The definition of damage functions from irradiation test data

NUCLEAR ENGINEERING AND DESIGN 33 (1975) 11-18. © NORTH-HOLLANDPUBLISHINGCOMPANY

T H E D E F I N I T I O N O F D A M A G E F U N C T I O N S F R O M I R R A D I A T I O N T E S T DATA*.. H.H. YOSHIKAWA, W.N. McELROY and R.L. SIMONS Hanford Engineering Development Laboratory, Richland, Washington 99352, USA

Received 23 April 1975 This report describes a method of determining irradiation effectiveness of different neutron spectra in causing radiation effects to fuel cladding and reactor structural materials. It involvesthe definit:on of a sem;.-empirical damage function or cro:" section using measured data from specimens irradiated in thermal and fast test r~actor spectra. The damage fun:tion it applied to design problems involvingirradiation effects to reactor structural and f~el cladding materials to pretxict the fluence which would produce a specific change in material properties.

I. Irradiation effects functions on cross sections

Those who use irradiation effects data on cladding and structural materials must ultimately answer the following question. Whal: fluence or reactor operating period will cause the same property change to a material in a specific reactor application as caused by an irradiation to 10 21 n/cm 2 in an irradiation test? To answer this question, the effect of neutron spectral differences between the irradiation facility and the service position must be taken into account. • This paper presents the method [ 1,2] used for accounting for such differences and examples of its application. The so-called damage function or cross section ~.hus derived, along with the spectrum where the material is used, defines the fluence required to cause a given level of property change. The definition of such fluences is the end result of this method.

2. General procedures The overall procedure is described in fig. 1. The following text serves as a guide through the figure: (1) dosimetry - methods for determining tbe (2) spectrum - the energy distribution, and fluence, total number, of neutrons during an *This paper it, based on work performed under USAEC Contract AT(45-I)-2170.

irradiation test. This experimental information is compared with (3) calculated spectra and fluence - derived from (4) test reactor design information - and (5) calculation methods - the comparison of experimental and calculated spectra and fluence provide a basis for judging the adequacy of the calculation techniques. These techniques are used with information on the projected (6) reactor design-- to derive the (7) spectrum and Iluence - expected at the point cf application. In order to assess the damaging effectiveness of irradiations during application. (8) irradiation effects data - from irradiation tests, the fluence and spectra, and results from (9) damage m o d e l i n g - involving analytical studies and computer simulation, are used in the (1 O) damage analysis - to generate a (11) damage function - which gives the effectiveness of neutron in causing the irradiation effect as a function of its energy. This damage fimction and the spectrum and fluence at the point of application are used to make a (12) damage p r e d i c t i o n - this prediction is the fluence required to cause the level of irradiation induced property change used in the derivation of the damage function. In subsequent sections, individual steps in this m.-.thod will be treated in fuller detail.

i2

H.H. Yoshtkavyz et ~1., Damage functions from irradiation test data

IRRADIATION TESTS

APPLICATIONS

I

TEST REACTOR INFORMATION

DESIGN

CALCULATED SPECTRUM FLUENCE

SPECTRUM FLUENflE (

SPECTRUM

DAMAGE UNCTION_ ~

IRRADIATION EFFECTS DATA (~)

REAcT'Oe

I

DAMAGE PREDICTII

GOAL: PREDICTIONS OF MATERIAL PERFORMANCE DURING APPLICATIONS FROM TEST IRRADIATION DATA

Fig, 1. Process for damage function analysis.

2.1. Test data

Irraaiation test data, which are input to this method, ideally should be in the form of sets of curves of property change versus fluence for each of several different irradiation conditions. Identical materials should have been used in all irradiations conducted at the same temperature and property measurements conducted at a fixed temperature and on fully calibrated equipment. Unfortunately, all these conditions are rarely fulfilled completely. Hence some extrapolation or interpolation in fluence or some adjustment for temperature or material variable is made to the data to secure the fluence required to cause a specific property change in each s~ctrum. 2.2. Test e vironment clzaracterization

The fluence and spectrum determination in some instances must be assigned on the basis of characterization studies performed after the irradiation test. However, the recommended procedure is the use of a number of neutron monitors to def'me the flux and spectrum [3]. As illustrated in fig. 2, a variety of monitors provides sensitivity in different neetron energy ranges. The activation induced in these differ-

ent materials thus provides the basis for assigning the energy distribution of neutrons or spectrum at the irradiation test position. In these studies, the SAND-ll code was used to make that assignment [4]. Such multiple foil dosimetry provided information on the spectral differences at different irradiation facilities. This multiple foil dosinietry method can be used during reactor start-up testing to determine the neutron spectrum actually present at service locations. Such information conf'Lrmsthe correctness of',he calculated results used in the design analysis.

