Assessment of lifetime of hot-water polyethylene pipes based on oxidation induction time data.
Lifetime predictions for pipes are typically based on data obtained by long-term hydrostatic pressure testing at several elevated temperatures. The procedure is schematically described in Figures 1 and 2. There are several attractive features of this method. Temperature is the single acceleration factor. In other respects, the testing conditions are very similar to the conditions prevailing during service. The extrapolation is straightforward in the case shown in Fig. 2; a linear extrapolation. However, in other cases with a limited oxygen supply, the relationship between the logarithm of the failure time and the reciprocal of the temperature is nonlinear and this makes extrapolation more difficult (1). The major disadvantage of the pressure testing is that it is time-consuming and expensive. Pressure testing does not directly permit the assessment of the condition of a given pipe system in service. It is also difficult to predict the lifetime of a pipe system subjected to complex thermo-mechanical conditions. The question is whether the lifetime can be assessed on the basis of data obtained during a shorter period of time. This paper presents a method based on the measurement of oxidation induction time (OIT) by differential thermal analysis/differential scanning calorimetry on samples taken from polyethylene pipes that have been pressure tested for time periods significantly shorter than the failure time. Important questions that are dealt with concern the requirements of the data taken and the type of extrapolation method used for the lifetime assessment.
The degradation characteristics of hot-water polyolefin pipes have been studied and reported in a series of papers (1-12). At low stresses, the effect of the mechanical loading becomes less important and it was proposed that the lifetime could be divided into Regimes A, B, and C [ILLUSTRATION FOR FIGURE 3 OMITTED]. The loss of antioxidant protection occurs by internal precipitation (Regime A) and by migration to the surrounding media (Regime B) (7, 11, 12). When the antioxidant system is depleted at a spatial point, rapid autocatalytic degradation of the polymer component occurs (Regime C) causing embrittlement of the material and ultimately brittle failure of the pipe. It was established for medium-density polyethylene that Regime C constituted only 5% to 10% of the total lifetime (9). Mathematical models for Regimes A and B were developed and successfully applied to a number of polyolefin pipes pressure tested at elevated temperatures (7, 11, 12).
This paper presents a new method for lifetime assessment of polyethyelene hot-water pipes that fail according to the stage III mechanism. Current standard methods, pressure testing at a range temperatures followed by numerical analysis of the results according to the Standard Extrapolation Method (SEM) (13) and extrapolation to lower temperatures are now well accepted. A drawback of the Standard Extrapolation Method is its phenomenological character. The method proposed in this paper is based on known chemical/physical processes. It is less time-consuming than pressure testing.
Oxidation induction time (OIT) measurements should be carried out according to the procedures described in Refs. 6 and 12. This test method is basically in accordance with an ASTM standard (14). Samples weighing 5 [+ or -] 2 mg are microtomed from a cut cross section of the pipe wall and are encapsulated in aluminum pans, with covers containing three 1 mm holes. A pipe wall thickness of 2 mm requires about 10 samples taken at different depths. The samples are heated in the differential thermal analyzer (DTA) or the differential scanning calorimeter (DSC) in a nitrogen atmosphere to a temperature close to 200 [degrees] C. The chosen temperature will depend on the stability of the particular sample studied. Suitable OITs are between two and thirty minutes. The atmosphere is changed from nitrogen to oxygen two minutes after the establishment of isothermal conditions. The OIT is obtained as the time at which a certain specified exothermal deviation from the isothermal baseline is present [ILLUSTRATION FOR FIGURE 4 OMITTED]. The OIT data are then shifted to a common temperature ([T.sub.ref]), here 190 [degrees] C, assuming the validity of the Arrhenius equation:
[OIT.sub.ref] = [OIT.sub.test] [multiplied by] [e.sup.[Delta]E/R(1/[T.sub.ref] - 1/[T.sub.test])] (1)
where "test" refers to the temperature at which the OIT measurement was performed, [Delta]E is the activation energy which is determined for the actual combination of antioxidant and polymer in the test, and R is the gas constant.
It is important to establish that the OIT is proportional to the antioxidant content. Samples with different antioxidant contents are prepared for this purpose by proper melt mixing followed by rapid cooling of the melt to avoid phase separation of the antioxidant during the cooling phase.
LIFETIME EXTRAPOLATION METHOD
The OIT profiles of pipes pressure tested for different time periods are the data input to the Regime A (11) and B (7, 12) models, of which the latter is the most important for lifetime extrapolations. This is due to that Regime B dominates the antioxidant depletion throughout the larger part of the Stage III life. It is important to establish the crossover from Regime A and Regime B, which can be done by integration of the OIT profiles and by plotting the average OIT (<OIT>) versus the square root of the exposure time [ILLUSTRATION FOR FIGURE 5 OMITTED]. The break provides information about the onset of Regime B dominance in the antioxidant depletion. Different starting conditions for the Regime B modeling are used and the OIT profiles associated with the longer exposure times are selected for lifetime extrapolation with the Regime B model (12).
