Experimental study of stress cracking in high density ...

Experimental Study of Stress Cracking in High Density Polyethylene Pipes

A Thesis

Submitted to the Faculty

of

Drexel University

by

Jingyu Zhang

in partial fulfillment of the

requirements for the degree

of

Doctor of Philosophy

November 2005

ii

Dedication

To my family with love.

iii

Acknowledgement It is a test of effort and persistence to complete a PhD research. I would like to take this

opportunity to express my sincere appreciation to those who have assisted and supported

me to make it a possibility during the last four years.

First and foremost, I would like to thank my advisor Dr. Grace Hsuan for her guidance

and advice. I also would like to extend my thanks to Dr. Robert Koerner; his advices and

encouragement have helped me tremendously during the last four years. In addition, I

would like to express my gratitude to Dr. George Koerner for his encouragement.

I would like to thank deeply my colleagues and friends, Mr. Greg Hilley, Mr. Lei Lou,

Mr. Songtao Liao, Mr. Mengjia Li, Mr. Sangsik Yeo, Ms. ShiQiong Tong, and Ms.

Cynthia Baxindine for their help by performing the experiments, sharing experiences, and

offering valuable discussions.

The project is made possible by the support of the Florida State Department of

Transportation. My appreciation also goes to the faculty in the Civil, Architectural, and

Environmental Engineering Department at Drexel University for providing a great

learning environment.

Finally, I would like to thank my family in China for their everlasting love and support.

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Table of Contents

List of Tables……………………………………………………………………………viii

List of Figures……………………………………………………………………………x

Abstract………………………………………………………………………………….xiv

1. Background and Literature Review…………………………………………………….1

1.1 Introduction………………………………………………………………………...1

1.2 Pipe material………………………………………………………………………..2

1.3 HDPE pipe application……………………………………………………………..3

1.4 Cracking of HDPE products……………………………………………………......5

1.5 Stress cracking mechanism………………………………………………………..10

1.5.1 Lustiger’s microscopic model……………………………………………..10

1.5.2 Crazing…………………………………………………………………….12

1.5.3 Environmental stress cracking…………………………………………….14

1.5.4 Fatigue-related stress cracking…………………………………………….15

1.6 Stress cracking test methods……………………………………………………...16

1.7 Residual stress…………………………………………………………………….22

1.8 Lifetime prediction methods……………………………………………………...25

1.8.1Fracture mechanics method…………………………………………………26

1.8.2 Shifting method……………………………………………………………..26

1.8.3 Rate process method………………………………………………………..28

2. Stress Cracking in HDPE Protection Ducts in Segmental Bridges……………………32

2.1 Introduction……………………………………………………………………….32

v

2.2 Background……………………………………………………………………….33

2.2.1 Segmental bridges…………………………………………………………..33

2.2.2 Tendon failures in segmental bridges………………………………………35

2.2.3 Corrosion mechanism………………………………………………………37

2.3 HDPE ducts included in this study……………………………………………….38

2.4 Assessment of cracking mechanisms……………………………………………..39

2.4.1 Introduction…………………………………………………………………39

2.4.2 Macroscopic and microscopic evaluation…………………………………..41

2.4.2.1 Cracked samples from the MB Bridge……………………………...41

2.4.2.2 Cracked samples from the SSK Bridge…………………………….55

2.4.3 Summary of cracking mechanism evaluation………………………………58

2.5 HDPE duct properties…………………………………………………………….59

2.5.1 Specifications for HDPE materials…………………………………………59

2.5.2 Specifications used for the ducts…………………………………………...64

2.5.3 Test results of the HDPE ducts……………………………………………..67

2.5.4 Correlation of SCR to other material properties of the ducts………………69

2.5.5 Recommended specification………………………………………………..70

2.6 Assessment of stresses in the ducts………………………………………………72

2.6.1 Temperature-induced stresses………………………………………………72

2.6.1.1 Laboratory test model……………………………………………...72

2.6.1.2 Results from test model……………………………………………75

2.6.1.3 FEM analysis………………………………………………………76

2.6.2 Residual stresses……………………………………………………………80

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2.7 Evaluation of fatigue failure……………………………………………………...83

2.7.1 Fatigue test………………………………………………………………….83

2.7.2 Discussion of fatigue test results…………………………………………...85

2.8 Summary………………………………………………………………………….87

3. Stress Cracking in Corrugated HDPE Pipes…………………………………………..89

3.1 Introduction……………………………………………………………………….89

3.2 Background……………………………………………………………………….89

3.2.1 Corrugated HDPE pipes……………………………………………………89

3.2.2 Failures in HDPE corrugated pipes…………………………………………91

3.3 Test materials……………………………………………………………………..93

3.4 SCR of liner………………………………………………………………………95

3.4.1 Introduction………………………………………………………………..95

3.4.2 Experimental design of liner test…………………………………………..97

3.4.3 Data analysis……………………………………………………………….99

3.4.3.1Data analysis method………………………………………………..99

3.4.3.2 Test results in water environment………………………………….100

3.4.3.3 Test results in air environment……………………………………..102

3.4.2.4 Test results in Igepal environment....................................................103

3.4.2.5 Comparison of SCR in different environments……………………103

3.5 Residual stresses………………………………………………………………...107

3.5.1 Residual stress measurement……………………………………………...107

3.5.2 Residual stresses effect on SCR……………………………………….…..109

3.5.2.1 Effect shown from four specimen configurations…………………109

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3.5.2.2 Effect shown from comparison on liner and plaque specimens…..111

3.6 SCR of junction…………………………………………………………………116

3.6.1 Introduction……………………………………………………………….116

3.6.2 Experimental design of junction test……………………………………...117

3.6.3 Data analysis………………………………………………………………118

3.7 Comparison of deferent tests……………………………………………………120

3.7.1 Comparison of liner and junction test……………………………………..120

3.7.2 Comparison of notched liner with liner and junction tests………………..125

3.8 Lifetime prediction………………………………………………………………127

3.8.1 Data extrapolation methods……………………………………………….127

3.8.2 Comparison of prediction methods……………………………………….129

3.8.3 Prediction using RPM……………………………………………………..133

3.9 Summary………………………………………………………………………...134

4. Conclusion and Future Work………………………………………………………...137

4.1 Summary………………………………………………………………………...137

4.1.1 HDPE ducts in segmental bridges…………………………………………137

4.1.2 Corrugated HDPE ducts…………………………………………………...138

4.2 Conclusion………………………………………………………………………140

4.3 Future work……………………………………………………………………..143

List of Reference………………………………………………………………………..144

Appendix A: Data Analysis Method and Matlab Code………………………………...150

Appendix B: Residual Stress Calculation………………………………………………160

Vita……………………………………………………………………………………...164

viii

List of Tables

1.1 Comparison of test methods………………………………………………………….21

2.1 Information on samples retrieved from the bridges………………………………….39

2.2 Specification designated in ASTM D3350…………………………………………..62

2.3 Equivalency of ATM D3350 and D1248……………………………………………64

2.4 Original material specification for the HDPE ducts in each bridge………………….65

2.5 Detailed original specification for the HDPE duct material…………………………66

2.6 Test results for the duct material properties………………………………………….68

2.7 Recommended specification for HDPE ducts………………………………………..71

2.8 Summary of the analytical model results…………………………………………….79

2.9 Combined temperature-induced stress and residual stress…………………………...82

3.1 Properties of the studied pipe samples……………………………………………….94

3.2 Failure times of the four specimen configurations…………………………………..96

3.3 Test environments for liner test……………………………………………………...98

3.4 Summary of fitted curves of liner test on A36……………………………………...101

3.5 Residual stress measurements and effect on failure times………………………….110

3.6 Summary of fitted curves of plaque and liner tests on A36………………………...113

3.7 Activation energies from different tests…………………………………………….115

3.8 Summary of fitted curves of junction test on A24………………………………….118

3.9 Comparison of the brittle region of liner and junction tests on A24……………….124

3.10 Comparison of acceleration effect of liner and junction tests……………………..127

ix

3.11 The three constants used for RPM method……………………………….……….134

4.1 Comparison of the two types of HDPE pipes……………………………………...143

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List of Figures 1.1 Ductile failure in a HDPE pipe………………………………………………………..6

1.2 Brittle failure in a HDPE pipe…………………………………………………………7

1.3 Impact fracture surface under 1000x magnification…………………………………..8

1.4 SC fracture surface under 1000x magnification………………………………………9

1.5 Failure modes that could occur in HDPE pipes………………………………………9

1.6 Graphic illustration of ductile failure at molecular level…………………………….11

1.7 Graphic illustration of brittle failure at molecular level……………………………..11

1.8 Craze at the crack tip………………………………………………………………...13

1.9 Test equipment for NCTL test……………………………………………………….19

1.10 Residual stress distribution caused by cooling……………………………………..22

2.1 Precast concrete “box”……………………………………………………………….34

2.2 Construction of a segmental bridge………………………………………………….34

2.3 Inside view of a segmental bridge……………………………………………………35

2.4 Cross-section of a tendon in segmental bridges……………………………………...35

2.5 Corroded steel strands in segmental bridge tendons…………………………………36

2.6 Close-up view of the corroded steel strands…………………………………………37

2.7 Corrosion mechanism of steel tendons………………………………………………38

2.8 Cracking in HDPE ducts……………………………………………………………..40

2.9 Duct section that contains a full crack……………………………………………….40

2.10 Duct section that contains part of the length of crack………………………………40

2.11 Drawing of sample MB 67-5-A…………………………………………………….43

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2.12 Specimen 1 from sample MB 67-5-A………………………………………………43


2.14 Drawing of sample MB 38-4-A…………………………………………………….45





2.19 Drawing of sample MB 126-4-A…………………………………………………...50

2.20 Specimen 1 from sample MB 126-4-A……………………………………………..51




2.24 Drawing of column sample SSK 131-SB-SE-6…………………………………….55

2.25 Specimen 1 from sample SSK 131-SB-SE-6……………………………………….56



2.28 Correlation between SCR and MI………………………………………………….69

2.29 Correlation between SCR and density……………………………………………..70

2.30 Test model built by FAU…………………………………………………………..73

2.31 Strain gage arrangements in the test model………………………………………...73

2.32 Void in the test model………………………………………………………………74

2.33 Strain gage measurement…………………………………………………………...76

2.34 Two-dimensional FEM model of duct-grout system……………………………….77

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2.35 Mesh in analytical model…………………………………………………………...78

2.36 First principal stress distribution when the void is 10%...........................................79

2.37 Void size effects on the principal stress……………………………………………80

2.38 Measurement of residual stress by slitting………………………………………….81

2.39 Combined temperature-induced stress and residual stress………………………….83

2.40 Fatigue test system………………………………………………………………….84

2.41 Specimen in the fatigue test………………………………………………………...84

2.42 S-N curves on logarithmic scale for different duct samples………………………..86

3.1 Creep and stress relaxation behavior of HDPE pipes………………………………..91

3.2 Cracking in a field corrugated HDPE pipe…………………………………………..91

3.3 Typical fracture morphology from a cracked field corrugated HDPE pipe…………92

3.4 Geometry of type S corrugated pipe…………………………………………………93

3.5 Liner specimen location……………………………………………………………...95

3.6 Liner specimen……………………………………………………………………….95

3.7 A36 liner test at 60, 70, and 80oC in water…………………………………………101

3.8 A36 liner test at 60, 70, and 80oC in air…………………………………………….102

3.9 A36 liner test at 50oC in Igepal solution……………………………………………103

3.10 Compiled graph for A36 line test in all environments…………………………….104

3.11 Activation energy calculation for A36 liner test in water at 600 psi……………...106

3.12 Measurement of arc height of the specimen………………………………………108

3.13 Comparison of test results from liner and junction test in Igepal solution………..114

3.14 Comparison of test results from liner and junction test in water………………….114

3.15 Comparison of test results from liner and junction test in air……………………..115

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3.16 Junction configuration…………………………………………………………….116

3.17 Junction test specimen location…………………………………………………...117

3.18 Typical configuration of junction specimen………………………………………117

3.19 A24 junction test at 60, 70, and 80oC in water……………………………………119

3.20 The fitted curves and 97.5% lower confidence limits for junction test in water….120

3.21 Comparison of test results at 60oC in water on A24………………………………122



3.24 Dependence of the ratio between junction failure time and liner failure time on

stress and temperature……………………………………………………………..124

3.25 Difference of activation energy in liner and junction tests………………………..125

3.26 Comparison of liner and junction tests at 80oC on A24…………………………...126

3.27 Comparison of predictions for liner test in water on A36………………………...130

3.28 Comparison of predictions for liner test in air on A36……………………………130

3.29 Comparison of predictions for junction test in water on A24……………………..131

3.30 Comparison of predictions for liner test in water on A24………………………...132

3.31 A24 junction test data and prediction at 23oC…………………………………….134

B.1 Specimen configuration after annealing…………………………………………...160

xiv

Abstract Experimental Study of Stress Cracking in High Density Polyethylene Pipes

Jingyu Zhang Grace Hsuan, PhD

Stress cracking (SC) is recognized as one of the major concerns for high density

polyethylene (HDPE) pipes. SC is a brittle failure that occurs at a stress level lower than

the short-term mechanical strength of the material. Many cases of SC have been reported

in two types of HDPE pipes: HDPE ducts used in segmental bridges and corrugated

HDPE drainage pipes. The causes of SC in these two types of pipes and their stress

cracking resistance (SCR) properties are evaluated in this dissertation.

Longitudinal cracking was observed in HDPE ducts and it was resulted by

circumferential stress inducing from temperature cycles in the field and residual stress in

the pipe. Conversely, the circumferential cracking in corrugated HDPE pipes was caused

by longitudinal stress from bending and residual stress of the pipe. Majority of the

fracture surfaces were covered by the fibril structure indicating that cracks propagated via

a slow crack growth (SCG) mechanism. The study confirmed that the notched constant

tensile load (NCTL) test can effectively distinguish the SCR of different HDPE ducts and

the NCTL test is incorporated into the recommended material specification for quality

control of HDPE ducts. Since fatigue lines were observed on the fracture surface, fatigue

tests were adopted to estimate the lifetime of the duct under thermal cyclic loading in the

field. For the corrugated HDPE pipes, the SCR evaluation focused on the finished pipe

in order to incorporate processing effects. Two test methods were developed and

xv

evaluated in the study, namely liner and junction tests. The liner test utilizes notched

specimens to generate short and consistent failure times, and is good for QA/QC. On the

other hand, the junction test challenges the junction where field cracking is observed.

Thus, the junction data were used for predicting the long-term SCR of the pipe, and the

reliable method was found to be the rate processing method (RPM).

1

Chapter 1: Background and Literature Review 1.1 Introduction The use of high density polyethylene (HDPE) pipes has increased significantly in last

fifty years in different sectors of civil and environmental engineering. Generally, HDPE

pipes have provided satisfactory performance; however, stress cracking (SC) was

reported in various types of HDPE pipes. ASTM D883 defined SC as an external or

internal rupture in a plastic caused by tensile stresses less than its short-term mechanical

strength. According to the report by Hartt and Hsuan (2004), cracking was observed on

some of the HDPE ducts in the segmental bridges located in the state of Florida. Another

report by Hsuan and McGrath (1999) revealed many cases of cracking in corrugated

HDPE drainage pipes. The causes of the SC in these two types of pipes are associated

with material properties, geometry, manufacturing process, and field loading conditions.

The objective of this study is to identify the cracking mechanism, develop effective test

methods for evaluating stress crack resistance (SCR), and provide appropriate approaches

to estimate the lifetime for both types of HDPE pipes.

1.2 Pipe material The conventional materials that are used for piping purposes are concrete and metal. The

oldest material is vitrified clay; the newest materials are polymeric materials, in which

HDPE is widely-used.

Polyethylene has the simplest molecular structure of all polymers. It consists of two

carbon and four hydrogen atoms in the basic repeating unit. Polyethylene is polymerized

2

from ethylene gas that is obtained from natural gas or crude oil. The polymerization

conditions of low temperature, low pressure, appropriate catalysts (such as Ziegler-Natta

catalyst), and co-monomers result in a linear polyethylene. Linearity indicates that there

are limited branches in the polymer chains, so that the molecules can pack tightly. High

density polyethylene (HDPE) is one type of linear polyethylene with a density range from

0.941 to 0.965 g/cc as per ASTM D883. HDPE exhibits high strength and modulus; thus,

it is preferred for use in the manufacture of plastic pipes.

Other common plastic materials used for piping include polyvinyl chloride (PVC),

polypropylene (PP), polybutylene (PB) and acrylonitrile-butadiene-styrene (ABS).

Along with HDPE, these thermoplastic pipes exhibit toughness, flexibility, high chemical

resistance, light weight, easy installation, and low Manning coefficient, which make them

suitable for engineering applications.

1.3 HDPE pipe application Plastic pipes have been used in pressure piping applications for many years. Sarkes and

Smith (1983) pointed out that the use of plastic pipes began in the gas industry from 1955.

In the early 1970s, plastic pipes started being used in highway drainage applications.

Currently, HDPE drainage pipes are installed more frequently than all other plastic pipes

combined. In the past thirty years, HDPE pipes have also been used as a protection layer

for cables in segmental bridges, encasing steel strands and concrete to prevent corrosion.

The three primary applications of HDPE pipes are described as follows.

3

Fuel pipes HDPE is now the dominant material used for fuel gas conveyance pipes. These pipes are

smooth-walled, with relatively small standard dimension ratio (SDR), which is the ratio

between the outside pipe diameter and the minimum pipe wall thickness. SDR is related

to internal pressure capability, as shown in Equation (1.1):

21

2−

=−

=SDRP

ttDPS (1.1)

Where, S = circumferential stresses in the pipe wall, P = gas pressure,

D = average outside diameter, t = minimum pipe wall thickness.

The design involves keeping the working pressure in the pipe lower than the pressure

rating of the pipe, which is defined by ASTM 2837 as “the estimated maximum pressure

that the medium in the pipe can exert continuously with a high degree of certainty that

failure of the pipe will not occur”. Due to the critical application of the gas pipe, the

quality of the pipe is carefully evaluated. Significant amounts of research, funded by the

Gas Research Institute, were carried out in the 1980s. The results of that research have

greatly benefited the application of HDPE pipes in different fields.

Drainage pipes Corrugated HDPE pipe is the most widely-used plastic pipe for gravity flow water

systems, which include storm sewers, perforated under-drains, storm drains, slope drains,

cross drains, culverts, and sanitary sewers. The diameters of these pipes span from 4 to

60 inches. In the majority of the applications, the pipes are buried underground. As such,

they are designed to support the soil load and live load. The flexibility of the HDPE pipe

4

allows limited deformation, which will transfer a portion of the overburden onto the

surrounding soil. Furthermore, because the stress relaxation is greater for the HDPE

pipes than the soil, more overburden could be taken over by the soil with time. However,

excessive deformation can lead to buckling of the pipes or/and jeopardizing of the

stability of the pipe/soil structural system. Therefore, satisfactory performance requires

HDPE pipes with sufficient stiffness. In order to increase the structural stiffness of the

pipe and reduce the material cost, corrugation is incorporated into the pipe profile.

According to AASHTO M294, there are three types of HDPE pipe profiles:

Type C: This pipe shall have a full circular cross-section, with an

annular corrugated surface both inside and outside.

Type S: This pipe has a full circular dual-wall cross-section, with an

outer corrugated pipe wall and a smooth inner liner.

Type D: This pipe has a circular cross section consisting of an

essentially smooth inner wall joined to an essentially smooth outer wall

with annular or spiral connecting elements.

Protection Ducts In this application, the HDPE pipes, called ducts, function as a moisture barrier. One

particular example of this application is the sheathing of cables in segmental bridges.

The HDPE duct surrounds the cement grout and steel to isolate them from the outside

environment. The duct and grout then form a double corrosion-protection system for the

steel strands. The ducts are smooth-walled pipes with diameters generally around 4

inches.

5

1.4 Cracking of HDPE products HDPE pipes have performed successfully in many applications; however, SC was found

to be the cause of primary premature failure in all three types of applications described

above. The Gas Research Institute published a report that summarizes many stress crack

field failure cases of gas pipes and their forensic analysis (Gas Research Institute, 1984).

Hsuan and McGrath (1998) investigated 19 stress crack field failure cases in corrugated

HDPE pipes for highway applications. Recently, Hsuan and Hartt (2004) completed a

report on the evaluation of SC of HDPE ducts in seven segmental bridges in the State of

Florida. The cracking phenomenon raises concerns regarding the long-term integrity in

some of the HDPE ducts.

Recognizing the SC issue in the HDPE pipe, researchers have carried out extensive

investigations. Their efforts and findings have contributed to the understanding of the

cracking mechanisms of the HDPE material. According to Lustiger (1985), the cracking

of HDPE pipes in the field can be categorized into three types: 1) third-party damage, 2)

joint failure, and 3) material failure. The third-party damage is the result of improper

construction practices. Joint failures are caused either by improper joining conditions, or

by a material deficiency that inhibits proper fusion. Material failure is related to the

polymer’s inherent properties, poor pipe design and faulty manufacturing process.

Ductile versus brittle failure The cracking of polyethylene pipes consists of two modes: ductile or brittle mode.