2.3. Input functions Input functions are drawn from irradiation effects modeling studies [5]. A frequent initial function is the Kinchin-Pease [6] model for displacement production or that model as modified by Doran [5] taking into account ionization processes as described by Lindhard [7]. In addition, information from computer simulation studies of radiation damage processes has helped to def'me the initial damage function. These input data are used to define a damage function. Moreover, uncertainties assigned to measurements of the material property, flux and spectrum are incorponted into a Monte Carlo error analysis code [8]

H.H. Yoshikawa et aL, Damage functions from irradiation test data

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which defines the resultant uncertainty in the damage function. A separate analysis of the effect of different input approximations provides an estimate of the possible variability from that source. The end result is an assignment of an uncertainty to the fluence required to cause a specific change in property.

Z 4. Damage function definition Briefly, this involves first obtaining property change data from irradiations in different neutron spectra. From these data, the SAND-If code [4] is used to obtain a solution G(E) for the set of integral equations

different d;l(E)s, and the fluences (~t)/at which this property change was observed in the various spectra are the required input. The SAND-If code then derives an adjusted final G(E). The input function is adjusted until the ratio of calculated to measured property cha,ge approaches unity for all spectra, The word solution is not used in the usual sense of unique solution, Actually she procedure is used to iteratively reduce errors incurred in the initial guess for the solut.'an. Thus the procedure is a mezhod of smoothing similar to those used in treating experimental data. 60 KSi YIELD STRENGTH DAMAGE FUNCTION FOE 3O4SS IRRADIATEO AND TESTED AT 480'~C

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i

H,H, ¥oshikawa et al,, Damage functions from irradiation test data

14

Table 1. Status of damage function definition for stainless steels. Material 304 S.S.

Irradiation temp. (°C)

Test temp. (°C)

Remarks

change level 10% residual

450

450

both form and magnitude of function based on test data

450

450

both form and magnitude of function based on test data

450

450

both form and magnitude of function based on test data

450

450

both form and magnitude of function based on test data

370

370

form assumed, magnitude set by test data

250

250

form assumed, magnitude set by test data

450

-

both form and magnitude of function based on test data

Property

total elongation

304 S.S. 304 S.S. 304 S.S. 304 S.S. 304 S.S. 304 S.S.

5% uniform elongation yield strength 60 ksi ultimate tensile strength 70 ksi 10% residual total elongation irradiation induced creep swelling

The choice of the initial input function is not critical if data are available from many diverse spectra. In such a case, the procedure would yield the same solution i]ldependent of the input form. in other cases, however, the source of data might be limited to two or three spectra. Under such circumstance, the iterative procedure could adjust the magnitude of the input function but make only relatively minor adjustments in the sha~. T~erefore, the choice of an input function becomes most ,-'mportant and should be based on a physically reasonable des:ription of the irradiation effect process. This method of generating functions from irradiation test data is treated in detail in ref [1]. 2..5. Damage functions

able of a number of possible solutions. The dotted curve, a gross displacement production rate cross section developed by Russcher for austenitic steel [ 13], the indicated values of property change, and the multiple-foil derived EBR-I! and ETR spectra and fluences were used as input to the SAND-II code to derive the solid curve [ 14]. i~ the analysis of this property change, the number of spectra are limited. There was a single thermal reactor spectrum (ETR) and a large number of fast reactor spectra (EBR-II). Consequently, the damage functions are not well defined below ~ ! 0 -2 MeV but do show that low energy neutrons contribute to damage. They may contribute through such effects as n,c~ (helium) and n,T (recoil atom and transmutation atom) damage. The overall status of damage function definition for austenitic stairdess steels is shown in table I. Functions have been defined for swelling and creep as well as the mechanical properties of ultimate tensile strength of total elongation, 5% uniform elongation and yield strength. s

The functions G(E) have been defined for annealed 304 stainless steel irradiated and tested between 420 and 540°C. Fig. 3 is the function for a change in yield strength to 50 ksi t [9]. Other functions have been defined for a change in ductility to 10% total residual elongation for ultimate tensile strength of 70 ksi [9] and ~:orirra.liation.induced creep at 250°C [ I0]. The G(E) for a change in yield strength (YS) to 60 ksi replaces one reported earlier [ 1 I, 12]. In fig. 3, the solid curve represents the most reasont a t the 0.~,,%yield point.

