AN ELEGANT AND FAST METHOD TO PREDICT THE
SLOW CRACK GROWTH BEHAVIOUR OF HIGH DENSITY
POLYETHYLENE PIPE MATERIALS
D.J.M. (Linda) Havermans - van Beek*, Rudy Deblieck†, Mary McCarthy*,
Rainer Kloth*, Lada Kurelec*
*
SABIC, The Netherlands; ††DSM Resolve, The Netherlands.
ABSTRACT
Resistance to slow crack growth is an important material property of polyethylene which
determines the application lifetime, especially for utility pipe applications. Usually, the slow
crack growth resistance of materials is assed by time consuming testing methods such as NPT,
FNCT, PENT, etc. These methods require often the use of notched samples, the use of
specific fluids (e.g. detergents) and elevated temperatures.
In this paper, we present an elegant method to predict slow crack growth resistance in
materials in a simple, very accurate and fast way. The resistance to slow crack growth is
predicted from a simple tensile measurement at a temperature of 80 qC. It will be shown that
the slope of the stress-strain curve above its natural draw ratio (i.e. strain hardening)
correlates very well with the results obtained by the full notch creep test (FNCT) of the same
materials.
The strain hardening method is an elegant method which does not require notched specimen
and/or detergents. Besides the advantage that the method is easy to implement in laboratories,
its main advantage is the dramatic decrease of measurement times from thousands of hours to
only a few. This method is very suitable in the development of new grades by researchers, but
also very valuable as batch release test for both resin suppliers and pipe converters.
INTRODUCTION
High density polyethylene (HDPE) is widely used in highly demanding utility pipe
applications because of its versatile properties profile. Traditionally, the long-term properties
of HDPE pipes are determined using accelerated internal pressure tests at different
temperatures from which a lifetime of 50 years shall be guaranteed.
However, one of the most prominent properties determining lifetime of HDPE in pipe
applications is its resistance to slow crack growth (SCG), estimated by environmental stress
crack resistance (ESCR). To access this property, a number of different accelerated testing
methods have been developed such as the notched pipe test, FNCT, PENT and these methods
are widely used in the HDPE pipe industry.
In the last years, the slow crack growth resistance of HDPE grades has gained increased
attention, as it is recognized that control over this property is extremely important in order to
guarantee lifetimes of 50 years and beyond in the advance of trenchless installation
techniques. Nowadays, the European market requirements for HDPE grades used in these
applications, so-called PE100 RC grades, require measurement times of at least one year
(>8760 hrs) for the traditional notch test and FNCT. These extremely long measurement times
form a serious concern in using these testing methods for determination of SCG behaviour of
1
resins and manufactured pipes. In a market with increasing demand with respect to SCG
behaviour a fast, regular and reliable test method for quality control of raw materials is an
absolute necessity especially for resin producers.
Strain hardening modulus as SCG predictor
SABIC took the challenge to develop a SMART (SMall Accelerated Reliable Test) predicting
the SCG behaviour of HDPEs. Therefore, the physical phenomena behind brittle failure in
polymers were considered so as to establish which failure mechanism is responsible for SCG.
The reasoning behind the relation between the strain hardening modulus and the craze-crack
mechanism leading to brittle failure has already been elaborately described by Kurelec 1 ,
McCarthy 2 and Deblieck 3 . Hence we will limit ourselves to a brief explanation of why strain
hardening modulus can be used as a predictor of prowess of SCG behaviour.
SCG has been physically analysed by existing deformation models3 from which it was shown
that the brittle failure of applications is caused by a craze-crack mechanism in which the
fibrils bridging the craze play a central role in the eventual failure by craze crack transition.4,
5, 6
The importance of the network of tie molecules governing the creep resistance of these fibrils
is supported by Raman Spectroscopy experiments under tensile load where it was shown that
the interlamellar tie molecules in high SCG resistant polyethylene samples bear less load than
in low SCG resistant samples. 7 Finally, the similarity between a fibril in a craze and a bulk
sample drawn beyond the yield point was shown by a tensile bar drawn to its natural draw
ratio. 8, 9, 10, 11
In 2005, Kurelec at al1 built on that knowledge to propose a simpler and more robust measure
of fibril deformation and failure resistance, i.e. the amount of strain hardening as observed in
a tensile test. This tensile test is performed at a temperature of 80 qC, which is the Į-transition
of polyethylene. This elevated temperature is necessary to access the response of the effective
molecular entanglements within the material at creep rate when the molecular chains become
mobile with respect to the crystals within the fibrils. The strain hardening modulus <Gp> as
defined by Kurelec et al1 turns out to correlate well with the resistance to SCG for a series of
different PE grades. In addition, the validity of the correlation between strain hardening and
ESCR data for a set of highly SCG resistant bimodal pipe grades was demonstrated by
McCarthy et al.2
In previous publications,1, 2, 3 we have shown that the strain hardening modulus correlates with
various traditional methods of determining the ESCR behaviour of HDPEs. However, a good
statistical interpretation of the data could not be performed due to the limited available data
set, which is a consequence of the very long testing times of the conventional testing methods.