It is essential that the values obtained for the adjustable parameters become stable and independent of the starting conditions used in the modelling, i.e. that pure Regime B mechanism is prevailing, Extrapolated OIT profiles are obtained by using the actual values for the five adjustable parameters (i.e., inner and outer diffusivities for the antioxidants, reaction consumption of antioxidant and parameters characterizing the inner-wall and outer-wall boundary condions) obtained from the modeling, and a lifetime including both the times for Regime A ([t.sub.A]) and B ([t.sub.B]) dominance can be estimated using a antioxidant concentration (OIT) criterion for the onset of Regime C. This is the most difficult task. It is unlikely that a universal critical OIT value exists because different polymers may "live" for different time periods owing to variations in fracture toughness, intrinsic chemical stability, mechanical stress and environmental factors. The total lifetime (t) is obtained on the assumption that the Regime C lifetime constitutes 10% of the sum of the Regimes A and B lifetimes (9):
t = 1.1([t.sub.A] + [t.sub.B] (2)
Figure 6 provides a schematic representation of the methodology used for the extrapolation procedure.
APPLICATION OF EXTRAPOLATION METHOD TO POLYETHYLENE PIPES
Figures 7 and 8 show a series of OIT profiles of medium-density polyethylene pipes. In the first case [ILLUSTRATION FOR FIGURE 7 OMITTED], the profiles show only little scatter and this is the characteristics of the systems suitable for Regime B modeling. The second case [ILLUSTRATION FOR FIGURE 8 OMITTED] exhibits profiles with a substantial scatter in the data, and in fact it was not possible to carry out Regime B modeling on the basis of the data displayed in Fig. 8. The reason for the scatter in the OIT data is a nonuniform dispersion of the antioxidant in the polymer.
The next critical phase is to establish the time period during which the Regime A loss is negligibly small. An estimate can be made on the basis of the type of data presented in Fig. 5. The breaking point in this graph is thus the approximate demarcation line between the periods dominated by the Regime A and B loss mechanisms. The data in Fig. 5 show a transition point at approximately 4500 h. OIT profiles from 4500 h onward were then used as the initial profile in the Regime B model. In this case stable parameter values were obtained already when using the profiles from 4500 h as the initial profile (12). Defining the starting conditions at 1000 h led to an overestimation of the outer-wall surface diffusivity by one order of magnitude whereas the inner-wall diffusivity was almost correct (12). Experience from Regime B modeling of OIT profiles from other materials (12) shows that it is not enough to use the Regime A/B transition point as a measure for a suitable initial profile for the modeling. It should be used only as a tool for the estimation of the first profile that may be a suitable initial profile. After that all other profiles will have to be evaluated as initial profiles to find the first profile that gives stable parameter values in the modeling. Using the transition point as the only tool for establishing the initial profile may result in an overestimation of diffusivities, thus giving shorter predicted lifetimes.
Table 1 presents a comparison between the pressure testing time required for performing "proper" Regime B modeling (to obtain stable adjustable parameter values) and the Stage III failure times. For the thin-walled medium-density polyethylene pipes at 95 [degrees] C or higher, the testing time required for the Regime B modeling is only half the failure time under the corresponding conditions. The time-saving is even greater for pipes tested at 80 [degrees] C, the testing time for Regime B modeling constituting only 23% to 32% of the failure times. The time saving for the thick-walled crosslinked polyethylene pipe tested at 110 [degrees] C is very substantial, 80%.
The outcome of a successful Regime B modeling is a "correct" set of optimized adjustable parameter values: inner and outer wall diffusivities, parameters characterizing the inner and outer boundary conditions and a parameter describing the chemical consumption of antioxidant. The latter has in no case, so far, displayed a non-zero value (7, 12). It is then possible to use the same Regime B model to perform extrapolation to longer times than those used in the actual modeling. The OIT profiles obtained should be compared with a predetermined critical OIT value, denoted [OIT.sup.*] that defines the onset of Regime C. The OIT profiles are not box-shaped, and the question is at what depth in the pipe wall the critical value should [TABULAR DATA FOR TABLE 1 OMITTED] be defined. Based on data for the thickness of typical oxidation spots and of the depth of initiating cracks (1, 6) a value of 0.5 mm was chosen. The critical OIT (antioxidant concentration) may be viewed as the concentration of antioxidant at which the radicals do not come into contact with the antioxidant molecules. For a given polymer under specified conditions (temperature, oxygen supply, etc), this concentration should be proportional to [D.sup.3/2] (D = diffusivity of the antioxidant). This scaling law is not, however, particularly helpful for calculating the critical antioxidant concentration, because a number of other factors, reaction rate constants for the oxidations reactions, etc., are largely unknown. The best that can be done currently is thus an empirical approach, i.e. to "calibrate" the method using experimental failure time data. Figure 9 shows schematically the method used to determine the time for the onset of Regime C, i.e. [t.sub.A] + [t.sub.B].
The time associated with the knee-point for the onset of Stage III failure is first established [ILLUSTRATION FOR FIGURE 9 OMITTED]. The time period associated with Regime C, constituting approximately 10% (0.1/1.1 [approximately equal to] 10%) of the knee-point-time ([t.sub.III]) (from the creep rupture curve) is then subtracted from the knee-point-time to give the Regimes A and B lifetime ([t.sup.*]). The OIT profile for [t.sup.*] is calculated using the Regime B model inserting the values for the optimized adjustable parameters values, as demonstrated in Fig. 10.