According to Lu and Brown (1990), ductile failure is associated with macroscopic

yielding. The time to failure of ductile failure is determined by creep rate. On the other

6

hand, brittle failure is associated with crack growth. Lu and Brown suggested that the

two processes occur simultaneously; and the final failure depends on which process is

faster under given stress, temperature and notch depth.

Ductile failure Ductile failures exhibit large material pull-out (or yielding) adjacent to the failure

location. The extreme example is the tensile test of the plastic samples. This type of

failure requires relatively high applied stresses and failure takes place in a relatively short

time. The mechanism is related to the viscoelastic behavior of HDPE materials and

specifically refers to the creep rupture. The resulting failure shows large deformation

accumulating in this process. Figure 1.1 shows the ductile failure in a gas pipe.

Figure 1.1 Ductile failure of a HDPE Pipe

Brittle failure The majority of cracking taking place in the field does not exhibit large deformation.

There is no pull-out or thinning down of material adjacent to the crack. Figure 1.2 shows

a field pipe with a brittle failure. This type of failure is defined as brittle (or brittle-like)

failure.

7

Brittle failure in HDPE usually occurs under low stresses and takes a long period of time

to propagate through the material’s thickness via the process of slow crack growth (SCG).

Lustiger (1987) stated that the SCG process can vary from hours to years at rates less

than 0.1m/s. SCR is the least-desirable failure mode for HDPE products because it shows

no sign prior to the failure. As a result, enormous attention is directed to the study of

SCG. SCG can be resulted of creep- and fatigue-loading.

Figure 1.2 Brittle failures in a HDPE pipe (From Hsuan, 1998)

Brittle failure in HDPE pipes can also be caused by impact. The phenomena of SCG and

impact facture tend to have similar failure appearance. However, they possess

fundamentally different failure mechanisms. Lustiger (1985) compared the differences,

which are listed as follows:

8

a. Impact failure happens fast, with the crack-growth rate close to the speed of sound

(300m/s), called rapid crack propagation (RCP); SCG usually takes a relatively

long time, ranging from minutes to decades (at a speed less than 0.1m/s).

b. Impact failure tends to occur at lower temperatures and at high loads, whereas

with increasing temperature at loads below yield strength, the tendency for SCG

is increased.

c. Impact fracture surfaces in PE display a flaky, scaly appearance (Figure 1.3),

whereas SCG reveals a fibrous texture (Figure 1.4).

Figure 1.5 summarizes the failures that could occur in HDPE pipes. In this study, the

focus is on the phenomenon of SCG, which has been found to be responsible for many

SC of HDPE pipes.

Figure 1.3 Impact fracture surface under 1000x magnification (from Hsuan and McGrath, 1999)

9

Figure 1.4 SC fracture surface under 1000x magnification (from Hsuan and McGrath, 1999)

Figure 1.5 Failure modes that could occur in HDPE pipes

10

1.5 Stress cracking mechanism

Understanding the failure mechanism is a key component to improving the SCR of

HDPE pipes. This section describes the stress cracking process based on macroscopic

and microscopic perspectives.

1.5.1 Lustiger’s microscopic model The microscopic aspect of the stress cracking mechanism is not yet fully understood. In

1985, Lustiger proposed a simple model to explain the microscopic deformation in

ductile and brittle failures.

The HDPE material comprises an ordered crystalline region and a random amorphous

region. The crystalline region consists of packs of folded molecules named lamella,

which are separated by the amorphous region. The intercrystalline polymer chains play

an important role in the deformation. There are three types of intercrystalline chains:

Cilia—chains suspended from the end of a crystalline chain

Loose loops—chains that begin and end in the same lamella

Tie molecules—chains that begin and end in adjacent lamellae

When tensile load is applied normally to the face of the lamellae, the tie molecules are

pulled and deformed. Since the tie molecules are intricately tangled, they can be viewed

as reinforcing elements. This model is sometimes called the “mortar and brick” model, in

which lamellae may be viewed as bricks and the tie molecules as mortar. The mortar

holds the bricks together. At high stresses, the tie molecules are pulled until they cannot

11

support the applied stresses. Then the lamellae break up into smaller units, as illustrated

in Figure 1.6. In this case, ductile failure happens.

Figure 1.6 Graphic illustration of ductile failure at the molecular level (From Lustiger, 1985)

When the stress level is low, tie molecules can gradually disentangle and relax with time.

As a result, interlamellar failure will occur. The process is shown in Figure 1.7. This

failure yields a brittle-like fracture surface

Figure 1.7 Graphic illustration of brittle failure at the molecular level (From Lustiger, 1985)

12

The key component of this model is the role of tie molecules during the fracture process.

Because tie molecules bridge adjacent lamellae, their density, integrity and ability to

remain entangled are critical. Assuming the abilities of all the tie molecules are the same,

the model suggests that materials with fewer tie molecules are more susceptible to brittle

failure than those with greater number of tie molecules. However, if the density of tie

molecules is too high, it is usually at the expense of the material stiffness. Some of the

parameters that influence the number of tie molecules in the HDPE follow:

• Molecular weight:

Higher molecular weight indicates longer polymer chains, which can result in more

tie molecules and more effective tie molecule entanglements.

• Comonomer content:

Polyethylene is a product of the copolymerization of ethylene and comonomers. The

comonomers form short branches along the linear polyethylene molecules that tend to

inhibit crystallization. A higher comonomer concentration leads to more tie

molecules. Furthermore, the branches contained in the chains inhibit the ability of the

tie molecules to slip past one another.

1.5.2 Crazing Crazing can be considered as the macroscopic aspect of stress cracking. The craze, or

damage zone, is the region ahead of the crack tip which consists of voids and stretched

fibrils. The structure of the craze is illustrated in Figure 1.8. Brown et al. (1985)

suggested that the brittle failure process can be categorized into a series of events. First,

a craze is formed at the root of the notch immediately following the application of

13

loading. At the root of the craze, a plastic zone is generated due to the localized yielding

of the material.

Yielding

Micro-fibrils

Crack tip

Figure 1.8 Craze at the crack tip

The craze remains stable, with the micro-fibrils sustaining the stresses. As time passes,

the craze grows slowly by stretching the micro-fibrils. The rupture of the micro-fibrils

near the base of the craze leads to a growing crack. When the remaining ligament

reaches the critical size, complete failure occurs. Chudnovisky et al. (2003) suggested

that crack propagation can be viewed as a step process. They named the craze itself the

process zone (PZ), and the craze and crack together the crack layer (CL). Under tensile

stresses, the fibers inside the PZ creep. After a period of time, the fibers break down, and

the crack extends into the PZ. The time until the PZ breaks down corresponds to the

arrest time in the crack propagation process. After that, a new PZ is developed from the

14

intact material ahead of the crack. The newly-created PZ stops the cracking process while

the micro-fibrils undergo creep deformation. The process repeats itself. The time to

formation of a new PZ is significantly shorter than the arrest time. This process of steps

will end when the crack becomes unstable.

Most literature divides the SC process into crack initiation and crack growth. The

initiation period is the stage before the craze is formed. Once the craze is formed, the

crack propagation begins. Cracks initiate from defects in the material such as flaws,

notches created by installation, impingement, and bending loads. In the laboratory tests,

notched specimens were used to generate consistent failure time. The failure time

represents time for both crack initiation and propagation (Cassady and Uralil, 1985).

Bragaw (1980) indicated that for HDPE pipes, one-third of the time to failure is

consumed by crack initiation. Others suggested that the initiation of the cracking can

represent as much as 90% of the total cracking process. Bragaw (1983) stated that the

initiation time becomes infinite when the stress is below a certain threshold.

1.5.3 Environmental stress cracking Environmental stress cracking (ESC) occurs when PE is subjected to stresses in the

presence of various environmental agents. The fundamental molecular mechanism of

ESC in PE is still debated. Nevertheless, ESC and SCG share many similarities, such as

load and temperature dependence of failure time, and brittle-like failure surface.

Therefore, it is thought that they probably have a common molecular deformation

mechanism. If so, it would be valuable to use ESC as a tool to evaluate the long-term

15

behavior of polyethylene material, since the ESC process takes a much shorter time to

complete than conventional SC tests.

The acceleration effects of environmental agents in SC have been studied by many

researchers. Hopkins et al. (1950) suggested that the surfactant exerts a spreading

pressure on intrinsic flaws and cracks on the polymer surface. The pressure works with

the applied stress and results in crack initiation. Isaksen et al. (1963) suggested that ESC

occurs because the agent is absorbed preferentially by the most highly stressed

crystallites, which act as a stress concentration raiser. Some researchers believe that the

environmental agent induces the plasticization of tie molecules and enhances their

disentanglement, subsequently accelerating the SC process.

1.5.4 Fatigue-related stress cracking While previous sections discuss cracking under static loading conditions (creep),

dynamic loading (fatigue) can also induce cracking. It has been observed that dynamic

loading can significantly increase crack propagation. Nishimura and Shishich (1985)

found that fatigue testing can shorten the creep failure time by more than two orders of

magnitude, while Shah et al. (1998) indicated acceleration of up to three times in the

fatigue test. Zhou and Brown (1993) found that the fastest failure in the fatigue test

occurs when the loading is in tension-compression mode, and is probably due to the

buckling of the fibrils under the compressive load. Parsons et al. (1999) found that the

size of craze is controlled by mean stress alone, and the crack growth rate is related to

both the maximum and mean stress through a power-law relationship.

16

Since fatigue loading can significantly accelerate the cracking rate, the test can be

conducted at room temperature while still achieving reasonably short testing time.

However, questions arise regarding the similarities between fatigue and SCR. Some of

the similarities include: 1) their fracture surfaces have a similar appearance; 2) the fatigue

crack growth exhibits step propagation, i.e., a craze is formed at the crack tip, which

relieves the stress, and the crack growth is stopped as long as the craze stays stabilized; 3)

correlation between creep and fatigue has been observed. Zhou et al. (1989) performed a

series of fatigue and creep tests and found that there is a linear relationship on a log-log

scale between the cycles to failure under a fatigue test and the time to failure under a

constant load test. Their finding suggested that fatigue test can be used to predict the

creep fracture of polyethylene. Nevertheless, current practice of fatigue test is limited to

material rating purpose only.

1.6 Stress cracking test methods The cracking of HDPE pipes can take place as early as a few months after installation,

but the majority of the cracking failure occurs after years. This makes it impractical to

study the SC by simulating the service condition in the laboratory. Thus, a variety of

acceleration methods have been developed to target a reasonably short testing time (or

failure time). The common approaches to achieving this objective include introducing a

stress concentration (e.g. notching), and utilizing elevated temperatures, environmental

solutions, high stress, or fatigue loading. A brief introduction of various test methods

used to evaluate the SC of HDPE materials is presented in this section.

17

Bent strip test (ASTM D1693) This test was the dominant QA/QC test for polyethylene materials in the ‘60s and ‘70s. It

involves cutting ten rectangular specimens notched on the surface longitudinally. The

specimens are then bent into a 180o arc and confined within the flanges of a small metal

channel. The entire assembly, with notched specimens, is immersed in either 10% or

100% Igepal solution at temperatures of 50oC or 100oC. There are three test conditions,

defined by the test specimen size, notch depth, and test temperature. The specimens are

examined after certain periods of time and the percentage of the failed specimens is

recorded. The test duration varies from 24 hours to 1000 hours, depending on the

specification set by different HDPE industries. The bent strip test is simple and easy to

perform. However, significant stress relaxation occurs during the test, and rate of stress

relaxation is difficult to quantify. This test has been found to be insufficient to

distinguish the SCR property of current HDPE materials; furthermore, the test results

contains a large standard deviation.

Pennsylvania notched test (ASTM D1473) The Pennsylvania notched test (PENT) was developed by Dr. Norman Brown at the

University of Pennsylvania, (Brown et al., 1989). Test specimens can be taken from

compression molded plaques or manufactured pipes. The compression molded plaques

are made according to ASTM D4703, with some modifications. After the resin is heated

to the set temperature, pressure is applied and removed several times to eliminate voids.

The plaque is then slowly cooled to room temperature to achieve a high crystallinity and

to minimize residual stresses. Specimens of 10x25x50mm (0.4x1x2 inches) bars are

taken from the plaque. Two side notches of 1mm deep and one side main notch of

18

3.5mm (0.14 inches) are produced in the same plane. The two side notches are referred

to as “side grooves”, which are used to promote the plane strain condition. The main

notch is where the cracking is expected to initiate. The specimens from manufactured

pipes are prepared based on the pipe diameters. For pipes larger than 25mm (1inch) in

diameter, rectangular bars are cut from the pipe walls; for those with diameters less than

25mm (1 inch), sections of the pipe are used for the test. The notches on the specimens

are made according to the pipe wall thickness. The specimens are tested at 80oC in air

under a single stress of 2.4 MPa (348 psi).

Full notch creep test (ISO16770) The full notch creep test (FNCT) was developed by Nishio et al. (1982), and is the

preferred test method in Europe due to its shorter failure time compared to the PENT test.

The FNCT specimen is a square section of 10x10mm (0.4x0.4 inch) bar (about 3.5 inches

long) with four coplanar notches 1.5mm (0.06 inch) deep, made by a razor. The test is

performed in a liquid environment at 80oC under a single stress level. One common

choice for the liquid is the 2% Igepal CO-630 mixed in 98% demineralized water. The

test is suitable to evaluate the latest pipe resins, such as PE100, because it takes a few

hundred hours to fail the specimens, compared to a few thousand hours for the PENT test.

Notched constant ligament stress test (ASTM F2136) The notched constant ligament stress (NCLS) test was developed from the notched

constant tensile load (NCTL) test and is designed to evaluate corrugated HDPE pipes and

pipe resins. The test uses dumbbell-shaped specimens with notch on one side of the

specimen’s surface. The depth of the notch is 20% thickness of the specimen. The

19

major difference between this and other tests is that the specimens are taken from

compression molded plaques in the NCLS test, instead of the end products in the NCTL

test. Also, a single applied stress of 600 psi is used in the NCLS test. The test is

performed in 10% Igepal solution at 50oC. Figure 1.9 shows the test equipment.

Figure 1.9 Test equipment for NCLS test

Hydrostatic stress rupture test (ASTM D1598) This is a performance test and is used for pressure pipes. A section of manufactured pipe

with caps on both ends is subjected to a constant internal water pressure at a desired test

temperature. The test continues until the pipe fails. Even with elevated test temperatures

and high stresses, this test takes a long time to finish. The crack initiation time based on

material defects themselves occupied a significant part of the testing. The test truly

reflects the performance of the pipe under the designed pressure; however, a large scatter

in the test data.

20

Notched pipe test (ISO 13479) The potential scatter in the hydrostatic rupture can be avoided by introducing notches in

the pipes. In the United Kingdom, both gas and water industries have adopted the

notched pipe test (NPT) for quality assessment. This is an elevated temperature stress

rupture test on a pipe with machined axial “V” notches. Four notches are equally-spaced

around the circumference of the pipe. The notches run along the longitudinal axis of the

pipe, with length equal to the pipe’s outside diameter, and the depth is to give a

remaining ligament of 80%±2% of the minimum wall thickness of the pipe. The pipe is

tested at a stress level of 4 MPa (580 psi) for PE80 and at 4.6 MPa (667 psi) for PE100

materials. It is recommended that at least three tests be performed with no failure before

165 hours for both PE80 and PE100. The test environment is air at 80oC.

Fatigue test All of the above-described test methods are creep-related. As discussed earlier, fatigue

testing is an alternative method that accelerates crack growth by applying cyclic stress.

The test is best performed at a high frequency in order to decrease test time. However,

increasing frequency can induce heat effect in the specimen. Most fatigue tests for

polymers use frequencies around 1 Herz. The specimen geometry and stresses vary from

study to study, depending on the test material. However, notched specimens have been

commonly used to accelerate the crack initiation time. The fatigue cycles could be

controlled by either load or strain.

Table 1.1 summarizes the SC test methods.

21

21

22

1.7 Residual stress Aside from externally- applied stresses, residual stress can also be a stress factor causing

SC. It is known that all plastic pipes contain residual stress introduced during the

manufacture processes. The magnitude and distribution of residual stress vary

significantly depending on manufacturing process. One of the main factors causing

residual stresses is differential shrinkage through the pipe wall during the cooling process.

Figure 1.10 shows the residual stress generated from two cooling approaches.

Figure 1.10 Residual stress distribution caused by cooling

Maxwell (2001) suggested that if cooling takes place from only one side of the wall, the

cooled side will shrink rapidly. The newly-solidified section constrains its adjacent part

from shrinking freely. As a result, compressive residual stress is created in the cool side

and tensile residual stress is formed in the opposite side (Fig. 1.10(a)). However, if both

sides are cooled simultaneously, compressive stress will be created near the two surfaces

and tensile stress in the center (Fig. 1.10(b)).

23

Residual stresses can also be introduced by the drawing of the polymer chains during the

manufacturing process. Wong (1983) found that biaxial tensile stresses are presented on

the inner wall and biaxial compressive stresses on the outer wall for certain types of

smooth pipe. Williams (1993) measured the residual stresses in both longitudinal and

circumferential directions of extruded isotropic smooth pipes, and found the tensile

residual stresses ranging from 2.12 to 4.07 MPa (307 to 590 psi). For anisotropic drawn

pipes, residual stresses on the inner surface varied significantly, from tensile stress of

0.25 MPa (36 psi) to compressive stress of 2.91 MPa (422 psi). Chaoui and Moet (1987)

studied the distribution of residual stress through the smooth pipe wall thickness and

found that 24% of the inner wall consisted of tensile residual stresses, while the

remaining thickness had compressive residual stresses, with the maximum value at the

outer surface of the pipe wall. Kanninen et al. (1993) found that the distribution of

circumferential residual stresses exhibited a parabolic shape through the smooth pipe wall,

with tensile stress in the inner wall.

High residual stress in the pipe could have significant impact on the SC property of the

pipe. Therefore, quantifying the residual stresses in the pipe is essential in predicting the

long-term behavior of the pipes. In this study, residual stresses in the smooth HDPE duct

and corrugated HDPE pipe are evaluated.

Tremendous efforts have been made to understand the residual stresses in metal pipes.

Conversely, the evaluation of residual stress in plastic pipes is very limited. Many

24

methods used to assess the residual stress in plastic pipes were adopted from those used

for metal pipes. Some of these methods are presented here.

Slitting and parting-out method

In order to measure residual stress in the circumferential direction of the pipe, a ring

specimen with width of one-inch is removed from the pipe. The ring is then slit open. If

the pipe has tensile stresses on the inside wall, the ring will tend to close and decrease the

diameter. By measuring the changing diameter over time, the maximum residual stress

can be calculated. For measuring the longitudinal residual stress, a small rectangular

shaped section is cut into the end of the pipe. The displacement at the end of the

removed section is monitored with time.

Layer removal method The layer removal method is the most widely-used technique to measure residual stresses.

A rectangular specimen is taken from the region of interest in the pipe, and then layers

are removed from one side of the surfaces. The specimen undergoes dimensional change

after removal of each layer. The average stress in each layer is calculated based on the

dimensional change. A plot of the residual stress across the thickness can be obtained.

However, the machine sectioning can introduce undesirable stresses to the test sample

that can be either surface residual stresses or gross yielding stresses, reducing the

accuracy of the measurement.

25

Hole drilling method (ASTM E837)

This method involves drilling a hole into the material and measuring the surface strains in

the vicinity of the hole during the drilling. Electric resistance gages are usually used to

determine quantitatively the strains close to the drilling. The strains are used to calculate

the biaxial stresses and their distribution at and near the surface of the part. There are a

number of limitations to this method: the test sample must be wide compared with the

diameter of the drilled hole; the residual stresses must be constant in the drilling area;

inelastic flow should not occur during and after the drilling; and the method can measure

only the residual stresses on the surface or at very limited depth.

Annealing method

This method is based on the assumption that a temperature increase does not change the

molecular structure of the material significantly. The operation involves taking the

specimens from the test section of the pipe and heating them to a suitable temperature.

After a certain amount of annealing, the residual stress is thought to be completely

relieved. The residual stresses are then measured according to the change of dimensions

of the specimen prior to and after the annealing.

There are other test methods, such as X-ray diffraction, ultrasonic method, indentation,

and stress corrosion method. They are either still under development or used less often.

1.8 Lifetime prediction methods All of the SC tests described here use high temperatures to accelerate the failure process.

Prediction methods are required to extrapolate the test data to the service temperature.

26

These methods can be categorized into three groups: the fracture mechanics method, the

shifting method, and the rate process method (RPM).

1.8.1 Fracture mechanics method Fracture mechanic theories can be used to model the failure time of SC. Liner elastic

fracture mechanics (LEFM) have often been used to analyze the cracking of pipes.

Numerous studies have been conducted in an effort to explore the relationship between

the stress intensity factor (K) and the crack growth rate. Some semi-empirical models

have been developed; however, the reliability of these models is not certain. Chan and

Williams (1983) found that the steady state of the crack growth rate assumed by most of

the fracture mechanics models exists only when the growth rate is at and above 10-9

m/sec. However, the actual crack growth rate in field application is well below that value.

