Значение и использование

A pressure vessel surveillance program requires a methodology for relating radiation-induced changes in materials exposed in accelerated surveillance locations to the condition of the pressure vessel (see Practice E853). An important consideration is that the irradiation exposures be expressed in a unit that is physically related to the damage mechanisms.

A major source of neutron radiation damage in metals is the displacement of atoms from their normal lattice sites. Hence, an appropriate damage exposure index is the number of times, on the average, that an atom has been displaced during an irradiation. This can be expressed as the total number of displaced atoms per unit volume, per unit mass, or per atom of the material. Displacements per atom is the most common way of expressing this quantity. The number of dpa associated with a particular irradiation depends on the amount of energy deposited in the material by the neutrons, and hence, depends on the neutron spectrum. (For a more extended discussion, see Practice E521.)

No simple correspondence exists in general between dpa and a particular change in a material property. A reasonable starting point, however, for relative correlations of property changes produced in different neutron spectra is the dpa value associated with each environment. That is, the dpa values themselves provide a spectrum-sensitive index that may be a useful correlation parameter, or some function of the dpa values may affect correlation.

TABLE 1 ENDF/B-VI-based Iron Displacement Cross Section

BinEng^A (MeV)σ_d (barns)BinEng^A (MeV)σ_d (barns)BinEng^A (MeV)σ_d (barns) 10.100E-09158.354320.1050E-09154.620930.110E-09151.1395 40.1150E-09147.889550.120E-09144.105460.1275E-09139.9202 70.1350E-09136.086080.1425E-09132.544590.150E-09128.7502 100.160E-09124.7860110.170E-09121.1728120.180E-09117.8527 130.190E-09114.8137140.200E-09111.9561150.210E-09109.3199 160.220E-09106.8646170.230E-09104.5694180.240E-09101.8930 190.2550E-0998.93331200.270E-0996.65981210.280E-0994.12717 220.300E-0991.05218230.320E-0988.24872240.340E-0985.68787 250.360E-0983.33912260.380E-0981.17265270.400E-0978.92472 280.4250E-0976.63646290.450E-0974.53734300.4750E-0972.59930 310.500E-0970.81827320.5250E-0969.14790330.550E-0967.59222 340.5750E-0966.13822350.600E-0964.64189360.630E-0963.12039 370.660E-0961.70157380.690E-0960.37332390.720E-0958.92732 400.760E-0957.39681410.800E-0955.97892420.840E-0954.65984 430.880E-0953.43220440.920E-0952.28703450.960E-0951.21545 460.100E-0850.07727470.1050E-0848.89598480.110E-0847.79609 490.1150E-0846.76870500.120E-0845.57125510.1275E-0844.25006 520.1350E-0843.03653530.1425E-0841.91761540.150E-0840.71708 550.160E-0839.46333560.170E-0838.32018570.180E-0837.26968 580.190E-0836.30967590.200E-0835.40710600.210E-0834.57391 610.220E-0833.79705620.230E-0833.06956630.240E-0832.22424 640.2550E-0831.28942650.270E-0830.57002660.280E-0829.76999 670.300E-0828.79791680.320E-0827.91048690.340E-0827.10139 700.360E-0826.35879710.380E-0825.67357720.400E-0824.96309 730.4250E-0824.23960740.450E-0823.57548750.4750E-0822.96268 760.500E-0822.39920770.5250E-0821.87094780.550E-0821.37982 790.5750E-0820.91994800.600E-0820.44705810.630E-0819.96509 820.660E-0819.51724830.690E-0819.09670840.720E-0818.63984 850.760E-0818.15581860.800E-0817.70708870.840E-0817.29049 880.880E-0816.90205890.920E-0816.54074900.960E-0816.20166 910.100E-0715.84242920.1050E-0715.46908930.110E-0715.12094 