PPI TN-7-2005 Nature of Hydrostatic Stress Rupture Curves《流体静应力破坏曲线的性质》.pdf

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1、 Nature of Hydrostatic Stress Rupture Curves TN-7/2005 1825 Connecticut Ave., NW Suite 680 Washington, DC 20009P: 202-462-9607F: 202-462-9779www.plasticpipe.org Foreword This report was developed and published with the technical help and financial support of the members of the PPI (Plastics Pipe Ins

2、titute, Inc.). The members have shown their interest in quality products by assisting independent standards-making and user organizations in the development of standards, and also by developing reports on an industry-wide basis to help engineers, code officials, specifying groups, and users. The pur

3、pose of this technical note is to provide general information on stress rupture curves used for plastic piping materials. This report has been prepared by PPI as a service of the industry. The information in this report is offered in good faith and believed to be accurate at the time of its preparat

4、ion, but is offered without any warranty, expressed or implied, including WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. Any reference to or testing of a particular proprietary product should not be construed as an endorsement by PPI, which do not endorse the proprietary product

5、s or processes of any manufacturer. The information in this report is offered for consideration by industry members in fulfilling their own compliance responsibilities. PPI assumes no responsibility for compliance with applicable laws and regulations. PPI intends to revise this report from time to t

6、ime, in response to comments and suggestions from users of the report. Please send suggestions of improvements to the address below. Information on other publications can be obtained by contacting PPI directly or visiting the web site. The Plastics Pipe Institute http:/www.plasticpipe.org June, 2005

7、 PPI TN-7 Nature of Hydrostatic Time to Rupture Curves I. Introduction Service life prediction or estimation is an important tool used by design engineers to safely plan, install and operate plastic piping systems. Piping system service life is dependent upon resistance to stress and chemicals from

8、the internal and external environment. Stresses may be internal from pressure or external from embedment, bending or shear. These stresses may be constant or varying. Internal pressure surges, temperature changes, and varying loads from traffic, tidal flows, and the like can also stress the material

9、. Resistance to external or internal chemicals, temperature, and variations in these effects can combine to affect the service life of the piping system. One component of service life, resistance to stress from constant internal pressure, can be estimated using hydrostatic stress-rupture testing. Th

10、is Technical Note (TN) explains hydrostatic time to rupture curves, their use, how they are developed under ASTM D 2837 and ISO 9080 protocols, and a brief explanation of the differences between these two methods. This TN is not intended as a guide to determine pressure ratings; the user should cons

11、ult the appropriate industry standard. II. The Nature of Hydrostatic Time to Rupture Curves The testing of pipe samples at different internal pressures in a laboratory environment generates time/stress failure data. However, these data do not form a straight line when plotted on regular graph paper,

12、 often called Cartesian coordinates (Figure 1). Detailed studies were performed to determine the best mathematical function to convert the data and the log-stress log-time linear equation was chosen. When plotted on log-log axes, the time/stress failure point data define a straight line, enabling a

13、linear regression analysis (Figure 2). The nature of a time to rupture versus stress hydrostatic curve for a plastic piping material is that as the stress on pipe decreases the time-to-failure increases. Figure 1 Stress Rupture Data Plotted on CartesianCoordinatesTime (hours)HoopStress(psi)By evalua

14、ting stress rupture test data from pressure test of pipe made from the subject material, a piping materials stress rating can be determined from the materials ASTM D 2837 Hydrostatic Design Basis (HDB) or ISO 9080 / ISO 12162 Minimum Required Strength (MRS). The HDB from ASTM D 2837 or MRS from ISO

15、9080 / ISO 12162 is the categorized long-term hydrostatic strength (LTHS) used to calculate the hydrostatic design stress (HDS) of a plastic piping material. The Plastics Pipe Institute lists the materials HDB and HDS, or MRS value in TR-4, “PPI Listing of Hydrostatic Design Bases (HDB), Pressure De

16、sign Bases (PDB) and Minimum Required Strength (MRS) Ratings for Thermoplastic Piping Materials or Pipe”. Hydrostatic testing performed under ASTM or ISO methodologies is applicable to all known types of thermoplastic pipe materials and for any suitable temperature and medium. PPIs TR-4 lists the HD

17、B and MRS values for specific formulations of the thermoplastic materials listed below. PVC Polyvinyl Chloride CPVC Chlorinated Polyvinyl Chloride PE Polyethylene PEX Crosslinked Polyethylene PB Polybutylene POM Polyoxymethylene, polyacetal PFA Perfluoroalkoxy PA Polyamide, nylon PVDF Poly(vinyliden