In the present paper, the potential of the strain hardening method is further expanded by a
careful statistical evaluation of available and new data on the relation between the ESCR
response of HDPEs determined by the Full Notched Creep Test (FNCT) and the strain
hardening method.
2
Experimental
Materials
For this study a range of commercial HDPEs, unimodal, high polydispersity Philips catalyst
based HDPEs as well as bimodal Ziegler-Natta HDPEs, have been selected. The selected
commercial HDPEs range find their application in blow moulding items (e.g. industrial
containers and bottles) or utility pipe applications (PE80 and PE100). The selected materials
were either natural (uncoloured) grades or black (= carbon black filled) grades.
Sample preparation for tensile measurements
The materials were compression moulded to a sheet at a temperature of 160 °C with a
thickness of about 0.3 mm. The compression moulding procedure: 5 min heating up at 0 kN
load, 3 min at 10 kN load, 3 min at 50 kN load and cooling down to room temperature at a
load of 180 kN. After pressing, the samples were annealed for 1 h at 120 °C and slowly
cooled down to room temperature by switching off the temperature chamber. Finally, test
samples were punched from the pressed sheets. The ISO37 type 3 sample shape was adapted
with a larger clamping area (width changed from 8.5 +/- 0.5 mm to 20 +/- 1.0 mm) in order to
prevent grip slip. Grip slip is especially an issue for materials that feature a high strain
hardening modulus.
Tensile measurements
The measurement is a standard tensile test performed on a ZWICK Z010/TH2A, tensile
machine equipped with a 200 N load cell, at a temperature of 80 qC. The test sample was
extended at a constant traverse speed (20 mm/min) until the strain reaches 1200% unless the
sample fractures before reaching that strain. The constant traverse speed implies that the
intrinsic strain rate is not constant. This may not be unimportant because in the course of a
measurement the true strain rate decreases with a factor Ȝ. Hence the strain rate decreases
about an order of magnitude towards the end of the measurement, which implies that the
strain hardening moduli obtained at true constant strain rate may be larger than the reported
ones.
The maximum strain value is limited by the length of the climate hood. During the test the
load sustained by the specimen and the elongation were measured. The elongation was
determined with an optical extensometer (ZWICK 066975B, class 1: 3.0-500 mm). Therefore
two reflecting and self-adhesive gauge marks were attached to the test specimens via a
marking apparatus (ZWICK 066921B). The initial distance l0 between these marks (gauge
length) was determined after reaching the pre-load before each test. Prior to testing the test
specimens were kept for about 30 min in the temperature chamber at the test temperature of
80 qC so as to allow thermal equilibrium. Each sample was measured in fivefold and major
attention was given to the constancy of thickness of the samples which is extremely critical
for this measurement.
Strain hardening data treatment
True strain expressed as the draw ratio was calculated on the basis of the gauge length:
O (t ) l (t ) / l 0
(1)
where Ȝ is the draw ratio, a dimensionless ratio, l0 [mm] is the initial distance between the
gauge marks and l(t) [mm] is the distance between the gauge marks during deformation.
The true strain is usually represented as a Hencky strain, ln(Ȝ(t)), but for the present paper Ȝ(t)
is adopted as a measure of true strain.
3
The true stress was calculated from the load force assuming conservation of sample volume
between the gauge marks and homogeneous deformation which is generally only valid
beyond the natural draw ratio.
V T O ( t )F ( t ) / A0
(2)
where ıT [MPa] is the true stress, F(t) [N] is the instantaneous force load, A0 [mm2] is the
initial cross-sectional area of the specimen and Ȝ is the true strain value from equation 1.