Popelar and Staab (1983) state that LEFM frequently fails to predict the cracking

behavior of polyethylene pipes because it cannot properly account for the creep effect.

Due to the semicrystalline nature of HDPE, the validity of linear elastic fracture

mechanics (LEFM) is still controversial. More appropriate fracture mechanics

techniques are needed to analyze cracking in plastic piping. The J-integral method has

been extensively studied; however, the complexity of the method keeps the model from

practical application.

1.8.2 Shifting method Boltzmann (1872) developed the fundamental equation for linear viscoelasticity, and one

of the applications is the time temperature superposition (TTS) principle. By measuring a

mechanical property at a series of temperatures, a master curve at a targeted temperature

27

can be obtained through shifting of the curve at each test temperature. The master curve

can span decades of time, from which the material’s lifetime at the targeted temperature

can be predicted.

Any individual test temperature, T, and the targeted temperature Tr, have the following

relationship:

(1.2) ),/(),( rT TatDTtD =

Where is the time-temperature shift factor, and is given by the Williams-Landel-Ferry

(WLF) equation:

Ta

)()(log

2

1

r

rT TTC

TTCa++−⋅

= (1.3)

Where, C1 and C2 are constants.

The assumption of TTS is that the material structure does not change during the test.

Faucher (1959) showed that TTS is only valid in the linear deformation range below the

material’s melting temperature. He believed that when the temperature is above the

melting point, the crystallinity in the PE will change. Onogi et al. (1967) suggested that

the temperature affects the mobility of the crystallites. Other researchers (Popelar et al.

1990; Thomas, 1997) suggested that the high temperature leads to recrystallization, in

which small crystallites grow into large crystallites. Popelar et al. (1990) found that

horizontal shifting (temperature) alone cannot achieve a coherent master curve, due to the

effect of temperature on crystallinity. However, with the help of vertical shifting, a

master curve can be obtained. Since the method involves both the horizontal and vertical

shifting of the curves, it is called bi-directional shifting. Popelar et al. (1990) analyzed a

28

large number of laboratory test data on relaxation moduli, stress rupture, and slow crack

growth, and found that horizontal and vertical shift functions are universal for MDPE and

HDPE used for gas pipes. The expressions for the shift factors are

)](109.0exp[ rT TTa −−= (1.4)

)](0116.0exp[ rT TTb −= (1.5)

Where = horizontal shift factor; = vertical shift factor; Ta Tb T = lab test temperature;

= arbitrary reference temperature (or targeted temperature). rT

Lu and Brown (1991) also proposed another shifting equation. These equations are based

on the Arrhenius equation discussed in the next section.

⎥⎦

⎤⎢⎣

⎡−⋅=∆

TTRQh

r

1143.0 (1.6)

⎥⎦

⎤⎢⎣

⎡−=∆

rTTCv 11

(1.7)

Where = horizontal shift factor; h∆ v∆ = vertical shift factor; Q = activation energy; R =

gas constant; C = coefficient.

1.8.3 Rate process method (RPM) The Swedish chemist Arrhenius found empirically that the logarithm of the chemical

reaction rate varies as the reciprocal of absolute temperature, provided that the range of

the temperature does not effect large structure change in the material. It can be expressed

in Equations 1.8 and 1.9.

RTEekk /0

−= (1.8)

29

Or

RTEkk /lnln 0 −= (1.9)

Where k = kinetic rate constant; k0 = pre-exponential kinetic rate constant; E = apparent

activation energy; R = universal gas constant, which is 8.314J/mole; T = absolute

temperature.

Equation 1.9 can be simplified and used to describe the relation between failure time, t

and temperature, T:

TBAt +=log (1.10)

The interested failure time at a certain temperature can be obtained by the transformation

of the Arrhenius equation:

)11(logrr TTR

Ett

−⋅= (1.11)

Where t= failure time at test temperatue ; tr = failure time at reference temperature;

T= test temperature; Tr = reference temperature; A, B = constants

The Arrhenius equation provides the theoretical basis bridging the time to failure at

different temperatures. The fundamental theory for the rate process method (RPM) is the

Arrhenius equation. The development of RPM is illustrated as follows:

It has been found that failure time and applied stress have a linear relationship on log-log

axis

σloglog ⋅+= BAt (1.12)

30

Where σ = applied stress; t= corresponding failure time

Combinig Equations 1.10 and 1.12, we arrive at the RPM model introduced by Bragaw

(1983):

σloglog ⋅++= CTBAt (1.13)

A similar approach has been used to develop other RPM mathematical models, as follows.

Three coefficient models include:

TC

TBAt σloglog ⋅++= (1.14)

TC

TBAt σ⋅++=log (1.15)

Four coefficient models :

TDT

CTBAt ⋅+

⋅++=

σloglog (1.16)

σσ logloglog ⋅⋅+⋅

++= TDT

CTBAt (1.17)

σσ logloglog ⋅+⋅

++= DT

CTBAt (1.18)

Six coefficients model :

]log)([21]log)([

21log

TFC

TEBDA

TFC

TEBDAt σσ ⋅−

+−

+−−⋅+

++

++=

(1.19)

Where A, B, C, D, E, F = constants

31

Eugene et al. (1985) discussed the pros and cons of these models. It is found that the four

coefficient models lead to better “lack-of-fit” values, which means the highest probability

for regression line extrapolation. However, the three coefficient model can provide good

fitting as well, without the complexity of a fourth term. Furthermore, while adding more

terms may improve the fit, it also increases the uncertainty of the predictions. Therefore,

Equation (1.14) is the model recognized as the most suitable in predicting the failure time,

and is adopted by both ASTM and ISO.

32

Chapter 2: Stress Cracking of HDPE Ducts in Segmental Bridges

2.1. Introduction This chapter focuses on the SCR of the HDPE pipes that serve as a protective layer for

post-tensioning tendons in segmental bridges. These pipes are commonly called HDPE

ducts. Post-tensioned tendons are a key structural component of the segmental bridge,

holding the precast concrete boxes together. The tendons consist of three parts: multiple

high-strength steel strands, cement grout fill, and HDPE ducts. The cement grout and the

HDPE duct serve as double protection layers for the steel strands encased inside.

However, cracking of HDPE ducts can lead to corrosion of the steel strands by allowing

moisture to penetrate the double protection layers. Cracking of the ducts should,

therefore, be prevented. A recent survey on post-tensioned tendons (Hartt and Hsuan,

2004) reported that cracking appeared in the HDPE ducts of several segmental bridges in

the State of Florida. A project was therefore initiated by the state of Florida to

investigate the causes of the duct cracking. The project was carried out by Drexel

University and Florida Atlantic University (FAU). This chapter consists of two parts,

each covering one part of the investigative project. During part one of the project, Drexel

University investigated the field-cracked HDPE ducts by identifying the cracking

mechanisms, selecting appropriate test methods to assess the stress-crack resistance of

HDPE ducts and recommending specifications to improve the quality of HDPE ducts.

Part two (performed by both FAU and Drexel University) concentrated on the evaluation

of stresses in the HDPE duct, together with service life assessment by fatigue test.

33

2.2. Background 2.2.1. Segmental bridges Construction of precast segmental bridges is a relatively new technology. The

technology was invented in France in the early ‘60s, and used widely in Europe during

the late ‘60s and ‘70s. The first segmental bridge constructed in the United States (US)

was the John F. Kennedy Memorial Causeway near Corpus Christi, Texas, in 1971. In

the ‘80s, segmental bridges were constructed in many states. A precast segmental bridge

is an assembly of precast concrete members, which are manufactured in a concrete plant,

often near the construction site. First, the piers are built by stacking one precast block on

top of the other. The segments of concrete “boxes” (Figure 2.1) are then hoisted and

lowered on top of the piers to form the bridge deck. Figure 2.2 shows a segmental bridge

under construction. Figure 2.3 is a picture taken inside the box, showing the tendons.

The steel tendons are designed to connect the box girders and reinforce the structure.

There are two types of tendons: internal and external. The internal tendons are cast inside

the concrete box and cannot be inspected. The external tendons are outside the concrete,

as shown in Figure 2.3. The construction method for external tendons involves housing

the steel strands in the HDPE duct. The steel strands are gripped at both ends, pulled and

anchored. Cement grout is then introduced into the duct, filling up the space and

encasing the tensioned steel strands.

Compared with conventional bridges, precast segmental bridges are more economical

(especially when covering large spans), require less construction time and easy

34

maintenance, provide improved durability and appealing aesthetics. In 1999, the

American Segmental Bridge Institute (ASBI) performed a comprehensive survey, and

found satisfactory performance in 99% concrete segmental bridges.

Figure 2.1 Precast concrete “box”

Figure 2.2 Construction of a segmental bridge

35

Tendons

Figure 2.3 Inside view of a segmental bridge 2.2.2. Tendon failures in segmental bridges The integrity of the tendons is key for the safety of segmental bridges, since they are the

reinforcing elements that hold the superstructure together. Therefore, corrosion of the

steel strands must be prevented. The HDPE duct and cement grout act as double

protection layers for the encased steel strands. Figure 2.4 shows the cross-section of a

typical tendon.

Figure 2.4 Nomenclature for cross-section of a segmental bridge tendon

36

Two corrosion-induced failures occurred in England: the Bickton Meadows footbridge in

1967 and the Ynys-Y-Gwas Bridge in 1985. The failures resulted in a ban on the use of

post-tensioned bridges in the United Kingdom from 1992 to 1996. In the US, during the

spring of 1999, a corrosion-related failure of an external tendon was found in the Niles

Channel Bridge, Florida, after the bridge had seen 16 years of service (Powers, 1999).

Niles Channel Bridge is one of a series of low-level segmental bridges stretching over

seawater in the Keys area. Further inspection revealed that two steel strands were

corroded in the tendon anchorage. In 2000, due to corrosion problems, eleven tendons

out of a total of 846 were replaced in the Mid Bay Bridge after seven years of service.

Also, in the same year, numerous corroded steel strands were discovered in segmental

piers of the Sunshine Skyway Bridge, built in 1986. The corrosion was a result of

seawater entering the ducts through the split in the ducts. Figure 2.5 and 2.6 show the

corroded steel strands.

Figure 2.5 Corroded steel strands in segmental bridge tendons (Mid Bay Bridge)

37

Figure 2.6 Close-up view of the corroded steel strands

2.2.3. General Corrosion mechanism In good-quality grout, the encased steel strands are protected against corrosion by the

alkalinity of the cement paste, whose pH is typically between 12 and 14. In a highly-

alkaline environment, the surface of the steel is passivated and protected by the formation

of an oxide film. The passive oxide film is stable at pH values greater than

approximately 9.5 in a chloride-free environment. The pH value that is necessary to

maintain the passive oxide film increases with increasing chloride content. The initiation

of corrosion of the steel requires the breaking down of this oxide film, and this can occur

by either diffusion of chlorides into the concrete or carbonation of the concrete.

Carbonation is the result of a reaction of CO2 in the air with Ca(OH)2 in the concrete. As

a result, the pH of the concrete gradually decreases. When the pH value of the concrete

falls below 9.5 (in a chloride-free environment), the oxide film starts breaking down.

The corrosion process is illustrated in Figure 2.7.

.

38

Figure 2.7 Corrosion mechanisms of steel tendons (From Hamilton et al., 1995)

Tendons are in greater danger in bridges that are built above or near seawater, due to the

high chloride content of sea water. Furthermore, the potential for steel corrosion is

greater when the protective HDPE duct cracks. Thus, the integrity of the HDPE ducts

must be maintained throughout the service life of the bridge.

2.3. HDPE ducts included in this study In this study, the HDPE ducts of seven bridges in the state of Florida were evaluated.

Samples were retrieved from both cracked and uncracked ducts. Information on the

bridges and the number of retrieved field samples is shown in Table 2.1. The ducts in

MB and SSK bridges had significant cracking problems.

39

Table 2.1 Information on samples retrieved from the bridges

Bridge County Location

Cracking Condition

Field Sample Age (yr.)

Total No. of Field

Samples

No. of Cracked Samples

Mid Bay (MB) Okaloosa Severe

Cracking 10 3 3

Garcon Point Santa Rosa No Cracking 4 1 0

Seven Mile Monroe No Cracking 21 1 0

32 column 4 Skyway (SSK) Pinellas Severe

Cracking 17 34 span 3

Channel Five Monroe No Cracking 21 1 0

Long Key Monroe No Cracking 22 3 0

Niles Channel Monroe No

Cracking 20 2 0

The seven bridges are located in different regions of the state. The MB Bridge is situated

in the northern part of Florida, where maximal ambient temperatures range from -10 to

40oC. Seven Mile, Channel Five, Long Key, and Niles Channel bridges are located in the

Keys region, with maximal temperatures ranging from 2 to 38oC. Garcon Point, Skyway

bridges are located in the central part of the state, with temperatures ranging from -5 to

40oC.

2.4. Assessment of cracking mechanism 2.4.1. Introduction The cracked ducts are coded with respect to their positions in the bridge. Figure 2.8

shows a cracked duct. The cracked section of the duct was removed from the tendon

according to a specific sampling procedure so that the fracture surface of the crack would

40

be protected. Figures 2.9 and 2.10 show the sampling protocol for obtaining a full crack

or part of the crack, respectively.

Figure 2.8 Cracking in HDPE ducts

1stCut

2ndCut

2ndCut

Crack ~ 4 feet

1stCut

Figure 2.9 Duct section that contains a full crack

1stCut 2ndCut

2ndCut

Crack ~ 4 feet

Figure 2.10 Duct section that contains part of the length of the crack

41

The cracking mechanisms were assessed by both macroscopic and microscopic

examinations of the cracks. Once the mechanism is identified, the appropriate test

methods can be employed to assess the SC properties. Furthermore, the cause of the

crack initiation can be identified by the microscopic examination.

2.4.2. Macroscopic and microscopic evaluation The retrieved field samples were shipped to the laboratory for examination. Each

cracked duct was photographed and sketches of the cracks were drawn. Specimens for

microscopic examination were then taken at various locations along the cracks. The

fracture surfaces of the specimens were examined under a scanning electron microscope

(SEM). Three cracked samples from MB and one cracked sample from SSK were

selected for presentation.

2.4.2.1 Cracked samples from the MB Bridge The MB Bridge presented the most severe cracking problem in the HDPE ducts. Three

samples retrieved from the MB Bridge were chosen for examination: 67-5-A, 38-4-A,

and 126-4-A.

• Sample MB 67-5-A

MB 67-5-A (Figure 2.11) features a short crack oriented longitudinally along the duct.

The crack is located near the 8 o’clock position of the duct circumference. The crack

length on the inner surface of the pipe is about 5 inches, and the crack length on the outer

surface of the pipe about 4.5 inches. Specimens 1 and 2 are located near the crack tips.

Figure 2.12(a) shows the general view of the fracture surface of Specimen 1. The

detailed fracture surface under 1000x magnification illustrates the fibril structure (Figure

42

2.12 (b)). This is an indicator of SCG mechanism. The small size of these fibers

suggests that the applied stress is relatively low during crack propagation. There are

many impurities observed on the fracture surface, as seen in Figure 2.12 (c). These

impurities may be the origin of the crack initiation.

43

Figure 2.11 Drawing of sample MB 67-5-A

Figure 2.12 Specimen 1 from sample MB 67-5-A: (a) general view of fracture surface; (b) fibril fracture morphology in area “A”; (c) a detailed view of an impurity.

44

Figure 2.13 shows the fracture morphologies of the specimen, which are very similar to

those in Figure 2.12. Small fibrils on the fracture surface in Figure 2.13 (b) indicate the

slow crack growth mechanism. Again, impurities (Figure 2.13 (c)) are found in areas

“B” and “C”, and these could initiate the crack.

Figure 2.13 Specimen 2 from sample MB 67-5-A: (a) general view of fracture surface; (b) fibril fracture morphology; (c) a detailed view of an impurity in area “B” and “C”.

45


In sample MB 38-4-A (Figure 2.14), two cracks can be observed, Crack B1 and B2. Both

of them occurred at the 12 o’clock position. They run along an irregular line and overlap

each other by about 1 inch at the end without connecting. Crack B1 is about 13” long on

both the inner and outer surfaces, and B2 is about 34 inches on both surfaces.


Four specimens were taken at different positions on the crack in sample MB 38-4-A.

Specimen 1 is located near the end of Crack B1, where the Crack B1 and B2 join.

Specimens 2, 3, and 4 were taken from Crack B2 and located in the right, middle and left

section of the crack, respectively. The fracture morphology of Specimen 1 is shown in

Figure 2.15. The overall microstructure on the fracture surface is fibril structure, as can

be seen in Figure 2.15(b). In this duct, air bubbles can be observed. No clear crack

initiation point can be determined. In the upper half of the fracture, a horizontal line can

be identified. This is believed to be a sign of the crack arresting during a fatigue process.

46

Figure 2.15 Specimen 1 from sample MB 38-4-A: (a) general view of the fracture surface; (b) fibril fracture morphology.

The fracture morphology of Specimen 2 is shown in Figure 2.16. Figure 2.16 (b) shows

the overall microstructure, which reveals fibril structures. No crack initiation can be

defined in this section of the crack. In the surface near the inner duct wall, fatigue lines

can be observed (Figure 2.16(c)). The fatigue lines indicate the existence of fatigue

process.

47

Figure 2.16 Specimen 2 from sample MB 38-4-A: (a) general view of the fracture surface; (b) fibril fracture morphology; (c) a detailed view of the fatigue line morphology.

The fracture morphology of Specimen 3 is shown in Figure 2.17. The fracture surface

also reveals the fibril structure (Figure 2.17 (b)). There is a hemispherical pattern on the

fracture surface. The center of the circles is approximately at point “A” near the inner

surface of the duct wall, and this is believed to be the initiation point of the crack. The

detailed view of area “A” shows an impurity (Figure 2.17 (c)).

48

Figure 2.17 Specimen 3 from sample MB 38-4-A: (a) general view of the fracture surface; (b) fibril fracture morphology; (c) a detailed view of area “A”.

On the fracture surface of Specimen 4 shown in Figure 2.18, the fibril structure (Figure

2.18 (b)) was also observed. Some fatigue lines were observed at the inner duct surface

near area “B”; these are shown in Figure 2.18 (c). Figure 2.18 (d) shows an impurity

located at both areas “A” and “B”.

49

Figure 2.18 Specimen 4 from sample MB 38-4-A: (a) general view of the fracture surface; (b) fibril morphology; (c) a close view of fatigue lines near the inner duct surface;

(d) a close view of the area “A”.


Sample MB 126-4-A (Figure 2.19) also shows two cracks, C1 and C2. They occurred at

the 10 o’clock position. Crack C1 is about 14 inches long on the inner surface and 13

inches on the outer surface Crack C2 is about 40 inches on the inner surface and 38

inches on the outer surface. The two cracks are separated from each other about one inch

of distance, measured from the inner surface.

50


Four specimens were taken at different positions along the crack in Sample MB 126-4-A.

Specimens 1 and 2 are located near two ends of Crack C1. Specimen 3 is in the middle

of Crack C2 and Specimen 4 is close to the end of Crack C2. Figure 2.20(a) shows the

general view of Specimen 1. The morphology of Specimen 1 is dominated by fibril

structure (Figure 2.20 (b)). Area “A” appears to be the initiation point, and the close

view of area “A” shows an impurity (Figure 2.20 (c)).

51

Figure 2.20 Specimen 1 from sample MB 126-4-A: (a) general view of the fracture surface; (b) fibril fracture morphology; (c) a detailed view of area “A”.

Figure 2.21 shows the fracture surface of Specimen 2. Impurity and fibril structures in

area “A” can be observed in Figure 2.21 (b) and Figure 2.21(c), respectively. In area

“C”, fatigue lines are revealed (Figure 2.21 (d)). In area “B”, flaky structure is observed

(Figure 2.21 (e)), which indicates an impact failure.

52

Figure 2.21 Specimen 2 from sample MB 126-4-A: (a) general view of the fracture surface; (b) fibril fracture morphology in area “A”; (c) a detailed view of the impurity in

the area “A”; (d) a detailed view of the fatigue line in area “B”; (e) the flaky fracture morphology of rapid crack propagation in area “C”.

The morphology of Specimen 3 is shown in Figure 2.22. The fracture surface is covered

by the fibril structure (Figure 2.22 (b)). Also, the fracture surface is covered by many

white particles, which make the observation difficult.

53

Figure 2.22 Specimen 3 from sample MB 126-4-A: (a) general view of the fracture surface; (b) fibril fracture morphology; (c) a detailed view of the area “A”.

Figure 2.23 shows the microstructure of Specimen 4. The overall fracture morphology is

a fibril structure (Figure 2.23 (b)). An initiation point can be seen in area “A”, where an

impurity is located (Figure 2.23 (c)). Figures 2.23(d) and (e) show the detailed view of

areas of “B” and “C”, respectively. Both of these areas reveal the existence of fatigue

lines.

54

Figure 2.23 Specimen 4 from Sample MB 126-4-A: (a) general view of the fracture surface; (b) fibril fracture morphology; (c) a detailed view of the imperfection in the area “A”; (d) a detailed view of fatigue line in area “B”; (e) a detailed view of fatigue line in

area “C”.

