Improved Methods for Determining The Design Basis of Polyethylene Piping Materials Ernest Lever Plastic Pipe Conference, SPE Philadelphia Section West Conshocken, PA April 16-17, 2019
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials
Ernest LeverPlastic Pipe Conference, SPE Philadelphia SectionWest Conshocken, PAApril 16-17, 2019
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 2
Agenda
1. How do polyethylene pipes fail?2. Quantifying creep3. Arrhenius principle and shift factors4. Where are shift factors used in current ASTM and ISO methods for
determining performance levels for polyolefin pipe5. DTMA derived shift factors6. Improving the regression models used for material characterization7. Conclusions and Questions
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 3
How Do PE Pipes Fail?
• Ductile Rupture• Joint Failures• Slow Crack Growth
• All the above failure modes are due to Creep:
– Large scale as in ductile rupture
– Constrained as in slow crack growth
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 4
Creep Can be Quantified and Modeled
• The stress/strain response of the material is measured by:
– Displacement controlled tensile testing to determine the true stress strain curve dependent on
• Strain rate• Temperature
– Force controlled tensile testing to determine creep rates dependent on
• Force• Temperature
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 5
What Governs the Creep Response of PE?
• PE is semi-crystalline• Creep involves an interaction
between the amorphous and crystalline regions
• A single CH2 unit needs to move through the crystalline region to allow rearrangement of the stressed amorphous region
• The activation energy for this elementary process can be measured by NMR or dynamic mechanical methods
Bower, D.I., An Introduction to Polymer Physics. 2002: Cambridge University Press.
Strobl, G.R., The Physics of Polymers: Concepts for Understanding Their Structures and Behavior. 2013: Springer Berlin Heidelberg.
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 6
Arrhenius Shift Factors• Processes governed by an activation
energy yield straight lines when the logarithm of process rate is plotted against inverse temperature
• Equating the ratio of rates at two different temperatures to the difference between the inverse temperatures allows us to calculate the activation energy of the process directly
https://www.chemguide.co.uk/physical/basicrates/arrhenius.html
https://chemistry.tutorvista.com/inorganic-chemistry/arrhenius-equation.html
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 7
Bi-directional Shift Factors
• Shift factors describe the time-temperature superposition characteristics of a polymeric material
• They allow master curves to be developed from data generated at multiple temperatures
• Polyethylene needs to undergo bi-directional shifting
– Stress shift– Time shift
• These two shift factors are independent and material specific
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 8
Popelar Shift Factors
• In the 1980’s and early 1990’s C. F. Popelar and C. C. Popelar empirically derived bi-directional shift factors for polyethylene from creep experiments using the formulation
𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒 𝐅𝐅𝐅𝐅𝐅𝐅𝐒𝐒𝐅𝐅𝐅𝐅 = 𝐞𝐞𝐞𝐞𝐞𝐞(𝐂𝐂𝐅𝐅𝐂𝐂𝐂𝐂𝐒𝐒𝐅𝐅𝐂𝐂𝐒𝐒 ∗ (𝐓𝐓 − 𝐓𝐓𝐅𝐅𝐞𝐞𝐒𝐒)
• Mavridis proposed a methodology for determining independent stress and time shift factors based on the Arrhenius relationship in 1992
𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒𝐒 𝐅𝐅𝐅𝐅𝐅𝐅𝐒𝐒𝐅𝐅𝐅𝐅 = 𝐞𝐞𝐞𝐞𝐞𝐞 (𝐀𝐀𝐅𝐅𝐒𝐒𝐒𝐒𝐀𝐀𝐅𝐅𝐒𝐒𝐒𝐒𝐅𝐅𝐂𝐂 𝐄𝐄𝐂𝐂𝐞𝐞𝐅𝐅𝐄𝐄𝐄𝐄
𝑹𝑹 ∗ (𝟏𝟏𝑻𝑻 −
𝟏𝟏𝐓𝐓𝐅𝐅𝐞𝐞𝐒𝐒
)
1. Mavridis, H. and R. Shroff, Temperaturedependence of polyolefin melt rheology. PolymerEngineering & Science, 1992. 32(23): p. 1778-1791.