940.1150E-0714.79594950.120E-0714.41855960.1275E-0714.00095 970.13050E-0713.61661980.1425E-0713.26338990.150E-0712.88403 1000.160E-0712.487591010.170E-0712.126331020.180E-0711.79428 1030.190E-0711.490391040.200E-0711.207601050.210E-0710.94298 1060.220E-0710.697451070.230E-0710.468041080.240E-0710.20132 1090.2550E-079.9067171100.270E-079.6794491110.280E-079.427035 1120.300E-079.1187451130.320E-078.8388191140.340E-078.582926 1150.360E-078.3479621160.380E-078.1316181170.400E-077.907534 1180.4250E-077.6788091190.450E-077.4688051200.4750E-077.276812 1210.500E-077.0975981220.5250E-076.9307671230.550E-076.775607 1240.5750E-076.6307011250.600E-076.4820831260.630E-076.330435 1270.660E-076.1889631280.690E-076.0566311290.720E-075.913148 1300.760E-075.7602981310.800E-075.6186171320.840E-075.486900 1330.880E-075.3643371340.920E-075.2500291350.960E-075.143171 1360.100E-065.0292541370.1050E-064.9114271380.110E-064.801945 1390.1150E-064.6997141400.120E-064.5815851410.1275E-064.450361 1420.1350E-064.3296141430.1425E-064.2182221440.150E-064.099185 1450.160E-063.9743041460.170E-063.8604021470.180E-063.756055 1480.190E-063.6607611490.200E-063.5713131500.210E-063.488699 1510.220E-063.4116161520.230E-063.3394661530.240E-063.256051 1540.2550E-063.1632761550.270E-063.0916281560.280E-063.013147 1570.300E-062.9169451580.320E-062.8294031590.340E-062.749808 1600.360E-062.6767501610.380E-062.6088351620.400E-062.527930 1630.4250E-062.4408971640.450E-062.3743841650.4750E-062.313606 1660.500E-062.2574621670.5250E-062.2053311680.550E-062.154114 1690.5750E-062.1087331700.600E-062.0601341710.630E-062.011735 1720.660E-061.9660451730.690E-061.9235861740.720E-061.877395 1750.760E-061.8285961760.800E-061.7830081770.840E-061.741254 1780.880E-061.7034171790.920E-061.6677921800.960E-061.632082 1810.100E-051.5957541820.1050E-051.5587201830.110E-051.522295 1840.1150E-051.4902001850.120E-051.4515541860.1275E-051.409592 1870.1350E-051.3702471880.1425E-051.3346351890.150E-051.296298 1900.160E-051.2561431910.170E-051.2198241920.180E-051.187621 1930.190E-051.1560281940.200E-051.1267461950.210E-051.099981 1960.220E-051.0752261970.230E-051.0518851980.240E-051.026221 1990.2550E-050.99657192000.270E-050.97222222010.280E-050.9476671 2020.300E-050.91571182030.320E-050.88767992040.340E-050.8611951 2050.360E-050.83773142060.380E-050.81538362070.400E-050.7928756 2080.4250E-050.76959232090.450E-050.74817112100.4750E-050.7286609 2110.500E-050.71075152120.5250E-050.69416002130.550E-050.6778895 2140.5750E-050.66350142150.600E-050.64807752160.630E-050.6327240 2170.660E-050.61820522180.690E-050.60474352190.720E-050.5900444 2200.760E-050.57456042210.800E-050.56003182220.840E-050.5467011 2230.880E-050.53459842240.920E-050.52323912250.960E-050.5118709 2260.100E-040.50029172270.1050E-040.48849022280.110E-040.4769112 2290.1150E-040.46668982300.120E-040.45435602310.1275E-040.4409762 2320.1350E-040.42842232330.1425E-040.41706482340.150E-040.4048129 2350.160E-040.39194772360.170E-040.38029932370.180E-040.3699498 2380.190E-040.35982112390.200E-040.35044752400.210E-040.3418580 2410.220E-040.33390292420.230E-040.32638102430.240E-040.3181047 2440.2550E-040.30854132450.270E-040.30068802460.280E-040.2927655 2470.300E-040.28245932480.320E-040.27339162490.340E-040.2648267 2500.360E-040.25721752510.380E-040.24997032520.400E-040.2426542 2530.4250E-040.23507712540.450E-040.22809362550.4750E-040.2217044 2560.500E-040.21584712570.5250E-040.21040362580.550E-040.2050605 