The Dependence of Rapid Crack Propagation in Polyethylene Pipes

on the Plane Stress Fracture Energy of the Resin

NORMAN BROWN andXICI LU

Department of Materials Science and Engineering University of Pennsylvania

Philadelphia, PA 191 04

The critical temperature [CT] for rapid crack propagation [RCP] was measured in 11 polyethylene [PE] 200 mm diameter gas pipes each with different resins. The plane stress fracture energy [PSFE] in thin Charpy impact specimens of the resin was found to correlate with the CT. The higher the PSFE, the lower the CT. This re- sult was related to the observation that the PSFE decreases as the temperature de- creases. It was found that the impact energy of specimens from compression molded pipe that was remelted at 180°C gave a better correlation with the CT than specimens that were machined from the inner wall of the pipe. Consequently, it is now possible to predict the CT of a pipe by measuring the PSFE of the resin without making the pipe.

1. INTRODUCTION

n general, if a structure under stress receives a vio- I lent impact, the resulting crack may propagate through the structure at a high speed. In this paper we are concerned with the case of a pressurized PE gas pipe where the resulting crack could propagate a long distance at speeds on the order of 100 m/s. This phenomenon, called Rapid Crack Propagation [RCP] , is a rare event in the field, but the consequences can be catastrophic. The five primary factors that deter- mine whether or not RCP may occur are 1) the nature of the impact that initiates RCP, 2) the gas pressure, 3) the temperature, 4) the geometry of the pipe and 5) the material. This paper is mainly concerned with the relationship between the material and the critical temperature [CT] above which RCP does not occur. In the case of PE gas pipes, RCP is observed in the labo- ratory by driving a sharp blade into the pipe at a speed of about 15 m/s. If the pressure in the pipe is above the critical pressure [CP] and the temperature is below the CT the crack will propagate to the end of the pipe at a very high speed. Typical CT versus CP curves are shown in Fig. I for a series of pipes with different resins and the same geometry as obtained by Vanspeybroeck (1). All curves have approximately the same shape. There is a lower shelf CP where the CP is essentially constant and an upper CT above which RCP is not possible at any pressure. The important difference between resins is in their lower shelf CP and the upper CT. Since CT is a function of CP the

difference between the CT among the resins can be defined with respect to the same arbitrary pressure which should be greater than the lower shelf CP of all the resins and less than their instantaneous burst pressure. In this work the arbitrary pressure was 6 bar.

RCP may be viewed as a two-stage process. The first is associated with the impact of the knife and the sec- ond with the long range steady state rapid propaga- tion of the crack. The details of the transition from the initiating impact to the steady state propagation are extremely complex and not well understood. However, the conditions for steady state propagation phase are well understood and have been initially described by the Irwin-Corten equation (2).

(1)

Subsequent refinements based on experiments by Venizelos et al. (3) have produced the following equa- tion

(21

where D = pipe diameter; SDR = ratio of D/t where t is pipe thickness: Y = Young's modulus ; G, = frac- ture energy during propagation. The left side of these equations is the driving force and the right is the frac- ture resistance of the high speed crack.

We now suggest that the initiation stage is associ- ated with the CT because above the CT, RCP cannot occur no matter how high is the pressure. As Q. 1

T (CP)2D (SDR)' / 8Y = Gp

(CP)1.8D (SDR - 2)' /Yo.' C( Gp

1140 POLYMER ENGINEERING AND SCIENCE, JULY 2001, Vol. 41, No. 7

Dependence of Rapid Crack Propagation in PE Pipes

-40 -30 -20 -10 0 10 20

TolnperntureFC

Ftg. I . Critical temperature us. critical pressure for a variety of copokynerpolyethylmes with short chain branches.

shows, CT obviously depends on the resin. The dis- tinction between initiation and propagation and their association with CT and CP can be simply viewed in terms of the ideal characterization of RCP in Fig. 2 by Leevers (4). We interpret Fig. 2 as follows. Region I below CT and above CP is where RCP occurs because the conditions for initiation and propagation are satis- fied. In Region 11 below CP and below CT. the condi- tions for initiation are sufficient, but the pressure is too low for propagation. In Region III above CT the con- ditions for initiation are not satisfied, and therefore RCP cannot occur no matter how high is the driving force for steady state Propagation. In this paper some of the details that influence initiation will be discussed, with the central feature being the PSFE of the resin.

I I I I

II NQ RCP

CT

Temperature

Fig. 2. Ideal characterization of rapid crack propagation [RCPI. Domain I-initiation and propagation, Domain U-initi- ation-no pmpagation, Domain III--no initiation CP is critical pressure and CT is critical temperature.