55

2.4.2.2 Cracked samples from the SSK Bridge The SSK Bridge also presented severe cracking problems in the ducts in both the column

and span parts of the bridge. Sample SSK 131-SB-SE-6 from the column was chosen for

presentation. Figure 2.24 shows a sketch of the crack in Sample SSK 131-SB-SE-6,

which is about 9 inches long on both inner and outer surfaces. The crack runs

longitudinally along the duct.

Figure 2.24 Drawing of column sample SSK 131-SB-SE-6

Three specimens were taken from the crack for microstructure examination. Specimens 1

and 2 are located in the middle section of the crack, and Specimen 3 at the left tip of the

crack. Figure 2.25 (a) shows the general view of Specimen 1. The crack initiated from

the inside surface and propagated through the thickness of the duct wall as suggested by

the hemisphere pattern on the fracture surface. Figure 2.25 (b) reveals the fibril structure

on the fracture morphology. The imperfection can be found at the initiation point shown

in Figure 2.25 (c).

56

Figure 2.26 (a) shows the general view of Specimen 2. Figure 2.26 (b) is an imperfection

existing in area “A”. The impurity is thought to be the initiation point for the crack.

Figure 2.27 shows the general view of the fracture surface of Specimen 3. Figure 2.27 (b)

reveals the fibril structure.

Figure 2.25 Specimen 1 from Sample SSK 131-SB-SE-6: (a) general view of the fracture surface; (b) fibril fracture morphology; (c) a close view at crack initiation point.

57

Figure 2.26 Specimen 2 from sample SSK 131-SB-SE-6: (a) general view of fracture surface; (b) a close view of the impurity at area “A”.

Figure 2.27 Specimen 3 from sample SSK 131-SB-SE-6: (a) general view of the fracture surface; (b) fibril fracture morphology.

58

2.4.3. Summary of cracking mechanism evaluation The information obtained from the general appearance of the cracks can be summarized

as follows:

• All cracks ran longitudinally along the duct, suggesting the presence of

circumferential tensile stress.

• In ducts taken from the superstructure of the bridge, the majority of the cracking

occurred in the region between 10 o’clock and 2 o’clock, on the top portion of the

ducts.

• Some of the long cracks were formed by the convergence of a series of small

cracks.

• The crack is usually longer on the inner surface than the outer surface, suggesting

that cracking was initiated in the inner wall of the ducts.

The microstructure of the fracture surfaces provided significant information on the

cracking mechanism of the HDPE ducts. The similarities of the fracture morphology of

the cracks in both the MB and SSK bridges indicate that the ducts failed by the same

mechanism. Fibril structure is the dominant microstructure on the fracture surface,

suggesting that slow crack growth is the main mechanism in the cracking. However,

impact failure was also involved, as indicated by the flaky morphology. The two long

cracks taken from the MB Bridge were formed by the convergence of small cracks,

indicating that these cracks were initiated from multiple points.

59

The initiation of the cracks was caused by defects such as impurities, air bubbles, or

imperfections. These defects were observed at the inner surface of the pipe wall. It

appears that cracks mostly likely start from these defects at the inner surface and then

propagate through the wall and then in a longitudinal direction. The longitudinal

cracking indicates that the driving force is oriented circumferentially. In Samples 126-4-

A and 38-4-A of the MB Bridge, fatigue lines were identified; thus, cyclic loading was

also a component of the driving force during the cracking process. It is believed that the

cyclic loading is induced mainly by the temperature fluctuations between day and night.

2.5. HDPE duct properties 2.5.1. Specification for HDPE materials The current specification used to assess polyethylene pipe materials is ASTM D3350,

“Standard Specification for Polyethylene Plastic Pipe and Fittings Materials”. According

to ASTM D3350, polyethylene plastic pipe materials are classified by density, melt index,

flexural modulus, tensile strength at yield, environmental stress-crack resistance, and the

hydrostatic design basis at 23oC. The specimens used in all of the tests have the same

thermal history, having been taken from mold plaques which were prepared according to

ASTM D4703 Procedure C at a cooling rate of 15±5oC. Each of the properties and the

corresponding test method are briefly described in the following section.

• Density - The density of polyethylene indicates the amount of crystallinity in the

material. Higher density indicates larger crystallinity in the material. Either ASTM

D1505 or D792 can be used to determine the density. In this study, ASTM D792,

Procedure B was used. The test involves immersing the specimen in a liquid which is

60

Isopropyl, since the density of HDPE is less than that of water and greater than

Isopropyl. The density was obtained by comparing the weight of the specimen in air

and in immersed conditions.

• Melt index (MI) - MI can be qualitatively related to the molecular weight of the

polymer. A lower MI value translates to higher molecular weight. The test method

for measuring MI is ASTM D1238. The temperature for the test of polyethylene is

190oC. A load of 2.16 kg (4.76 lb) is applied. The test records the mass that flows

out of the die after a period of time. Then the flow rate can be calculated with a unit

of g/10min.

• Flexural modulus - Flexural modulus is the ratio of stress to strain in flexural

deformation within the elastic limit. It indicates the ability of the material to resist

deformation under load. For polymers, it is closely-related to density; high density

translates into high flexural modulus. ASTM D790 uses three-point bending to

determine the flexural modulus.

• Tensile strength at yield – The test method is described in ASTM D638. A type IV,

dog-bone shaped specimen is applied under tensile load to find the yield point during

the process. For polyethylene material, higher density indicates higher tensile

strength.

• Environmental stress-crack resistance (ESCR) – ASTM D1693 is the standard for

measuring ESCR. In this study, condition C is used: the test specimens are

immersed in 100% Igepal at 100oC. The specimens are inspected periodically for

failure.

61

• Slow crack growth resistance (SCGR) – ASTM F1473 (PENT) is the test used by the

pressure pipe industry to evaluate SCR. The test involves applying a constant tensile

stress of 2.4MPa (348psi) on the specimen at 80oC in air.

• Hydrostatic data basis (HDB) – ASTM D2837 is the test method used to obtain HDB.

The test method involves subjecting the pipe to a series of internal pressures. HDB is

the stress that corresponds to a failure time of 100,000 hours.

• Carbon black content – Carbon black is mixed in the pipe resin to increase the UV

resistance. ASTM D4218 is used to measure the content of carbon black in the pipe.

The specimen is heated in a muffle furnace at 600oC for three minutes. By doing so,

the polymer is burnt off and the residue left is the carbon black.

Cell classes are created based on different ranges of values from each of the eight tests.

There are six numerical cell classes, and class “0” refers to unspecified. Carbon black

content is expressed by a letter. The material properties are specified by a series of cell

numbers. Table 2.2 shows the ASTM D3350 designation.

62

62

63

Another less-popular specification for identifying the polyethylene material uses types,

classes, categories, and grades. This method is described in ASTM D1248, “Standard

Specification for Polyethylene Plastics Molding and Extrusion Materials”. According to

this specification, density determines type. The following terms have long been used in

practice:

Type I = Low Density, when density is between 0.91 and 0.925 g/cc

Type II = Medium Density, when density is between 0.926 and 0.94 g/cc

Type III = High Density, when density is between 0.941 and 0.965 g/cc

Each of the types is subdivided into three classes according to composition:

Class A Natural color

Class B Colors including white and black

Class C Black, containing not less than 2% carbon black

The category is based on flow rate obtained from the melt index test. There are five

categories according to ASTM D1248.

Category 1 flow rate > 25 g/10min

Category 2 flow rate between 10 and 25 g/10min

Category 3 flow rate between 1 and 10 g/10min

Category 4 flow rate between 0.4 and 1 g/10min

Category 5 flow rate > 0.4 g/10min

64

Both ASTM D3350 and ASTM D1248 can be used to specify polyethylene materials.

ASTM D3350 uses two letters to indicate the material, followed by two numbers

indicating density cell and ESCR cell, respectively. Table 2.3 shows the equivalency of

the two specifications.

Table 2.3 Equivalency of ASTM D3350 and D1248

Specification Grade designations

ASTM

D3350 PE10 PE20 PE23 PE30 PE33

ASTM

D1248 P14 P23 P24 P33 P34

Note: PE = Polyethylene; P = pipe Two more numbers can follow the designation to define the material with greater detail.

For example, in PE3408, “08” indicates the hydrostatic design stress of 800 psi.

2.5.2. Specifications used for the ducts For each of the bridges, material specifications were developed and required for the

HDPE ducts prior to the construction. These specifications are showed in Table 2.4.

Table 2.5 illustrates the material properties in each of the specifications.

65

Table 2.4 Original material specification for the HDPE ducts in each bridge

Bridge Source Material Specification

Mid Bay Construction specification ASTM D3350 with a cell

classification PE345433C

Garcon Point Printed on the exterior wall PE3408

Seven Mile Supplied by duct manufacturer

ASTM D3350 with a cell classification PE335433C

Skyway No material specification available

AASHTO specification was used ASTM D3350 with a cell

classification PE345433C

Channel Five Printed on the exterior wall

ASTM 3350 with a cell classification PE335433C

Long Key Printed on the exterior wall PE3406 and PE3408

Niles Channel Printed on the exterior wall PE3406

67

All of the above properties except HDB were evaluated in this study. HDB is excluded

from the test matrix, since the test must be performed on a complete pipe.

In addition to the above tests, the SP-NCTL test (ASTM D 5397) was performed to

evaluate the SCR of the duct materials. The specimens were dog-bone. A notch of 20%

of the specimen thickness was introduced on one side of the surfaces. The specimens

were immersed in 10% Igepal solution at 50oC, and subjected to 600 psi stress. Five

specimens were required for each of the duct samples.

2.5.3. Test results of the HDPE ducts The properties of retrieved field samples from the seven bridges were tested according to

the test methods in the ASTM D3350, together with the SP-NCTL test. The test results

were then compared with their corresponding material specification.

Table 2.6 shows the test results. All of the field samples conform to the specified values

for density, flexural modulus, and tensile strength. However, samples from the MB and

SSK Bridges exhibited higher MI values than the specified values. Additionally, all the

samples from the MB Bridge failed the ESCR requirement.

The SCR of the HDPE ducts from the seven bridges can be assessed by comparing failure

times of the SP-NCTL tests. The shortest failure time is obtained in ducts from the MB

Bridge, followed by those from the SSK Bridge. Ducts from the Seven Mile, Channel 5

and Nile Channel Bridges show a significantly longer failure time than those from the

MB and SSK bridges. Nevertheless, the longest failure time was measured in ducts made

68

from pressure-rated resins (PE3408). The SP-NCTL results demonstrate a good

correlation with the field performance of the ducts. A poor SCR led to cracking in the

field for ducts in both the MB and SSK Bridges, while fewer cracks or none were found

in other bridges.

Table 2.6 Test results for the duct material properties Result

Test Method MB Garcon

Point Seven Mile SSK Channel-5 Long-Key Niles

Channel

Density Passed Passed Passed Passed Passed Passed Passed

Melt Index Higher Passed Passed Majority

Higher Passed Passed Passed

Flexural Modulus Passed Passed Passed Passed Passed Passed Passed

Tensile strength Passed Passed Passed Passed Passed Passed Passed

ESCR Failed Passed Passed na na na na

Carbon black Lower Passed Passed Lower Some

lower Some lower Some lower

SP-NCTL (hr) at 15% σy

3 to 4 > 1000 80 3 to 11 na na na

SP-NCTL (hr) at 25% σy

na 524 19 na 13

16 (PE3406);

243 (PE3408)

50 - 70

Note: na = not available

69

2.5.4. Correlation of SCR to other material properties of the HDPE ducts

It is known that the SCR of HDPE is in some way related to the molecular weight and

crystallinity of the material. The molecular weight of the polymer can be assessed by the

MI test and the crystallinity by the density. The SCR of the material is determined by the

SP-NCTL test.

The correlation between SCR and molecular weight is evaluated by plotting the MI value

against the failure time for the SP-NCTL test. The data certainly show a trend indicating

that a high MI value tends to yield a short failure time (Figure 2.28).

0

0.2

0.4

0.6

0.8

1

0 10 20 30

Failure time (h)

MI (

g/10

min

)

40

Figure 2.28 Correlations between SCR and MI

In the same manner, the correlation between SCR and crystallinity is evaluated by

plotting the density value against the failure time for the SP-NCTL test. Figure 2.29

shows the graph plotting density against failure time. The relationship between these two

70

parameters is relatively poor, although materials with a lower density tend to yield a

longer failure time.

0.9440.9460.948

0.950.9520.9540.9560.958

0 10 20 30

Failure time (h)

Den

sity

(g/c

c)

40

Figure 2.29 Correlation between SCR and density

Although both molecular weight (MI) and crystallinity (density) can affect the SCR, the

scatter makes it difficult to predict confidently the SCR of the material.

2.5.5. Recommended specification As shown in Table 2.5, there is no unified specification for HDPE ducts used in

segmental bridges. Based on the previous study, a reliable and unified specification is

recommended, which is shown in Table 2.7.

Compared with the original specifications, the required density, tensile yield strength,

and carbon black content remain the same. Original specifications have MI values in cell

3 or 4. Recommended MI was unified in cell 4 to obtain a relatively high molecular-

71

weight material. Original specifications required flexural modulus in cell 4 or 5. The

unified specification suggested cell 4, since it is not necessary for the ducts to have high

flexural modulus. HDB was raised to cell 4 in the recommended specification for

conservative reasons. Furthermore, the current specifications require the ESCR test to

assess the SCR property. As stated in Chapter 1, the ESCR test is known to have large

standard deviation and is inadequate to distinguish today’s HDPE resins. Thus,

alternative tests should be implemented in the recommended specification. The SP-

NCTL test used in this study has been proven to be able to distinguish the SCR property

of different duct materials; however, the SP-NCTL test is not used by the pressure pipe

industry; instead the PENT test (ASTM F 1473) is commonly used as the QA/QC test.

The correlation between the SP-NCTL test and the PENT test was performed on the duct

sample from the Garcon Point Bridge. A failure time greater than 100 hours, which

corresponds to cell 6, was obtained from the PENT test.

Table 2.7 Recommended specification for HDPE ducts

Property Test Method Cell class Required Value

Density (g/cc)

ASTM D 1505 or D 792 3 >0.940-0.955

Melt index (g/10 min) ASTM D 1238 4 < 0.15

Flexural

modulus (psi) ASTM D790 4 80,000 - <110,000

Tensile yield strength (psi)

ASTM D 638 Type IV 4 3000 - <3500

Slow crack growth (h)

ASTM F 1473 (PENT Test) 6 100

HDB (psi) ASTM D2837 4 1600

Carbon black content ASTM D 1603 C > 2%

72

2.6. Assessment of stresses in the HDPE ducts The cracking should occur where the largest tensile stresses are located if the material is

isotropic. As suggested by the microstructure evaluation in Section 2.4, the driving force

is believed to be induced by temperature changes. The distribution of the temperature-

induced stress in the duct was evaluated by both a laboratory-simulated performance test

and the Finite Element Method (FEM). In addition, the residual stresses in the duct were

measured. As stated in the introductory section, the stress evaluation part of this project

was performed by Dr. Hartt’s group at Florida Atlantic University (FAU). Their study is

summarized in Section 2.6.1 and 2.6.2.

2.6.1. Temperature-induced stresses 2.6.1.1. Laboratory test model A simulated tendon consisting of steel-grout-duct was built by Dr. Hartt’s group at FAU

to simulate the field tendon (Hartt et al., 2004). The model was 22-inch long with a

nominal diameter of 4 inches. The duct was manufactured using pressure-rated resin of

PE3408 with a SDR of 21. The diameter of the strands was 0.5 inches. Strain gages and

thermocouples were mounted at various locations on the assembled tendon, as shown in

Figure 2.30. Figure 2.31 indicates the locations of the strain gauges mounted on the

HDPE ducts. In addition, a void was produced intentionally on the top part of the

hydrated grout due the bleeding water during grouting process, as can be seen in Figure

2.32.

73

Figure 2.30 Test model built by FAU (From Hartt et al., 2004)

Figure 2.31 Strain gage arrangements in the test model (From Hartt et al., 2004)

74

Figure 2.32 Void in the test model (From Hartt et al., 2004)

The temperature cycles were introduced according to the following four steps:

1. The specimen was grouted at 60 psi at temperatures of 22 to 24oC, and the pressure

was maintained for approximately 22 hours to allow the grout to hydrate.

2. The specimen was then placed in a freezer at -39°C ± 2°C for seven days.

3. After the freezing cycle, the specimen was exposed outdoors for seven days at

temperatures between 20 and 35°C.

4. The fourteen-day thermal cycle was repeated to monitor the strain changes.

Because the simulated tendon was prepared at 22 to 24oC and the coefficient of thermal

expansion of the duct is much greater than that of the grout, the measurements from strain

gages at temperatures higher than 24oC reflected thermal expansion of the duct only.

Conversely, at temperatures below 22oC, i.e., from -39 to 22oC, the duct was subjected to

75

internal stress from the grout. The actual change in temperature in each thermal cycle

was from 61 to 63oC. Compared to the actual field environment, the maximal range of

temperature changes varies from 36oC (2 to 38oC) in the Keys region to 50oC (-9 to 41oC)

in the northern region. Therefore, the laboratory simulation test was performed in a

temperature range 20 to 70% higher than service conditions in the field.

2.6.1.2. Results from test model Figure 2.33 shows a plot of micro-strain versus time of three gage locations (SG1, SG2

and SG3). The results indicate that SG2 and SG3 have similar tensile strains. Both of

them have the highest strain at low temperatures and the lowest at high temperatures.

The strain variation range for SG2 is smaller than SG3. SG1, however, has a

compressive strain, which could be attributed to the existence of the void below SG1 and

SG2 (Figure 2.31). Thus, the induced strain from SG1 and SG2 are thought to be

affected by the additional bending effect. For SG3, the strain change is induced solely by

the relative contraction of the duct and grout. If the modulus of 1.46x105 psi is used for

the duct material, the temperature-induced stresses for SG1, SG2, and SG3 are -1020,

440, and 730psi, respectively.

76

Figure 2.33 Strain gage measurements (From Hartt et al., 2004)

2.6.1.3. FEM analysis

As discussed previously, as temperature decreases, the thermal contraction of the three

components in the tendon will not be the same due to their different coefficients of

expansion. The coefficient of thermal expansion for HDPE is much larger than those for

the steel and grout (the linear coefficients of expansion for grout, steel, and HDPE being

approximately 10x10-6 in/in/K, 11.5x10-6 in/in/K, and 117x10-6 in/in/K, respectively.)

Because of this, the duct shrinks more than the grout when temperature drops, which

induces a tensile hoop stress in the duct.

In order to find out the distribution of stresses in the pipe wall, ANSYS, a FEM program,

was utilized. A two-dimensional model was established, as shown in Figure 2.34. The

77

model was a two-dimensional representation of the cross-section of a SDR 21 HDPE duct

with an interior grout void comprised of 3, 8, or 10% of the interior volume. Triangular,

six-node elements were implemented in the analysis. The general illustration of the mesh

is shown in Figure 2.35. Stress-strain response of both grout and HDPE was considered

to be linearly elastic. The modules used in the model are 1.46x105 psi for the HDPE and

4.06x105 psi for the grout. Poisson’s ratios for the duct and grout were taken as 0.28 and

0.21, respectively.

Figure 2.34 Two-dimensional model of duct-grout system

78

Figure 2.35 Mesh in analytical model

Results of the analytical model are shown in color-contoured plots of the first principal

(hoop) stresses. Figure 2.36 shows the result with 10% void, from which stress

distribution can be seen in the color configuration. The tensile stresses were computed at

locations SG2 and SG3 on the simulated tendon. The maximum tensile stresses are

located at SG2 as well as on the outer duct surface at two sides of the grout void corner.

Table 2.8 lists the FEM-computed stress at each of these three locations for three

different void volumes. Correspondingly, in Figure 2.37, the stresses are plotted at each

of these three locations as a function of void size. For the smallest void size (three

percent), stress was greatest at the corner locations followed by SG2. These stresses

decrease with increasing void size.

79

Figure 2.36 First principal stress distribution when the void is 10%

Table 2.8 Summary of the analytical model results

Computed stress (psi) Void volume (%) SG2 SG3 Corner

10 780 974 974

8 938 938 1206

3 1228 921 1382

80

0200400600800

1000120014001600

0 5 10 15

Void volume (%)

Prin

cipa

l stre

ss (p

si)

Corner SG2 SG3

Figure 2.37 Void size effects on the principal stress

The results of the FEM suggest that the most possible areas that initiate the SC is at SG2

and at the outer duct surface of the void corners. Both the FEM and simulated test

indicate that the tensile stresses also distribute around the duct section that contact with

the grout.

2.6.2. Residual stresses It is well-known that residual stresses are generated in pipes during the manufacturing

process. The measured residual stresses in HDPE pipes generally fall into the range of

470-1200psi. The magnitude is certainly too significant to be neglected. Therefore, the

effect of residual stress on the material property must be evaluated. The simplest method

for measuring the residual stress in the small diameter duct is to slit the duct and measure

the diameter change. Dr Hartt’s group measured the residual stresses on a section of 10

81

inch-long PE3408 duct with a SDR of 21 (Hartt et al., 2004). Figure 2.38 illustrates the

splitting test method.

