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8 One of the advantages of hydrostatic testing on plastic pipe resins used for corrugated drainage pipe. It has been validated is that one can generate both Stage I and Stage II failures with for PP by comparing SIM results to conventional creep results. the same basic test. Additionally, a resin and carbon black A plot of duplicate SIM results compared with two, 10,000 h formulation is certified through the room temperature testing. conventional creep tests is shown in Figure 5. Then, as long as the formulation stays the same, there is no The main difference between PET and HDPE is their respec- additional testing. In the present case, where we want to eval- tive temperature dependencies at temperatures from ambient uate pipe resins containing recycled materials, every lot may to 80C. HDPE's properties change at a higher rate with tem- be different and accelerated tests must be used to estimate the perature than PET's properties. In fact, the low-temperature long-term performance of the materials. Moreover, there will dependency of PET strength was the main reason SIM was have to be two accelerated tests performed, one for Stage I developed in the first place. The sample-to-sample variability (ductile) and another for Stage II (brittle). could be as large as the difference in creep rates at two different Along with the long-term strength (Stage I), AASHTO temperatures. A comparison for the two materials is shown requires long-term creep modulus and long-term creep strain in Figure 6. as part of the design for corrugated pipe. The approach to TTS has been used for decades and it is the basis for the determine both the creep and creep rupture properties of pipe validation procedures for PE pipe materials in ASTM D2837 containing recycled PE is through the SIM accelerated test. and Plastics Pipe Institute (PPI) Technical Report TR-3 (10). TTS can be used to project the long-term hydrostatic strength of pressure pipe. The SIM for Predicting Creep and Basically, increasing the temperature of a process like creep, Creep Rupture (Stage I) Properties stress relaxation, or slow crack growth is equivalent to per- forming the test at longer times. The higher the temperature, The SIM is a special form of TTS that has been used to the longer the accelerated time. extrapolate short-term creep results (24 h) into long-term In the case of traditional TTS, tests are performed at various estimates of creep behavior (50, 100 years). It was originally elevated temperatures on different samples and the results developed in these laboratories on polyester (PET) geogrids shifted to a lower target temperature. Because of the sample- used for reinforcement applications (6, 7). The application of to-sample variability, the result of TTS can be uncertain and SIM to PET has been verified and validated by several other requires tests on many specimens. Two examples of TTS are laboratories comparing the SIM results to conventional creep the Rate Process Method and Popelar Bi-Directional Shifting tests performed at room temperature (8). It has also been Method. used by others on other PET fibers, Kevlar, and polyethylene SIM is a form of TTS where behavior at multiple tempera- naphthanate (PEN)(9). tures is observed on a single test specimen, which reduces It has also been used in these laboratories to examine poly- the uncertainty of the behavior due to sample-to-sample propylene (PP) buried structures and most recently on HDPE variability. 8.0 Reference Temperature - 23C 7.0 1000 psi Stress 10,000 hours 6.0 2 ea SIM 5.0 % Strain 4.0 3.0 2 ea Conventional Creep-Modulus 2.0 50 years 1.0 0.0 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 Log Time (hr) Figure 5. Comparison between conventional creep and SIM for a PP storm chamber under 1,000 psi of stress.

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9 1.2 PET 1 y = -0.003x + 1.069 Relative Property 0.8 0.6 0.4 PE 0.2 y = -0.0117x + 1.2639 0 10 20 30 40 50 60 70 80 90 Temperature (C) Figure 6. Temperature dependence of PET and PE. An example SIM test for HDPE was performed under the temperature step, the creep rate increases. This is due to the following conditions: increased temperature, but also because PE gets softer as the temperature rises. So, in reality, there is a double acceleration. Sample: Type I Dumbbell. The next step in the analysis is to determine what is referred Strain Measurement: Extensometer. to as the virtual starting time (t) for each step above the first Initial Temperature: 20C. one. This accounts for the effects of the creep that occurred Temperature Steps: 7C (20, 27, 34, 41, 48, 55, 62, 69, 76, 83). at the lower temperature. This step is necessary because the Stress: 500 psi. specimen "remembers" what had occurred at the previous Dwell Time: 10,000 seconds (2.77 h). creep step. This also allows one to rescale the individual creep curves and get them all on a common time scale. The raw, unshifted data are shown in Figure 7. The t is found by plotting creep modulus vs. log time for There are 10 temperature steps shown on the plot. Notice the end of one step and the beginning of the next step. Then, that the sample yielded catastrophically during the early part one can adjust the t iteratively until the slopes of the two of the 83C step. It's also easy to see that at each successive curves are parallel. A vertical shift is also added at this time 5 4.5 83C 4 3.5 76C 3 69C % Strain 2.5 62C 2 55C 1.5 48C 41C 1 34C 0.5 27C 20C 0 0 10000 20000 30000 40000 50000 60000 70000 80000 90000 100000 Time (sec) Figure 7. Raw SIM data.

