studied. According to ISO 18488, the strain rate is 20

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mm·min−1, but for this study we applied two additional strain rates, 3 mm·min −1 and 10 mm·min−1. For some polymers, we also tested specimens with additional thickness values. 2.4.WAXS measurements

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We obtained wide-angle X-ray scattering (WAXS) diffractograms of the samples at room temperature using a Bruker Microstar rotating-anode generator with a copper target. WAXS patterns were recorded using a Mar345 dtb image plate with a resolution of 3450 × 3450

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pixels and 100 µm/pixel, using a sample-to-detector distance of 200 mm. The experimental data were corrected for X-ray absorption and background scattering. The patterns were

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analysed using FIT2D software.

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3. Results and discussion 3.1.Modified PENT test Four principal variables influence the PENT test: specimen geometry, notch depth, load and temperature. In this study, we did not modify geometry and notch depth, because they were

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the focus of previous studies and were necessary to maintain the plane-strain conditions that favour brittle failure. However, we did modify applied stress and temperature and then studied the results for the 14 polyethylene grades.

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All polyethylene resins underwent the standard PENT test (2.4 MPa, 80 °C) and the modified PENT test (2.8 MPa, 90 °C). Figure 1 shows a good linear fit between both tests for a wide range of materials, from PE 80 to PE 100+. The sample failure times ranged

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from 20 to 8,000 hours using the standard PENT test. Using the modified PENT test, the stress-cracking failure times for all resins were six times shorter. In all cases, the fracture surfaces showed a fibrillar morphology in which slow crack growth is the dominant process. Thus, the ageing or melting processes are negligible, and the failure mechanism is ruled by slow crack growth, at least up to the maximum failure time obtained (8,000 hours at 80 °C and 1,500 hours at 90 °C). Table 1 summarises the results according to the time

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reduction achieved for the different material specifications. Note that the modified PENT test significantly reduced failure time, even with high-resistance materials such as PE 100+ and PE 100 RC resins. Thus, the evaluation of the materials’ stress-cracking propagation

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was achieved in a reasonable time, confirming that the modified PENT test reliably predicts

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SCG performance.

3.2.Strain hardening modulus test This section examines the strain hardening modulus for 14 different resins as an alternative investigative test of SCG performance. Using the protocol described in ISO 18488, the strain hardening modulus () can be determined from the true stress–true strain curve and the neo-Hookean constitutive model, considering the final part of the curve between λ = 8 and λ = 12.

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Several authors [12, 17, 22-24] have reported a good relationship between the strain hardening modulus and the FNCT, ESCR and NPT methods. Therefore, different types of polyethylene pipe materials were ranked according to their respective SCG performance. The strain hardening modulus results were compared with those of the PENT test. Figure 2

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shows the failure times of several HDPE pipes; these results were obtained with the standard PENT test and modified PENT test versus the strain hardening modulus () with the ISO 18488 standard conditions (temperature: 80 °C; specimen thickness: 20 mm·min−1 and 300 µm). PENT determination and strain hardening modulus determination

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were compared at 80 °C to remove the temperature factor, and all 14 resins showed good correlation between the PENT test and strain hardening modulus. Figure 2 shows that the

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standard PENT test and the modified PENT test both have the same relationship with the strain hardening modulus. These results indicate that the modified PENT test conditions align with those of the standard PENT test, but failure time evaluation was six times shorter. Therefore, with the modified PENT test conditions, the resins could be evaluated in one to two months instead of the one-year period required by the standard PENT test. Other researchers have calculated the strain hardening values using this same protocol but

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with modified specimen geometry or modified test conditions [12, 25]. In the next section, the strain hardening test conditions (e.g., strain rate and specimen thickness) are discussed in greater depth, and we rank materials and correlate them with the conventional tests to

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promote the strain hardening modulus as a good evaluator of SCG performance. Effect of strain rate

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Strain rate is known to significantly affect a material’s mechanical properties [26-29]. In the stress–strain curves of the material, as the strain rate increases, the stress also increases and the strain at break decreases. The strain hardening modulus, determined from the slope at the final part of the stress–strain curve, also increases. During the tensile test, the polymer undergoes orientation and relaxation processes. Depending on the strain rate, one process is favoured over the other. As the strain rate increases, the orientation process is favoured, and the strain hardening modulus increases. The polymer does not have enough time for the relaxation process, and, consequently, the