2590.5750E-040.20034032600.600E-040.19527002610.630E-040.1902102 2620.660E-040.18542212630.690E-040.18097562640.720E-040.1761094 2650.760E-040.17097262660.800E-040.16614742670.840E-040.1616956 2680.880E-040.15765492690.920E-040.15384602700.960E-040.1500470 2710.100E-030.14616012720.1050E-030.14219332730.110E-030.1382971 2740.1150E-030.13485282750.120E-030.13067992760.1275E-030.1261477 2770.1350E-030.12188732780.1425E-030.11801862790.150E-030.1138330 2800.160E-030.10942872810.170E-030.10542792820.180E-030.1018602 2830.190E-030.9837523E-012840.200E-030.9515446E-012850.210E-030.9224781E-01 2860.220E-030.10484592870.230E-030.10282882880.240E-030.8397242E-01 2890.2550E-030.8057346E-012900.270E-030.7782596E-012910.280E-030.7506079E-01 2920.300E-030.7147984E-012930.320E-030.6842791E-012940.340E-030.1581741 2950.360E-030.7452445E-012960.380E-030.6020231E-012970.400E-030.5752645E-01 2980.4250E-030.5484677E-012990.450E-030.5239946E-013000.4750E-030.5017326E-01 3010.500E-030.4855164E-013020.5250E-030.4750492E-013030.550E-030.8634498E-01 3040.5750E-030.36845673050.600E-030.72306623060.630E-031.085166 3070.660E-031.4330573080.690E-031.7537643090.720E-032.100540 3100.760E-032.4288953110.800E-032.7227883120.840E-032.998771 3130.880E-033.2584613140.920E-033.4653723150.960E-033.618973 3160.100E-023.7870813170.1050E-023.9642713180.110E-0213.13789 3190.1150E-0210.693823200.120E-024.2626933210.1275E-024.338387 3220.1350E-024.4353673230.1425E-024.5342253240.150E-024.592575 3250.160E-024.7831803260.170E-024.7016233270.180E-024.841220 3280.190E-024.9990093290.200E-025.1113353300.201E-025.183993 3310.220E-025.2790693320.230E-025.4089103330.240E-025.523736 3340.2550E-025.6954423350.270E-025.8268533360.280E-025.975410 3370.300E-026.1735233380.320E-026.3954153390.340E-026.658582 3400.360E-027.1839393410.380E-0210.011683420.400E-029.194485 3430.4250E-028.1782663440.450E-028.2296573450.4750E-028.508525 3460.500E-028.9108763470.5250E-029.5253953480.550E-0210.59739 3490.5750E-0213.204113500.600E-0221.174663510.630E-0219.67340 3520.660E-0218.592033530.690E-0224.366273540.720E-0239.42936 3550.760E-0256.386213560.800E-0248.661023570.840E-0235.11790 3580.880E-0227.248923590.920E-0223.521593600.960E-0220.66808 3610.100E-0119.983923620.1050E-0118.418693630.110E-0118.51923 3640.1150E-0116.803653650.120E-0116.409453660.1275E-0116.00651 3670.1350E-0116.067923680.1425E-0115.558763690.150E-0115.08970 3700.160E-0114.618093710.170E-0113.995113720.180E-0113.21823 3730.190E-0112.019593740.200E-0110.615303750.210E-018.888706 3760.220E-016.8576863770.230E-014.4352993780.240E-014.034283 3790.2550E-0151.588563800.270E-01462.42043810.280E-01374.2036 3820.300E-01138.85823830.320E-0191.992423840.340E-0175.21491 3850.360E-0166.928963860.380E-0162.406113870.400E-0165.56062 3880.4250E-0159.518933890.450E-0161.428973900.4750E-0155.61853 3910.500E-0180.549943920.5250E-0184.937463930.550E-0161.63473 3940.5750E-0161.835473950.600E-0161.394863960.630E-0151.44463 3970.660E-0141.055203980.690E-0135.187873990.720E-01195.2115 4000.760E-0172.972704010.800E-01139.38014020.840E-01276.0543 4030.880E-01138.45684040.920E-01104.07434050.960E-01113.7160 4060.100105.54894070.105078.430954080.11078.06753 4090.115060.445434100.12070.474304110.1275134.1587 4120.1350255.36304130.1425293.01614140.150133.0900 4150.160122.75964160.170156.01434170.180244.4100 4180.190370.76274190.200205.33394200.210101.0349 4210.220307.51114220.230146.96134230.240171.8077 