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10 200000 180000 Sample B1 160000 50 Yrs 100 Yrs CREEP MODULUS (psi) 140000 120000 100000 80000 60000 23,250 psi 40000 22,531 psi REFERENCE TEMPERATURE - 23C 20000 500 psi Stress 0 -3 -2 -1 0 1 2 3 4 5 6 7 8 LOG TIME (hr) Figure 8. Creep modulus master curve under 500 psi of stress. until the two parallel lines line up. The matching of the slopes someter. The researcher excludes the data from the transi- of the end of one step with the beginning of the next step is tion region, but keeps the time scale in place. The transi- the critical step for accurate extrapolations. tions then show up as blank spots in any plot with time as Once this is done for each step, master curves can be pre- the abscissa. sented as either creep modulus or strain. Master curves for SIM can also be performed under higher loads to create a this data set are shown in Figures 8 and 9. creep-rupture environment. Recall that the SIM test above From these two curves, one can obtain both the 50-year was performed under an applied stress of 500 psi (about 12.4% creep modulus and 50-year creep strain. In this case, they of ultimate). If one does the same test at 1,000 psi, the master are 23,250 psi and 2.15% respectively. These represent the curve can produce the time it would take for the sample to behavior of the material when placed under a 500 psi load for yield under the applied load. This is shown in Figure 10. The 50 years. extrapolate time to Stage I failure under these conditions is Notice that there are gaps between the extrapolated about 1,900 years. Shorter times are found for applied stresses steps. The transition from one temperature to the next is an of 1,500 and 2,000 psi (Figures 11 and 12). important variable in SIM testing. The time it takes for the These three results can then be put together on a plot of Log specimen to equilibrate at the new temperature should Stress vs. Log Time, to generate a Creep Rupture Master Curve. be just a few minutes. Other things that occur during the The one for the results above is shown in Figure 13. transition time are thermal expansion or contraction of the The results from these tests show that the 50-year yield specimen as well as re-equilibration of the grips and exten- strength will be about 1,161 psi. 3 Sample B1 2.22 % 2.5 2.15 % 2 STRAIN (%) REFERENCE TEMPERATURE - 23C 1.5 100 Yrs 500 psi Stress 1 50 Yrs 0.5 0 -4 -3 -2 -1 0 1 2 3 4 5 6 7 LOG TIME (hr) Figure 9. Creep strain master curve under 500 psi of stress.

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11 40 REFERENCE TEMPERATURE - 23C 35 1000 psi 30 STRAIN (%) 25 20 15 7.22 10 5 0 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 LOG TIME (hr) Figure 10. Long-term yield stress by SIM at 1,000 psi. 40 REFERENCE TEMPERATURE - 23C 35 1500 psi 30 STRAIN (%) 25 20 15 2.43 10 5 0 -4 -3 -2 -1 0 1 2 3 4 5 6 7 LOG TIME (hr) Figure 11. Long-term yield stress by SIM at 1,500 psi. 40 REFERENCE TEMPERATURE - 23C 35 2000 psi 30 STRAIN (%) 25 20 15 1.11 10 5 0 -4 -3 -2 -1 0 1 2 3 4 5 6 7 LOG TIME (hr) Figure 12. Long-term yield stress by SIM at 2,000 psi.