Nezbedova2001 Article Relationofslowcrackgrowthfailu

Mechanics of Time-Dependent Materials 5: 67–78, 2001. © 2001 Kluwer Academic Publishers. Printed in the Netherlands.

67

Relation of Slow Crack Growth Failure Time to Structure of HDPE E. NEZBEDOVA, J. KUCERA and A. ZAHRADNICKOVA Polymer Institute Brno, Tkalcovska 2, CZ-656 49 Brno, Czech Republic; E-mail: [email protected] (Received 15 March 1999; accepted in revised form 21 January 2000) Abstract. Long-time brittle failure limits the lifetime of polyethylene pipes for water and gas distribution. The same type of failure was observed in single-edge-notched tensile specimens under plane strain conditions. The crack opening displacement (COD) was measured as a function of time and temperature, and the time to complete fracture (tf ) was measured. An empirical failure time extrapolation relation based on temperature was developed using the Arrhenius equation. The experimental and extrapolated data for 80◦ C were found to correlate very well. Using this relation, structural parameters were characterised by the Stepwise Isothermal Segregation/Differential Scanning Calorimetry (SIS/DSC) method. The correlation between fracture and structural parameters was found. Key words: crack growth, PENT test, polyethylene, structure

Nomenclature A Ac COD DSC FST GPC 1H HDPE NPT PE PENT Q R SCB SDR SENT SIS T tf tf † , tf k

= = = = = = = = = = = = = = = = = = = =

stress-frequency factor anisotropy factor for brittle failure crack opening displacement (mm) differential scanning calorimetry full scale test gel permeation chromatography enthalpy of fusion (J·g−1 ) high density polyethylene notch pipe test polyethylene Pennsylvania notch test activation energy (kJ·mol−1 ) gas constant (J·mol−1 ·K−1 ) density of short chain branches (CH3 /1000C) standard dimension ratio, nominal ratio of the outside diameter to the wall thickness single edge notch tensile specimen stepwise isothermal segregation temperature (◦ C) time to failure (min) time to failure for crack growth perpendicular, parallel to the extrusion direction (min)

68

E. NEZBEDOVA ET AL.

1. Introduction The lifetime of plastic pipes is controlled by material, service temperature, defect sizes, environment, and loading factors (Tränker et al., 1996). It is well known (Egan and Delatycki, 1995) that the structure of polymer chains, mainly (a) molecular weight and distribution, and (b) number, type, and distribution of short and long chain branches, are the primary material factors. Further, the structure and morphology of the polymer are influenced significantly by processing (palletising, pipe extrusion). Structure, together with temperature, environment, and loading conditions, determine the type of fracture. Polyethylene can fail at pipe service temperatures under low stresses in a brittle mode after a long period of time. The failure mode is called ‘long-term brittle failure’ (Lu and Brown, 1992). The crack initiation stage and slow crack growth play an important role in determining the lifetime (Tränker et al., 1996; Huang and Brown, 1988). The currently used quality check test for slow crack growth (ISO 13479, 1997) generally takes 1000 hours, after which the test is terminated. Similarly, to qualify a new resin, the conventional hydrostatic pressure test must last 104 hours (ISO 1167). Some accelerated tests, utilising fracture mechanics, have been developed during the last ten years (Lu and Brown, 1992; ISO/TC 138/SC 4N. 144, 1998). The PENT test developed by Lu and Brown (1992) produces the same type of brittle fracture that occurs in pipes after a long time in service. The main aim of this study was to judge the quality of pipes being in service for a long time. The structure of the resin of PE pipes was characterised by the Stepwise Isothermal Segregation/Differential Scanning Calorimetry (SIS/DSC) method (Adison et al., 1992; Nezbedova et al., 1997, 1998) and gel permeation chromatography (GPC) (Nezbedova et al., 1998) in an attempt to link structure with service performance. The PENT test was used to determine the time to failure (tf ) of the resin. Further fracture parameters can be estimated from the crack opening displacement (COD) as a function of time: (i) the time of the beginning of brittle fracture (tb ) as the inflection point of this function, (ii) the minimum rate of COD (min d(COD)/dt) (Nezbedova et al., 1997). Only tf was measured for the purpose of this work. The extrapolation of tf data from higher temperatures to 20◦ C enables one to judge the fracture parameters at temperatures expected in service. 2. Experimental A set of pipes supplied by the Czech Gas Company was investigated. The pipes, having been in service since 1969, had an outside diameter from 40 to 225 mm (SDR 11). Samples taken from the pipe’s surface were analysed by SIS/DSC, some of them also by GPC analysis. The reason for using GPC analysis was to exclude bimodal materials because the SIS/DSC record for bimodal materials is the same as that for the homopolymer with a unimodal distribution (Nezbedova et al., 1998).