Figure 2.38 Measurement of residual stresses by slitting (From Hartt et al., 2004)

The change in outside diameter was measured after the splitting. The residual stresses

were calculated according to the equation presented in the standard ASTM E 1928-99.

DDDDEt

IMc

01

0121

−⋅

−±==

µσ (2.1)

Where,

M is the residual moment in the duct,

c is the distance from the neutral axis to the point of maximum strain,

I is the moment of inertia of the cross-section of the specimen,

E is the Flexural Modulus,

t is the specimen thickness,

µ is Poisson’s ratio,

Do is the mean outside diameter before splitting, and

D1 is the mean outside diameter after splitting.

82

The residual stress measured on the duct was 5.42 MPa (786 psi), with tensile mode on

the inner surface and compressive mode on the outer surface. Such stresses are on the

same order of magnitude as those obtained from the test model and FEM model.

Combining both residual stresses and thermal-induced stresses, it is clear that the highest

tensile stress was on the inner surface of the duct. Table 2.9 and Figure 2.39 show the

results. This is consistent with the field observation that cracks always originate in the

interior surface of the ducts.

Table 2.9 Combined temperature-induced stresses and residual stresses

Stress (psi) Void volume (%) SG2 Corner Inner duct

surface Outer duct

surface

10 1566 188 1760 188

8 1724 420 1724 152

3 2014 596 1707 135

83

0

500

1000

1500

2000

2500

0 2 4 6 8 10 12

Void volume (%)

Prin

cipa

l stre

ss (p

si)

Corner SG2 Outer duct surface Inner duct surface

Figure 2.39 Combined temperature-induced stresses and residual stresses

2.7 Evaluation of fatigue failure

2.7.1 Fatigue test

Since fatigue is one of the driving forces behind the cracking of the HDPE ducts, the

fatigue property of the HDPE materials was evaluated. Duct samples were cut into small

pieces, and then compression-molded into 2.5 mil-thick plaques. Specimens 4 inches

long by 1 inch wide were cut from the compression-molded plaque prepared by ASTM

D4703 procedure C. A 0.5 mil (20% of thickness)-deep notch was introduced at the

center of the specimens, at a notching rate of 0.2mil/min. Fatigue tests were performed

by three-point bending using an Instron Model 1331 machine under load control. The

frequency adopted is 3 Hz, so that no significant heat can be accumulated, and the test

can be completed in a short time period as well. To maintain the specimen in position, an

initial load of 9.9 lb was applied. The loading was performed by using a half-sine wave

loading function. Fatigue failure was defined as the number of cycles to reach a vertical

84

deflection of 1 inch. Maximum loads of 19.8-110.2 lb were employed. Figure 2.40

shows the test equipment. Figure 2.41 shows the specimen under testing.

Figure 2.40 Fatigue test system

Figure 2.41 Specimen in the fatigue test

85

The tensile stress σ can be calculated by

223bdPL

=σ (2.2)

Where: P = applied load (lb),

L = span length (2 inches),

b = width of specimen cross-section (1inch), and

d = depth of specimen cross-section (0.25 inch).

2.7.2. Discussion of fatigue test results

Results of the fatigue tests are presented as a plot of stress range versus cycles-to-failure

(S-N plot). The relationship conforms to a Power Law equation expressed as

(2.3) bAN=σ

Where: σ = stress,

N = cycles-to-failure, and

A and b are material constants,

The S-N curves on a log-log coordinate for five duct materials were plotted in Figure

2.42. The MB and SSK specimens exhibited similar fatigue behavior, having the lowest

fatigue resistance. The PE3408 duct specimens exhibited the highest resistance. The

specimens from the Seven Mile and Long Key Bridges were intermediate. This ordering

of fatigue resistance (i.e. cycles to failures) agrees with the SCR measured by the SP-

NCTL test.

86

Combining the maximum tensile stresses (about 1200 psi) evaluated from FEM and the

measured residual stress (786psi) suggests that the maximum tensile stresses in the duct

can be as high as 2000 psi. 2000 psi is then used as the reference stress to compare the

cycles to failure for the different duct samples in the fatigue tests. The plots in Figure

2.42 indicate that a stress level of 2000 psi led to the failure of the SSK and MB

specimens after 300 and 900 cycles, respectively. Considering that the in-service ducts

experienced one thermally-induced stress cycle per day, the cracking could occur in the

ducts in less than one and three years after construction, respectively. Specimens from

the Long Key Bridges had cycles to failure of 2.0x104 at 2000 psi , which translates to a

service life of 50 years in the field. The Seven Mile Bridge sample exhibited 4.0x104

cycles. Therefore, 100 years of service life could be possible. For PE3408 resin,, the

cycles to failure at 2000psi were 1.0x106, making it the most reliable resin for the ducts

used in segmental bridges.

1.0E+02

1.0E+03

1.0E+04

1.0E+00 1.0E+01 1.0E+02 1.0E+03 1.0E+04 1.0E+05 1.0E+06 1.0E+07

Cycles to failure

Stre

ss r

ange

(psi

)

Sunshine Skyw ay Seven Mile Mid Bay Long Key PE 3408

Figure 2.42 S-N curves on logarithmic scale for various duct samples

87

2.8. Summary

This chapter focuses on the SC of the HDPE ducts in segmental bridges. The cracking of

the ducts is critical to the safety of the bridges, since the ducts protect the steel strands

supporting the superstructure of the bridge. Seven bridges in Florida were involved in

this study. The ducts in the MB Bridge and the SSK Bridge presented severe cracking

problems. Consequently, the cracking was examined both macroscopically and

microscopically. Observation shows that cracking starts on the inner surface of the ducts

and propagates through the wall thickness and longitudinally. The microstructure shows

that fibril structure dominates the fracture morphology, suggesting the SCG failure

mechanism. The fatigue lines can also be found on the fracture surface. It is believed

that the driving force for the SC is day-night temperature cycles.

To evaluate the effect of duct material properties on SCR, the properties of the materials

were tested according to the test methods in ASTM D3350. The results show that some

of the properties did not meet the construction specifications. Also, the ESCR test used

in these specifications is thought to be inadequate to assess the SCR. A unified

specification was then recommended. The major modification in the recommended

specification is to replace the ESCR with the SP-NCT test, because it can effectively

distinguish the SCR of different ducts, and its results exhibit a good correlation with the

field performance. However, the SP-NTCL test is not used by the pressure-pipe industry.

Alternatively, the PENT test was adopted in the unified specification. The difference

between the SP-NCTL and PENT tests is the test environment. However, they are

88

designed based on the same loading mechanism--constant tensile loading. Therefore,

either of them is more appropriate to evaluate SCR than the ESCR test.

It is of interest to know the stress distribution through the ducts. The laboratory-

simulated test and FEM were thus used. Results of both analyses confirm that the most

likely initiation positions of the cracking in the duct are the inner surface in the void

region. Combined with the residual stresses, large tensile stresses are distributed in the

inner surface of the ducts, while the outer duct surface has either compressive stresses or

very low residual stresses. These stress analyses agree with the field observation, since

the cracking happens where the maximum tensile stresses are distributed.

Neither the SP-NCTL nor PENT tests can simulate the cyclic loading occurring in the

field. Fatigue tests were thus used to simulate the fatigue process. The cycles to failure

were used to estimate the failure times in service conditions. The results show that duct

materials from the MB and SSK bridges have the smallest number of failure cycles, and

PE3408 has the largest. This presents a good correlation with the field observation,

which shows that the MB and SSK bridges have severe cracking problems, while other

bridges’ ducts have minor or no cracking problems. It is concluded that the fatigue test

can be used as an effective approach for evaluating the SCR of the HDPE duct material.

89

Chapter 3: Stress Cracking in Corrugated HDPE Pipes

3.1 Introduction Corrugated HDPE pipes are the most widely used plastic pipes for drainage applications

due to their inherent advantages discussed in Chapter 1. However, like other types of

HDPE pipes, the long-term properties of corrugated HDPE pipes are cause for concern.

A recent report by Hsuan and McGrath (1999) revealed widespread cracking of

corrugated HDPE pipes. Although these pipes are intended to last for approximately 50

years, significant cracking had occurred within a period of a few decades after installation.

Unlike the longitudinal cracking observed in the HDPE ducts used in segmental bridges,

cracking in drainage pipes was oriented circumferentially within the pipe liner. This

pattern suggests that the primary stress acting in the pipes is longitudinal, in contrast to

the circumferential stress experienced by HDPE ducts. The purpose of this part of the

study was to establish reliable tests and methods to analyze SCR and guarantee a

satisfactory lifetime of corrugated HDPE pipes.

3.2 Background 3.2.1 Corrugated HDPE pipes Corrugated HDPE pipes are typically used in drainage applications. Most pipes are

covered by soil and subjected to substantial compressive loads. Since HDPE is a flexible

material, deflection under load is expected. While rigid pipes are considered to be under

structural distress when the deformation is above 2% of the pipe diameter, the maximum

allowable deformation for flexible HDPE pipes is 5% of the pipe diameter, according to

90

AASHTO design standards. Deformation above maximum allowable levels may lead to

stability issue of the soil/pipe system, even in the absence of cracking.

Corrugated HDPE pipes can range from 4 to 60 inches in diameter, and the liner

thickness is relatively thin, regardless of diameter, ranging from approximately 0.06 to

0.15 inches. The pipe stiffness is a function of the corrugation profile, of which there are

three types: type C, S, and D. In this study, only type S corrugated pipes were evaluated.

In cases where the pipe is buried underground, the pipe and the surrounding soil interact

with each other as a composite structure, in which the stiffer element (soil) will respond

to a greater fraction of the load. In order to decrease the load transferred onto the pipe,

the surrounding soil must be well compacted (95% standard compaction). .

Due to the viscoelastic properties of HDPE, the pipe would experience two types of time-

dependent behavior, creep and stress relaxation, which are shown in Figure 3.1. The load

generated at the time of placement is expected to determine the long-term deflection of

the pipe and ensure that the pipe does not creep. After the deflection reaches equilibrium,

stress relaxation takes place and the stress in the pipe gradually decreases with time.

91

(a) (b)

Figure 3.1 Creep and stress relaxation behaviors of HDPE pipes

3.2.2 Failure in corrugated HDPE pipes According to the report by Hsuan and McGrath (1999), cracked pipes were found in 20

out of 62 sites surveyed in various regions of the US. The majority of the cracks

occurred along the circumferential direction on the pipe, indicating the existence of a

longitudinal tensile stress. Figure 3.2 shows the cracking in one of the field pipes.

Further examination indicates that most of the cracking occurred in the liner, adjacent to

the junction, and that the cracks grew from the outer pipe liner surface through the

thickness of the liner.

Figure 3.2 Cracking in a field corrugated HDPE pipe

92

SEM was used to examine the fracture morphology, and revealed that the cracks were

dominated by fibril structures, as shown in Figure 3.3. This suggests that SCG was the

cracking mechanism.

Figure 3.3 Typical fracture morphology from a cracked field corrugated pipe (From Hsuan and McGrath, 1999)

Many of the cracking problems were ascribed to improper installation, which results in

excessive deflection and buckling of the pipe. However, SC was observed in situation

that the deflection of the pipe is less than 5%. Therefore, both the quality of the material

and installation are critical in order to achieve a crack-free lifetime.

Corrugated HDPE pipes have complex wall geometry, as illustrated in Figure 3.4

depicting a type S corrugated pipe. The complex geometry introduces large variability in

residual stresses at different parts of the pipe. Therefore, an adequate performance test

should use finished pipes to properly account for pipe geometry and residual stresses.

93

Figure 3.4 geometry of type S corrugated pipe 3.3 Test Material The tests were performed on several type S commercial pipes, ranging in diameter from

24 to 60 inches. These pipes included A24, A24, A36, A48, A60; B24, B36, B48, B60,

in which the first letter denoted the manufacturer and the subsequent digits indicated the

pipe diameter in inches. Most of the tests in this study were conducted on specimens

from pipe A36 and A24.

The properties that are closely related to SCR are presented, i.e., density, MI, and NCLS.

The current specification for the HDPE drainage pipe is AASHTO M 294 specification.

M294 requires cell classification of 3 for both density and MI. M294 requires the NCLS

test performed on five specimens under an applied stress of 600 psi (4.1 MPa); the

average failure time of five test specimens must be greater than 24 hours for virgin pipe

resins with no single specimen failure time less than 17 hours.

94

Table 3.1 illustrates the tested values. The results indicate that all the pipes meet the

density and MI values. However, A60, B24, and B48 pipes do not meet the NCLS

requirements.

Table 3.1 Properties of the studied pipe samples

Sample Density (g/cc) MI (g/10min) NCLS on plaque (hour)

Test value 0.95 0.2 30.7 A24

Classification 3 3 pass

Test value 0.951 0.28 34.6 A36


Test value 0.95 0.13 29.4 A48


Test value 0.948 0.13 10.5 A60

Classification 3 4 fail

Test value 0.949 0.2 19.6 B24


Test value 0.951 0.16 28.2 B36


Test value 0.951 0.19 18.5 B48


Test value 0.947 0.16 25 B60


95

3.4 SCR of liner 3.4.1 Introduction The liner test focused on the liner of the pipe. This test was conducted according to the

NCLS protocol, with the exception of pre-test preparation of the specimens. Instead of

taking the test specimens from the compression molded plaques, the specimens were

taken directly from the liner part of the pipe. A notch of 20% of liner thickness is

introduced in the center of the specimen. Figure 3.5 shows the specimen location, and

Figure 3.6 shows the specimen dimension.

Figure 3.5 Liner specimen locations

Figure 3.6 Liner specimen

96

There are four different configurations in preparing the liner specimen for the NCLS test,

which are categorized by the following names:

LO—specimen cut longitudinally and notched on outer surface;

LI—specimen cut longitudinally and notched on inner surface;

CO—specimen cut circumferentially and notched on outer surface;

CI—specimen cut circumferentially and notched on inner surface.

The SCR of the pipe liner is governed by the weakest configuration of the four.

Therefore, the configuration that exhibits the least SCR would be used to assess the long-

term SCR of the pipe. The average failure times are listed in Table 3.2. The results show

that the minimum failure times tended to occur in the LO specimens. Consequently, all

liner tests were performed on specimens using type LO configuration for the evaluation

of SCR in the involved pipes.

Table 3.2 The failure times of four specimen configurations

Failure time tested in Igepal solution at 50oC (hour) Specimen

A24 A36 A48 A60 B24 B36 B48 B60

LO 30.4 28.3 10.6 7.6 12.2 12.7 14.6 13.9

LI 88.5 79.2 13.3 42.7 97.9 37.2 42 39.2

CO 37 -- 17.5 11.6 13.6 20.8 20.1 16.9

CI 26.8 -- 13.9 10.8 10.5 15.4 14.7 15.8

Note: -- indicates that the tests were not performed due to the shortage of test material

97

3.4.2 Experimental design for liner test The liner test was developed to evaluate SCR of the finished pipe by incorporating the

processing effect into the test. In this study, a number of approaches were adopted to

ensure that testing times would be within a practical range. These approaches included

increasing test temperatures, using surfactants, and introducing notches into the liners.

The following section describes the different test environments.

Test agent The use of a 10% Igepal CO630 solution is widely-accepted for SC tests. Although the

Igepal solution accelerates the SC process, this does not accurately represent natural

conditions. Therefore, extrapolation of experimental data to field performance becomes

problematic. A more accurate representation would involve tests that incorporate

environmental factors, such as soil, water, and air that are normally in contact with pipes

in the field. Since HDPE is highly resistant to chemical corrosion, soil poses little risk to

pipe longevity, therefore, only water and air were used in the tests. For comparison, tests

in Igepal solution were also performed.

Temperature Research had shown that HDPE undergoes material changes in temperatures above 80oC.

Therefore, temperatures were kept below 80oC for all tests. However, temperatures that

are too low risk increasing testing times to levels that are impractical. Tests conducted in

water or air requires relatively high temperatures to ensure relatively short failure times.

High temperatures are also preferable for testing performed in the presence of Igepal

solution; however, temperatures above 50oC are known to inhibit the effect of Igepal-

98

CO630. Therefore, test environments were selected that represent a compromise of

effectiveness and practicality. Table 3.3 summarizes the environments used for the liner

tests.

Table 3.3 Test environments for liner test

Test agent Water Air 10% Igepal® Solution

60 60

70 70 Temperature (oC)

80 80

50

In each test environment, pipes were subjected to a series of stress levels in order to

obtain a full ductile-to-brittle curve. The range of stress levels were determined by the

failure times, which were designed to fall within 200 hours in order to make the test

practical. Thus, the stress levels used in these tests were between 300 and 1600 psi, at

increments of 100 psi.

Liner tests were performed on A36 and A24 pipes. For the A36 pipe, the test was

performed in all three test agents in order to generate the full ductile-to-brittle curve. For

the A24 pipe, the test was only performed in water environment and only the brittle

region was generated. The test results for the A36 pipe are presented in three parts. The

first part represents the results of tests conducted in water at all three temperatures, the

second part represents the results of tests performed in air at all three temperatures, and

third part represents data from tests conducted in 10% Igepal solution at 50oC. The

99

results of these tests were compiled in order to compare the effect of the test conditions

on the stress cracking.

3.4.3 Data and Analysis 3.4.3.1 Determination of the ductile-to-brittle curve The test data were assembled in graphical form by plotting log stress against log failure

time. The ductile-to-brittle curves were determined using the analytical method

described in ISO 9080 – Annex B (3). Briefly, this method utilizes a trial-and-error

approach to establish the transition point that separates the ductile and brittle portions of

the curve, in which 50 points at even increments over the range of log stresses are

selected. By assuming that any of these 50 points could be the transition point and

assigning the test data in two groups (corresponding to the ductile and brittle behavior,

respectively); the data are fitted into the model shown in Equation 3.1:

( ) eccct ki +−++= σσσ 10103102110 loglogloglog (3.1)

Where:

t = time to failure, in hours,

σ = applied stress, in psi,

σk = assumed knee stress, in psi (knee stress is the transition stress at which failure

changes from ductile to brittle mode)

c1, c2, c3i = constants; i = 1 or 2, corresponding to the ductile or brittle region,

respectively.

e = error variable with zero mean and constant variance

100

For each assumed transition point, the constants were computed by the least squares

method. The residual variance was calculated based on the fitted lines. After 50 sets of

calculations, the best model was the one corresponding to the minimum residual variance.

The transition point and fitted lines for ductile and brittle regions were subsequently

established from this data. A Matlab code was developed based on this approach to find

the best fitting curves (Appendix A).

3.4.3.2 Test results in water environment The liner tests were performed in a deionized water environment at temperatures of 60,

70 and 80oC. The test data were fitted with ductile and brittle bilinear lines according to

ISO 9080 method. Figure 3.7 presents the results of these tests in a single graph.

The ductile-to-brittle transition was well-defined in all three curves. The transition stress

and time along with the slopes of the ductile and brittle regions at each test temperature

are presented in Table 3.4. The slopes in the ductile region increased with temperature,

while the slopes in brittle region were less sensitive to temperature. The curves in the

brittle region at 70 and 80oC had similar slopes, while the slope at 60oC was slightly

lower than the other two.

101

at 60oC

at 70oC

at 80oC

Figure 3.7 A36 liner test at 60, 70, and 80oC in water

Table 3.4 Summary of fitted curves of liner tests on A36

Transition Point Slope Environment Temperature

(oC) Stress (psi)

Time (hr)

Ductile Region

Brittle Region

60 1248 6.3 0.041 0.33

70 1077 4.5 0.055 0.38 Water

80 875 3.2 0.082 0.38

60 1206 6.1 0.059 0.28

70 1081 4.5 0.082 0.36 Air

80 944 2.0 0.092 0.35

10% Igepal 50 1427 4.9 0.043 0.52

102

3.4.3.3 Test results in air environment Liner tests were also performed in forced air ovens at temperatures of 60, 70 and 80oC.

Figure 3.12, 3.13, and 3.14 show the test data in air and the fitted curves at the three

individual temperatures, respectively. Figure 3.8 depicts these results in a single graph.

The data suggested that the results at each temperature could be fitted with ductile and

brittle bilinear lines. The ductile-to-brittle transition was well-defined in all three curves.

Similar to the water data, the slopes in the ductile region increased with temperature. The

slopes in the brittle region at 60oC were significantly lower than those at 70 and 80oC.

at 60oC

at 70oC at 80oC

Figure 3.8 A36 liner test at 60, 70, and 80oC in air

103

3.4.3.4 Test results in Igepal solution The test data and the fitted curve for the tests performed in Igepal solution at 50oC are

presented in Figure 3.9. The transition stress, time, and slopes in the ductile and brittle

regions are shown in Table 3.4.

