A Practical Model for Prediction of the Lifetime of Elastomeric Seals in

Chapter 33

A Practical Model for Prediction of the Lifetime of Elastomeric Seals in Nuclear Environments

Downloaded by UNIV OF ARIZONA on August 6, 2012 | http://pubs.acs.org Publication Date: November 12, 1991 | doi: 10.1021/bk-1991-0475.ch033

S. G. Burnay Advanced Engineering Materials Department, AEA Industrial Technology, Harwell Laboratory, Didcot, Oxfordshire OX11 0RA, United Kingdom A predictive model of radiation degradation in elastomeric materials has been developed, based on time-temperature-dose rate superposition. Examples of the application of the model to practical elastomers used in the nuclear industry are given. The model does not require a detailed knowledge of the degradation mechanisms. Elastomeric seals are widely used in nuclear power stations and other nuclear plant; such seals can be exposed to elevated temperatures and low dose rate irradiation for times up to the lifetime of the plant. In assessing the long term behaviour of elastomeric seals, accelerated tests are necessary to enable estimates of lifetime to be made under the anticipated service conditions. It is well established that many polymeric materials exhibit dose rate effects or synergism between temperature and radiation; any seal lifetime prediction method used needs to take these effects into account. The physical parameters which are most relevant to seal leakage under irradiation have been previously assessed (2); compression set has been found to be the most useful parameter for routine monitoring of seal performance. This paper describes the development of a lifetime prediction model based on time-temperature-dose rate superposition which has proved to be useful in assessing the behaviour of elastomeric seals in nuclear environments. The new model is of practical use to design engineers in assessing maintenance schedules for replacement of such seals. Lifetime Prediction Models Empirical Model. An empirical model based on time-temperature-dose rate superposition was developed at Harwell for lifetime prediction of elastomeric seals (2). This early model attempted to separate the thermal and radiation components of the degradation by determining the shift factors under a range of conditions. The thermal shift factors were determined experimentally at a series of dose rates, all relative to the same reference temperature, producing a series of master curves at each dose rate. The radiation shift factors were then determined by shifting these master curves to a single master curve relative to zero dose rate. The empirical model used this single master curve of compression set versus time combined with a set of empirical equations relating the thermal and radiation shift 0097-6156/91/0475-0524$06.00/0 Published 1991 American Chemical Society

In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.


33. BURNAY

Prediction of Lifetime of Elastomeric Seals

525

factors to the temperature and dose rate (2). The master curve was determined experimentally by superposition of data and its time dependence was an arbitrary function. In this early work it was found that the thermal and radiation shift factors were not independent, the thermal shift factor having an apparent dose rate dependent activation energy. This early model contains 4 empirical parameters which must be determined experimentally for each elastomer, the model is described in more detail in reference (2). The model parameters in this empirical model are specific to the elastomer formulation tested. Although this simple model has proved useful in practical applications, there are several disadvantages to the technique (i) the number of parameters needed to describe the model mean that a large amount of experimental data are required to fully characterise any one elastomer formulation; (ii ) because of the empirical nature of the model, the parameters do not have a physical significance and cannot be used to predict the behaviour of similar materials; (iii ) the arbitrary shape for the master curve means that interpolation of data can only be done graphically; (iv) the model cannot fully explain the behaviour of some materials. New Superposition Model. The empirical equations describing the thermal and dose rate shift factors can be simplified by using the approach of Rudd (?) who suggests the use of a single shift factor a(T,D)relativeto the reference conditions to superpose data (Figure 1), rather than the two shift factors of the empirical model. This single shift factor is equivalent to a^.a^ in the earlier model. His approach makes use of the fact that superposition is a symmetry property of the damage parameter, this will determine the functional formrequiredof the temperature and dose rate dependence of the shift factor a(T,D) for superposition to be possible. Rudd describes two types of superposition that are possible, designated type 1 and type 2. For type 1 superposition, plots of a damage parameter (such as compression set) versus time will superpose with a shift factor a(T,D) whose functional form is not critical. For type 2 superposition, plots of dose to equivalent damage versus dose rate will superpose with a shift factor b(T) which is a function of temperature only. This is the type of superposition behaviour which has been observed and modelled by Gillen and Clough (4,5). The two types of superposition are independent, but if a system displays both types then the type 1 shift factor a(T£>) and the type 2 shift factor b(T) arerelatedand must have the form,