RELATION OF SLOW CRACK GROWTH FAILURE TIME TO STRUCTURE OF HDPE

69

Figure 1. An example of a DSC record after using the SIS procedure. The sample taken from a HDPE pipe after ten years in service – sample No. 14.

The SIS procedure is described in detail in Adison et al. (1992) and Nezbedova et al. (1997). The principle of this procedure is the fractionation of the sample during the course of a selected temperature programme. The DSC record (following SIS) gives several peaks according to the number of temperature pauses, which reveals the short branch distribution (Figure 1). The location and the area of these peaks correspond to the average density of short chain branches (SCB) in each individual fraction and to the representation of this fraction in the polymer, respectively. Peak I corresponds to a homopolymer fraction in the polymer and indicates the stiffness of the resin. Too low a content of the homopolymer fraction decreases stiffness, too high a content of the homopolymer fraction supports brittle fracture. Peak II corresponds to a copolymer fraction with a very low content of SCB and a relatively high molecular weight. Peak III corresponds to a copolymer fraction with a higher content of SCB and a medium molecular weight. Fraction IV that crystallised during cooling of the sample to room temperature, consists mostly of low molecular weight chains with a high content of co-monomer. The method of Lu and Brown (1992) was applied to evaluate parameters of ‘long-term brittle failure’. The geometry of the specimens was single edge notch tensile specimen (SENT). The shape and dimensions of the specimens are shown in Figures 2a and 2b. The specimens were machined from the pipes parallel to the extrusion axis (Figure 2a) and perpendicular to the extrusion direction axis (Figure 2b) as recommended in ISO/TC 138/SC 4N. 144 (1998). The notch depth was chosen to minimise the failure time without producing excessive creep on the remaining ligament. The notch was made by pressing a fresh razor blade into the specimen at a constant speed of 330 µm·min−1 . The specimens were conditioned for 40 hours prior to testing. It was found (Lu and Brown, 1992) that a notching speed of less than 500 µm·min−1 does not affect the lifetime.

70

E. NEZBEDOVA ET AL.

Figure 2. The shape and dimensions of specimens machined from a pipe.

The kinetics of the failure process was observed under a constant nominal applied stress of 2 MPa and temperature 80 and 40◦ C, respectively. Only specimens which had the shortest time to fracture at 80◦ C were examined at 40◦ C. The COD was measured with the aid of an optical microscope (Figure 3) in the middle of the notch and measured at the surface of the specimen and at the bottom of the notch. The COD versus time curves measured at the surface and at the bottom of the notch were similar, but a difference in the slope of the initial curve parts was found (Nezbedova et al., 1997). For the purpose of this paper, only the COD measured at the surface of the specimen were considered. The error of this COD measurement was about 2 µm. The testing conditions are important for the following reasons: the temperature of 80◦ C is usually the highest temperature for testing polyethylene, because significant morphological changes occur above 80◦ C. The nominal stress of 2 or 2.4 MPa (recommended by Lu and Brown, 1992) is about the upper limit at 80◦ C for production of the same type of brittle fracture as occurs at room temperature under long-time service conditions. The test under these conditions is one of the quickest for PE in air under constant load. The measurement at two temperatures enables the time to fracture to be extrapolated to other temperatures. The method based on the Arrhenius equation (Equation (1)) was used for this extrapolation. 