Figure 3.9 A36 liner test at 50oC in Igepal solution

3.4.3.5 Comparing SCR in Different Test Environments

The ductile-to-brittle curves in the three different test environments are shown in Figure

3.10. Table 3.4 summarizes the transition points and the slopes for each test. At each

temperature, the ductile-to-brittle curves for tests performed in water and air appeared to

104

be similar. The transition stresses and failure times were similar at 60 and 70oC. In

contrast, tests at 80oC, suggest that the tests performed in water had a transition point at

lower stress point and at longer time. The difference between the tests in water and air

was reflected in the slopes of the curves. In the ductile region, the curve in air was

steeper than that in water, whereas the opposite phenomenon was observed during the

brittle region. The curves for the test performed in Igepal solution were significantly

different from those in the other two test environments. These curves had a significantly

steeper slope than those in air or water. These results indicate that Igepal can

significantly accelerate the SC process in HDPE pipes.

Tested in Igepal solution at 50oC

at 60oC

at 70oC

Figur

Solid line --tested in water or Igepal solution Dotted line--tested in air

at 80oC

e 3.10 Compiled graph for A36 liner test in all environments

105

The difference between the test results under each test condition could also be determined

by calculating the corresponding activation energy, which is defined as the minimum

energy required to initiate the reaction. The Arrhenius model expressed in Equation 3.2

was used to calculate the activation energies.

⎟⎠⎞

⎜⎝⎛ −

= RTE

f

Aet1 (3.2)

Where:

tf = failure time at a specific applied stress, in hr,

E = activation energy, in kJ/mol,

T = test temperature, in K,

R = gas constant (8.314 J/mol-K),

A = material constant

Activation energies are usually determined experimentally by measuring the reaction rate

(ft1 ) at different temperatures (T), plotting the logarithm of

ft1 against 1/T on a graph,

and determining the slope of the straight line that best fits the points. Figure 3.11 shows

the relation between natural log (ft1 ) and 1/T for the test data in water at 600 psi. Based

upon the calculated slope of -11123, Equation 3.2 yeilds activation energy of 92.5 kJ/mol.

106

y = -11123x + 29.355

-4.5-4

-3.5-3

-2.5

-2-1.5

-1

-0.50

0.0028 0.00285 0.0029 0.00295 0.003 0.00305

1/T

ln(1

/t)

Figure 3.11 Activation energy calculation for A36 liner test in water at 600 psi

For tests conducted in water, the activation energies ranged from 228 to 232 kJ/mol for

the ductile curves, and 92 to 104 kJ/mol for the brittle curves. For tests conducted in air,

the activation energies ranged from 185 to 189 kJ/mol for the ductile region, and 100 to

113 kJ/mol for the brittle region. A low applied stress yields a high activation energy,

and vise versa. Extensive investigations on all polyethylene by Lu and Brown (1986,

1987, and 1990) and Huang and Brown (1988) demonstrated that the activation energy

for SCG (brittle region) was approximately 100 kJ/mol. Lu and Brown (1990) stated that

the activation energy in the ductile region ranged from 172 to 270 kJ/mol. Our results

strongly recapitulate these previous findings. However, a previous report by Lu and

Brown (1990) suggested that the activation energy is independent of stress, while an

inverse proportion between the stress and activation energy was found in this study.

107

3.5 Residual stress 3.5.1 Residual stress measurement The difference in the failure times among the four configurations of liner specimens

indicated that the residual stress in the pipe may have an influence on SCR. Thus, the

residual stresses in the pipe were measured. However, the geometry and large diameter

of the pipe limited the application of the simple slitting method that was used to measure

residual stresses for small diameter smooth pipes. As an alternative, residual stresses

were measured on specific regions cut from the larger diameter pipes. Although the most

popular and accurate method is layer removal, the thinness of the pipe liner (mostly less

than 0.12 inches) made this method impractical. Therefore, a thermal annealing method

was performed in this study. Unfortunately, this process could potentially result in

changes to the molecular structure of the material. However, since the SC tests were

performed at relatively high temperatures of up to 80oC with little change to the

molecular structure, annealing below 80oC is presumed to be acceptable.

The annealing approach involves two steps: releasing the residual stress by heating at a

certain temperature, and estimating the residual stress by comparing the specimen

geometries before and after annealing. Specimens of 3 inches by 0.5 inches were cut

from pipe liner in both longitudinal and circumferential directions. If the crest of the

corrugation was wide enough, specimens were also cut from the crest. The specimens

were subsequently placed in heated ovens for various time intervals. Four trial

temperatures were adopted for the annealing: 50oC, 60oC, 70oC, and 80oC. These

temperatures were chosen because they were the temperatures at which the stress

108

cracking tests were performed. The annealing interval was determined by direct

observation of specimen shape changes. After approximately 6 hours, the specimen

shape experienced no further changes at any of the above four temperatures, suggesting

that 6 hours of annealing was sufficient to release all residual stress. The initial shape of

the specimens was roughly flat, however following the release of residual stress, a

curvature on the specimen was observed. The change in the curvature corresponded to a

certain amount of strain, from which residual stress could be calculated. The change of

the curvature was measured by the dial gauge. Figure 3.12 shows the measurement of the

arc height. The procedures that were used to calculate residual stresses are included in

Appendix B.

Figure 3.12 Measurement of arc height of specimen

109

3.5.2 Residual stresses effect 3.5.2.1 Effect shown from four specimen configurations The residual stresses measured by the annealing method are listed in Table 3.5. All the

values shown are residual stresses on the outer surface of the liner. The data indicate

tensile residual stresses in the longitudinal direction of the pipes. In the circumferential

direction, the stress mode varies from pipe to pipe. Generally, the absolute values of

residual stresses in longitudinal direction are much larger than those in circumferential

direction. This indicated that the extrusion rate has a larger effect than the cooling

process on generating the residual stresses.

110

110

111

McGrath (2003) conducted a parametric study using corrugated HDPE pipes in which

effects of soil compaction conditions, depth of fill, and support under the pipe haunches

was investigated. The result showed that both circumferential and longitudinal long-term

service strain should be less than 1.6%, corresponding to a stress of approximately of 320

psi assuming a long-term modulus of 20,000 psi. The measured residual stresses are

certainly too large to neglect, especially in the longitudinal direction, where the residual

stresses typically range from 40 to 815 psi. The effect of residual stresses can be seen by

the NCLS test data included in Table 3.5. These data indicated that the large tensile

residual stresses correspond to shorter failure times. Since the largest tensile residual

stresses are found on the outer surface of the longitudinally oriented specimens, the

shortest failure times always occurred in the LO specimens. However, the longest failure

times occurred in the LI specimens, due to the maximum compressive residual stresses on

the inner surface. The residual stresses in the circumferential direction are not as

significant as those in longitudinal direction. Therefore, the failure times are between

those of LO and LI specimens. It should be pointed out that the measured residual

stresses are only on the pipe surfaces and that the distribution of the residual stresses

across the pipe liner thickness is unknown. Thus, the relationship between the failure

times and residual stresses can only be evaluated qualitatively.

3.5.2.2 Effect shown from comparison of liner and plaque specimen It is believed that compression molded plaques could relieve most of the residual stresses

in the pipe. By comparing the failure times between specimens taken from plaque and

liner, the effect of residual stresses on SCR can be assessed. The A36 pipe was used in

112

this evaluation study. Table 3.6 presents the parameters for the plaque and liner test

results.

Figure 3.13, 3.14, and 3.15 compare the test results from both liner test and plaque test

results in Igeapl solution, water, and air environments, respectively. The figures show

that the two sets of tests have similar transition points at the same test conditions.

However, there is a significant difference in the calculated slopes of the fitted curves.

The difference in slopes is smaller at 80oC than at 60 or 70oC. In the ductile region,

plaque tests tended to have steeper slopes, while in the brittle region, plaque tests tended

to have shallower slopes. The steeper slopes in brittle region for liner test translated into

lower activation energy. The calculated activation energies in the brittle region are listed

in Table 3.7. Since the tests were performed under identical conditions, the difference in

activation energies between liner and plaque tests are primarily ascribed to the residual

stresses in the specimens. Residual stress varies within the specimens, therefore the

effect of the residual stresses on cracking initiation and propagation are unclear.

113

113

114

Figure 3.13 Com

Figure 3.14 Com

Solid line--liner test Dotted line--plaque test

parison of test results from liner test and plaque test in Igepal


parison of test results from liner test and pl

at 60oC

at 70oC

at 80oC

aque test in water

115

at 60oC


at 70oC at 80oC

Figure 3.15 Comparison of test results from liner test and plaque test in air

Table 3.7 Activation energies from different tests

Test Test environment

Activation energy range (kJ/mol)

water 92-104 Liner test on A36

air 100-113

water 101-113 Plaque test on A36

air 108-126

116

3.6 SCR of junction 3.6.1 Introduction Although the liner tests offer consistent results with short failure times, the application of

these data to the prediction of pipe lifespan suffers from two main limitations. First,

these tests do not consider the complexity of the pipe geometry. Field observations

indicate that the SC in corrugated HDPE pipes commonly occurs at the junction area

between the liner and the corrugation. Second, liner test required a 20% deep notch on

the specimen, which is rarely observed in field pipes. Furthermore, the correlation

between the notch and the defect in the service pipe remains unclear. The development

time for the defect on the pipe surface to 20% thickness represent a significant proportion

of total failure time.

Junction tests were designed to overcome the shortcomings of the liner test. The

discontinuity of the junction generates a stress concentration, making it more susceptible

to SC. Figure 3.16 illustrates the configuration of the junction.

Figure 3.16 Junction configuration

117

3.6.2 Experimental design for junction test To evaluate the SCR of the junction, specimens were taken from this part of the A24 pipe.

Figure 3.17 shows the location of the specimens. Figure 3.18 shows the typical junction

specimen. The junction tests were limited to water environment at temperatures of 60, 70,

and 80oC. The applied stresses ranged from 350 psi to 1150 psi with increments of 100

psi.

Figure 3.17 Junction test specimen location

Figure 3.18 Typical configuration of junction specimen

118

3.6.3 Data analysis The junction test data were also fitted to lines by the least square method on a log-log

scale. The transition stresses and failure times together with slopes of the ductile and

brittle regions at each test temperature are shown in Table 3.8. Figure 3.19 shows the

ductile-to-brittle curves of junction tests on pipe A24 in the water environment at all three

temperatures. The slopes of both the ductile region and the brittle region appeared to be

similar at 60 and 80oC. The slopes of both the ductile and brittle regions at 70oC were

steeper than those at 60 and 80oC.

Table 3.8 Summary of fitted curves of junction tests on A24

Transition Point Slopes Environment Temperature

(oC) Stress (psi)

Time (hr)

Ductile Region

Brittle Region

60 1088.3 157.8 -0.02 -0.186

70 979.3 42.5 -0.026 -0.206 Water

80 941.5 9.6 -0.023 -0.179

119

at 60oC

at 70oC

at 80oC

Figure 3.19 A24 junction test at 60, 70, 80oC in water on A24

The scattering of data in junction tests was significantly greater than in the liner tests due

to the irregularity of the junction geometry in junction specimens. Statistical methods are

necessary to analyze the test data. Commonly, two-sided 95% confidence interval is used

for the estimated means (i.e. fitted lines for the test data). In this study, only the lower

confidence limit is of interest in order to obtain a conservative estimate. This required

calculation of the 97.5% lower confidence bound using the method described in ISO

9080. Matlab code for the analysis is included in Appendix A. Figure 3.20 shows the

test data and 97.5% lower confidence bound in the brittle region on the junction data on

the A24 pipe. At each stress level, the failure times of the fitted curves are approximately

120

1.5 to 5 times greater than at the lower confidence limit. These results suggest that a

reduction factor of 1.5 to 5 should be used in order to obtain the lower limit of failure

time.

Solid line---fitted curve Dotted line---lower confidence limit

at 60oC

at 70oC

at 80oC

Figure 3.20 The fitted curve and 97.5% lower confidence limit for junction test in water

on A24 3.7 Comparison of different tests 3.7.1 Comparison of liner and junction test The results from the A24 pipe material were used to compare SCR between liner and

junction tests. The comparison was made for the brittle region only, since the brittle

121

failures are dominant in the field pipes. Figures 3.21, 3.22, and 3.23 show the difference

of the two tests at 60, 70, and 80oC, respectively.

Large differences in the slopes between liner and junction tests were observed at all three

temperatures. The failure times of the liner tests were significantly shorter and generated

less scatter than those of the junction tests at the same stress level and temperature. As

indicated in Figure 3.24, the difference in the failure times between liner and junction

tests increased as the temperature decreased. At each temperature, the acceleration effect

decreases dramatically as the stress decreases. Figure 3.24 demonstrates that the low

temperature had the largest rate of change in the acceleration effect. Table 3.8 lists the

difference in the curve parameters for the two tests. The activation energies were

calculated using Equation 3.2, and values ranged from 169 to 180 kJ/mol in the brittle

phases, which were larger than those of liner tests. The activation energies for both tests

on A24 are shown in Table 3.9.

Researchers (Chan and Williams 1983, Brown et al. 1991) have stated that the SCG

propagation rate was similar for the same polyethylene material. Therefore, the long

failure times in the junction test are due to the long cracking initiation periods for the

junction corner. Figure 3.25 shows the difference in activation energies between liner and

junction tests. This figure indicates similar activation energies (slopes) were obtained in

each set of the tests with liner test having smaller activation energy. The difference in

activation energies is attributed to the difference in stress concentration between the

122

specimens. The junction corner has a lower stress concentration than the notch in the

liner specimen, which results in higher activation energy.

Figure 3.21 Comparison of test results at 6

Junction test at 60oC

Liner test at 60oC

0oC in water on A24

123


Liner test at 70oC

Figure 3.22 Comparison of test results at 70oC in water on A24


Liner test at 80oC

Figure 3.23 Comparison of test results at 80oC in water on A24

124

0

100

200

300

400

500

600

0 200 400 600 800 1000 1200

Stress level (psi)

Junc

tion

failu

re ti

me

Line

r fai

lure

tim

eat 60Cat 70C

at 80C

Figure 3.24 Dependence of the ratio between the junction failure time and liner failure

time on stress and temperature

Table 3.9 Comparison of the brittle region of liner and junction tests on A24

Constants Slopes Test on A24

in water A B C 60oC 70oC 80oC

Activation energy range

(kJ/mol)

Liner test -13.57 7264 -749 -0.445 -0.458 -0.471 89-113

Junction test -25.9 14724 -1772 -0.186 -0.206 -0.179 169-180

125

-8-7-6-5-4-3-2-10

0.0028 0.00285 0.0029 0.00295 0.003 0.003051/T

ln(1

/t)

junction test at 650 psi junction test at 750 psi junction test at 850 psi

liner test at 600 psi liner test at 700 psi liner test at 800 psi

Figure 3.25 Difference of activation energies in liner and junction tests

3.7.2 Comparison of unnotched liner test with notched liner and junction test The notches in the liner test are used to generate short and consistent failure times. When

unnotched liner specimens were used in the test, the failure times are expected to be

much longer. In order to demonstrate the effect of stress concentration in both the liner

and junction specimens, some unnotched liner specimens from A24 were tested at high

stresses.

Figure 3.26 shows the three test results (unnotched liner test, notched liner test, and

junction test) in the brittle region under identical test conditions (80oC in water). The

junction test and unnotched liner test exhibited similar failure times and slopes relative to

the notched test. The unnotched liner test had longer failure times and shallower slope

126

than the junction test. Data from unnotched and junction tests exhibited greater scattering

relative to the notched liner test. Therefore, the 97.5% lower confidence interval for the

junction test was broader than that for liner test (Figure 3.26). The acceleration factors

(failure time of unnotched liner test over failure time of liner or junction test) were

calculated at different stress levels and presented in Table 3.10. For both junction and

unnotched liner tests, the acceleration factors increased as the applied stress decreased.

From 300 to 1000 psi, the acceleration factor ranged from 1.4 to 110 for liner test, and

1.2 to 2.5 for the junction test.

Solid line—fitting curve Dotted line—97.5% lower confidence bound

Unnotched liner test

Notched liner test Junction

test

Figure 3.26 Comparison of liner and junction tests at 80oC on A24

127

Table 3.10 Comparing of the acceleration effect of liner and junction tests

Unnotched liner Liner test Junction test Stress (psi)

Failure time (h) Failure time (h)

Acceleration factor

Failure time (h)

Acceleration factor

1000 6.9 4.8 1.4 5.8 1.2

900 12.4 5.9 2.1 9.8 1.3

800 23.9 7.5 3.2 17.6 1.4

700 50.5 9.8 5.2 34 1.5

600 119.9 13.3 9.0 74.1 1.6

500 332.9 19.1 17.4 184.4 1.8

400 1162 29.8 39.0 562.6 2.1

300 5823 52.9 110.1 2370.8 2.5

3.8 Lifetime prediction 3.8.1 Data extrapolation methods

The prediction of pipe lifetime required extrapolation of the data from high testing

temperatures to service temperatures. In this study, two popular methods were used for

this purpose; the rate process method (RPM) and the Popelar shift method (PSM).

The rate process method (RPM)

The ductile and brittle regions were defined as described above. Data from each phase

(either ductile or brittle) was extrapolated to lower temperatures using RPM, as expressed

in Equation 3. 3. This method has been described in both ISO 9080-Annex A and ASTM

128

D2837. The three constants in the equation are determined using a least squares multi-

variable regression analysis. The equation with known constants can then be applied to

predict the ductile-to-brittle curve at any temperature and stress under similar test

conditions.

TC

TBAt σloglog ++= (3.3)

Where:

t = time to failure, in hours,

σ = applied stress, in psi

T = test temperature, in K

A, B and C = constants

Popelar shift method (PSM) This method can shift individual test data from one temperature to another using two shift

factors, as defined by Popelar, et al. (1988), and shown in Equations 3.4, and 3.5. The

shifted data can then be analyzed by ISO 9080 to define the ductile-to-brittle curve.

( )[ RTTT ea −−= 109.0 ] (3.4)

( )[ RTTT eb −= 0116.0 ] (3.5)

Where:

aT = horizontal shift function (time function)

bT = vertical shift function (stress function)

T = temperature of the test

TR = target temperature

129

3.8.2 Comparison of prediction methods Results from the two extrapolation methods were applied to the liner test data at 70 and

80oC in order to predict the ductile-to-brittle curve at 60oC for A36. The predictions were

then compared with the experimental data at 60oC to verify the accuracy of the methods.

The calculation was performed by a Matlab code included in Appendix A. Results from

liner tests performed in water and the predicted curves are displayed in Figure 3.27. The

solid line at 60oC was generated by RPM using A, B, and C values obtained from data at

70 and 80oC. The predicted curve was similar to the actual experimental data. For PSM,

the predicted curve at 60oC was created by shifting the data point at 70 and 80oC using

corresponding shifting factors given by Popelar. The shifted data at 60oC were then fitted

by the ISO method to determine the ductile-to-brittle curve. The RPM produced a good

prediction, however the PSM over-predicted the failure time at 60oC by a considerable

amount (1.8 times of the actual test failure times).

The same procedure was used on data from tests performed to A36 in air. Figure 3.28

shows the test data and predicted curves. Similar to the liner tests in water, RPM

produced an accurate prediction of actual test results. However, PSM predicted failure

times that were approximately 1.6 times greater than those determined from the actual

test data.

130

PSM curve

RPM curve Exp. curve

at 60oC at

70oC 80oC

Figure 3.27 Comparison of predictions for liner test in water on A36

PSM curve

RPM curve Exp. curve

80oC

70oC

60oC

Figure 3.28 Comparison of predictions for liner test in air on A36

131

Comparison of the two extrapolation methods was also conducted on test data from A24

pipe material. Both junction test and liner test data were used to verify the predictions.

For the junction test, the 70 and 80oC data were used to predict the 60oC data. Figure

3.29 illustrates the test data and the results from both prediction methods. The curve

predicted by RPM correlated well with actual test data, while the curve predicted by PSM

was approximately half of the actual test data.

PSM curve

RPM curve Exp. curve 60oC

70oC 80oC

Figure 3.29 Comparison of predictions for junction test in water on A24

The liner tests for A24 pipes were performed in water at 80, 70, 60, and 40oC. Only

brittle failures were obtained in this test. Figure 3.30 shows the predictions from both

132

RPM and PSM. Again, the results indicated that RPM produced a strong prediction

while PSM offered little predictive value. The PSM predictions were approximately 2.5

times greater than the actual failure times.

PSM prediction at 40oC

RPM prediction at 40oC

at 80oC

at 70oC

at 60oC

Figure 3.30 Comparison of predictions for liner test in water on A24

The verification evaluation, demonstrated that RPM is a reliable method for prediction.

The PSM method tended to over-predict the pipe lifetime for the liner test and under-

predict the lifetime for the junction test. Therefore, PSM should not be used for

predicting the behavior of the pipes discussed in this study. PSM has been used

successfully for developing master curves for a variety of physical properties including

133

SCG (Popelar et al., 1991). However, the significant error associated with PSM

predictions was also reported. Chudnovsky et al. (1995) stated that the PSM-predicted

lifetime for brittle failure on a PE material at 24oC based on 80oC data was 10 times

greater than the actual lifetime. Therefore, it is thought that PSM is not accurate for the

SCG tests.