18、e difluoride) III. Brief Comparison of ASTM and ISO Methods Both ASTM D 2837 and ISO 9080 analyze stress rupture data to estimate the long-term strength of a plastic piping material. In ASTM D 2837, the HDB for the material is determined by categorizing the mean LTHS value at 100,000 hours (11 years

19、). In ISO 9080, the lower prediction limit (LPL) of the LTHS at 50 years (438,000 hours) is determined then categorized into a MRS as defined in ISO 12162. Both ASTM D 2837 and ISO 9080 / ISO 12162 have served users well for many years. Whether HDB or MRS is determined for a material, the actual lon

20、g-term performance will be the same under the same service conditions. While both ASTM D 2837 and ISO 9080 are used to develop hydrostatic time to rupture curves, there are some differences between the methods. Table 1 presents a summary of differences. Table 1 Comparison of ASTM D 2837 and ISO 9080

21、 ASTM D 2837 ISO 9080 Classification HDB MRS Linearity Assumes linearity (validation required for polyethylene materials) (Note 1) No assumption (Note 2) Regression Individual temperatures All points combined Coefficients 2 3 or 4 Extrapolation temperature 23C is normal, but many others are used 20C

22、 Extrapolation time 100,000 hours and 50 years 50 years Intercept Mean LTHS 97.5% LPL of LTHS Units psi MPa Note 1 ASTM D 2837 assumes a linear extrapolation to the 100,000-hour intercept. For polyethylene materials, a validation procedure is applied to confirm this assumption. Polyethylene material

23、s that exhibit a knee in the 73F stress rupture curve before 100,000 hours do not “validate” the extrapolation and are not given a HDB rating. Note 2 ISO 9080 uses an extrapolation that includes characterization of a possible knee in the stress rupture curve before the 438,000-hour intercept. The kn

24、ee in the regression curve typically, but not always, corresponds to a change between ductile failure and brittle (slit) failure modes in polyolefin materials. Temperature has an inverse effect on the LTHS for thermoplastic materials; that is, at higher temperature, the LTHS is lower for the same ex

25、trapolation time. ASTM D 2837 does not specify the LTHS temperature, but 23C is typically used when characterizing the LTHS for stress rating. ISO 9080 specifies 20C. IV. ASTM D 2837 A. Methodology ASTM D 2837 does not stipulate the size of pipe to be tested or the number of material lots. ASTM D 28

26、37 specifies the minimum number of failure points at a particular temperature with a distribution over three log-decades on the time axis to give the regression more statistical significance. The established method of regression analysis is a 2-coefficient equation: Log t = A + B * log S Where: A, B

27、 = constants t = time (hours) S = Hoop Stress (psi) Once the regression equation describing the line is determined, the line is extrapolated to 100,000 hours and the corresponding mean stress can be calculated. This mean stress intercept at 100,000 hours is the LTHS of the material (Figure 3). Since

28、 ASTM D 2837 uses a 2-coefficient equation with the time (t) and stress (S) as variables, the temperature (T) is constant. The LTHS, therefore, is for the temperature at which the data are obtained. For many materials the common temperature selected is 73F (23C), but other temperatures may be used.

29、(Recommended temperatures are 73F, 140F, 180F and 200F). The data are checked for suitability of use through 1) calculation of the 97.5% lower confidence limit at 100,000 hours and comparing it to the LTHS. If the values differ by less than 15%, the data are considered statistically significant and

30、suitable for use, and 2) calculation of the 50-year long-term hydrostatic strength. The 100,000-hour LTHS must be less than 125% of the 50-year value. If the 50-year LTHS is less than 80% of the 100,000 hour LTHS, then use the 50-year LTHS to establish the HDB. If the data are suitable, the Hydrosta

31、tic Design Basis (HDB) for the material is determined by categorizing the LTHS within limits specified in ASTM D 2837. Standard HDB categories are based on the R10 preferred number series and result in stress increments of 25%. The lower limit of the HDB range is set to include mean LTHS stresses th

32、at are 4% below the HDB value in order to take into account some inherent testing variation B. Validation using ASTM D 2837 When extrapolating a time/stress data regression line to a point in the future, it is assumed that this regression line will continue in a linear manner. This assumption holds

33、true for most thermoplastics except for the polyolefins, which include polyethylene, polypropylene, and polybutylene. These polyolefin materials may exhibit a change in failure mode from ductile to brittle, or slit failures. This change in failure mode typically decreases the materials long-term str