 Q tf = A · exp , R · (T + 273◦ C)

(1)

where A is an empirical parameter (called the stress frequency factor) which includes the effect of nominal stress and branch density (Brown and Lu, 1990), Q is the activation energy, T is the temperature in ◦ C and R is the gas constant.

RELATION OF SLOW CRACK GROWTH FAILURE TIME TO STRUCTURE OF HDPE

71

Figure 3. The COD measuring equipment: an open temperature chamber, two specimens in grips, a weight, the microscope with measuring eyepiece, and a lighting optical cable.

3. Results Two parameters for basic structural classification were chosen (Nezbedova et al., 1998): (a) the average density of SCB, and (b) the value of the ratio 1H1 /1H2 , where 1H1 and 1H2 are the enthalpy of fusion connected with the peaks I and II respectively (see Figure 1). The parameter SCB was calculated from the following equation SCB =

4 X 133.2 − Tpeak i i=1

1.6

·

1Hi , 1H

(2)

where Tpeak i is the temperature of fusion of the fraction i (see Figure 1), 1Hi is the enthalpy of fusion connected with the peak i, and 1H is the total enthalpy of fusion. The values of Tpeak i and 1Hi were determined from DSC records with the aid of a peak analysis software. The GPC analysis confirmed that none of the analysed samples was bimodal. The results of the PENT tests are summarised in Table I for 80◦ C and in Table II for 40◦ C, respectively. The times to produce complete fracture (tf ) are designated by tf † and tf k for crack growth perpendicular (axial specimens) and parallel (tangential specimens) to the extrusion direction, respectively. Some typical COD measurements for axial specimens (tf † ) are shown in Figures 4 and 5. As expected, tf † > tf k holds for each pipe because the molecules are generally oriented parallel

72

E. NEZBEDOVA ET AL.

Table I. The specimen dimensions, the structure parameters, the activation energy Q for selected samples, the time to fracture, and the anisotropy factor at 80◦ C. Number Outside SCB 1H1 /1H2 Q Type of Wall Notch tf † Ac = diameter [kJ·mol−1 ] specimen thickness depth tf k tf † /tf k [mm] [mm] [mm] [mm] [min] 1

110

3.98

0.33

–

2

110

2.97

2.43

–

3

110

4.40

2.43

–

4

110

0.46

6.32

65

5

110

2.20

3.72

–

6

110

1.34 10.21

7

110

3.14

8

110

1.26 8.74

65

9

160

1.95 1.74

–

10

160

1.15 4.6

62

11

160

1.66 2.79

–

12

160

1.45 4.41

112

13

160

3.19 3.21

106

14

225

4.27 0.72

–

15

225

4.16 2.27

–

3.38

98 102

ax tn ax tn ax tn ax tn ax tn ax tn ax tn ax tn ax tn ax tn ax tn ax tn ax tn ax tn ax tn

6.01 6.10 6.36 7.56 6.42 6.47 6.45 6.45 6.48 6.56 6.99 6.37 7.10 6.94 7.45 7.40 9.22 9.41 9.31 9.54 9.86 9.39 10.07 10.09 10.24 10.25 13.52 13.41 14.24 14.38

2.52 2.54 2.63 2.94 2.63 2.65 2.65 2.65 2.65 2.68 2.79 2.63 2.80 2.76 2.92 2.89 3.34 3.38 3.36 3.41 3.50 3.38 3.54 3.54 3.57 3.59 4.25 4.23 4.39 4.41