2. 6. Error analysis The uncertainty in the definition of the low and high energy portions of these G(E)s has been studied. Preliminary results of an error analysis for the YS G(E)

H.H. Yoshikavm et al., Damage functions from irradiation test data indicate that an error o f +30% in the ETR data point would increase the derived G(E) as much as a factor o f ten in the thermal region (-~2.5 X 10 - 8 MeV). Similarly, an error o f - 3 0 % would reduce the G(E) by a factor o f ten in that region. This occurs since the solution is well defined in the high energy region;

15

that is, the combined ETR and EBR-II data points fix the shape and magnitude of the G(E)s between ~ 1 0 - 2 and 4 MeV, the region of major response. Below "-10 - 2 MeV, the ETR data dominate the deftnition. Consequently, any error in the ETR data is accommodated p~imarily as a large change at low

Table 2. Calculation of fluence required to attain 60 ksi yield sUength at the FTR vessel wall (irradiation teraperature of 430-540°C).

Group

EL ( M e V )

Normalized group flux (~/)

Gi[ ksi/(n/cm 2)]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1~ ;9 20 21 22 23 24 25 26 27 28 29 30 31 32

7.79 +00 6.07 +00 4.72 +00 3.68 +00 2.87 +00 2.23 +00 1.74 +00 1.35 +00 1.05 +00 8.21 -01 6.39 -01 4.98 -01 3.88 -01 3.02 -01 2.35 -01 1.83 -01 1,43 -01 1.~,1 -01 6.74 -02 2.48 -02 9.12 -03 3.36 -03 1.23 -03 4.54 -04 1.67 -04 6.14 -05 2.26 -05 &32 -06 3.06 -06 1.12 -06 4.14 -07 1.00 - 1 0

2.16 - 10 5.18 -10 7.86-10 1.09 -09 1.05 -09 3.47-09 2.57-08 1.37-07 3.49 -07 9.43 -07 4.34 -06 1.01 - 0 5 2.48 -05 7.61 --05 1.54 -04 3.59 -04 1.20 - 03 2.62 -03 6.44 -03 1.32 -02 1.64 -02 9.01 -03 9.67 -03 5.78 -02 8.95 -02 1.23 -01 1.50 -01 1.50 -01 1.37 -01 1.11 -01 7.46 - 0 2 4.52 -02

1.94 -20 2.16 -20 2.16 -20 2.13 -20 2.18 -20 1.99-20 1.74-20 1.48-20 1.25 -20 1.05 -20 9.24 -21 8.04 - 2 1 6.~ 5 -21 5.21 -21 4.It, - 21 3.65 -21 3.24 -21 2.80 -21 2.26 -21 1.66 -21 6.91 -22 2.58 - 22 1.59 -22 3.68 -23 2.02 -24 2.41 -24 2.77 -24 4.98 -24 9.73 -24 1.71 -23 2.92 - 23 6.44 -23

Group response Gi X ¢/ 2 [ksi/(n/cm )] 4.21 -30 1.11 -29 1.70-29 2.32 -29 2.29 -29 6.90-29 4.47 -28 2.03-27 4.36 -27 9.90 -27 4.01 -26 8.12 -26 1 *~6 -26 4.00 -25 6.38 -25 1.31 -24 3.89 -24 7.33 -24 1.46 -23 2.19 -23 1.13 -23 2.32 -24 1.54 -24 2.12 - 24 1.81 -25 2.96 -25 4.16 -25 7.47 -25 1.33 -24 1.89 -24 2.19 -24 2.92 -24 ~.~':.Oi = 7.75 -23 ksi/(n/cm2), /

Ot = 60 k~i/7.75 X 10 -23 ksi/(n/cm2),

Ot = 7 7 X 1023 n/cm 2.