Ingham and Marshall (5) originally proposed that the plane stress fracture energy [PSFE] of the resin influ- ences the CT. Brown et aZ. (6) correlated the Charpy impact energy on thin specimens with CT where the specimens were machined from the inner wall of the pipe. In this paper it was found that a better corre- lation could be obtained if the impact specimen was obtained from a compression molded plaque of the remelted pipe.

2. EXPERIiKENTAL The CT was measured on 200 nun diameter SDR 1 1

gas pipes from the 11 different resins produced in North America. The pigmented resins were ethylene- hexene or butene copolymers whose densities ranged from 0.943 to 0.965 gm/cc. The RCP test known as the S-4 is described in the international standards specification I S 0 13477. The tests were done at a con- stant pressure of 6 bar, and the temperature was var- ied to obtain the CT. The CT was determined with an accuracy of i 1°C.

Charpy impact specimens were made from the pipe in different ways. Specimens were machined from the inner wall of the pipe in the longitudinal and circum- ferential directions. Other specimens were machined from compression molded plaques from pipe that was remelted at 180°C and slowly cooled at a rate of 0.5 "C/min or fast cooled at a rate of 15"C/min. The geometry of the impact specimen is shown in Fig. 3. The dimensional tolerances were 10 2 0.2 mm for width; 80 5 1 mm for length and 2.5 ? 0.02 mm for notch depth. The effect of specimen thickness was in- vestigated by varying the thickness from 1.6 to 4.5 mm with the final design having a thickness of 3 ? 0.2 mm.

The Charpy impact energy was measured on a Zwick tester with a 40 nun span and impact velocity

POLYMER ENGINEERING AND SCIENCE, JULY 2001, Vol. 41, No. 7 1141

Norman Brown and Xici Lu

FYg. 3. Geometry of charpy impact specimen Llimensions in m Length = 80; width = 10: thickness = 3.0; notch depth = 2.50; span = 40.

of 2.9 m/s at 0 and 23°C. Five to ten impact tests were made per duplicate set of specimens for which the standard deviation was 4%. The toss energy of a hctured specimen was 0.013 J.

3. RESULTS The typical effect of specimen thickness on the im-

pact energy is shown in Flg. 4 for three resins. Each resin has a critical thickness above which the impact energy was practically constant. Below this critical thickness the energy rises to a maximum value and then decreases. It was observed that the specimens twisted during impact in the range of thickness below the point of maximum energy. The critical thickness, above which the total energy remained constant, was greater the greater the fracture energy of the resin. The region of constant energy will be called the plateau region, and where the energy rises, the peak region. kom these data it was decided to standardize the thickness at 3 mm so that the impact energy for all resins would be in the plateau region, and the im- pact energy would not be sensitive to small variations in thickness. The maximum values of the energy in the peak region have the same ranking as those in the plateau region, but since the scatter in the test data was appreciably greater in the peak region, it is better to standardize the test method using the plateau val- ues.

Observations of the fractured surfaces in the plateau region showed thin shear lips of essentially constant thickness which enclosed a smooth bnffle type of frac- tured surface. The area of brittle fracture increased with thickness. Below the critical thickness, the shear lips began to broaden and merge until the area of brit- tle fracture was eliminated at the maximum value of the energy. The decrease in energy with thickness below its peak value is associated with the observation that the specimens twisted during impact.

The CT of the 11 resins are shown in Table 1. Note that the CT increased as the density of the resins de- creased. In Table I, the impact energies are U(23) and U(0) at 23 and O°C for compression molded and slow cooled specimens from pipe remelted at 180°C whose thickness was 3 t 0.2 mm. The average value is based on five to ten duplicate tests whose standard deviation was 4%. The correlation between the CT and the impact energies for slow cooled and rapidly cooled specimens is shown in Flg. 5. The impact energies of the specimens that were machined from the inner wall of the pipe in the longitudinal and circumferen- tial direction also correlated with the CT as shown in Flg. 6, but not as well as for compression molded specimens. The scatter in the impact test data was much larger than for the compression molded speci- mens. Also considering that it was much more diffi- cult to machine specimens from the inner wall of the

1.6 2.1 2.6 3.1 3.8

Specimen Thickness (mm)

Rg. 4. Charpy impact e~ergy us. specimen thickness for various resins.

1.1

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Dependence of Rapid Crack Propagation in PE plpes

Table 1. S-4 Critical Temperature, Charpy Impact Energy, and Density in 200 mm SDR 11 Polyethylene Gas Pipes.