The average strain hardening slope (<Gp>, MPa) was calculated as defined by Kurelec et al1.
That definition requires that strains between Ȝ=8 to Ȝ=12 are experimentally available, which
may be troublesome for bimodal HPDEs for pipe applications where the strain hardening
values are considerably higher and lower strains are reached. To circumvent this difficulty, a
Neo-Hookean constitutive model is assumed to fit the data to obtain Gp as shown in equation
3:
1
V T C G p ( O2 )
O
(3)
<Gp> was then straightforwardly calculated from fitting the experimental data with equation
3, in which C is a mathematical parameter of the constitutive model describing the yield stress
interpolated to Ȝ=1. This constant is of no consequence for the calculation because it is
vanishing in the derivative or the difference quotient to calculate <Gp> which is then found to
be:
(4)
Gp
20 u G p
8 O 12
ESCR by Full Notch Creep Test
Full Notch Creep Test (FNCT) experiments were performed according to ISO16770 in
accredited laboratories. Generally the tests are performed using 2% detergent at a stress of 4
MPa at a temperature of 80 qC. Time to failure (hours) of each test sample was registered.
Each test was carried out in triplo and the geomean of these values is reported for each
experiment.
RESULTS AND DISCUSSION
Tensile response
It is known that the SCG behaviour of a polymer is influenced by its molecular structure and
that even very subtle variations of the molecular structure lead to variation in ESCR
performance.1, 12
In order to cover an as large as possible extent of ESCR, a large set of different commercial
polyethylenes were selected for investigation by both the strain hardening method and FNCT.
The selection ranges from Philips based HDPE grades for blow moulding applications to
bimodal Ziegler-Natta grades for utility pipe applications. The molecular structures of these
polyethylenes differ in density, molecular weight, comonomer type, comonomer distribution
and/or polymerisation process.
ESCR requirements of HDPE grades correspond to the demands of the end application with
respect to SCG behaviour. In other words, the ESCR requirements for a blow moulding
application are less stringent compared to those for utility pipe applications. As a result a clear
distinction between the grades for these specific applications can be made by the differences
in failure times by FNCT.
Figure 1 shows the true stress –– true strain tensile curves of a bimodal blow moulding grade
and a bimodal pipe grade, which were recorded at a temperature 80 qC and serve as the basis
4
for the strain hardening modulus determination. Significant slope difference between the
curves can be observed above the natural draw ratio, indicating significant differences in
strain hardening moduli of the two grades.
Figure 1: True stress - true strain response for two arbitrary bimodal grades at 80°C.
All selected materials were investigated for their ESCR behaviour by both the strain
hardening modulus and FNCT.
A note of caution concerns the fact that all of the current strain hardening modulus
assessments are performed at a constant traverse speed of 20 mm/min. This basically means
that the average strain rate is kept constant. When one wants to rank the performance of
materials with respect to a specific application this will not jeopardise the ranking derived
from this measurement. However the performance of a material depends on the time scale of
the application load. Indeed, the demands on a pipe grade application extend over much
longer times than the ESCR failure of say, a food packaging application. It is clear that rate
dependence over some orders of magnitude of the strain hardening response has also to be
envisaged.
Statistical regression analysis of FNCT versus <Gp>
The objective is to perform regression analysis while taking the uncertainty of both variables
(FNCT and <Gp>) into account, which requires a dedicated approach.
First the FNCT results are investigated more closely. Failure times in FNCT above 8760
hours (grey area in Figure 2) are discarded from the analysis because of the ongoing depletion
of the stabilisers, and the consequent possibility of premature failure due to molecular
degradation. 13 Statistical evaluation of the FNCT dataset does not show any distinction
between the dataset obtained using either detergent Arkopal N100 (black diamonds) or
detergent Arkopal N110 (open diamonds). As a result, the statistical evaluation is continued
considering the results of the FNCT tests as one dataset.
In standard least-squares regression, the distance of an individual data point to the regression
line is assessed by calculating the vertical distance between the point and the line. This
procedure is useful as it is assumed that there is no error in the x-variable; the point is not on
the line because the y-value is subject to random variation and hence can be (will be)
5
numerically wrong, but the x-value is correct. In Deming regression, the distance is assessed
along a diagonal rather than vertical line between data point and regression line. The slope of
this diagonal measuring line is defined by the ratio of the standard deviations in the x and y
value.
