The main coolant piping system is one of the base case systems. The failure probability of the large piping of this system is dominated by the hot leg to pressure vessel weld, because this location is at the highest temperature and sees the highest stress.

F. 3.2.1 Dimensions and Welds — From the piping isometrics made available to the panel members, the hot leg has a 29 inch inner diameter, and a thickness of 63.5 mm (2.5 inch) (OD=34 inches), fabricated from SA-376 (which is an austenitic stainless steel). The example plant has two coolant loops. There are several welds in the hot leg, including shop and field welds and safe ends. There is a safe end and field weld at the pressure vessel.

F.3.2.2 Stresses and Cycles — Table 1-2, page 9 of Reference F.1 summarizes the deadweight, pressure and restraint of thermal expansion stresses for the 14 field welds in one loop of the large primary piping in the plant considered in that report. Joint 1 is the hot leg to pressure vessel joint, and it has the highest stresses. The seismic stresses are included in Table 1-3, page 10 [F.1]. They are generally quite low. The postulated list of transients is provided in Table 4-1, page 152 [F.1], and is the transients occurring over the 40 year design life, which corresponds to reactor years. The list contains 11 types of transients. There is sufficient information in Reference F. 1 to consider all of these transients, but only the heat-up cool-down transient will be considered in this case, because it is the dominant transient contributing to fatigue crack growth [F.1]. The heat-up cool-down transient was postulated to occur 200 times in 40 years (5/year). This is excessive, and 3/year is used herein.

The seismic stresses are given in terms of the maximum load controlled stress (deadweight + pressure + max seismic), and the summary of the stress history needed for fatigue crack growth analysis is also provided. This summary, denoted as S, is the sum of the cyclic stresses as follows

S4 = Z^x Ao2 [F.4]

se ism icstressh isto ry

This is what controls the amount of fatigue crack growth during a seismic event for a fourth power crack growth law that includes Я-ratio effects (See Reference F.1). Table F.4 summarizes the suggested stress history for the hot leg to pressure vessel joint.

Table F.4 Summary of Stress History for Hot Leg to Pressure Vessel Joint
deadweight stress = 2.08 ksi
pressure stress = 6.49 ksi (axial)
restraint of thermal expansion stress = 6.50 ksi
3 times per year

	max oLC ksi	S4 ksi4	Ao, ksi
OBE	8.76	521.6	1.27
SSE	9.06	2958.3	1.96
3SSE	10.26	63430	4.22
5SSE	10.62	162000	5.33

The right-hand column in the above table is the cyclic stress if the seismic event contains 200 stress cycles all of the same amplitude, with a low minimum load. This column is derived from the value of S4 and Equation F.4, with omax=Ao, and is included just to provide an idea of the size of the seismic stresses. They are not large.

Residual stresses, when considered, are taken to be the default values for large lines, as reported in Reference F.2.

F.3.2.3 Results — WinPRAISE runs were made for the hot leg to pressure vessel weld using the above stresses and default material properties. Table F.5 summarizes the results. “Good” inspections at 0, 20 and 40 years were considered. These results are the cumulative leak probability. The left hand column gives the leak rate in gallons per minute. The next column in gives the time (25, 40 and 60 years), and the probabilities are directly from the PRAISE output for these times. For the Monte Carlo simulation, the crack size plane (a/h — a/b) was divided into 20 by 20 strata, with a maximum of 2000 trials drawn from each stratum. Sampling from a given stratum was stopped when 20 failures occurred in that stratum. Sampling began at the corner of the a/h-a/b plane corresponding to long deep cracks (1,0), and continued to shorter, then shallower cracks until no failures occurred in a stratum within 2000 trials. Sampling was then stopped. This procedure is referred to as automated stratification, and is a feature unique to WinPRAISE [F.4]. Earlier versions of the PRAISE software require the user to define each stratum and the sampling from each.

Table F.5 Cumulative Probability PRAISE Results for Hot Leg-Pressure Vessel Weld for Fatigue

