relaxation modulus master curve of HDPE and long-term failure pressure of PSP with time
Description
figure 4-Curve fitting to the test data of HDPE tensile relaxation modulus with time figure 4 is the relaxation modulus master curve of HDPE (trade mark YEM4803T). figure 8-Variation of long-term failure pressure with the elapsed time figure 8 shows the long-term failure pressure of a composite pipe (its name is plastic pipe reinforced by cross helically wound steel wires, and the type is DN200 PN1.6).
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Steps to reproduce
(1) How to reproduce figure 4 Curve fitting to the test data of HDPE tensile relaxation modulus with time. The long-term behavior of HDPE(trade mark YEM4803T) is represented by the relaxation modulus acquired by dynamic mechanical analysis (DMA) test. Based on the time-temperature equivalence principle, the relaxation modulus of HDPE under a certain reference temperature can be ascertained. So DMA tests at different temperatures were carried out using the single cantilever deformation mode, according to ASTM D4065-2006[American Society for Testing Materials. Standard practice for plastics-Dynamic mechanical properties-Determination and Report of Procedures. ASTM D4065: 2006.]. The DMA specimen has the size of 34.96mm*12.01mm*1.001mm. In order to ensure that the PSP and the DMA specimens were of the same physical age, the DMA specimens were machined from the inner liner of the prototype PSP. Test data corresponding to the angular frequency could be obtained after DMA tests. According to the literature[Yang Tingqing. Theory of Viscoelasticity. 1990, Wuhan: Huazhong University of Science & Technology Press; Christensen R. M. THEORY OF VISCOELASTICITY-AN INTRODUCTION. 1982, New York: Academic Press; Emri I., von Bernstorff B. S., Cvelbar R., Nikonov A. Re-examination of the approximate methods for interconversion between frequency- and time-dependent material functions. Journal of Non-Newtonian Fluid Mechanics, 2005, 129 (2): 75-84.], transformation between angular frequency and time was implemented, and the master curve of HDPE relaxation modulus with respect to 20℃ was obtained. The generalized Maxwell model was used to fit the data, to form the functional relationship between relaxation modulus and time. (2) How to reproduce figure 8-Variation of long-term failure pressure with the elapsed time. Hydrostatic experiments were performed on DN200 PN1.6 PSP specimens to obtain the long-term failure pressure of PSP under 20℃. Structural parameters of pipe specimens were listed in table 3. All specimens were made of the same materials and of the same production batch. Table 3 PSP structural parameters Nominal diameter/mm 200 Steel wire diameter/mm 0.8 Number of steel wires 160 Total thickness/mm 9.5 Winding angle/° 35.3 Long-term hydrostatic tests were carried out according to ISO 1167-1:2006. Before the test all the PSP specimens were kept in the incubator fulfilled with 20℃ water for at least 6h, to make the temperature of the specimens consistent inside and outside. The fixture for the test was an axial constraint-free end sealing device. Hydrostatic tests were carried out in the incubator to keep the test temperature stable with a precision of ±2℃. Subsequently, the specimen was quickly loaded to the required inner pressure, and the pressure was maintained. After the pressure was stable, the time was continuously recorded till the PSP specimen fails.