3.8.3 Prediction using RPM For extrapolating the ductile-to-brittle curve to temperatures lower than the test

temperatures, a least square method was applied to data at 60, 70 and 80oC to calculate

the three required constants in Equation 3.3. The values are included in Table 3.11. By

substituting these constants into the RPM equation, the ductile-to-brittle curve at working

temperatures (e.g., 23oC) can be generated. McGrath (2003) analyzed tension stresses in

the corrugated HDPE pipe under field stress conditions and found that the maximum

tensile stress was approximately 320 psi. By applying a factor of safety, 500 psi was

recommended as the long-term design stress.

Figure 3.31 shows the prediction of A24 junction test at 23oC by PRM. At 500 psi, the

predicted failure time is thousands of years. Even incorporating the 97.5% confidence

limit, the lifetime would still be greater than 100 years. Therefore, the A24 pipe should

not be susceptible to stress cracking based on the design stress.

134

Table 3.11 The three constants used for RPM methods Test

Material

Test

Environment Failure Mod A B C

Brittle -25.9 14724 -1772 A24

Junction Water

Ductile -79.97 71426 -14517

Figure 3.31 A24 junction test data and prediction at 23oC

3.9 Summary

The cracking in corrugated pipes occurs circumferentially around the junction between

the liner and corrugation. The microstructure of the fracture surface indicated a SCG

failure mechanism. Two tests were designed to evaluate the SCR of the pipes.

135

Liner test were performed on specimens taken from the liner part of the pipe. Four

specimen configurations were used in this study. The specimens cut along the

longitudinal direction of the pipe with notch on the outer liner surface (i.e., LO) had the

shortest failure times for all pipes. The difference in SCR of the four specimen

configurations is caused by the residual stresses in the pipes. Using the annealing method,

the maximum tensile residual stresses were localized to the outer surface of the pipes,

resulting in short failure times for the LO specimens. LO specimens were used for all the

liner tests. The effect of residual stresses was also assessed by comparing the test results

on the specimens with residual stresses (liner test) and those without residual stresses

(plaque test). The results indicated that tests on the specimens without residual stresses

have a shallower slope within brittle region and a steeper slope within ductile region.

The notched liner test generated short and consistent failure times, and is thus suitable for

QA/QC purposes.

To better represent the performance of HDPE pipes, junction tests were also conducted.

These tests use specimens taken directly from the junction area of the pipe. The junctions

between the corrugation and liner are the areas of highest stress concentration in the pipe.

Junction test data had large scatter due to the variability of junction geometry between

specimens, therefore, the lower confidence limit should be used for the junction data.

In the brittle region, the junction test corresponded to higher activation energy than in the

liner test. The difference resulted from the longer cracking initiation period for the

junction, which generated less stress concentration than the notch in the liner specimens.

136

The lifetime prediction was based on the junction test data due to the better representation

of actual pipe performance. RPM and PSM represent two widely used methods to predict

the lifetime of HDPE pipe material. PSM tended to over-predict in the liner test and

under-predict in the junction test. In contrast, RPM predictions were in strong agreement

with actual test data. Therefore, RPM represents a more reliable method to predict all the

failure curves. The lifetime of A24 was predicted at the design stress of 500 psi at 23oC,

and was found to be well over 100 years.

137

Chapter 4: Conclusion and Future Work

4.1 Summary This study investigated the SC of two different types of HDPE pipes: HDPE ducts used

in segmental bridges and Type S corrugated HDPE drainage pipes. Summary of the

results is presented below.

4.1.1 HDPE ducts in segmental bridges HDPE duct samples from seven bridges in Florida were evaluated. All of the cracking

was oriented longitudinally, indicating a circumferential tensile stress. Fracture

morphology of the fracture surfaces revealed a dominant fibril structure and few cases of

flaky structure. The fibril structure resulted from a SCG failure mechanism and the flaky

structure indicated an impact failure. In addition, fatigue lines were observed on the

fracture surface in some of the duct samples, indicating a cyclic loading acting on the

ducts. It is believed that the cyclic loading was caused by temperature changes between

day and night. Since there is a large difference in the thermal coefficients of expansion

between HDPE duct and cement grout, a circumferential internal stress is generated when

the temperature drops and this stress is gradually released when the temperature rises. In

order to determine the stress distribution in the duct, both laboratory performance testing

and FEM modeling were used. Furthermore, the residual stress in the pipe was measured

by the slitting method. It was found that the residual stress in the circumferential

direction of the duct was similar to the applied stress obtained from the laboratory test

and the FEM model. As a result of the residual stress and temperature-induced stress, a

maximum tensile stress was generated in the inner surface of the duct.

138

The material properties of HDPE ducts were tested according to ASTM D3350. MI and

density are two physical properties that relate to the SCR of the material. However, it

was found that neither of them could confidently predict the SCR. Also the bent strip test

(ASTM D1693) in the original material specifications was inadequate to predict field

behavior. In this study, the NCTL test (ASTM D5397) was used to evaluate duct

samples retrieved from the field, and the results were consistent with the field

performance. Thus, the NCTL test was recommended and included in the unified

material specification for the HDPE ducts. In addition, fatigue tests were performed to

evaluate the SCR of the HDPE ducts, and the results yielded the same ordering of SCR

for the duct materials as those of the NCTL tests.

The SC lifetime was estimated based on S-N curves from fatigue tests, by assuming that

one load cycle corresponded to one day-and-night temperature cycle in the field pipe.

The stress used in the prediction was 2000 psi, which was the combined stress of residual

stress and maximum thermally-induced stress. Only the Seven Miles Bridge sample and

the PE-3408 sample could reach a service life of 100 years, with only PE-3408 having a

large safety margin.

4.1.2 Corrugated HDPE pipes Cracking in corrugated HDPE pipes occurred adjacent to the corrugation junction along

the circumferential direction, indicating longitudinal stress acting on the pipe. The

fracture morphology of cracked surfaces revealed a fibril structure resulting from a SCG

mechanism. The longitudinal stress in the corrugated HDPE pipe was introduced by

deflection due to surrounding soils. In addition, the residual stress measured by the

139

annealing method indicated that the residual stress in the longitudinal direction was much

larger than that in the circumferential direction, with tensile stress on the inner liner

surface.

The effect of residual stress on the SCR of the corrugated pipe was evaluated using the

NCTL test, on specimens taken from compressive molded plaques and pipe liners. Four

different configurations were tested, based on specimen orientation with respect to the

pipe and notching positions. It was found that the LO configuration (cut along

longitudinal direction with notch on the outer liner surface) gave the lowest SCR for the

liner, consistent with the findings from the annealing method. Thus, specimens with LO

configuration were used for all of the liner tests.

The liner test is ideal for QA/QC due to the relatively short and consistent failure times.

However, the arbitrary sharp notch on the specimen does not represent the true scenario

of the pipe in the field. The junction test was developed to challenge the stress

concentration raised due to discontinuities of the junction geometry. However, due to the

variability of junction geometry from specimen to specimen, a large scatter in failure

times was observed from the junction tests. Also, the failure time of the junction tests

was much longer than that of the notched liner test at the same applied stress, because of

the long cracking initiation period.

The methods described in ISO 9080 were used to analyze data from both the liner and

junction tests. The transition point between ductile-to-brittle regions was identified, and

140

then the curves were fitted using the least square method. Furthermore, the lower

confidence limits for the junction tests were determined. Two extrapolation methods,

PSM and RPM, were investigated to predict the SC lifetime of corrugated HDPE pipes,

and RPM was found to be a more reliable method.

4.2 Conclusion

Based on the work conducted in this study, the following conclusions can be reached:

• The SC failure in the HDPE ducts and corrugated HDPE pipes was caused by SCG.

• The stress on the HDPE ducts was partly caused by thermal cyclic loading. The

temperature-induced stresses in the ducts ranged from 400 to 1400 psi. On the other

hand, deflection of the corrugated HDPE pipes induced a 300 psi stress in both

longitudinal and circumferential directions.

• The residual stress was measured using the slitting method for HDPE ducts and the

annealing method for corrugated HDPE pipes. For the HDPE ducts, the maximum

tensile residual stress is approximately 786 psi on the inner surface, oriented

circumferentially. The maximum tensile residual stresses in the corrugated HDPE

pipes range from 80 to 815 psi in the longitudinal direction and from 0 to 180 psi in

the circumferential direction. The magnitude of the residual stresses is comparable

with the applied stresses and would play a significant role in the SC for both types of

HDPE pipe.

141

• For HDPE ducts, both the NCTL test and the fatigue test yielded the same SCR

ranking for the samples from the seven bridges, and the result was consistent with

field performance. In the unified specification, the NCTL test is adopted for QA/QC

to replace the conventional bent-strip test. The fatigue test simulates the cyclic

loading in the field ducts; therefore, it can be used for lifetime prediction.

• For the corrugated HDPE pipes, the liner and junction tests were developed to

evaluate the SCR of the finished pipes. The liner test generates short and consistent

failure times, and is appropriate for QA/QC purposes, while the failure times in the

junction test are significantly longer with a large scatter compared to the liner test.

The long failure time in the junction test was caused by the prolonged cracking

initiation period. The scattering of the data was caused by the variability of the

junction geometry. However, the junction test better represents pipe performance in

the field, and therefore the test data are more realistic for predicting lifetime of SC

performance.

• Lifetime prediction was performed using both PSM and RPM. RPM was found to

provide a more reliable prediction, while PSM tended to over-predict the lifetime in

the liner test and under-predict the lifetime in the junction test. To be conservative, a

safety factor obtained from the 97.5% lower confidence limit was applied to the

junction data in SC lifetime prediction. The SC lifetime prediction based on the

junction test on pipe sample A24 by RPM indicates that SC will not occur within the

design life.

142

• The comparison of the two types of HDPE pipe and their respective SC studies is

listed in Table 4.1.

Table 4.1 Comparison of the two HDPE pipes

Features HDPE ducts Type S corrugated HDPE pipes

Function Moisture protection Drainage

Geometry Smooth-walled Corrugated

Cracking initiation location Inner duct surface Outer surface at the

junction area

Cracking orientation Longitudinal Circumferential

Cracking mechanism SCG SCG

Driving force Cyclic load (fatigue-related) Static load (creep-related)

Residual stress measurement Slitting method Annealing method

Max. residual stress Circumferentially Longitudinally

SCR test NCTL, fatigue test Liner test, junction test

Lifetime prediction method S-N curves RPM

4.3 Future work The unaddressed studies that are of interest for future research include:

• Residual stress distribution across the pipe wall (liner) thickness and in different

directions. The residual stresses discussed in this study are only maximum stresses

143

measured on the pipe surfaces. Therefore, a quantitative relationship between the

SCR and residual stresses cannot be established. Furthermore, the effect of the

thermal process and extrusion process during pipe manufacturing on residual stresses

should be addressed.

• Fatigue test for HDPE ducts. The samples were obtained from compression molded

plaques and were notched on the surface. Therefore, the residual stresses effect was

not included in the SCR evaluation. Furthermore, the acceleration effect of the notch

on the SC process remains unclear. It is also of great interest to find the relationship

between the SCR obtained from the creep test and fatigue test.

• The relationship between the liner and junction test data. It is desirable to establish a

quantitative relationship between the QA/QC tests and the lifetime prediction test.

• The validation of both the tests (liner and junction tests) and analytical approach

(RPM) require confirmation from pipe performance in the field.

144

List of Reference

1. Akiyama,S., Takagi, N. , Nagatani, F. , Ishimaru, N. , (1991), “A method for life

prediction of polyethylene under the constant strain condition”, Twelfth Plastic Fuel Gas Pipe Conference Symposium, 170-179

2. Annual Book of ASTM Standard 08.03: Plastics (III), (2001) 3. Baxindine, C., (2004), Crack investigation in HDPE post tensioning ducts in

Florida bridges 4. Bernal,C., Montenegro,H.L., Frontini, P., (2002), Failure prediction analysis for

polyethylene flawed pipes, Engineering Fracture Mechanics, 1-14 5. Bhatnagar, A., Broutman, L.J, (1985), “Effect of annealing and heat fusion on

residual stresses in polyethylene pipe”, Annual Technical Conference-Society of Plastics Engineers, 545-549

6. Bhattacharya, S.K., Brown, N., (1984), “Micromechanisms of crack initiation in

thin films and thick sections of polyethylene”, Journal of Materials Science, 2519-2532

7. Bragaw, C.G., (1980), “Prediction of service life of polyethylene gas piping

system”, Seventh Plastic Fuel Gas Pipe Conference Symposium, 20-24 8. Bragaw, C.G., (1980), “Service rating of polyethylene piping systems by the rate

process method”, Seventh Plastic Fuel Gas Pipe Conference Symposium, 40-48 9. Brown, N. , (1985), “Relationship between initiation of slow crack growth and

ultimate failure of polyethylene”, Nineth Plastic Fuel Gas Pipe Conference Symposium, 283-290

10. Brown, N., Bhattacharya, S.K., (1985), “The initiation of slow crack growth in

linear polyethylene under single edge notch tension and plane strain”, Journal of Materials Science, 4553-4560

11. Brown, N., Lu, X., (1995), “A fundamental theory for slow crack growth in

polyethylene”, Polymer, 543-548 12. Brown, N., Donofrio, J., and Lu, X., (1987), “The transition between ductile and

slow-crack-growth failure in polyethylene”, Polymer, 1326-1330 13. Cassady, M.J., Uralil, F.S., (1985), “Initiation in stress rupture test failures”,

Nineth Plastic Fuel Gas Pipe Conference Symposium, 281-283

145

14. Chang, P., Donovan, J.A., (1990), “Detergent Assisted Stress Cracking in Low Density Polyethylene”, Polymer Engineering and Science, Vol. 30, No.22, pp 1431-1441.

15. Chaoui, K., Chudnovsky, A,. Moet, A., (1987), “Processing effect on the crack

propagation resistance of PE pipes”, Annual Technical Conference-Society of Plastics Engineers, 468-471

16. Chaoui, K., Moet, A. (1987), “Residual stress analysis in fuel gas pipes”, Tenth

Plastic Fuel Gas Pipe Symposium Proceedings, New Orleans, 315-323. 17. Choi, S.,Broutman, L.J, (1983), “Residual stresses in polyethylene pipe”, Annual

Technical Conference-Society of Plastics Engineers, 378-379 18. Chudnovsky, A. Shulkin, Y.,Zhou, Z., (2003), “Characterization of polyethylene

resistance to slow crack growth”, Annual Technical Conference-Society of Plastics Engineers, 2976-2981

19. Chudnovsky, A., Baron, D., Shulkin, Y., Sehanobish, K., Bosnyak, C.P., (1996),

“Lifetime, toughness, and reliability of engineering thermoplastics”, Annual Technical Conference-Society of Plastics Engineers, 2712-2717

20. Chudnovsky, A., Shulkin, Y., (1996), “New model of slow crack growth in

viscoelstic thermoplastics”, Annual Technical Conference-Society of Plastics Engineers, 3284-3288

21. Derringer, G.C., Cassady, M.J., Epstein, M.M., (1980), “A reassessment of the

strength-failure time regression extrapolation for estimating the long-term strength of plastic pipe”, Seventh Plastic Fuel Gas Pipe Conference Symposium, 15-19

22. Faucher, J.A., (1959), “Viscoelastic behavior of polyethylene and polypropylene”,

Transportation Society Rheology III, 81-93 23. Hartt, W. , Suarez, J., David, F. , Hsuan,Y.G., Zhang, J. , (2005), “The role of

polyethelene duct cracking in failure of post tensioning cables in Florida segmented bridges (BD220)”, Florida Department of Transportation report

24. Hopkins, I.L., Baker, W.D., Howard, J.B., (1950), “Complex Stressing of

polyethylene”, Journal of applied physics, v2, n3, 206-213 25. Hsuan, Y.G., McGrath, T.J., (1998), HDPE pipe material specifications and design

requirements 26. Hsuan, Y. G., Zhang, J. , (2005), “Residual stress effects on stress crack resistance

in HDPE corrugated geopipe”, Geofrontiers Confrence Proceedings, Austin, TX

146

27. Hsuan, Y.G., Zhang, J., (2005), “Stress crack resistance of corrugated HDPE pipes in different test environments”, Transportation Research Board (TRB) Annual Meeting, Washington D.C.

28. Hulbert, L.E, Mamoun, M.M. , (1983), “A perspective of current technology on

the time-dependent deformation and fracture of plastic gas piping materials”, Eighth Plastic Fuel Gas Pipe Conference Symposium, 4-8

29. Iimura,S., Akiyama,S., Kasahara,K., (1989), “Application of linear fracture

mechanics to service life prediction of polyethylene with full notch creep test”, Eleventh Plastic Fuel Gas Pipe Conference Symposium, 411-430

30. Ingen J.F., Housz, (1982), “Residual stresses in extruded pipe”, Polymer extrusion,

26.1-26.9 31. ISO/FDIS 9080, Plastics Piping and Ducting Systems - Determining of Long-term

Hydrostatic Strength of Thermoplastics Materials in Pipe Form by Extrapolation. (2002).

32. Ivan K.B., (1980), “Plastic pipe demonstrated performance evaluates predictive

methods”, Seventh Plastic Fuel Gas Pipe Conference Symposium, 12-14 33. Kamal, M.R., Lai-fook, R.A., Hernandez-aguilar, J.R., (2002), “Residual thermal

stresses in injection moldings of thermoplastics: a theoretical and experimental study”, Polymer Engineering and Science, Vol. 42, No. 5, 1098-1114

34. Kamei,E.,Brown,N., (1984), “Crazing in polyethylene”, Journal of Polymer

Science, 543-559 35. Kanninen, M.F., Peggs, I.D.,.Popelar, C.H, (1993), “A methodology for forcasting

the lifetimes of geomembranes that fail by slow crack growth”, Geosynthetics ’93, Vancouver, Canada, 831-844

36. Koerner, R.M. , (1999), Designing with geosynthetics, 4th edition, Prentice Hall 37. Lu, X., Brown, N., (1990), “The ductile-brittle transition in a polyethylene

copolymer”, Journal of Materials Science, 29-34 38. Lu, X., Brown, N., (1990), “The transition from ductile to slow crack growth

failure in a copolymer of polyethylene”, Journal of Materials Science, 25, 411-416 39. Lu, X., Brown, N., (1997), “Abnormal slow crack growth in polyethylene”,

Polymer, 5749-5753 40. Lustiger, A., (1985), “The molecular mechanism of slow crack growth in

polyethylene”, Ph.D dissertation, Drexel Unviersity

147

41. Lustiger, A., Markham,R.L., (1983), “Importance of tie molecules in preventing polyethylene fracture under long-term loading conditions”, Polymer, 1647-1654

42. Lustiger,A., Corneliussen, R.D., (1987), “The role of crazes in the crack growth of

polyethylene”, Journal of Materials Science, 2470-2476 43. Lustiger,A., Corneliussen, R.D.,Kantz, R., (1978), “Environmental stress crack

growth in low density polyethylene”, Materials Science and Engineering, 117-123 44. Maxell, A.S., (2001), “Practical guide for designers and manufacturers of moldings

to reduce the risk of environment stress cracking”, NPL Report MATC (A) 05. 45. McGrath, T. J., (2003), “Protocol for 100 year service life of corrugated HDPE

part I - evaluation and control of stresses in buried corrugated HDPE drainage pipe”, Florida Department of Transportation.