[TABULAR DATA FOR TABLE 2 OMITTED]
The critical [OIT.sup.*] is finally obtained as the lowest value at depths 0.5 mm from the inner and outer walls. Table 2 presents the results of this analysis on a series of polyethylene pipes.
The average value for the thin-walled medium-density polyethylene pipes is 2.5 min with a standard deviation for single data of 2.2 min. A pipe of crosslinked polyethylene showed considerably lower critical values, the average value being only 0.4 min. Both the difference in pipe wall thickness, 2.2 mm for the medium-density polyethylene pipes and 4.5 mm for the crosslinked polyethylene pipe, and the higher fracture toughness of crosslinked polyethylene are probable reasons for the difference in the [OIT.sup.*]s obtained.
The method was tested by using the average [OIT.sup.*]s (2.5 min for medium-density polyethylene and 0.4 mm for crosslinked polyethylene) and obtaining from the extrapolated O/T profiles the onset time for Regime C and the total lifetime associated with the Stage III knee-point. Table 3 shows a comparison between calculated [TABULAR DATA FOR TABLE 3 OMITTED] lifetimes (extrapolated based on the average [OIT.sup.*]) and lifetimes determined by hydrostatic pressure testing.
The maximum difference between the calculated and experimental lifetime was 20% of the experimental value. The average deviation between the two sets of data was 15% of the experimental values. These promising results should only be considered as a starting point for further development. To make the method more generally applicable, additional data are needed including pipes with other dimensions (wall thicknesses) and other materials, particularly materials with high fracture toughness.
A method is presented for the assessment of the lifetime of polyethylene pipes undergoing thermal oxidation (stage III failure) on the basis of oxidation induction time (OIT) data obtained by differential thermal analysis. The method requires pressure testing for limited time periods, sampling from unexposed and exposed pipes, the establishment of a linear relationship between OIT and the antioxidant concentration, and the taking of OIT profiles through the pipe wall. The method is not applicable to pipes with extensive variations in antioxidant concentration due to improper dispersion of the antioxidant in the polymer. The pressure testing required to obtain proper data for modeling takes only a fraction of the failure times of the pipes. For medium-density polyethylene: only [approximately] 20%-30% at 80 [degrees] C and - 50% at 95 [feet] C or at higher temperature. For crosslinked polyethylene tested at 110 [degrees] C, the corresponding time saving was [approximately] 80%. The average difference between factual and predicted (using a universal critical OIT value) lifetimes amounted to 15% for medium-density polyethylene pipes studied.
This study was sponsored by the fund for fundamental research at Studsvik AB, Sweden and by the National Swedish Board for Industrial and Technical Development (NUTEK; grant P5728-2). We thank Mr. M. Ifwarson, Studsvik Polymer AB for valuable discussions.
1. U. W. Gedde, J. Viebke, H. Leijstrom, and M. Ifwarson, Polym. Eng. Sci., 34, 1773 (1994).
2. M. Ifwarson and P. Eriksson, Kunststoffe, 76, 245 (1986).
3. P. Eriksson and M. Ifwarson, Kunststoffe, 76, 512 (1986).
4. M. Ifwarson, Kunststoffe, 76, 525 (1989).
5. U. W. Gedde and M. Ifwarson, Polym. Eng. Sci, 30, 202 (1990).
6. K. Karlsson, G. D. Smith, and U. W. Gedde, Polym. Eng. Sci., 32,649 (1992).
7. G. D. Smith, K. Karlsson, and U. W. Gedde, Polym. Eng. Sci., 32, 658 (1992).
8. K. Karlsson, P.-A. Eriksson, M. Hedenqvist, M. Ifwarson, G. D. Smith, and U. W. Gedde, Polym. Eng. Sci., 33, 303 (1993).
9. J. Viebke, E. Elble, M. Ifwarson, and U. W. Gedde, Polym. Eng. Sci., 34, 1354 (1994).
10. J. Viebke, E. Elble, and U. W. Gedde, Polym. Eng. Sci., 36, 458 (1996).
11. J. Viebke, M. Hedenqvist, and U. W. Gedde, Polym. Eng. Sci., 36, 2896 (1996).
12. J. Viebke and U. W. Gedde, Polym. Eng. Sci., 37, 896 (1997).
13. "Themoplastics pipes for the transport of fluids. Methods of extrapolation of hydrostatic stress rupture data to determine the long-term hydrostatic strength of thermoplastics pipe materials." ISOITR 9080: 1992(E).
14. ASTM Standard D 3895-80.
|Printer friendly Cite/link Email Feedback|
|Author:||Viebke, J.; Gedde, U.W.|
|Publication:||Polymer Engineering and Science|
|Date:||Aug 1, 1998|
|Previous Article:||Photochemical modification of polymers - photocrosslinking, surface photografting, and lamination.|
|Next Article:||Biodegradable polymers and environmental interaction.|