2. Popelar, C.F., Characterization of mechanicalproperties for polyethylene gas pipe materials.1989, The Ohio State University.
3. Popelar, C., C. Popelar, and V. Kenner,Viscoelastic material characterization andmodeling for polyethylene. Polymer Engineering& Science, 1990. 30(10): p. 577-586.
4. Popelar, C. A Comparison of the Rate ProcessMethod and the Bidirectional Shifting Method. inProceedings of the Thirteenth InternationalPlastic Fuel Gas Pipe Symposium. 1993.
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 9
Where Do Shift Factors Come In to Developing Design Bases for PE Pipe?
• ASTM develops single temperature regression models for pipe• ASTM requires validation of the single temperature regression models
using higher temperature data• The test pressures and minimum time to failure in the high temperature
validation tests are calculated using Popelar shift factors• ISO calculates regression models using data from multiple temperatures• ISO imposes limits on how far higher temperature data can be
extrapolated to lower reference temperatures• The extrapolation limits are calculated using Arrhenius shift factors and an
assumed activation energy of 110kJ/mol
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 10
Current PPI HSB Process for Developing a Design Basis for Plastic Pipe
Reliant on Popelar Bi-Directional Shift Factors
Extrapolate to 100,000 h -> LTHSRequire 97.5% LCL ≥ 0.9*LTHS
ASTM D 2837 Table 1 -> HDBIf no brittle failure < 10,000 h, then validate
Else RPM validation of ductile failure mode Or RPM determination of brittle slope and require intercept with ductile > 100,000 h
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 11
Shift Factors from DTMA Testing vs. Popelar Shift Factors
• Material specific shift factors can be developed from DTMA testing using a method based on the Mavridis method
• There is material to material and batch to batch variation in the measured shift factors
• The impact on high temperature validation test pressures and required test times is shown in the figure
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 12
ISO Extrapolation Limits Based on Arrhenius Shift Factors
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 13
ISO Extrapolation Limits Appear to be Conservative
• Directly calculating the k factors from an activation energy of 110 kJ does not match Table 1 in ISO 9080
• They appear to have applied a reduction factor that increases with larger temperature differentials
• The reduction factors appear to follow a Renard R40 preferred number series
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 14
Applying the ISO 9080 Method to Actual Data
• Depiction of actual test data from PE4710 pipe tests
• Time to ductile rupture @– 23°C (73°F)– 60°C (140°F)– 80°C (176°F)
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 15
ISO 9080 Regression Model
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 16
ISO 9080 Extrapolation Limits
• Calculated using ISO 9080 k factors:
– 100 for 80°C to 23°C– 30 for 60°C to 23°C
10-1
100
101
102
103
104
105
106
107
108
Time to Ductile Failure [h]
5
6
7
8
9
10
11
12
13
Stre
ss [M
Pa]
PE4710: ISO9080 RPM Regression
23°C Regression
23°C Prediction Limits
23°C Prediction Limits
23°C PE4710 Test Data
PE4710 23 °C Test Data Shifted
60°C Regression
60°C Prediction Limits
60°C Prediction Limits
60°C PE4710 Test Data
PE4710 60 °C Test Data Shifted
80°C Regression
80°C Prediction Limits
80°C Prediction Limits
80°C PE4710 Test Data
PE4710 80 °C Test Data Shifted
ISO 9080 60°C to 23°C Extrapolation Limit
ISO 9080 80°C to 23°C Extrapolation Limt
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 17
DTMA Derived Activation Energy Data Shift
• Bi-directional shifting • Activation energies
derived from DTMA testing of pipe extruded with same material