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entanglement density increases. As a result, the strain hardening modulus also increases because it is proportional to the entanglement density [26, 27, 30]. On the other hand, slower strain rates favour the relaxation process, and lower strain hardening moduli are

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obtained. Figure 3 shows the relationship between the PENT test failure time and the strain hardening modulus for 14 different polyethylenes (PE 80, PE 100, and PE 100+). Measurements were performed at a different strain rate and specimen thickness to compare them with the values

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proposed by ISO 18488 (i.e., a 20 mm·min −1 strain rate and 0.3 mm specimen thickness). Regardless of the strain rates chosen, the PENT test failure time and strain hardening modulus values adjust well to a linear fit regression. The slopes and correlation coefficients

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are similar for all strain rates, but the strain hardening modulus values are remarkably different. Increasing the strain rate from 3 mm·min−1 to 10 mm·min−1 and then to 20 mm·min−1 yields a strain hardening modulus value increment of 20% or higher. At 20 mm·min−1, the strain hardening modulus is the highest value obtained. According to these results, the calculation of the strain hardening modulus must take into account the tensile

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test speed.

Figures 3a and 3b show the influence of specimen thickness on the strain hardening modulus value. Thicker specimens have better repeatability and less scatter than thinner ones. Thicker specimens improved the test repeatability by reducing the distortions caused

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by specimen imperfections and inhomogeneities during the drawing process [31]. Although there are no reported studies on the influence of thickness, our results indicate that clear

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differences can be established. When the specimen is thinner (e.g., 0.30 mm), the strain hardening modulus value slightly increases, giving a poorer correlation coefficient because of greater scatter.

Effect of thickness

This section evaluates the influence of specimen thickness. For this, it is essential to perform the measure with an accuracy of ± 0.005 mm, as the ISO 18488 standard indicates.

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Three different polyethylene grades, PE 80, PE 100 and PE 100+, were analysed. For each polyethylene resin, thickness values from 0.30 mm to 3.0 mm were tested. All experiments applied constant strain rates of 20 mm·min−1. To calculate the strain hardening modulus mean value for each thickness, at least seven independent specimens were tested. Figure 4

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shows that, for the PE 100+ resin at low draw ratios, the same curve trend is independent of the specimen thickness. However, significant differences are established in the upper region where the strain hardening modulus is calculated. Figure 4 also shows that, as specimen thickness increases, the resin can reach higher strain before breaking, while the strain

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hardening modulus value decreases. If the strain rate remains constant and the relaxation process is the same for all materials, then, as mass increases (i.e., the specimens are

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thicker), the strain hardening modulus decreases. The strain hardening modulus was calculated for thickness values from 0.15 mm up to 3.3 mm. Figure 5 shows the strain hardening modulus variation for the three different polyethylene grades tested (PE 80, PE 100,and PE 100+). The results indicate that increases as specimen thickness increases.

For the three resin grades, the representation of the strain hardening modulus versus

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specimen thickness fits well on an asymptotic curve. As specimen thickness increases, the curve reaches a plateau and the strain hardening modulus hardly declines. Consequently, the dependence between thickness and the strain hardening modulus is negligible for thickness values above 1.0 mm. However, the most significant decrease is observed at

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smaller specimen thicknesses (less than 1.0 mm), and this trend is apparent in all resins studied. ISO 18488 establishes thickness values of 0.30 mm or 1.0 mm, but our results

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indicate that this range of specimen thickness values is where the differences in the strain hardening modulus become apparent. To verify whether the observed decrease is statistically significant, an ANOVA was performed to compare the strain hardening mean values as a function of specimen thickness. All the samples fulfil the homoscedastic criterion, checked through an F test, which is necessary for performing an ANOVA test. A one-way ANOVA test was calculated for each pair of samples. The null hypothesis H0 in the ANOVA test states that there is no difference in means; that is, all samples came from populations with the same mean. Table 2 presents the statistical results, but to simplify,

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only the results for specimen thickness values of 0.30 mm and 1.0 mm are shown. In all cases, an ANOVA test produced a p-value below 0.05, thus rejecting the null hypothesis H0. This indicates that, with 95% confidence, the sample comes from different populations and finds a dependence between the strain hardening modulus and specimen thickness.