Percent response per group 0.0 0.0 0.0 C.0 0.0 6.0 0.0 0.0 0.0 0.0 0.0 O.1 0.2 0.5 0.8 1.6 5.0 9.4 18.7 28.3 14.5 2.9 1.9 2.7 0.2 0.3 0.5 0.9 1.7 2.4 2.8 3.7

16

H.H. Yothikawa et al., Damagefunctions [rom irradiation test data 105 TOTAl ELONGATION DAMAGE FUNCTION ON ANNEALED 304SS IRRADIATED AND TESTED AT 370°C

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t~t(- ~pper uncertainty limit (95%confidence). in GEE) rather than as a small change at h i g h energy. Similarly, the solutions above - ' 4 MeV are sensitive to errors. Only additional irradiation data from spectra with a significant component of low energy neutrons will ~ignificantly reduce the uncertainty of these G(E)s below ~ 10-2 MeV. This uncertainty, however, is not of major concern since the integral, as opposed to differential, form of these initial semi-empirical derived G(E)s is of primary importance in predicting property changes in reactor structural materials. In most applications where radiation damage is a concern, neutrons in this low energy .range cause negligible damage. Figure 4 shows a damage function for 10% total elongation in 304 stainless steel irradiated and tested at 700°F. This damage function was determined in response to a need to define the irradiation effects on the removable portion of the FTR core support structure. Since only few data were available, the initial G°(E) guess was critical to the solution GEE). Experimental evidence suggests that the damage process is nearly the same in the temperature range 700-900°F [ 15]; consequently, the best guess GO(E)was the 900°F GEE) for 10% total elongation. Th~ solution GEE) (solid curve) is essentially the 900°F GEE) norrealized in magnitude by the 700°F data.

uncertainty limit to the GEE) solution at the 95% confidence level. Three factors were considered in the GEE) solution uncertainty: errors in the material property measurement; errors in the flux-spectra; and uncertainty due to non-uniqueness of the solution. The first two factors were treated by a Monte Carlo error analysis code [8] which propagates these erro~ to the GEE) solution. Uncertainty due to non-uniqueness was treated by •starting from several different initial input functions, such as a constant for all energies, and subsequently c~ermingan envelope of solutions. The two error analyses are linearly combined at a 95% confidence level to give the total upper bound uncertainty. The uniqueness error dominates the region of low damage ~sponses whereas the errors determined by the Monte Carlo analysis dominate the region of major damage response.

nt-rgy

2. 7. Uncertainty estimates

The dotted curve in fig. 4 is an estim-te of the upper

2.8. Application o f damage function

The damage function is used to calculate the fluence required to produce a specified property change during exposure of the reference material in the service neutron spectra. Such calculations require spectral

YIELD STRENGTH CHANGES AT FIR LOCATIONS

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*(OTALNEUTRONFLUENCE, nlcm2tE> 10"10 MeV)

Fig. 5. Yieldstrength for 304 stainless steel versus total fluence for different FTR spectra (test and irradiation temperatme of ~450°C).

ti.H. Yoshikawa et al., Damage functions from irradiation test data 30

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~700¢~F).

data from reactor physics calculations or measurements. The fluence is obtained from the equation

I o,

¢ t - ,V

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17

perimentally determined yield strength versus fiuence curves for spectra characteristic of the core, grid p!ate and vessel of FTR. Since the meaa neutron energy varies from 0.5 MeV at the core to 0.03 MeV at the grid plate and about 0.002 McV at the vessel, quite different total neutron fluences are required to produce the same level of property change. Roughly 1022 neutrons are required at the core, 8 X 1022 at the grid plate, and 8 X 1023 at the vessel. A second example is that from the analysis of total elongation damage at 700°F for application to the removable portion of the grid plate. Fluence predictions for different spectra are shown iv, fig. 6. The predicted fluence required to attain 10% to al elongation at the grid p!ate is "-4 × 1022 n/cm 2 for an irradiation temperature of 7000F. in contrast, the same level of damage would be o ~tained in EBR-II :n one-third to onetenth of the fluente. The fission"spectrum is the hardest spectrum Li.e. highest mean neutron energy) and therefore requL es the last fluence.