• Data shifted across all temperatures
• Result not coherent with ISO 9080 regression model
10-1
100
101
102
103
104
105
106
107
108
Time to Ductile Failure [h]
5
6
7
8
9
10
11
12
13
Stre
ss [M
Pa]
PE4710: ISO9080 RPM Regression
23°C Regression
23°C Prediction Limits
23°C Prediction Limits
23°C PE4710 Test Data
PE4710 23 °C Test Data Shifted
60°C Regression
60°C Prediction Limits
60°C Prediction Limits
60°C PE4710 Test Data
PE4710 60 °C Test Data Shifted
80°C Regression
80°C Prediction Limits
80°C Prediction Limits
80°C PE4710 Test Data
PE4710 80 °C Test Data Shifted
ISO 9080 60°C to 23°C Extrapolation Limit
ISO 9080 80°C to 23°C Extrapolation Limt
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 18
Adding ASTM D2837 Regression Plots
• 23°C regression model appears to be coherent with DTMA derived bi-directional shift factors
• 60°C data could be anomalous
– Very different slope
– Very little scatter10
-110
010
110
210
310
410
510
610
710
8
Time to Ductile Failure [h]
5
6
7
8
9
10
11
12
13
Stre
ss [M
Pa]
PE4710: ISO9080 RPM and ASTM D2837 Regression
23°C Regression
23°C Prediction Limits
23°C Prediction Limits
23°C PE4710 Test Data
PE4710 23 °C Test Data Shifted
60°C Regression
60°C Prediction Limits
60°C Prediction Limits
60°C PE4710 Test Data
PE4710 60 °C Test Data Shifted
80°C Regression
80°C Prediction Limits
80°C Prediction Limits
80°C PE4710 Test Data
PE4710 80 °C Test Data Shifted
ISO 9080 60°C to 23°C Extrapolation Limit
ISO 9080 80°C to 23°C Extrapolation Limt
data2
ASTM D2387 Regression for 23°C Data
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 19
DTMA Shift Factor Based Regression Model
• A regression model that explicitly incorporates Arrhenius shift factors can be derived from first principles
• Some of the workings are shown on the right
• The regression model is fed by two independent data sources:
– DTMA data– LTHS testing
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 20
DTMA and LTHS Based Regression Model• Model is coherent
across all temperatures
• Slopes are constant across all temperatures
• Consistent with known weak dependence of activation energy for alpha relaxation on temperature
• Uncertainty is well defined and driven by all the data 10
010
110
210
310
410
510
610
710
8
Time to Ductile Failure [h]
5
6
7
8
9
10
11
12
13
Stre
ss [M
Pa]
800
1000
1200
1400
1600
1800
2000
Stre
ss [p
si]
PE4710: GTI RPM Regression model coherent with DTMA shift factors
23°C Regression
23°C Prediction Limits
23°C Prediction Limits
23°C PE4710 Test Data
PE4710 23 °C Test Data Shifted
60°C Regression
60°C Prediction Limits
60°C Prediction Limits
60°C PE4710 Test Data
PE4710 60 °C Test Data Shifted
80°C Regression
80°C Prediction Limits
80°C Prediction Limits
80°C PE4710 Test Data
PE4710 80 °C Test Data Shifted
80°C to 23°C ISO 9080 Extrapolation Limt
60°C to 23°C ISO 9080 Extrapolation Limt
ASTM D2827 1600 psi HDB @ 73°F Validation Point
ASTM D2837 1000 psi HDB @ 140 °F Validation Point
ASTM D2837 100,000 h
ISO 9080 50 year
ISO 9080 10MPa MRS @ 20°C (68°F)
ASTM D2837 1600 psi HDB @ 73°F
ASTM D2837 1000 psi HDB @ 140°F
ASTM D2837 Regression for 73°C Data
ASTM D2837 Regression for 140°F Data
ASTM D2837 LTHS range to qualify for 1600 psi
HDB is 1530 to < 1920 --- 10.91 MPa = 1582 psi
10 MPa @ 20°C shifts to 9.67
MPa @ 23°C. 438,300 h @ 20°C
shifts to 291,460 h @ 23°C
X 1e+05
Y 10.91
X 2.979e+05
Y 9.609
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 21
Speeding up the Process
• The DTMA and Shift Factor Regression Model works well with shorter term test data
• We will generate ISO 9080 and GTI models restricting the data to those that generated failures in less than 1500 hours (one sixth of the 10,000h required by current standards)
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 22