Crack Growth from Pre-Existing Defects

	Base	No hydro	Aging
Hydro	yes	no	no
Insp	good	good	good
tinsp	0,20,40	0,20,40	0,20,40
Aging	no	no	yes
Jic	5	5	1.5
dJ/da	23.44	23.44	15
	no EQ	SSE	5SSE	no EQ	SSE	5SSE	no EQ	SSE	5SSE
О A	25	1.20×10-18	2.34×10-16	2.45×10-16	6.61×10-15	7.04×10-15	7.08×10-15	1.43×10-14	1.47×10-14	1.47×10-14
40	1.29×10-18	2.35×10-16	2.45×10-16	6.61×10-15	7.04×10-15	7.08×10-15	1.43×10-14	1.47×10-14	1.47×10-14
60	1.29×10-18	6.01×10-18	6.19×10-18	6.61×10-15	6.62×10-15	6.62×10-15	1.43×10-14	1.44×10-14	1.44×10-14
	HLA0	HLB0	HLC0
>100	25	2.44×10-19	2.53×10-18	3.89×10-18	2.93×10-17	3.18×10-17	3.22×10-17	5.11×10-17	5.52×10-17	5.63×10-17
40	2.55×10-19	2.60×10-18	3.97×10-18	2.94×10-17	3.19×10-17	3.22×10-17	5.11×10-17	5.53×10-17	5.63×10-17
60	2.56×10-19	3.04×10-19	3.33×10-18	2.94×10-17	2.94×10-17	2.94710-17	2.12×10-17	5.12×10-17	5.13×10-17
	HLA1	HLB1	HLC1
>1500	25	1.20×10-20	6.48×10-19	1.31×10-18	1.31×10-18	1.99×10-18	2.64×10-18	2.72×10-18	4.33×10-18	5.99×10-18
40	1.26×10"20	6.62×10-19	1.32×10-18	1.31×10-18	2.00×10-18	2.65×10-18	2.72×10-18	4.36×10-18	5.97×10-18
60	1.27×10"20	2.61×10-20	3.93×10-20	1.31×10-18	1.33×10-18	1.34×10-18	2.72×10-18	2.75×10-18	2.79×10-18
	HLA2	HLB2	HLC2
>5000	25	1.19×10-20	6.48×10-19	1.31×10-18	1.31×10-18	1.99×10-18	2.64×10-18	2.72×10-18	4.33×10-18	5.99×10-18
40	1.26×10-20	6.62×10-19	1.32×10-18	1.31×10-18	2.00×10-18	2.65×10-18	2.72×10-18	4.36×10-18	5.97×10-18
60	1.27×10"20	2.61×10-20	3.93×10-20	1.31×10-18	1.33×10-18	1.34×10-18	2.72×10-18	2.75×10-18	2.79×10-18
	HLA3	HLB3	HLC3
>500000	25	1.20×10-20	6.48×10-19	1.31×10-18	1.31×10-18	1.99×10-18	2.64×10-18	2.72×10-18	4.33×10-18	5.99×10-18
40	1.26×10"20	6.62×10-19	1.32×10-18	1.31×10-18	2.00×10-18	2.65×10-18	2.72×10-18	4.36×10-18	5.97×10-18
60	1.27×10"20	2.61×10-20	3.93×10-20	1.31×10-18	1.33×10-18	1.34×10-18	2.72×10-18	2.75×10-18	2.79×10-18
	HLA4	HLB4	HLC4

noticeable effect of hydro

noticeable effect of seismic when hydro test is performed, less effect when no hydro aging has about x2 effect >1500 gpm same as DEPB

Runs were made with and without a hydro test, and it is seen that hydro testing has a noticeable effect. Moderate material degradation is considered, with the values of JIc and (dJ/da)matl identified in the table. The failure probabilities are all very small, even the leak probabilities. The influence or seismic events is seen to be quite small.

Table F.5 provides the base case results for the hot leg. Additional runs were made to study the following variables: [15]

• The effects of the fatigue crack growth relation employed were studied. The fatigue crack growth relation in PRAISE for austenitic stainless steel is based on information available during the original software development. More recent crack growth relations have been suggested [F.11]. For the simple stress history in this case, it is possible to run PRAISE with a crack growth relation that is equivalent to the more recent relation.

• PWSCC crack initiation and growth has been identified in the control drive mechanisms (CRDM) in PWRs. This occurs in the Alloy 600 weldment. This alloy is also used in the safe end of the pressure vessel to main coolant piping welds, so is present in the hot leg to pressure vessel weld under consideration. In order to model the initiation and growth of PWSCC cracks, the initiation kinetics were assumed to be the same as for Type 316NG stainless steel as currently in PRAISE [F.2], but the crack growth kinetics were changed to be representative of Alloy 600. Based on information in Reference F.12, the crack growth kinetics is represented by the relation

da__ CKr’

dt

where m equals 1.16, and C is lognormally distributed with a median value that depends on the temperature and material (weld, base metal, etc.). The median value of C for a weld at 315 C (600°F) is 7.86×10-7, when crack growth rates are in inches/hour and K is in ksi-in1/2. Combining the within-heat and heat-to-heat variation in C, the second parameter of the lognormal distribution is 1.193 (standard deviation of lnC = 1.193).

• The effects of more severe material degradation were studied, with the values of the degraded toughness given along with the results. Since PRAISE can not consider time-dependent material properties, the degraded material properties are present even in new pipe. The values of the degraded properties are from Reference F.13.

The results of these additional runs are summarized in Tables F.6 and F.7.