where b(T) is some function of temperature and D is the dose rate. Rudd (4) has suggested an alternative empiricalrelationshipwhich will satisfy equation (1), X

a(T,D)=exp^è - I ) [ 1 . e x p | ( i ref ref

X

-I).D ]

+ k

R T

T

1

R

T

T

(2)

J

where E, k and χ are empirical constants for the new model. Implied in this equation is that the type 2 shift factor, b(T), is given by


526

RADIATION EFFECTS ON POLYMERS

b(T) = exp§è 4> R T T

( 3 )


r e f

Equation (2) describes the new empirical model, which has fewer disposable parameters than the earlier model. The main advantage of this type of approach is that characterisation of an elastomer requires considerably less data than the earlier model since there are only three model parameters to be determined - E, k and x. The parameter Ε can be determinedfromdegradation in the absence of irradiation, leaving only k and χ to be determinedfromirradiation data. The functional form of the new model fits Rudd's criterion, equation (1), so that both types of superposition are valid. Figure 2 shows how a(TJD) will vary with dose rate and temperature for the new model. At low dose rates the degradation is dominated by the thermal component; at high dose rates, temperature has little effect on the degradation. This decrease in temperature dependence with increasing dose rate, which was interpreted as a change in apparent activation energy in the earlier empirical model (2,5), is now seen to arise automaticallyfromequation (2), without having to invoke a dose rate dependent activation energy. For the majority of elastomers that have been studied, the parameter χ has been found to be equal to one. For this case, equation (2) simplifies to a two parameter model,

aCT^) = exp^4 --i) k.D r

R T

ref

+

(4)

T

which can be interpreted in physical terms as the sum of a thermal component, described by the Arrhenius relationship with an activation energy E, and a dose rate component, with k representing a reaction constant for radiation degradation. This description of the shift factor also implies mat degradation involves competing thermally induced and radiation induced initiation processes to form radicals which can then participate in similar subsequent reactions. The model does not require a detailed knowledge of the reaction mechanisms but assumes that a single mechanism dominates the degradation behaviour. Dose to Equivalent Damage. An alternative way of approaching the model is to examine how the dose required to reach a particular level of the damage parameter will vary with temperature and dose rate, i.e. type 2 superposition. At a temperature Τ and dose rate D, the dose to equivalent damage, i.e. DED, is given by t .D DED = — — a(T,D) m

(5)

where ^ is the time required to reach the damage level on the master curve at the reference condition of D = 0 and Τ = T f. The parameter ^ is only a function of re

the damage level selected and is independent of Τ and D. Substituting for the shift factor a(T,D) and taking the special case of Τ = T f this equation simplifies to rc


33. BURNAY


527

ΌΛ

τη

DED =

(6) 1 + k. D

x


X

x

At high enough dose rates, when k.D » 1, DED will be proportional to D*" . This implies that for materials where χ = 1, DED will be independent of dose rate at high dose rates. However, at low dose rates there will be a marked dose rate effect, irrespective of the value of x, since the material will ultimately be limited by thermal degradation. This is illustrated in Figure 3 which shows the DED plotted as a function of the dose rate; the curve is equation (6) using the same values of E, k and χ as used in Figure 2. As the dose rate decreases, the curve tends assymptotically towards the straight line given by purely thermal degradation. In Figure 3 this is shown as a dashed line; for the example shown, thermal degradation dominates for dose rates less than about 0.01 Gy/s. Since DED is being plotted as a function of dose rate, i.e. type 2 superposition, data obtained at temperatures other than T f can be superposed by using the type 2 re