Time to Failure < 1500 h ISO 9080 Regression
• Unusable Model
10-1
100
101
102
103
104
105
106
107
108
Time to Ductile Failure [h]
5
6
7
8
9
10
11
12
13
14
Stre
ss [M
Pa]
PE4710: ISO9080 RPM Regression
23°C Regression
23°C Prediction Limits
23°C Prediction Limits
23°C PE4710 Test Data
PE4710 23 °C Test Data Shifted
60°C Regression
60°C Prediction Limits
60°C Prediction Limits
60°C PE4710 Test Data
PE4710 60 °C Test Data Shifted
80°C Regression
80°C Prediction Limits
80°C Prediction Limits
80°C PE4710 Test Data
PE4710 80 °C Test Data Shifted
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 23
DTMA and LTHS Based Model
• Usable Model
10-1
100
101
102
103
104
105
106
107
108
Time to Ductile Failure [h]
5
6
7
8
9
10
11
12
13
14
Stre
ss [M
Pa]
PE4710: GTI RPM Regression model coherent with DTMA shift factors. Outliers excluded
23°C Regression
23°C Prediction Limits
23°C Prediction Limits
23°C PE4710 Test Data
PE4710 23 °C Test Data Shifted
Excluded PE4710 23 °C Test Data Shifted
60°C Regression
60°C Prediction Limits
60°C Prediction Limits
60°C PE4710 Test Data
PE4710 60 °C Test Data Shifted
Excluded PE4710 60 °C Test Data Shifted
80°C Regression
80°C Prediction Limits
80°C Prediction Limits
80°C PE4710 Test Data
PE4710 80 °C Test Data Shifted
Excluded PE4710 80 °C Test Data Shifted
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 24
<1500 h Data Compared to Full Dataset
• The strong influence of the 60°C data points > 1500 hours is obvious
• All 23°C and 80°C data points are consistent with one another
• The short term data model provides a good sanity check for longer term data 10
-110
010
110
210
310
410
510
610
710
8
Time to Ductile Failure [h]
5
6
7
8
9
10
11
12
13
Stre
ss [M
Pa]
PE4710: GTI RPM Regression model coherent with DTMA shift factors. Outliers excluded
23°C Regression
23°C PE4710 Test Data
PE4710 23 °C Test Data Shifted
Excluded PE4710 23 °C Test Data Shifted
60°C Regression
60°C PE4710 Test Data
PE4710 60 °C Test Data Shifted
Excluded PE4710 60 °C Test Data Shifted
80°C Regression
80°C PE4710 Test Data
PE4710 80 °C Test Data Shifted
Excluded PE4710 80 °C Test Data Shifted
23°C Regression
23°C Prediction Limits
23°C Prediction Limits
23°C PE4710 Test Data
PE4710 23 °C Test Data Shifted
Excluded PE4710 23 °C Test Data Shifted
60°C Regression
60°C Prediction Limits
60°C Prediction Limits
60°C PE4710 Test Data
PE4710 60 °C Test Data Shifted
Excluded PE4710 60 °C Test Data Shifted
80°C Regression
80°C Prediction Limits
80°C Prediction Limits
80°C PE4710 Test Data
PE4710 80 °C Test Data Shifted
Excluded PE4710 80 °C Test Data Shifted
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 25
Conclusions• ISO 9080 is not a rigorous application of the Arrhenius principle
– The mathematical formulation of the model forces a temperature dependence of the slope– This temperature dependence of the slope is not consistent with other measurements of
molecular mobility (creep) in semi-crystalline polyolefins• ASTM D2837 develops separate, data driven regressions models for each temperature
– Decoupling the models for each temperature can lead to incorrect models of material behavior if there is a significant difference in slopes at each temperature
• Incorporating the shift factors into the regression model forces coherence across all temperatures– The independence of the DTMA and LTHS data adds credence to the combined model– Rigorous application of the Arrhenius principle allows useful models to be developed from short-
term LTHS data– This is entirely consistent with time-temperature superposition methods– The method affords a more critical review process for new data that are candidates for inclusion
in the model
Improved Methods for Determining The Design Basis of Polyethylene Piping Materials 26
Questions