(3) 3. Discussion

where the integral flux spectrum is normalized to one neutron, i.e. m

l- 1

S is the property change level used to define the damage function, and the group structure for the damage function must be the same as that for the spectrue~,. As an example of the application of the damage function, fig, 5 shows the fluences predicted for an increase in yield strength to 60 ksi for three core positions in the FTR. Table 2 shows an example of how the fluence to attain 60 ksi in the FTR vessel spectrum is calculated using eq. (3). The table gives the group lower energy bound E L , the normalized group flux 01, the group averaged damage function Gl, and the group response (Gf X Oi). The total response is 7.75 X 10-23 ksi/(n/cm2), and from eq. (3) the predicted fluence to reach the level of 60 ksi yield strength is 7.7 X 1023 n/cm 2. The last column shows the percent response attributed to each group. Most of the damage is due to neutrons between I and 150 keV. The calculated fluence points may then be used to establish the relative positions on a service fluence scale of ex-

The procedure described here provides a systematic means of utilizing irradiation effects data obtained in a 'ariety of spectra to the prediction of material performal~,ce. It is noted that the damage function is :lefined only for a specific temperature and level of property change. Its extension to higher fluence or different temperatures requires further analyses. Generally, the data used in the definition of the damage function have the same fluence dependence of damage for all the spectra considered. That is, the curve of property change versus fluence is parallel for irradiations in different spectra. If this relationship holds for the spectrum at the reactor application position, the damage function analysis also provides the fluence dependence of the property change. Ir. this case, fluence predictions could be made for p,:operty change levels different from those used in thf, damage function def'mition. As yet, tbe validity of st~ch an assumption has not been fully demonstrated.

4. Conclusions A method for materials performance predictions from

18

H.H. Y o t h i k ~ et al., 13en~e functions from irradiation test data

h-radiation test data has been developed and applied to the prediction of mechanical property change in a projected applica~on to a fast reactor. This method permits the systematic use of experiment~.l irradiation effects data and the prediction of material performance under reactor conditions without the need for arbitrary assumptions. It is recommended as a general method for relating irradiation test data among reactor locations characterized by different neutron spectra.

161 G.EL Kinchin and R.S. Pease, Rep. progr. Phys. 18 (1) (1955).

171 J. Lindhard, V. Nielsen, NL Scharf and P.V. Thomsen, Mat. Fys. Medd. Dan. Vid. Seisk. 33 (10) (1963).

181 C.A. Oster, W.N. McElroy and J. Mawr,A Monte Carlo

191

IlOl References

!111 [121

[ 1 ] W.N. McEIroy, R.E. Dahl, Jr 6nd C.Z. Serpan, Jr, NucL AIr0~. 7 (6) (1969) 561-571. [2J ILL Simons, Damage functions for determining irradiation effectiveness, HEDL Report, HEDL-TME 71-189, Westinghouse Hanford Company, Richiand, Washington, Nov. ~1971). 13l W.N. McEIroy and R.E. Dahi, Jr, Neutron dosimetty for fast reactor applications, ASTM Special Publication STP-484, Apr. (1971). [4] W.N. McEIroy et aL, NucL ScL Eng. 36 (1969) 15-27. [ 5 ] !).(3. Doran, Displacement c r o , sections for stainless steel and tantalum based on a Lindhatd model. HEDL Report, HEDL-TME 71-42, Westinghouse Hanford Company, Richland, Washington, Apr, (1971).

!131

1141

!151

program for SANDAl error analysis, HEDL Report to be published, Westinghouse Hartford Company, Richland, Washington. R.L Simons, W.N. McEIroy and LD. Blackburn, Damage function analysis of austenitie steel neutron induced mechanical property change data, HEDL Report, HEDLSA-291, Westinf0house Elanford Company, Richland, Washington, Mar. (1972). W.N. McElroy, ILE. Dahl, Jr and E.R. Gilbert, NucL Eng. Des. 14 (1970) 319. W.N. McEIroy, ILL. Simons and I.D. Blackburn, Trans. Amer. NucL Soc. 13 (1970) 144. W.N. McElroy, ILl.. Simons and I.D. Blackburn, Trans. Amer. NucL Soc. 13 (I970) 555. G.E. Russcher, Calculated damage functions for determining irradiation effectiveness~ BlqW Report, BNWL1093, Battelle-Northwest, Richland, Washington, Sept. (1969). W.F. Sheely (Ed.), WADCO quarterly technical report, voL 4, October, November, December 1970, HEDL Report, HEDL-TME 71-29, Westinghouse Hanford Company, Richland, Washington, Jan. (1971). A.L. Ward and J.J. Holmes, Prediction of fast reactor irradiation hardening in austenitie stainless steels, HEDL Report, HEDL-SA-198, Westinghouse Hanford Company, Richland, Washington, June (1971). Submitted for publication in Met. Tram,