Resin Density-kglm3 CT-"C U(23)J U(O)-J dUldTJPC

2406 949 33 0.247 0.127 0.0052 949 30 0.275 0.144 0.0057 946 28 0.270 0.137 0.0058 948 23 0.280 0.157 0.0053 943 18 0.390 0.260 0.0057

3408 960 19 0.357 0.255 0.0044 957 18 0.310 0.231 0.0034 956 16 0.337 0.234 0.0045 957 11 0.41 1 0.321 0.0039 959 9 0.434 0.330 0.0045 965 <-15 1.726 1.114 0.027

pipe, it was decided to concentrate on compression molded specimens. In general it was found that for all types of specimens the impact energy increased with the density.

4. DISCUSSION The important result is that the PSFE of the resin

varies inversely with CT of the resin, as shown in Flg. 5. Once curves such as those in Flg. 5 have been es- tablished for a given pipe geometry, the CT can be predicted from the Charpy test described herein. Based on the scatter in the data points in the curves in Fg. 5, and that the standard deviation of the aver- age value of about five Charpy tests is about 4%, and that the CT can be determined within 2 1"C, it is esti- mated that the CT can be predicted from the Charpy impact energy within 34°C. Since remelting the pipe at 180°C removes the prior processing history, the Charpy specimen can be made from the pellets with- out making a pipe. Industry now has an inexpensive test method for controlling the RCP behavior of the resin. In general, the higher the density of the resin, the higher the PSFE and the lower the CT of the pipe.

The following simplified view of the initiation stage reveals the basis for the dependence of CT on the PSFE and the pipe geometry. The impacting knife de- livers a total amount of energy, & ,which may be par- titioned as follows.

(31 & is the resistance to fracture of the pipe and is di- rectly related to the PSFE of the resin. ED is the macroscopic deformation in the pipe which depends on the diameter and thickness and on the plastic and elastic strain energy density in the resin. E, is the ki- netic energy of the crack and is related to its velocity. It is postulated that the initiation of RCP occurs if a crack is produced with an E, greater than a critical value, Wc), which is associated with a critical veloc- ity. As the crack velocity decreases, more gas escapes resulting in a greater reduction of the driving force for propagation .and there is an increase in the dynamic fracture energy as shown experimentally by Channel and Clutton (7) and theoretically by Leevers (8). Thus, there is a critical velocity below which the crack will not propagate as suggested by Kanninen et at. (9). The critical condition for the initiation of RCP is

&-ED-EFr &(c) (4)

At too high a temperature, Eq 4 may not be satisfied. The left side of Eq 4 can be increased by lowering the temperature since E, decreases with temperature. The greater the PSFE of the resin, the more the tem- perature must be lowered to initiate the critical veloc- ity. Consequently the CT varies inversely with the PSFE as in F?g. 5.

The effect of pipe geometry on CT can also be pre- dicted by Eq 4. Increasing the diameter with a constant thickness increases ED. Also, decreasing the thickness with a constant diameter increases because a thin pipe undergoes more macoscopic deformation prior to fracture than a thicker pipe. If E,, is too high, at a cer- tain temperature Eq 4 may not be satisfied. However, the left side of Eq 4 can be increased by lowering the temperature (decreasing q). For each resin the amount of decrease in temperature required to initiate RCP is greater the greater ED, Consequently, CT is lower the greater the diameter and the smaller the thickness. These predictions agree with experimental observations by Leevers et al (10). The fact that the CT increases with diameter at a constant SDR (ratio of diameter over thickness) as shown in Fig. 5 and by Leevers et aL (1 1) means that thickness has a greater effect on

The fact that compression molded specimens give a better correlation with the CT than the specimens machined from the pipe was a suprise. One definite reason is that the dimensional tolerances on speci- mens from the pipe wall are more difficult to maintain since they are curved. Consequently, there is more scatter in the impact energy. Also the effects of proc- essing the pipe such as orientation and residual stress may tend to randomize the correlation between PSFE and the CT.

The general trend of the data in Table I indicates that the PSFE increases with density, and Fig. 6 shows that all the higher density slow cooled states have a higher PSFE than the lower density rapidly cooled materials. These results do not conform to other data such as that by Chan and Williams (12) who found that the fracture toughness Kcl increased as the density decreased from 960 to 940 kg/m3. Also Plati and Williams (13) found that the Charpy impact

than does the diameter.