4268 580 269 47 297 122 106 67 122 57 112 25 114 78 84 69 145 139 56 51 374 132 105 70 89 78 33968 16882 246 166

7.36 5.72 2.43 1.58 2.14 4.48 1.46 1.22 1.04 1.10 2.83 1.50 1.14 2.01 1.48

RELATION OF SLOW CRACK GROWTH FAILURE TIME TO STRUCTURE OF HDPE

73

Table II. The specimen dimensions, time to fracture and the anisotropy factor at temperature of 40◦ C. Outside diameter [mm]

Type of specimen

Wall thickness [mm]

Notch depth [mm]

tf † tf k [min]

Ac = tf † /tf k

4

110 110

7

110

8

110

10

160

12

160

13

160

6.57 6.23 6.47 6.77 6.96 6.95 7.68 7.94 9.51 9.90 9.98 9.96 10.42 9.56

2.68 2.57 2.65 2.73 2.79 2.79 2.97 3.02 3.41 3.50 3.52 3.52 3.61 3.43

7294 2973 1442 563 8866 1531 1367 1044 1129 378 14389 4744 10494 4298

2.45

6

ax tn ax tn ax tn ax tn ax tn ax tn ax tn

Number

2.56 5.79 1.31 2.99 3.03 2.44

to the extrusion direction and the crack growth is generally slower in the direction perpendicular to the orientation. The crack growth anisotropy factor based on the lifetime, Ac = tf † /tf k , varies from 1.0 to 7.4 at 80◦ C. This range is wider than that published in Lu et al. (1994) for similar experiments. The range depends on the processing conditions and the grade of the PE resin, and can be affected by small variations in initial crack depth and uniformity. Equation (1) was applied to the experimental data for 80 and 40◦ C. If we suppose that A is temperature-independent, we can calculate Q for each pipe and crack orientation when the tests were conducted at both temperatures. We have taken the time of failure at 40◦ C as the characteristic parameter of a pipe and the crack direction. It was denoted tf (40). When the values of Q are plotted versus ln{tf (40)}, they are well approximated by a straight line (Figure 6) Q = a + b · ln{tf (40)},

(3)

with a = −66.2, b = 18.7 corresponding constants. The stress frequency factor A can be evaluated for each tf (40) applying Equation (1). Plotting A versus tf (40), it was concluded (see Figure 7) that an approximation to a straight line is again reasonable: ln(A) = c + d · ln{tf (40)},

(4)

74

E. NEZBEDOVA ET AL.

Figure 4. An example of COD dependencies versus time at 80◦ C.

Figure 5. An example of COD dependencies versus time at 40◦ C.

where c = 25.44, d = −6.20. Then Equation (1) was rewritten as ln(tf ) = c + d · ln{tf (40)} +

a + b · ln{tf (40)} . R · (T + 273◦ C)

(5)

Equation (5) was used for extrapolation of the time to failure at 20, 40, 60, 80◦ C (Figure 8). The extrapolation was compared with the experimental data measured at 80◦ C for different pipes at both directions. A good correlation in the range of meas-

RELATION OF SLOW CRACK GROWTH FAILURE TIME TO STRUCTURE OF HDPE

75

Figure 6. The dependence of activation energy Q versus the logarithm of time to failure at 40◦ C for different pipes.

Figure 7. The dependence of stress frequency factor A versus time to failure at 40◦ C for different tested pipes.