4240.2550135.33874250.270282.55014260.280187.6945 4270.300142.03914280.320315.57914290.340166.5530 4300.360302.11844310.380545.71174320.400528.4010 4330.4250400.44124340.450309.78254350.4750351.4453 4360.500381.00014370.5250327.40084380.550316.9469 4390.5750264.20914400.600190.80424410.630255.5292 4420.660529.87454430.690389.01674440.720680.4310 4450.760627.30194460.800427.23284470.840461.2467 4480.880327.13984490.920278.17194500.960479.7678 4511.00498.49224521.10477.68934531.20707.1735 4541.30616.46404551.40716.41014561.50734.1659 4571.60758.83534581.70784.55804591.80819.3325 4601.90989.32654612.00928.76814622.10923.3754 4632.20969.48004642.301079.7164652.401143.224 4662.501348.9544672.601192.1054682.701263.538 4692.801277.8014702.901271.5784713.001364.006 4723.101387.7244733.201358.4664743.301346.851 4753.401398.0344763.501334.7434773.601424.447 4783.701440.7084793.801483.8804803.901464.868 4814.001526.3714824.101560.4434834.201530.309 4844.301582.9164854.401523.3404864.501626.724 4874.601600.8634884.701617.4554894.801653.609 4904.901642.8334915.001600.0754925.101682.554 4935.201687.2864945.301716.4694955.401731.089 4965.501729.7854975.601760.8524985.701760.538 4995.801768.6565005.901792.1055016.001811.511 5026.101800.9405036.201811.5475046.301859.081 5056.401859.1255066.501879.2375076.601890.037 5086.701891.7625096.801909.4855106.901909.076 5117.001914.4425127.101936.4145137.201941.750 5147.301966.6635157.401963.3065167.501986.044 5177.601976.2135187.701989.2435197.802003.646 5207.902006.7715218.002009.0935228.102013.259 5238.202032.5885248.302064.7555258.402063.837 5268.502061.3655278.602059.5075288.702072.344 5298.802089.9765308.902107.5255319.002122.580 5329.102135.0775339.202147.5775349.302160.074 5359.402172.4825369.502185.8925379.602199.950 5389.702213.9185399.802226.6985409.902238.281 54110.02250.48254210.102263.39254310.202276.220 54410.302288.97154510.402301.72554610.502313.910 54710.602325.62854810.702337.34254910.802348.869 55010.902360.30155111.02371.74455211.102383.112 55311.202395.21255411.302407.95255511.402421.344 55611.502434.32555711.602446.24355811.702458.956 55911.802471.20556011.902482.24756112.02493.659 56212.102506.01656312.202519.59856412.302534.971 56512.402549.08656612.502562.97756712.602576.115 56812.702586.93656912.802600.01157012.902615.468 57113.02630.34357213.102644.45557313.202658.475 57413.302672.21857513.402685.52057613.502698.683 57713.602711.99057813.702725.31357913.802738.112 58013.902750.41858114.02763.16458214.102775.980 58314.202788.33158414.302800.21458514.402811.915 58614.502824.20858714.602837.18358814.702849.781 58914.802862.18459014.902874.42159115.02877.552 59215.102871.08459315.202864.61759415.302858.147 59515.402851.58159615.502844.83959715.602837.641 59815.702830.53859915.802823.42760015.902816.329 60116.02813.38660216.102814.81960316.202816.344 60416.302817.78260516.402819.12460616.502819.920 60716.602819.88360816.702819.84660916.802819.725 61016.902819.63161117.02823.43761217.102831.455 61317.202839.47561417.302847.22061517.402855.056 61617.502862.95661717.602870.91361817.702878.960 61917.802886.82662017.902894.59462118.02903.983 62218.102914.91362318.202925.79162418.302936.340 62518.402946.71262618.502956.44862718.602965.448 62818.702974.45062918.802983.45363018.902992.455 63119.02999.56163219.103004.58363319.203009.698 63419.303014.72163519.403019.74163619.503025.406 63719.603031.52663819.703037.73763919.803043.950 64019.903050.161641

