Improved Methods for Determining The Design Basis of Polyethylene Piping Materials … · 2019. 4. 19. · ASTM D2827 1600 psi HDB @ 73°F Validation Point ASTM D2837 1000 psi HDB

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


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


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


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.


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


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


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.


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


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


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


ISO Extrapolation Limits Based on Arrhenius Shift Factors


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


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)


ISO 9080 Regression Model


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

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108

Time to Ductile Failure [h]

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Pa]

PE4710: ISO9080 RPM Regression

23°C Regression

23°C Prediction Limits


23°C PE4710 Test Data

PE4710 23 °C Test Data Shifted

60°C Regression





80°C Regression





ISO 9080 60°C to 23°C Extrapolation Limit

ISO 9080 80°C to 23°C Extrapolation Limt


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

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23°C Regression





60°C Regression





80°C Regression








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

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PE4710: ISO9080 RPM and ASTM D2837 Regression

23°C Regression





60°C Regression





80°C Regression







data2

ASTM D2387 Regression for 23°C Data


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


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

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si]

PE4710: GTI RPM Regression model coherent with DTMA shift factors

23°C Regression





60°C Regression





80°C Regression





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


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)


Time to Failure < 1500 h ISO 9080 Regression

• Unusable Model

10-1

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23°C Regression





60°C Regression





80°C Regression






DTMA and LTHS Based Model

• Usable Model

10-1

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PE4710: GTI RPM Regression model coherent with DTMA shift factors. Outliers excluded

23°C Regression





Excluded PE4710 23 °C Test Data Shifted

60°C Regression






80°C Regression







<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

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PE4710: GTI RPM Regression model coherent with DTMA shift factors. Outliers excluded

23°C Regression




60°C Regression




80°C Regression




23°C Regression






60°C Regression






80°C Regression







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


Questions

Documents

Improved Methods for Determining The Design Basis of Polyethylene Piping Materials … · 2019. 4. 19. · ASTM D2827 1600 psi HDB @ 73°F Validation Point ASTM D2837 1000 psi HDB