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However, when thicker specimens are compared (1.0 mm and 2.0 mm), the differences between the strain hardening modulus values are minimal, and the p-value is very close to the critical value of 0.05. This implies that the strain hardening value does not clearly depend on thickness at this range of thickness.

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ISO 18488 indicates that, in dispute cases, the 0.30 mm thickness shall be used. However, according to our results, 0.30 mm is not the optimal thickness value. For thickness values

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greater than 1 mm, the dependence of the strain hardening value with thickness becomes negligible and the test repeatability improves.

Smaller thickness values demonstrate a clear correlation between thickness and the strain hardening modulus. What causes these differences? Specimen orientation is known to improve the strain hardening and reduce elongation at break [32, 33]. The specimen is

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annealed to remove any orientation or thermal history and to maintain isotropic sheets. However, because the annealing process runs for only 1 hour, this may not be long enough to completely remove the orientation, and these oriented segments could act as nucleating agents, thus promoting a higher degree of orientation in these materials.

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To investigate this hypothesis, the three resin grades (PE 80, PE 100, and PE 100+) were analysed. The specimen orientation was studied using the wide-angle X-ray scattering

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(WAXS) technique, which provides valuable information about a specimen’s crystalline morphology [34]. The specimens were measured in three different regions during the tensile test: (i) λ = 1, (ii) λ = 8, and (iii) λ = 12. In brief, (i) is the specimen immediately before the tensile test when it should have a fully isotropic pattern, and (ii) and (iii) are two areas of high deformation. We chose these draw ratio values because they are the limits of the region where the strain hardening modulus is determined. These experiments were performed for samples 0.30 mm and 2.0 mm thick.

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Figure 6 illustrates the room-temperature WAXS diffraction patterns for a PE 100 resin. The WAXS diffraction pattern indicates that the preferential orientation of the lamellar crystals is higher when the draw ratio (λ) value increases but, contrary to expectations, no differences between samples with different thickness values were found. In Figure 6, λ = 1

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shows a clearly unoriented profile and concentric circles for λ = 1 (each circle corresponding to a Bragg reflection), which suggests that the annealing process effectively removed any orientation from the sheets. As elongation increases, the orientation rapidly increases, and a fully developed fibre structure can be observed at λ = 8 and λ = 12.

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The diffraction circles may not have uniform intensity. At these draw ratio levels, the fibrillar orientation is too high to distinguish which WAXS diffraction pattern corresponds

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to λ = 8 and which to λ = 12, an observation also reported in the literature. Different authors have found that the transformation of the initial isotropic profile into a fully developed fibrillar structure in polyolefins is essentially completed by draw ratios between 5 and 9 [33, 35, 36].

Herman’s orientation function (fH) is the best way to quantify the molecular orientation

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degree [37]. To see the molecular chain orientation, the corresponding azimuthal scan of the (110) and (020) reflections have been analysed. Herman’s orientation function (fH) was determined from the integration of intensity over the azimuthal angles. However, the results were not relevant, finding no differences between the two sample sets. In all cases, at λ = 1

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the value of Herman’s function (fH) was close to 0, which corresponds with the typical value of a fully isotropic material, and the individual crystallites were oriented in all directions with equal probabilities. However, for high draw ratios (λ = 8 and λ = 12), the

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value of Herman’s function was close to −0.5, which is a limiting value for perfect perpendicular orientation. Figure 6 shows the value of Herman’s function for PE 100. From the WAXS results, we can conclude that specimen thickness does not play a special role in molecular orientation. The higher strain hardening moduli found in the thinner specimens are probably related to the smaller mass of the samples. The specimen can reach a lower strain before breaking and, consequently, obtain a higher strain hardening modulus.