shift factor b(T) given by equation (3). A plot of DED versus D/b(T) will then yield a single curve for data at different temperatures. This is precisely the form of the superposition model put forward by Gillen and Clough (5,6) where they used the activation energy for the breakdown of peroxides to shift their data on PVC. Time-Dependence of Compression Set. Another limitation to the earlier 4-parameter empirical model (2), the arbitrary shape of the master curve, can also be improved. Examination of a large number of data from several different elastomers has shown that the time dependence of compression set is frequently a simple power law. For a temperature Τ and dose rate D, the observed compression set is given by set = QCaOTJUtH

(7)

where q < 1, typically of the order of 0.5 or less, and Q is constant for a particular formulation. This can be used in conjunction with the superposition model to calculate the predicted compression set. Application to Practical Elastomeric Seals Practical Examples. Some examples of how the superposition model has been applied to elastomeric seal materials will illustrate the range of degradation behaviour which can be modelled in practice. These examples are for materials in use in the UK nuclear industry, i.e. they are compounded formulations not model systems. The type of behaviour which is observed will be determined by the relative values of the reaction constant k for radiation degradation and the activation energy Ε for thermal degradation. If k is sufficiently large for the radiation component in equation (2) to dominate in the temperature range of interest, then temperature is found to have little effect (Figure 4). However, if k is relatively small, temperature will have a much larger effect (Figure 5). Both of the materials illustrated in Figures 4 and 5 have been fitted to the simplified model, equation (4). Thefirsttwo examples were for a limited temperature range but the model can be used over a much wider temperature range provided that a single degradation mechanism is operating. Figure 6 illustrates a high temperature elastomer which has been modelled over a temperature range from 80°C to 250°C. For this particular



528 Φ Φ

Ε ο Ι

/

Ο α.

loga(T.D)

Φ

οι ο log (time)


Figure 1. Superposition principle - schematic.

ίο

- 3

2

-1

1er ίο Dose rate ( G y / s e c )

10

1

Figure 2. Calculated shift factors a(T,D) for compression set; temperatures T >T >T >T . 3

2

ref

1

1

1

1

10 hJ

Ο

-

Q LU Q

•

10 -Thermal degradation limit

/

/

/

/

/

/

/

I

/

-*—

-—

2

jy^

10 h

1

10"

I 10- 3

I

I 10"

10"

I 1

10

Figure 3. Dose to equivalent damage (DED) for compression set at T f. re




BURNAY

1

1

NITRILE [ T

Ref

1

' · 23°C ο 40 ν 55 * 75 •95

= 40°Cl

95°C 75

7

X

•

55 ^

40 _ r !I

ίο*

5

/ /

-^^^v'

23 HI

^

ίο"

4

I1

II

ίο

ισ

-3

II 2

10"

I 1

1

Dose rate (Gy/s)

Figure 5. Shift factor a(T,D) as a function of dose rate and temperature nitrile.



530


* 250 10 10"

10"

3

10"

2

10"

1

10

D o s e rate (Gy/s)

Figure 6. Shift factor a(T,D) as a function of dose rate and temperature · high temperature elastomer. material, data are available at high temperatures but superposition is known to break down for Τ > 250°C as the degradation mechanisms change (2). The original raw data for this material (2) has been reassessed using a power law time dependence for compression set, rather than an arbitrary curve shape, to redefine the shift factor a(TJD) in the new model for each data set. Plots of dose to equivalent damage (DED) versus dose rate can also be used to illustrate the model; the type 2 shift factor, equation (3), has been used to superpose data obtained at different temperatures. For the EPDM rubber, DED is virtually independent of dose rate down to 10 Gy/s at 20°C (Figure 7) whereas for the nitrile rubber DED is strongly dose rate dependent at 40°C below 1 Gy/s (Figure 8). In the high temperature elastomer shown in Figure 9, DED is still slighdy dose rate dependent even at high dose rates; this is because the exponent χ in equation (6) is 0.95 rather than the value of 1.0 found for the EPDM and nitrile. 5