^A Energies represent the lower bin boundary. The upper bin limit is 20.0 MeV

Since dpa is a construct that depends on a model of the neutron interaction processes in the material lattice, as well as the cross section (probability) for each of these processes, the value of dpa would be different if improved models or cross sections are used. The calculated dpa cross section for ferritic iron, as given in this practice, is determined by the procedure given in 6.3. The currently recommended dpa cross sections in this practice (Table 1) were generated using the iron ENDF/B-VI iron cross section (1). A recent calculation using ENDF/B-VII produced identical results.(2,3) Although the ENDF/B-VI based dpa cross section differs from the previously recommended ENDF/B-IV dpa cross section (1) by about 60 % in the energy region around 10 keV, by about 10 % for energies between 100 keV and 2 MeV, and by a factor of 4 near 1 keV due to the opening of reaction channels in the cross section, the integral iron dpa values are much less sensitive to the change in cross sections. The update from ENDF/B-IV to ENDF/B-VI dpa rates when applied to the H. B. Robinson-2 pressurized water reactor resulted in “up to ∼4 % higher dpa rates in the region close to the pressure vessel outer surface” and in “slightly lower dpa rates ... close to the pressure vessel inner wall” (5, 6). Table 2 presents a comparison of a previous edition (Practice E693-94) and currently recommended dpa estimates for several neutron spectra.

TABLE 2 Changes in Spectrum-Integrated dpa for Benchmark Neutron Spectra

Neutron SpectrumSpectrum-averaged dpa cross section (barns)^A “Old” ENDF/B-IV-based E693 response“Current” ENDF/B-VI-based E693 responseDifference ([Current - Old]/Old) (%) ENDF/B-VI ²³⁵U Thermal Fission (1, 4)875.55858.54–1.9 Materials Dosimetry Reference Facility (MDRF) (7)345.03343.58–0.42 CFRMF (8, 9)382.94387.081.08 Intermediate-energy Standard Neutron Field (ISNF) (9, 10)483.63480.00–0.75 Arkansas Nuclear ONE-1 (ANO) Cavity (11, 12)134.40139.443.75 ORNL Poolside Facility (PSF) T/4 position (11, 13)242.14238.33–1.57 Oak Ridge Research Reactor (ORR) (9)291.68288.86–0.97 Yayoi (9)613.12609.03–0.67 BIGTEN (9, 14)334.98341.251.87 H.B. Robinson-2, in the vessel wall, close to the inner surface (5, 6)219.43218.81–0.28 H.B. Robinson-2, ∼¼ T vessel wall (5, 6)245.17249.241.66 H.B. Robinson-2, ∼¾ T vessel wall (5, 6)203.68211.233.71

^A The spectrum-average dpa values in this table were computed using Eq 11 in a 640 SAND-II energy group representation and a lower integration bound of E_o = 10^–10 MeV.

Note—Table 2 is included to illustrate the effect on the dpa cross sections resulting from the change from the ENDF/B-IV to ENDF/B-VI cross sections. The spectrum-average cross section values given are not recommended for other uses because of their sensitivity to the assumed spectrum representations and the lower energy integration limit.

Область применения

1.1 This practice describes a standard procedure for characterizing neutron irradiations of iron (and low alloy steels) in terms of the exposure index displacements per atom (dpa) for iron.

1.2 Although the methods of this practice apply to any material for which a displacement cross section σ_d(E) is known (see Practice E521), this practice is written specifically for iron.

1.3 It is assumed that the displacement cross section for iron is an adequate approximation for calculating displacements in steels that are mostly iron (95 to 100 %) in radiation fields for which secondary damage processes are not important.

1.4 Procedures analogous to this one can be formulated for calculating dpa in charged particle irradiations. (See Practice E521.)

1.5 The application of this practice requires knowledge of the total neutron fluence and flux spectrum. Refer to Practice E521 for determining these quantities.

1.6 The correlation of radiation effects data is beyond the scope of this practice.

1.7 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.