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4. Conclusions This work investigates the SCG resistance of different grades of high-resistance polyethylene resins using a direct test method (the PENT test) and an indirect test (the

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strain hardening modulus). A modified PENT test with more severe conditions of stress and temperature (90 °C, 2.8 MPa) than the standard conditions (80 °C, 2.4 MPa) is a potential alternative for evaluating the SCG resistance of polyethylene resins. The modified PENT test is especially useful for high-resistance polyethylene grades, because it eliminates the ageing effect observed in the standard PENT test. For the bimodal ethylene-1-butene

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copolymers analysed, the failure time was six times shorter following, in all cases, an SCG failure process.

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On the other hand, the strain hardening modulus proves to be an excellent method for estimating the SCG resistance of polyethylene resins for pipe applications in a simple, precise and reproducible way. The strain hardening modulus method does not require specimen notching and/or surfactants and, therefore, achieves better reproducibility. We extensively investigated the influence of two experimental variables (i.e., tensile test speed

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and specimen thickness) on the strain hardening modulus; both variables proved to have remarkable influence on the strain hardening modulus value. The strain hardening modulus method (ISO 18488) establishes the tensile test at 20 mm·min−1 and the specimen thickness at 0.30 mm or 1.0 mm. Although the standard

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suggests using the 0.30 mm thickness in a dispute case, we proved that 0.30 mm is not the optimal thickness. We propose a specimen thickness greater than 1.0 mm as an alternative

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because, despite an overall strain hardening modulus decrease of around 5% to 10%, the repeatability of the tests could be improved. Nowadays, it is pivotal to define the qualities of polyethylene resins according to their SCG performance. Different methods and alternatives continually emerge to explore and predict the behaviour of polyethylene resins. In this work, an accelerated modified PENT test and a modified strain hardening modulus determination shed light on the unresolved field of polyethylene pipe failure prediction.

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Acknowledgements The authors kindly acknowledge the Repsol Company for providing the materials for this research and the Polymer Technology Laboratory (LATEP) staff from Rey Juan Carlos

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University for the resin characterisation. The authors also kindly acknowledge the Department of Crystallography (Instituto Química-Física ‘Rocasolano’, CSIC) for providing the facilities to conduct the wide-angle X-ray diffraction experiments. We are also indebted to Dr. Araceli Flores (Instituto de Estructura de la Materia, CSIC) for the

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equipment training.

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[19] R. Steenbakkers, L. Havermans, P. Voets, J. Rabiei, R. Deblieck, Strain hardening modulus: A measure for ranking time to failure of random polypropylene pipe materials, Plastic Pipes XVIIIBerlin, Germany, 2016. [20] C. Dominguez, N. Robledo, R.A. Garcia, Limits on the slow crack growth resistance evaluation for the PE100 and PE100RC polyethylene resins, Plastic Pipes XVIIIBerlin, Germany, 2016. [21] X. Lu, N. Brown, A test for slow crack-growth failure in polyethylene under a constant load, Polymer Testing, 11 (1992) 309-319. [22] R.A.C. Deblieck, D.J.M. van Beek, K. Remerie, I.M. Ward, Failure mechanisms in polyolefines: The role of crazing, shear yielding and the entanglement network, Polymer, 52 (2011) 2979-2990. [23] E. van der Stock, F. Scholten, Strain hardening tests on PE pipe materials, Conference Proceedings Plastic Pipes XVIBarcelona, Spain, 2012. [24] J.J. Cheng, M.A. Polak, A. Penlidis, Influence of micromolecular structure on environmental stress cracking resistance of high density polyethylene, Tunnelling and Underground Space Technology, 26 (2011) 582-593. [25] A. Adib, C. Dominguez, J. Rodriguez, C. Martin, R.A. Garcia, The Effect of Microstructure on the Slow Crack Growth Resistance in Polyethylene Resins, Polymer Engineering and Science, 55 (2015) 1018-1023. [26] H.G.H. van Melick, L.E. Govaert, H.E.H. Meijer, On the origin of strain hardening in glassy polymers, Polymer, 44 (2003) 2493-2502. [27] R.S. Hoy, M.O. Robbins, Strain hardening of polymer glasses: Entanglements, energetics, and plasticity, Phys. Rev. E, 77 (2008) 14. [28] J.J. Cheng, M.A. Polak, A. Penlidis, A tensile strain hardening test indicator of environmental stress cracking resistance, Journal of Macromolecular Science Part a-Pure and Applied Chemistry, 45 (2008) 599-611. [29] K. Chen, K.S. Schweizer, Theory of Yielding, Strain Softening, and Steady Plastic Flow in Polymer Glasses under Constant Strain Rate Deformation, Macromolecules, 44 (2011) 3988-4000. [30] M. Wendlandt, T.A. Tervoort, U.W. Suter, Non-linear, rate-dependent strain-hardening behavior of polymer glasses, Polymer, 46 (2005) 11786-11797. [31] A.S. Maxwell, G. Pilkington, Prediction of environmental stress cracking resistance in linear low density polyethylenes, Polymer Engineering and Science, 48 (2008) 360-364. [32] L. Pi, X. Hu, M. Nie, Q. Wang, Role of Ultrahigh Molecular Weight Polyethylene during Rotation Extrusion of Polyethylene Pipe, Industrial & Engineering Chemistry Research, 53 (2014) 13828-13832. [33] D. Milicevic, M. Micic, G. Stamboliev, A. Leskovac, M. Mitric, E. Suljovrujic, Microstructure and Crystallinity of Polyolefins Oriented via Solid-state Stretching at an Elevated Temperature, Fibers and Polymers, 13 (2012) 466-470. [34] I.H. Hall, Structure of crystalline polymers, Elsevier Applied Science Publishers1984. [35] C.P. Lafrance, R.E. Prudhomme, Characterization of the molecular-orientation in highly oriented rolled polypropylene sheets by X-ray-diffraction, Polymer, 35 (1994) 3927-3935. [36] M. Furuta, K. Kojima, Morphological-study of deformation process for linear polyethylene, Journal of Macromolecular Science-Physics, B25 (1986) 349-364. [37] P.H. Hermans, Contribution to the Physics of Cellulose Fibres: A Study in Sorption, Density, Refractive Power and Orientation, Elsevier1946.