Limitations to the Model. Although the superposition model does not require a detailed knowledge of the reaction schemes underlying the degradation, it does assume that a single mechanism is dominant. If this assumption breaks down, then the model will be invalid. An example of this is seen in the nitrile elastomer shown in Figure 5 where superposition breaks down at dose rates 5 0.1 Gy/s. A similar breakdown in superposition has previously been observed (2) in the high temperature elastomer illustrated in Figure 6. In this material there is a temperature limitation of 250°C for the validity of the superposition model. In general, the model has proved to be of practical use where extrapolations are made towards lower temperatures and lower dose rates than those tested experimentally. In combined environment radiation experiments such as these, diffusion limited oxidation is likely to play an important part (5,6), particularly at high dose rates. The breakdown of the model at dose rates > 0.1 Gy/s in the nitrile elastomer is likely to be due to such effects. Although measurements of oxidation profiles have not been carried out on the elastomeric materials tested so far, it is recognised that heterogeneous oxidation is likely to be significant at the highest dose rates In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

33. BURNAY


10*

1

EPDM [ T

Ref

10 /


ο

Ω

1

1

531

r

=20°C]

/

/

/ ^ \ ^ Thermal / ^-degradation / limit

10 /

10

6

-$

Φ

Η • • 20°C ο 55 χ 90

10'

10

ior

5

J

ιο"

Α

L

ίο

ίο

-3

-2

ίο

-1

A

1

D/b(T) (Gy/s)

Figure 7. Dose to 50% compression set versus dose rate for EPDM at 20°C.

ισ

5

ίο

-4

ισ

3

ίο

-2

1

10"

1

Dose rate (Gy/s)

Figure 8. Dose to 50% compression set versus dose rate for nitrile at 40°C.



532


used. For this reason, best estimates of the model parameters have been made based on the lower dose rate data where possible. Conclusions A new empirical superposition model has been developed with three disposable parameters. For many elastomers, this improved model can be further simplified to a two parameter model which can be interpreted as the sume of a thermal component and a radiation component. This model can be applied to a number of elastomeric materials of interest to the nuclear industry. In the new model, the temperature dependence which is observed under irradiation is determined by therelativevalues of the model parameters Ε and k. The dose rate dependence is determined by the parameter x, particularly at high dose rates. The use of a simple power law to describe the time dependence of compression set has been found to be a useful adjunct to the new superposition model. Acknowledgements This work was carried out under the Underlying Research Programme of the United Kingdom Atomic Energy Authority. The author would like to thank Nuclear Electric and British Nuclear Fuels pic for permission to use data on their materials. Literature Cited (1) Burnay, S.G.; Hitchon, J.W. J. Nucl. Materials, 1985, 131, p. 197. (2) Burnay, S.G.; Hitchon, J.W. in Influence of Radiation on Material Properties: 13th Inter. Symposium (Part II), ASTM STP 956, 1987, eds. In Radiation Effects on Polymers; Clough, R., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1991.

33. BURNAY


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F. A. Garner etal.,American Society for Testing and Materials, Philadelphia, p. 609-614. (3) Rudd, H.J. Time temperature dose rate superposition behaviour in irradiated polymers, AERE-R13746, 1990, Harwell Laboratory, Didcot, Oxon, UK. (4) Rudd, H.J. Harwell Laboratory, unpublished information. (5) Gillen, K.T.; Clough, R.L. Polym. Degrad. and Stabil., 24, 1989, p. 137. (6) Gillen, K.T.; Clough, R.L. J. Polym. Sci., Polym. Chem. Ed., 23, 1985 p. 2683. 1991


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A Practical Model for Prediction of the Lifetime of Elastomeric Seals in

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