POLYMER ENGINEERING AND SCIENCE, JULY 2001, Vol. 41, No. 7 1143

Fig. 5. Charpy impact energy us. critical temperature, for 110 m SDR 11 (re$ 6) impact specimens machinedfrompipe. 200 mm SDR 1 1 pipe, impact specimens com- pression molded and slow cooled 200 mm SDR 1 1 pipe, impact specimens compression molded andfast cooled

1.6

1.4

1.2 7

i . P

Fig. 6. Charpy impact energy us. critical temperature for 200 mm

from inner wall of pipe. pipe, imptldspecimens machined

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POLYMER ENGINEERING AND SCIENCE, JULY 2001, Vol. 41, No . 7

Dependence of Rapid Crack Propagation in PE Pipes

energy for a medium density polyethylene was 44% greater than that for a high density polyethylene. However, density does not uniquely determine the im- pact energy. All the polyethylenes in this study have short chain branches, and the density is determined primarily by the number and type of short chain branches. However, the distribution of the branches relative to the molecular weight distribution is also an important factor. For example, in Table 1 , the resin with a density of 965 kg/m3 has a PSFE of 1.726 J, whereas the resin with a density of 960 kg/m3 has a PSFE of 0.3575. The former resin is bimodal with all the short chain branches on the high molecular weight part of the distribution.

The probability for RCP in the field depends on the probability for initiation if the gas pressure is above the CP. This probability is very uncertain because it depends on the details of the violent impact to which the pipe may be subjected in the field. The weight, speed, sharpness and orientation of the impacting de- vice are important factors. Bragaw (14) investigated the initiation process by dropping differently shaped blades at various speeds and temperatures on pres- surized pipes. Of the three blades he tested, only one whose sharp edge pointed in the longitudinal direction of the pipe produced RCP. Thus, owing to the com- plexity of the factors required to initiate RCP, the probability is likely to be very small. However, the probability of RCP can be reduced to zero if the CT is below the operating temperature of the pipeline.

1.

2.

6. SUMMARY

The PSFE of the resin correlates inversely with the CT of the pipe.

From the correlation curve and the Charpy energy of thin impact specimens compression molded from pellets, the, CT c a n be predicted to within 34°C.

3. The PSFE increases with the density of the resin.

ACKNOWLEDGMENTS The support of The Gas Research Institute is appre-

ciated. Use was made of the MRSEC shared experi- mental facilities, which are supported by the National Science Foundation under award number DMR 00- 79909. The S4 tests were done at BECETEL by Prof. P. Vanspeybroeck.

REFERENCES 1. P. Vanspeybroeck, Plastic Pipes VIII, Einhoven, pub.

Inst. of Materials, London, paper D1/6 (1992). 2. G. R Irwin and H. T. Corten, Report to Northern Nat-

ural Gas Co. and El Pas0 Natural Gas Co. (1968). 3. G. P. Venizelos, C. J. Greenshields and A. Ivankovic

Plastic Pipes X, Goteborg, pub. Inst. of Materials, Lon- don, 291 (1998).

4. P. S. Leevers, ibid, Plask pipes X, 275 (1998). 5. E. J. Ingham and G. P. Marshall, Con- Deformation and

Racture ofPolymers, Cambridge pub. Inst. Materials, London (1997).

6. N. Brown, X. Lu. E. J. Ingham and G. P. Marshall. Pro- ceedings 15th Symposium on Plastic Fuel Gas Pipes, Lake Buena Vista, Florida, in pub. Gas Research Insti- tute, Chicago 157 (1997).

7. A. D. Channell and E. Q. Clutton, Plastic Pipes IXEdin- burgh, 213 (1995).

8. P. S. Leevers. Polyrn Eng. Sci, 56, 2296 (1996). 9. M. F. Kanninen, C.-P.Leung, S. C. Grigory. H. P.

Couque and C. F. Popelar, 12th Plastic Fuel Gas Pipe Symp. Boston, 70 (1991).

10. P. S. Leevers, G. P. Venizelos and R. E. Morgan, fioc. 13th PIastic Fuel Cas Symp. San Antonio, pub. AGA 172 (1993).

11. P. S. Leevers, C. J. Greenshields, G. P. Venlzelos and A. Ivankovics, ibid P.P.X. 197 (1995).

12. M. K. Chan and J. G. Williams, Polyym Eng. Sci, 21, 1019 (1981).

13. E. Plati and J. G. Williams, Polyrn Erg. Sci, 15, 470 ( 1975).

14. C. G. Bragaw. 7th Plastic Fuel Gas Pipe Symp.. New Orleans, pub Am. Gas Assoc., 68 (1979).

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