Table F.6 Cumulative PRAISE Results Additional Runs for Hot Leg Pressure Vessel Weld

	From Table F.5	Ref F.11 da/dN	Odl @ t-1	PWSCC Growth no Ores	PWSCC Growth Ores	PWSCC Initiation Ores
Hydro	yes	yes	yes	yes	yes	—
Insp	good	good	good	good	good	good
tinsp	0, 20,40	0,20,40	0,20,40	0,20,40	0,20,40	20,40
Aging	no	no	no	no	no	no
Jic	5	5	5	5	5	5
dJ/da	23.44	23.44	23.44	23.44	23.44	23.44
	no EQ	no EQ	no EQ	no EQ	no EQ	no EQ
О A	25	1.20×10-18	2.20×10-18	2.38×10-16	0.923	0.916	0.001
40	1.29×10-18	2.42×10-18	—	0.926	0.918	0.020
60	1.29×10-18	2.43×10-18	—	0.926	0.919	0.068
		HLD0	HLE0
>100	25	2.44×10-19	2.61×10-19	2.38×10-16	7.97×10-7	2.16×10-7	1.0×10-5
40	2.55×10-19	2.71×10-19	—	7.97×10-7	2.16×10-7	2.69×10-4
60	2.56×10-19	2.72×10-19	—	7.97×10-7	2.16×10-7	1.78×10-3
		HLD1	HLE1
>1500	25	1.20×10-20	1.63×10-20	6.41×10-20	9.68×10-10	2.78×10-11	<10-4
40	1.26×10-20	1.65×10-20	—	9.68×10-10	2.78×10-11	1.0×10-4
60	1.27×10-20	1.66×10-20	—	9.68×10-10	2.78×10-11	4.85×10-4
		HLD2	HLE2
>5000	25	1.20×10-20	1.63×10-20	6.41×10-20	2.78×10-11	4.66×10-11	<10-5
40	1.26×10-20	1.65×10-20	—	2.78×10-11	4.66×10-11	9.0×10-5
60	1.27×10-20	1.66×10-20	—	2.78×10-11	4.66×10-11	3.77×10-4
		HLD3	HLE3
break	25	1.20×10-20	1.63×10-20	6.41×10-20	2.19×10-14	2.59×10-13	<10-5
40	1.26×10-20	1.65×10-20	—	2.19×10-14	2.59×10-13	9.0×10-5
60	1.27×10-20	1.66×10-20	—	2.19×10-14	2.59×10-13	3.77×10-4
		HLD4	HLE4	DEPB	DEPB

The design limiting stress was 40.0 MPa (4.49 ksi). In the case of PWSCC growth, initial fabrication defects were considered with the default depth distribution discussed above. Both initiation and growth were considered for the column identified as PWSCC initiation. The higher large leak rates for the initiation relative to the PWSCC growth are due to the possibility of multiple initiation sites, whereas the growth considers only one initial crack.

Table F.7 Additional Hot Leg Pressure Vessel Runs Considering Material Aging

Good Inspection at 0, 20 ,40 Updated da/dN

3 HU-CD per year No Hydro Unless Specified

Type 304 Stainless

Degraded Properties Used for All Times

	Base	no Hydro	A	B	C	D	E
Jic kips/in	5	1.11	0.67	1.72	0.75	0.20
dJ/da ksi	23.44	13.4	8.0	22.6	6.5	0.05
ovs ksi	19.4	29.2
Cut ksi	—	76.7
Oflo ksi	44.9	53.0
D ksi	106	104.5
N	5	4.84
О A	25	1.20×10-18	6.61×10-15	1.34×10-14	1.96×10-14	9.73×10-15	2.07×10-14	4.02×10-13
40	1.29×10-18	6.61×10-15	1.34×10-18	1.96×10-14	9.73×10-15	2.07×10-14	4.02×10-13
60	1.29×10-18	6.61×10-15	1.34×10-18	1.96×10-14	9.73×10-15	2.07×10-14	4.02×10-13
>100	25	2.44×10-19	2.93×10-17	5.26×10-18	6.76×10-17	—	—	2.81×10-14
40	2.55×10-19	2.94×10-17	5.27×10-18	6.77x10_1/	—	—	2.81×10-14
60	2.56×10-19	2.94×10-17	5.27×10-18	6.77x10_1/	—	—	2.81×10-14
break	25	1.20×10-20	1.31×10-18	2.67×10-18	4.30×10-18	1.48×10-18	5.31×10-18	2.81×10-14
40	1.26×10-20	1.31×10-18	2.67×10-18	4.31×10-18	1.48×10-18	5.31×10-18	2.81×10-14
60	1.27×10-20	1.31×10-18	2.67×10-18	4.31×10-18	1.48×10-18	5.31×10-18	2.81×10-14
	earlier base case, default WinPRAISE properties, with hydro	no hydro	unaged weld metal J-T CF8M tensile	mult J-T by 0.6	all CF8M	more sensitive aged	extremely sensitive aged

The biggest effect in Table F.7 is not having a hydro test. This assumption is necessary, because when degraded material properties are used, everything that fails does so during the hydro test.

“Extremely sensitive aged” material properties are needed before degradation has a large effect.