46. Methods of Residual Measurement-SAE J936, Report of Iron and Steel Technical

Committee, (1965) 47. Moet, A., Chudnovisky, A., Strebel, J., Chaoui, K., (1989), “Slow crack fatigue

crack growth test for ranking polyethylene pipes”, Eleventh Plastic Fuel Gas Pipe Conference Symposium, 327-333

48. Nishimuro, H., Shishich, T., (1985), “A quality control test method for MDPE”,

Nineth Plastic Fuel Gas Pipe Conference Symposium, 70-84 49. Onogi, S., Asada, T., Fukui, Y., Fujisawa, T., (1967), “Time-temperature

superposition of time-dependent preference for low-density polyethylene”, Journal of Polymer Science, A-72, 5, 1067-1077

50. Palermo, E. F., DeBlieu, I. K., (1985), “Rate process concepts applied to

hydrostatically rating polyethylene pipe”, Seventh Plastic Fuel Gas Pipe Conference Symposium, New Orleans, 215-240

51. Palermo, E.F., (1980), “Rate process method as a practical approach to a quality

control method for polyethylene pipe”, Seventh Plastic Fuel Gas Pipe Conference Symposium, 96-101

52. Parsons, M. , Stepanov, E.V., Hiltner, A. , Baer, E. , (1999), “Correlation of

stepwise fatigue and creep slow crack growth in HDPE”, Journal of materials science, v34, n14, 3315-3326

53. Popelar, C.F., Popelar, C.H., Kenner, V.H., (1990), “Viscoelasic material

characterization and modeling for polyethylene”, Polymer Engineering and Science, Vol. 30, No. 10, 577-586

148

54. Popelar, C.H., (1993), “A comparison of the rate process method and the bi-directional shifting method”, Thirteenth Plastic Fuel Gas Pipe Conference Symposium, San Antonio, 151-161

55. Popelar, C.H., Kenner, V.H., Wooster, J.P., (1991), “An accelerated method for

establishing the long term performance of polyethylene gas pipe materials”, Polymer Engineering and Science, Vol. 31, No. 24, 1693-1700

56. Popelar, C.H., Kuhlman, C.J., Peggs, I.D., (1998), “A fracture mechanics

assessment for the long term durability of HDPE geomembranes”, Sixth International Conference on Geosynthetics, 365-369

57. Powers, R.G. (1999), “Corrosion Evaluation of Post-Tensioned Tendons on the

Niles Channel Bridge”, Florida Department of Transportation, Tallahassee, Florida 58. Rate process method for projecting performance of polyethylene piping

components, Plastic Pipe Institute, TN-16/99, (1999) 59. Sarkes, L.A., Smith, R.B., (1983), “Plastic pipe research-a historical perspective”,

Seventh Plastic Fuel Gas Pipe Conference Symposium, Arlington, VA, 2 60. Scott, H., Lee H., (1988), “The effect of various processing stages on the

crystallinity of post-consumer recycled HDPE”, Annual Technical Conference-Society of Plastics Engineers, 2935-2938

61. Shah, A., Stepanov, E.V., Klein, M. , Hiltner, A., Baer, E., (1998), “Study of

polyethylene pipe resins by a fatigue test that simulates crack propagation in a real pipe”, Journal of Material Science, 3313-3319

62. Shlton, W.S., Bright, D.G., (1993), “Using the Arrhenius equation and rate

expressions to predict the long term behavior of geosynthetic polymers”, Geosynthetics ’93, Vancouver, Canada, 789-802

63. Squrez, J. Zhang, J., Hsuan, Y.G., Hartt, W., (2005), “Polyethylene duct on post

tensioning tendons in Florida bridges”, ASCE Journal of Materials 64. Strong, A.B., (2000), Plastics materials and processing, 2nd edition, Prentice Hall 65. Thomas, R.W., Siebken, J., (1997), “Increasing the temperature of the notched

constant tensile load environmental stress crack resistance test”, Geosynthetics ’97, 191-200

66. Uralil, F. S., Markham, R.L., (1980), “Evaluation of polyethylene pipe using stress

intensity factor obtained in a simple laboratory test”, Seventh Plastic Fuel Gas Pipe Conference Symposium, 10-13

149

67. Ward, A.L., Lu, X., Huang, Y., and Brown, N., (1989), “The mechanism of slow crack growth in polyethylene by an environmental stress cracking agent”, Polymer Engineering and Science

68. Whittle, A.J., Burford, R.P, Hoffman, M.J., (2000), “Influence of residual stress

on the relationship between pipe pressure and C-ring tests”, Polymer Engineering and Science, Vol. 40, No. 11, 2311-2316

69. Williams, J. G. , Clutton, E. Q., (1993), “On the measurement of residual stresses

in plastic pipes”, Thirteenth Plastic Fuel Gas Pipe Conference Symposium, San Antonio, 194-203

70. Williams, J.G., (1987), Fracture Mechanics of Polymers, John Wiley and Sons,

Inc., New York 71. Wong, T.C., (1983), “Residual stress in polyethylene pipe and fittings”, Eighth

Plastic Fuel Gas Pipe Symposium Proceedings, Arlington, 124-127. 72. Wu, S., Sehanobish, K., Chudnovsky, A., (2003), “Accelerated testing for slow

crack growth in HDPE”, Annual Technical Conference-Society of Plastics Engineers, 2952-2956

73. Zhou, Y. , Brown, N. , (1993), “Evaluating the fatigue resistance of notched

specimens of polyethylene”, Polymer of engineering and science, v33, n21, 1421-1425

74. Zhou, Y., Brown, N., (1995), “Anomalous fracture behavior in polyethylene under

fatigue and constant load”, Journal of Materials Science, 30, 6065-6069 75. Zhou, Y., Lu,X., Brown, N., (1996), “The relative influence of molecular structure

on brittle fracture by fatigue and under constant load in polyethylene”, Polymer Engineering and Science, Vol.36, No. 16, 2101-2107

76. Zhou, Y., Lu, X., Brown, N., (1989), “Slow crack growth under fatigue and

constant stress for ethylene-hexene resins with different density of branches”, Eleventh Plastic Fuel Gas Pipe Conference Symposium, 321-326

150

Appendix A: Data Analysis Method and Matlab Code A.1 Principle and procedure The data obtained from liner and junction tests on corrugated HDPE pipes were analyzed

based on ISO 9080. The standard includes the methods of detecting the transition point

(knee) between brittle and ductile regions, fitting the data with bilinear lines,

extrapolating the data to lower temperatures, and calculating the lower prediction limits

for the stresses. The following describes the details:

• Knee detection and model fitting

At each temperature, the data can be modeled by the following equation:

eccct ki +−++= )log(logloglog 10103103110 σσσ (A.1)

Where

ic3 is the coefficient to express the effect of type of failure: for brittle failures i=1 and for

ductile failures i=2; and 3231 cc −= (to avoid singularity)

kσ is the stress corresponding to the knee;

e is the error variable;

A practical way of fitting this model is to assume 50 values of 10log kσ that are evenly

distributed over the experimental range of stress values. The residual variance for each

corresponding linear fit was then calculated. The minimum in the residual variance, ,

indicates the best fit. The corresponding

2s

kσ is the optimum knee point.

151

The following matrix notations are used for the calculation:

⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

−

−−

−

=

)log(log0log1

)log(log0log10)log(loglog1

0)log(loglog1

101010

10110110

101010

10110110

kmn

k

kmm

k

X

σσσ

σσσσσσ

σσσ

MMMM

MMMM

; ; ⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

+nmt

ty

10

110

log

logM

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡=

+nme

ee M

1

Where

m = number of points in the mode of brittle failure;

n = number of points in the mode of ductile failure;

Equation A.1 can be expressed as:

(A.2) eXcy +=

The least squares estimates of the parameters are:

yXXXc ')'( 1−=) (A.3)

The residual variance estimate is:

)/()()'(2 qnmcXycXys −+−−= )) (A.4)

Where q is the number of parameters of the model

• Extrapolating the data to lower temperatures

The approach uses the three-parameter model (RPM equation) expressed as follows:

eTcTcct +++= /)(log/log 1042110 σ (A.5)

The matrixes used for calculation are:

152

; ;

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

310103

31101103

210102

21101102

110101

11101101

/)(loglog/11

/)(loglog/11

/)(loglog/11

/)(loglog/11/)(loglog/11

/)(loglog/11

TT

TT

TT

TTTT

TT

X

rr

qq

pp

σσ

σσ

σσ

σσ

σσ

σσ

MMMM

MMMM

MMMM

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

=

++ rqpt

ty

10

110

log

logM

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

=

++ rqpe

ee M

1

Where , , and indicate three different temperatures; and p, q, and r are the number

of test data at each of the temperatures, respectively.

1T 2T 3T

Using the above matrices, the constants A, B, and C can then be obtained by applying

Equation A.2

• Calculating the lower prediction limits of the stress

The lower prediction limit of stress, LPLσ , can be developed from the following equation:

(A.6) 2/111041032110 )')'(1(/)(log)(log/log xXXxstTccTcct st

−+−+++= σσ

Where

stt is the Student’s t-statistic corresponding to a probability level of 0.975 and a degree of

freedom of (total number of observations – number of parameters);

x represents the vector )/)(log,log,/1,1( 1010 TT σσ .

By inverting Equation A.6, LPLσ10log can be obtained:

ααβββ

σ2

4log

2

10−−−

=LPL (A.7)

153

Where

)//2()/( 2444333

22243 TKTKKstTcc st ++−+=α

)//)((2)/)(log/(2 242324131

22431021 TKTKKKstTcctTcc st +++−+−+=β

)1//2(log/( 2222111

2221021 +++−−+= TKTKKsttTcc stγ

ijK = element of indices i, j of the matrix 1)'( −XX

A.2 Matlab code for data analysis %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Code A: Finding the transition point (knee) and fitting the data with bilinear curves%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % Input the test data sigma=[applied stresses for a certain test]'; time=[corresponding failure times]'; logsigma=log10(sigma); logtime=log10(time); logsigmamax=max(logsigma); logsigmamin=min(logsigma); step=(logsigmamax-logsigmamin)/(t+1); m=0; n=0; %Assume 50 points that are evenly distributed in the range of log10 of applied stresses as %the knee points t=50 for i=1:t;

logsigma_1(i)=logsigmamin+i*step;

%Divide the data points into two groups by each of the assumed knee point logsigma_1= []; logtime_1= []; logsigma_2= []; logtime_2= []; for j=1:length(sigma); if logsigma(j)<logsigma_1(i); m=m+1; logsigma_1(m)=logsigma(j); logtime_1(m)=logtime(j); else n=n+1; logsigma_2(n)=logsigma(j); logtime_2(n)=logtime_2(j);

154

end end

%Form the matrix with the first group of data for p=1:m; x(p,1)=1; x(p,2)=logsigma_1(p); x(p,3)=logsigma_1(p)-logsigma(i); x(p,4)=0; y(p,1)=logtime_1(p); end %Form the matrix with the second group of data for p=m+1:m+n; x(p,1)=1; x(p,2)=logsigma_2(p-m); x(p,3)=0; x(p,4)=logsigma(i)-logsigma_2(p-m) y(p,1)=logtime_2(p-m); end m=0; n=0; %Calculate the constants and residual variances c=inv(x'*x)*x'*y; s=(y-x*c)'*(y-x*c)./(length(sigma)-length(c)); end %Find the knee position a=0; b=10; for i=1:t; if s(i)<b; smin=s(i); a=i; end end %Calculate the stress and failure time at the knee point logsigmaknee=logsigmamin+a*step; sigmaknee=10^logsigmaknee logtimeknee=c(1,a)+c(2,a)*logsigmaknee; timeknee=10^logtimeknee %Draw the fitting curve corresponding to the minimum residual variance c_1(1)=c(1,a)

155

c_1(2)=c(2,a) c_1(3)=c(3,a) c_2(1)=c(1,a) c_2(2)=c(2,a) c_2(3)=-c(4,a) inte_1=-(c_1(1)-c_1(3)*logsigmaknee)/(c_1(2)+c_1(3)) slop_1=1/(c_1(2)+c_1(3)) inte_2=-(c_2(1)-c_2(3)*logsigmaknee)/(c_2(2)+c_2(3)) slop_2=1/(c_2(2)+c_2(3)) logsigma_1=(logsigmamin:(logsigmaknee-logsigmamin)/t:logsigmaknee); for p=1:t; x_1(p,1)=1; x_1(p,2)=logsigma_1(p); x_1(p,3)=logsigma_1(p)-logsigmaknee; end logtime_1=x_1*c_1'; logsigma_2=(logsigmaknee:(logsigmamax-logsigmaknee)/t:logsigmamax); for p=1:t; x_2(p,1)=1; x_2(p,2)=logsigma_2(p); x_2(p,3)=logsigma_2(p)-logsigmaknee; end logtime_2=x_2*c_2'; plot(logtime,logsigma,'kd',logtime_1,logsigma_1,'k-',logtime_2,logsigma_2,'k-','linewidth',2) xlabel('log time (hour)','fontsize',14) ylabel('log stress (psi)','fontsize',14) grid on %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Code B: Calculating the three constants A, B, and C% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Input the test data at different temperatures clear format long sigma60=[applied stresses at 60oC] time60=[corresponding failure times at 60oC] sigma70=[applied stresses at 70oC] time70=[corresponding failure times at 70oC] sigma80=[applied stresses at 70oC] time80=[corresponding failure times at 70oC] logsigma60=log10(sigma60) logtime60=log10(time60) logsigma70=log10(sigma70)

156

logtime70=log10(time70) logsigma80=log10(sigma80) logtime80=log10(time80) logsigma=[logsigma60,logsigma70,logsigma80]'; logtime=[logtime60,logtime70,logtime80]'; n1=length(logsigma60) n2=length(logsigma70) n3=length(logsigma80) n=n1+n2+n3; %Form the matrix and calculate the constants for i=1:n x0(i,1)=1; y0(i,1)=logtime(i); end for i=1:n1 x0(i,2)=1/333; x0(i,3)=logsigma(i)/333; end for i=n1+1:n1+n2 x0(i,2)=1/343; x0(i,3)=logsigma(i)/343; end for i=n1+n2+1:n x0(i,2)=1/353; x0(i,3)=logsigma(i)/353; end c0=inv(x0'*x0)*x0'*y0 A=c0(1) B=c0(2) C=c0(3) %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Code C: Predicting 60oC data by both RPM and PSM using 70 and 80oC data % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%% % RPM prediction% %%%%%%%%%% %Calculate the constants by Code B A_b=calculated A at brittle region from data at 70oC and 80oC B_b=calculated B at brittle region from data at 70oC and 80oC C_b=calculated C at brittle region from data at 70oC and 80oC A_d=calculated A at ductile region from data at 70oC and 80oC B_d=calculated B at ductile region from data at 70oC and 80oC

157

C_d=calculated C at ductile region from data at 70oC and 80oC %Predict the curve at 60oC by RPM logtimeknee=((-A_d*333-B_d)/(C_d)-(-A_b*333-B_b)/(C_b))/(333/(C_b)-333/(C_d)) logtime_b=logtimeknee:0.1:4 logsigma_b=(-A_b*333-B_b+logtime_b*333)/(C_b) logtime_d=-1:0.1:logtimeknee logsigma_d=(-A_d*333-B_d+logtime_d*333)/(C_d) plot(logtime_b,logsigma_b,'k-',logtime_d,logsigma_d,'k-','linewidth',2) xlabel('log time (hour)','fontsize',14) ylabel('log stress (psi)','fontsize',14) grid on hold on %%%%%%%%%% %PSM prediction % %%%%%%%%%% %Calculate the shift factors clear at80=exp(-0.109*(80-60)); logat80=log10(at80) bt80=exp(0.0116*(80-60)); logbt80=log10(bt80) at70=exp(-0.109*(70-60)); logat70=log10(at70) bt70=exp(0.0116*(70-60)); logbt70=log10(bt70); %Input the data dn shift the data to 60oC using the shift factors logsigma70=[log10 of applied stresses at 70oC]; logtime70=[log10 of corresponding failure times at 70oC]; logsigma80=[log10 of applied stresses at 80oC]; logtime80=[log10 of corresponding failure times at 80oC]; logsigma=[logsigma70'+logbt70,logsigma80'+logbt80]'; logtime=[logtime70'-logat70,logtime80'-logat80]'; %The PSM shifted data at 60oC are then fitted using Code A %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

%Code D: Calculate the 97.5% lower confidence bound% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Input data to be analyzed sigma=[applied stresses]';

158

time=[corresponding failure times]'; logsigma=log10(sigma); logtime=log10(time); % Form the matrix m=length(sigma); for i=1:m; X(i,1)=1; X(i,2)=logsigma60(i); Y(i,1)=logtime60(i); end c=inv(X'*X)*X'*Y; s=(Y-X*c)'*(Y-X*c)./(length(sigma60)-length(c)); %Draw the fitting curve logsigma_1=2.7:0.05:3.1; for p=1:9; xx(p,1)=1; xx(p,2)=logsigma_1(p); end logtime_1=xx*c; plot(logtime,logsigma,'kd',logtime_1,logsigma_1,'k-','linewidth',2) xlabel('log time (hour)','fontsize',14) ylabel('log stress (psi)','fontsize',14) grid on hold on

%Draw the 97.5% lower confidence bound a=length(sigma); b=length(c); tst=upper critical value of student’s distribution with (a-b) degrees of freedom K=inv(X'*X) for i=1:a alfa=c(2)^2-tst^2*s*K(2,2) beta(i)=2*(c(1)-logtime_1(i))*c(2)-2*tst^2*s*K(2,1) gama(i)=(c(1)-logtime_1(i))^2-tst^2*s*(K(1,1)+1) logsigmalpl(i)=(-beta(i)-(beta(i)^2-4*alfa*gama(i))^0.5)/(2*alfa) end plot(logtime_1,logsigmalpl,'k--','linewidth',2) xlabel('log time (hour)','fontsize',14) ylabel('log stress (psi)','fontsize',14) grid on

159

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%Code E: Predicting the lifetime at 23oC using RPM%

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %Predict the curve at 23oC logtimeknee=((-A_d*296-B_d)/(C_d)-(-A_b*296-B_b)/(C_b))/(296/(C_b)-296/(C_d)) logtime_b=logtimeknee:0.1:4 logsigma_b=(-A_b*296-B_b+logtime_b*296)/(C_b) logtime_d=-1:0.1:logtimeknee logsigma_d=(-A_d*296-B_d+logtime_d*296)/(C_d) plot(logtime_b,logsigma_b,'k-',logtime_d,logsigma_d,'k-','linewidth',2) xlabel('log time (hour)','fontsize',14) ylabel('log stress (psi)','fontsize',14) grid on hold on %Find the predicted failure time at 23oC corresponding to 500 psi design stress logstress=log10(500) loglifetime=A_b+B_b/296+logstress*C_b/296 plot(loglifetime,logstress,'d','linewidth',2) lifetime=10^loglifetime

160

Appendix B: Residual Stress Calculation

Figure B.1 shows the configuration of the specimen form after annealing. The

parameters illustrated in the figure use capital letters to indicate that they are measured

after annealing. Corresponding small letters are used for the same parameter in the

original shape.

Figure B.1 Specimen configurations after annealing

The following shows the steps to calculate the residual stresses:

161

From Figure B.1, it can be found that the basic relationship exists for the parameters.

222)( rbhr =+− (B.1)

And

( )2 2R H B R− + = 2 (B.2)

The radius

hhbr

⋅−

=2

)( 22

(B.3)

And

HHBR

⋅−

=2

)( 22

(B.4)

Approximately, b =B=L/2

Then, substitute the above into Equations B.3, and B.4,

hh

Lhh

brh

hbr 28222

)( 2222

−⋅

=−⋅

=⋅⋅

−= (B.5)

And

HHLH

HB

RHHBR 2

8222)( 2222

−⋅

=−⋅

=⋅⋅

−= (B.6)

It is noticed that on the right hand of the equations, the first term is much larger than the

second. Then the equations can be reduced into

hLr⋅

=8

2

(B.7)

And

162

HLR⋅

=8

2

(B.8)

Because the curvature is the reciprocal of the radius, Equations B.7 and B.8 can be

expressed as:

2

81L

hr

c ⋅== (B.9)

And

2

81LH

RC ⋅

== (B.10)

Generally, the arc height is less than 1/10 of the arc length. The approximation will give

the accuracy of 96%.

The arc length Ly and ly that have a distance of y from neutral axis of the beam specimen

can be calculated by the following equations

)1()(ryL

ryrLly −⋅=

−⋅= (B.11)

And

)1()(RyL

RyRLLy −⋅=

−⋅= (B.12)

Then the strain is

ryry

Ry

llL

y

yy

−

−=

−=

1ε (B.13)

Generally, y/r is far less than 1; then, B.13 can be reduced into

ry

Ry−=ε (B.14)

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Therefore

2

)(8)()11(L

hHycCyrR

y −⋅⋅=−⋅=−⋅=ε (B.15)

Usually, the original shape of the specimen is approximately in flat form (i.e., curvature

c=0). Then, Equation B.15 can be reduced to

2

8L

HyCy ⋅⋅=⋅=ε (B.16)

And the corresponding stress is

2

8L

EHy ⋅⋅⋅=σ (B.17)

The maximum stresses will occur at the surface of the specimen, where the strain is the

largest. In this case, y=t/2, then

2max4

LEHt ⋅⋅⋅

=σ (B.18)

The arc height H can be developed from the measured distance, A (Figure B.1).

tAH −= (B.19)

Therefore

2max)(4

LEtAt ⋅−⋅⋅

=σ (B.20)

The parameters needed to be measured are specimen length, L, thickness, t, and the sum

of arc height and thickness, A.

164

Vita Jingyu Zhang Education:

Ph.D., Geotechnical Engineering, Drexel University, Philadelphia, USA, 2005

M.S., Geotechnical Engineering, Xi’an University of Architecture &. Technology,

Xi’an, China, 2001

B.S., Civil Engineering, Xi’an University of Engineering, Xi’an, China, 1998

Publications:

1. Jorge Suarez, Jingyu Zhang, Grace Hsuan, and William Hartt, Polyethylene Duct cracking on Post Tensioning Tendons in Florida Segmented Bridges, submitted to ASCE, Journal of Materials

2. Y.G. Hsuan, J. Zhang, &. R. Koerner, Residual Stress Effects on Stress Crack

Resistance in HDPE Corrugated Geopipe, the Geofrontiers Conference, Austin, Texas, Jan. 26, 2005

3. Y.G. Hsuan, J. Zhang, Stress Crack Resistance of Corrugated HDPE Pipes in

Different Test Environments, Transportation Research Board (TRB) Annual Meeting, Washington D.C., Jan., 2005

4. William H. Hartt, Jorge Suarez, Florent David, Grace Hsuan and Jingyu Zhang,

The Role of Polyethylene Duct Cracking in Failure of Post Tensioning Cables in Florida Segmented Bridges (BD220), Florida Department of Transportation report, January 20, 2005

Professional affiliation:

American Society of Civil Engineers (ASCE)

North American Geosynthetics Society (NAGS)

Experimental study of stress cracking in high density ...

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