34、ength as the slope of the regression line changes in the brittle zone. Figure 4 shows a typical hydrostatic time versus stress plot for polyethylene with data taken at various temperatures. This plot illustrates both how temperature impacts the curves and the ductile-brittle transitions. Figure 4 Ty

35、pical Hydrostatic Curves for PEat Various TemperaturesHigher temperatures shorten the time-to-failure and the time to ductile-brittle failure mode transition (i.e. Arrhenius relationship) . This is the basis for validating the HDB to improve the confidence of the extrapolated regression line. In oth

36、er words, higher temperature tests show whether the ductile-brittle transition does or does not occur within the extrapolated time frame at lower temperatures. ASTM D 2837 and PPI TR-3 Policies and Procedures for Developing Hydrostatic Design Bases (HDB), Pressure Design Bases (PDB), Strength Design

37、 Bases (SDB), and Minimum Required Strengths (MRS) Ratings for Thermoplastic Piping Materials or Pipe, Part F.4 defines validation procedures for polyethylene materials. Three methods are described. The Standard method entails placing pipe samples on test at either 80C or 90C at a prescribed stress

38、depending on the categorized HDB to be validated. The log average failure time of the samples must exceed the minimum values shown in ASTM D 2837 and TR-3, Part F.4.1. For materials that exhibit brittle failures before 10,000 hours the Alternate Method is used for PE materials that have brittle mode

39、 failures at high temperatures in a reasonable time. This validation method includes testing pipe samples under three stress and temperature conditions. An example is shown in Table 2. Table 2 Typical Conditions for Validation Testing of PE for a 73F HDB Condition 1 80C 5.7 MPa (825 psi) Condition 2

40、 80C 5.0 MPa (725 psi) Condition 3 60C 5.7 MPa (825 psi) To validate the LTHS at the HDB temperature, the Rate Process equation is solved using data derived from Conditions 1 and 2. The calculated LTHS at 100,000 hours is used for the third point. Solving these three equations and unknowns yields th

41、e coefficients for the 3-coefficient rate process extrapolation equation: Log t = A + B/T + (C * log S) / T Where: A, B, C = constants t = time (hours) T = Temperature (K) S = Hoop Stress (psi) With these coefficients, the model is used to calculate the mean time to failure for pipes placed on test

42、under Condition 3. When the pipes placed on test under Condition 3 surpass the log average time-to-failure projection generated by the rate process equation, then the extrapolation at the HDB temperature has been validated. In other words, the ductile-brittle transition occurs after the 100,000 hour

43、 intercept at the HDB temperature (as shown in Figure 5). An example of this procedure is detailed in ASTM D 2837 Appendixes. A third method for validation of a 140F (60C) HDB is based on ISO 9080 K-factor principles. For this method a ductile failure regression line is established at either 80C or

44、90C. The log average failure time of the five longest running specimens must exceed the minimum time as shown in TR-3, Part F.4.3. When this minimum time is exceeded, the extrapolation of the 140F stress regression line is considered valid meaning the ductile/brittle transition is past 100,000 hours

45、. Figure 5 Validation by Standard Method per ASTM D 2837 and PPI TR-3 Part F.4 ASTM D 2513, Thermoplastic Gas Pressure Pipe, Tubing and Fittings, requires a further substantiation of the linearity of the stress regression line to 438,000 hours (i.e. 50 years). This supplemental validation shows that

46、 the ductile/brittle transition is beyond the 50-year intercept. This is a requirement of D 2513, in addition to validation of the HDB as described above. The procedure for this substantiation is in TR-3,Part F.5. V. ISO 9080 and ISO 12162 A. Methodology ISO 9080 “Plastic piping and ducting systems

47、Determination of the long-term hydrostatic strength of thermoplastics materials in pipe form by extrapolation”, requires data at two or three temperatures, such as 20, 60 and 80C. The data required are at least 30 failure points at each temperature with distribution over three log decades. There mus

48、t be at least five different stress levels with at least two specimens at each stress level for each temperature. This procedure does not stipulate size of pipe to be tested or number of material lots, though typically only one material lot is used to develop the data in order to minimize the statis

49、tical scatter in the data. ISO 9080 allows for two equations to calculate the LTHS and LPL depending on the statistical fit of the data. The procedure requires that the 4-coefficient model be used for the initial analysis. If after calculating the 4-coefficients the probability of c3 is greater than 0.05, then the 3-coefficient model may be used. 4-Coefficient Equation log t = c1 + c2/T + c3 logS + c4 (log S)/T 3-Coefficient Equation log t = c1 + c2/T + c4 (log S/)T Where: c1, c2, c3, c4 = constants t = time (hours) T = Temperature (K) S