76

E. NEZBEDOVA ET AL.

Figure 8. The extrapolation of time to failure for different temperatures (straight lines). This is compared with experimental data at 80◦ C.

ured times was found. It seems that for room temperature (20◦ C) and longer times, the extrapolated data are shifted to significantly long failure times. Unfortunately, we have no independent experimental data to confirm this trend. A discussion of this problem was found in Tränker et al. (1996) where the authors concluded that all data at 20◦ C are shifted to significantly longer (factors of 2–10), compared with the experimental data obtained directly at 20◦ C. Correlation between structural parameters and the time to failure is very difficult. We tried to correlate the logarithm of tf to SCB with respect to results published by Brown and Lu (1990). We obtained a more complicated graph (Figure 9). The dependence of tf for 80◦ C is simple for SCB < 3; it can be approximated by a straight line for all values of a second structural parameter 1H1 /1H2 . Above this value, the data split into two branches. The samples with 1H1 /1H2 > 1 (a high share of homopolymer fraction) lie on the original straight line, but the samples with 1H1 /1H2 < 1 (a low share of homopolymer fraction) lie on another branch which represents a substantial increase in time to failure from 500 to 104 min, which agrees qualitatively with results obtained by Brown and Lu (1990).

4. Conclusions • The measured anisotropy factors differed over a wide range (1–7.4) for the pipe material.

RELATION OF SLOW CRACK GROWTH FAILURE TIME TO STRUCTURE OF HDPE

77

Figure 9. The correlation between time to failure tf † (80) and SCB. The enthalpy ratio 1H1 /1H2 serves as a secondary structural parameter.

• The dependence of the activation energy and the stress-frequency factor on the failure parameter tf (40) were evaluated. An extrapolation of failure data was provided on this basis. This extrapolation is in good agreement with the experimental data at 80◦ C in the range of measured times. There is somewhat of an overestimation of failure times at temperatures of 20◦ C and below. • The log(tf ) depends linearly on SCB for SCB < 3. For SCB > 3 the data split into two branches corresponding with the other structural parameter 1H1 /1H2 .

Acknowledgement The authors thank the Czech Gas Industry for the sponsorship of this project. References Adison, E., Ribeiro, V. and Deffieux, A., ‘Evaluation of the heterogeneity in linear low-density polyethylene comonomer unit distribution by differential scanning calorimetry characterisation of thermally treated samples’, Polymer 33, 1992, 4337–4342. Brown, N. and Lu, V., ‘The kinetics and microscopic processes of long term fracture in polyethylene piping materials’, Annual Report 1989–90 GRI90/0104. University of Pennsylvania Philadelphia, PA, 1990.

78

E. NEZBEDOVA ET AL.

Egan, B.J. and Delatycki, O., ‘The morphology, chain structure and fracture behaviour of highdensity polyethylene’, J. Mater. Sci. 30, 1995, 3307–3318. Huang, Y.L. and Brown, N., ‘The effect of molecular weight on slow crack growth in linear polyethylene homopolymers’, J. Mater. Sci. 23, 1988, 3648–3655. ISO/TC 138/SC 4 N. 144, ‘Notch tensile test to measure the resistance to slow crack growth of polyethylene resins (PENT)’, first version of ISO document, 1998. Lu, X. and Brown, N., ‘A test for slow crack growth failure in polyethylene under a constant load’, Polymer Testing 11, 1992, 309–319. Lu, X., Zhou, Z. and Brown, N., ‘The anisotropy of slow crack growth in polyethylene pipes’, Polymer Engrg. Sci. 34, 1994, 109–115. Nezbedova, E., Salajka, Z. and Kucera, J., ‘Relation between toughness and structural parameters of PE-copolymers’, in International Conference Welding Technology, Materials Testing, Fracture Mechanics and Quality Management, Vol. 2, S. Felber, T. Varga and J.L. Zeman (eds), Vienna University of Technology, 1997, 507–515. Nezbedova, E., Zahradnickova, A. and Kucera, J., ‘Long time brittle fracture in HDPE’, in Polymerwerkstoffe ’98, Vol. 1, H.-J. Radusch and J. Vogel (eds), Martin-Luther-Universität, Halle-Wittenberg, 1998, 457–466. Tränkner, V., Hedequist, V. and Gedde, U.W., ‘Structure and crack growth in gas pipes of mediumdensity and high-density polyethylene’, Polymer Engrg. Sci. 36, 1996, 2069–2076.