In order to perform Deming regression, the ratio of the standard deviations is required. In the
current data, samples are tested in replicates, allowing the assessment of the standard
deviations. The observed mean of all individual sample variance is used as best available
estimate for the random variation of a given analytical technique. As such, the ratio of the two
average variances was assessed.
Before performing Deming regression, verification of constant standard deviations over the
given data range is required. The test of Cochran is convenient to test if the largest observed
variance is statistically significantly larger than the others. The Cochran test on the data set
shows that the variances could not be considered constant over the range. It appears that an
individual standard deviation is responsible. Therefore, this sample is removed from the
dataset.
Subsequently, Deming regression is performed using the statistical package SAS (version 9.2)
resulting in a linear relation between <Gp> and FNCT including a 95% confidence level.
Figure 2 shows the result of the statistical correlation analysis of the time to failure obtained
by FNCT, against strain hardening modulus.
Figure 2: Strain Hardening modulus <Gp> versus FNCT.
6
CONCLUSIONS
The result of the regression analysis elegantly demonstrates that the FNCT test data correlate
very well with <Gp> as it was predicted by the theoretical deformation mechanism
considerations. This correlation makes it plausible to state that the strain hardening response
is determined by the same molecular differences that govern SCG resistance in HDPE,
assessed by a traditional ESCR method. Advantages of the strain hardening method are the
very low measurement variation, absence of surfactants and notches, the limited amount of
required testing material (<50 g) and, above all, testing times of only a few hours.
Moreover, the use of a universal test set up allows for an easy and cost effective
implementation at all accredited testing laboratories for HDPE pressure pipe applications. The
correlation expresses the value of this elegant technique as a short term test for resin
development, batch release of high performance HDPE pipe grades and reduction of analysis
costs.
ACKNOWLEDGMENTS
The authors gratefully acknowledge Hans Martens (SABIC) for the discussions on the
practical applicability. Marcel Teeuwen from DSM Ahead is thanked for being our
conscience with respect to the tensile measurements and for his help with solving the problem
of sample grip slippage. Marcel Gehlen from Intertek Polychemlab Geleen for performing all
measurements reliably. Dr Jos Weusten of the Mathematics group of DSM Resolve showed
us the way towards statistical relevance of our results for regression. Finally, these results
were complemented elegantly by additional samples and FNCT measurements provided by
Frans Scholten of Kiwa Gas Technology, Apeldoorn.
REFERENCES
1. L. Kurelec, M. Teeuwen, H. Schoffeleers, R. Deblieck, Polymer, 2005, 46, 6369––6379
2. M. McCarthy, R. Deblieck, P. Mindermann, R. Kloth, L. Kurelec, H. Martens, Conference
Paper Plastic Pipes XIV, Budapest, Hungaria, 2008
3. R. Deblieck, D.J.M. van Beek, K. Remerie, I. Ward, Polymer, submitted for publication
4. C.J.G. Plummer, A. Goldberg, A. Ghanem, Polymer, 2001, 42, 9551-9564
5. T. Riemslag, PhD Thesis TU Delft, 1997, ISBN 90-407-1453-3.
6. C. Thomas, V. Ferreiro, G. Coulon, R. Seguela, Polymer, 2007, 48, 6041-6048
7. J. M. Lagarón, G. Capaccio, L. Rose, B. J. Kip, J. Appl, Pol. Sci., 2000, 77, 283-296.
8. M. J. Cawood, A. D. Chanell, G. Capaccio, Pol.. Comm., 1993, 32, 423––5.
9. L. J. Rose, C.J. Channell, G. Capaccio, J. Appl. Pol. Sci., 1994, 54, 2119––24.
10. P. A. O’’Connell, M. J. Bonner, R. A. Duckett, I. M. Ward, Polymer, 1995, 36, 2355––62.
11. P. A. O’’Connell, A. Duckett, I. M. Ward, J. Appl. Pol. Sci., 2003, 89, 1663––70.
12. J. Cazenave, R. Seguela, B. Sixou, Y. Germain, Polymer, 2006, 47, 3904––3914
13. J. Hessel, ’3R International’, 2001, 40 (6), 178-184
7