Lifetime prediction extrapolation

Lifetime prediction of plastic pipes is performed by extrapolating from higher loads and lower times to lower loads and higher times, remembering to use only data corresponding to brittle , low energy ruptures to the right of the knee in the curve (see Section 4.9). 

Two different approaches for lifetime prediction are presented. The underlying lifetime limiting processes have been identified in two cases. Mathematical expressions of chemical/physical relevance were used for the lifetime predictions for PE hot-water pipes and cables insulated with plasticized PVC. Accelerated testing, extrapolation and validation of the extrapolation by assessment of the remaining lifetime of objects aged during service conditions for 25 years were successfully applied to cables insulated with chlorosulfonated polyethylene. Polyolefin pipes exposed to chlorinated water showed a very complex deterioration scenario and it was only possible to find a method suitable for predicting the time for the depletion of the stabilizer system. 

Lifetime predictions of polymeric products can be performed in at least two principally different ways. The preferred method is to reveal the underlying chemical and physical changes of the material in the real-life situation. Expected lifetimes are typically 10-100 years, which imply the use of accelerated testing to reveal the kinetics of the deterioration processes. Furthermore, the kinetics has to be expressed in a convenient mathematical language of physical/chemical relevance to permit extrapolation to the real-life conditions. In some instances, even though the basic mechanisms are known, the data available are not sufficient to express the results in equations with reliably determined physical/chemical parameters. In such cases, a semi-empirical approach may be very useful. The other approach, which may be referred to as empirical, uses data obtained by accelerated testing typically at several elevated temperatures and establishes a temperatures trend of the shift factor. The extrapolation to service conditions is based on the actual parameters in the shift function (e.g. the Arrhenius equation) obtained from the accelerated test data. The validity of such extrapolation needs to be checked by independent measurements. One possible method is to test objects that have been in service for many years and to assess their remaining lifetime. 

Polyethylene has become one of the most widely used materials for electrical insulation due to its excellent dielectric properties and low cost. Original estimates of its probable lifetime using Arrhenius type extrapolation led to lifetime predictions of the order of forty years or more and yet a substantial number of failures in transmission and distribution cables have been observed at times under ten years. For 1977 failures on HMW URD cable totalled 1697 a failure rate of 3,08 per 100 miles while XLP cables were 0.53 per 100 miles and increasing (5). This work was undertaken to find out the role played by the polymer molecule under separate thermal and electrical stress. 

Although cyclic environmental chamber test procedures may suffice for failure processes Involving, for example, mechanical stress, kinetic controlled processes dependent upon time and temperature such as oxidation and diffusion do not lend themselves to adequate Identification and analysis based solely on number of cycles. Thus Sandia National Laboratories developed an accelerated aging protocol for environmental testing which (1) identifies material incompatibilities and subsequent failure modes in Phase I and (2) proceeds with kinetic analysis of the Arrhenius type of failure mode processes which allow extrapolation necessary for lifetime prediction of components in Phase II. Thus two phases are necessary in a complete analysis to accurately predict system lifetimes. The accelerated aging protocol requires the Identification of the stresses that are most likely to damage the performance of the component under test. However, data is frequently not available on the performance of a system under a particular stress. When this is the case, it becomes necessary to make predictions of those stresses most likely to cause degradation and then test to see if the stresses selected are dominant. 

Lifetime prediction is an applied technique, which is frequently needed in industry to find out the probable performance of a new material. The philosophy of lifetime prediction is to identify the critical reaction which limits the life of a material, then to measure its kinetics quantitatively at high temperature where the reaction is fast. Finally, using proper kinetic expressions, one extrapolates the kinetics to the much longer reaction times expected at the lower temperatures at which the sample will be in service. Naturally, the reverse process, extrapolating the kinetics to higher temperatures, could also be carried out to find shorter lifetimes—as for example, for ablation processes. 

In the present discussion it is tacitly assumed that the thermal analysis technique identifies the proper life-determining reaction and that the detailed chemistry and physics of the various failure mechanisms is as assumed, in order to allow us to concentrate on the kinetics and the precision of the chosen extrapolation methods. The safest lifetime prediction is necessarily the one with the shortest extrapolation — in other words, the test made under conditions close to those the material experiences in service. 

Lifetime prediction studies on polymeric materials rely heavily on the use of accelerated thermal aging exposures. Most accelerated aging methods first expose the virgin material to various accelerated environments. Then the changes that occur in the material are documented. The goal is to extrapolate the accelerated results obtained in order to predict the material lifetime imder ambient aging conditions (1). 

The transition from power-law creep with a stress exponent of about seven to a viscous creep regime occurs at a stress of about one below 30 MPa at 700°C. Any extrapolation from the power-law creep regime to stresses below 30 MPa may lead to serious underestimation of the creep rate and therefore overestimation of lifetime based on the Dyson nucleation law (Eq. (6.5)) which is accounted for in the lifetime prediction. As the strain rates measured at low stress are used as inputs of the Riedel model (Eq. (6.6)), the long-term creep lifetimes are more correctly predicted (Fig. 6.30(a,b)) and the experimental data are within the predicted scatter bounds. 

Extrapolate to 20°C for lifetime predictions based on 50% loss of strength and elongation and assess the results as well as comparisons with lahoratoiy predicted values, hoth at 20°C. 

In practice a method is established which estimates the limits of application by time-temperature-extrapolation of the measured damage processes. So a lifetime prediction is possible by using the time-temperature-shifting-principle (Figure 4). 

Accelerated testing depends critically on selecting a parameter whose effect on service life is so well understood that long lifetimes at low values of the parameter can be predicted from shorter lifetimes at higher values. The parameter may be the prime cause of degradation, such as in a stress-rupture test where longer lifetimes at lower loads are predicted by extrapolation from short lifetimes at higher loads. It can also be a secondary parameter, such as when temperature is increased to accelerate chemical attack while the principal factor, chemical concentration, is kept constant. This is because there is more confidence in the relation between rate of reaction and temperature than in the relation of rate of reaction to concentration. It is clearly essential that extrapolation rules from the test conditions to those of service are known and have been verified, such that they can be used with confidence. 

The purpose of the trial also affects the choice of degradation agents and the parameters used to monitor degradation. For comparison and quality control purposes, single agents are most frequently used. For prediction purposes multiple agents are more likely to be representative of service, but at the same time they make extrapolation rules more complicated. The parameters measured in trials to predict lifetime must be those critical to service, but in many instances of comparison or quality checks the choice of parameter can be heavily influenced by experimental convenience. 

Logarithmic scales and power laws make extrapolation look too easy. The wide confidence limits are often overlooked and particular care should be exercised because small deviations can result in large changes in predicted lifetime. Precise calculations can lose their value when the extent of the confidence limits is noticed ( predicted life 10 years, upper limit 600 years, lower limit two months ). 

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