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Figure Captions

Figure 1. Modified PENT test (90 °C, 2.8 MPa) as a function of the standard PENT test (80 °C, 2.4 MPa).

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Figure 2. Standard PENT test (80 °C and 2.4 MPa) and modified PENT test (90 °C and 2.8 MPa) failure times versus strain hardening modulus .

Figure 3. PENT test failure time versus strain hardening modulus () at different strain rates and thickness values: (a) 0.30 mm thickness; (b) 2.0 mm thickness.

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Figure 4. True strain–true stress curves for the sample PE 100+ (at 20 mm·min−1) with different specimen thickness values: 0.34 mm (black line), 1.14 mm (red line), and 2.26 mm (blue line). Figure 5. Strain hardening modulus () versus specimen thickness for three different polyethylenes.

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Figure 6. True strain–true stress curves for the sample PE 100 (at 20 mm·min−1) with different specimen thickness values (black line, 0.30 mm; red line, 2.0 mm) and corresponding WAXS patterns at selected draw

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ratio (λ) and Herman’s orientation function (fH).

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Tables

Table 1. Classification of polyethylene (PE) pipe grades

MPa) Minimum failure time >500 h (21 days)

PE 100+

>1000 h (42 days)

PE 470 Plus

>2,000 h (83 days/2.8 months)

PE 100 RC

>10,000 h (417 days/14 months)

Minimum failure time >78 h (3.3 days) >160 h (7 days)

>330 h (14 days)

>1,650 h (69 days/2.3 months)

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PE 100–PE 4710

Modified PENT (90 °C, 2.8 MPa)

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Standard PENT (80 °C, 2.4

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Table 2. Summary of p-values from one-way ANOVA test at 95% confidence level

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PE 100+ (1.0 mm) = 48.5 ± 0.9

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PE 100+ (0.30 mm) = 51.5 ± 1.1MPa

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p-value = 1.367*10−5 H0 is rejected --

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PE 100 (1.0 mm) = 43.5 ± 1.2

PE 100 (0.30 mm) = 47.1 ± 0.6 MPa

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PE 80 (1.0 mm) = 27.3 ± 0.5 MPa

PE 80 (0.30 mm) = 28.7 ± 0.5 MPa p-value = 5.419*10−4 H0 is rejected

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p-value = 2.602*10−4 H0 is rejected

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Figure 3-a

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Figure 3-b

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Figure 6