8.6. Computer Code Implementation

The DEFORM‑4 module is implemented in SAS4A as a group of subroutines. Section 8.6.1 gives a list of these subroutines and a brief description of the calculation performed by each. The direct coupling with SAS4A is through the subroutine SSFUEL for the pre‑transient calculation, and DFORM3 for the transient calculation.

The input parameters necessary for DEFORM‑4 to perform its calculations are given in Table 8.6.3. This table also includes cross‑references to the equation or section number where the parameter is used, the input location and variable name, a suggested value (assuming mixed‑oxide fuel with 20% cold-worked, stainless‑steel cladding), and the external reference where the suggested value originated. Further information on the input parameters is given in the Input Description (see Chapter 2 Section 2.2).

In Section 8.6.3 a brief description of the output generated by DEFORM‑4 is given. The sample output given in Figure 8.6.1 through Figure 8.6.13 are included for illustration only, and should not be used as a sample case.

8.6.1. Subroutine and Function List

Table 8.6.1 DEFORM‑4 Associated Subroutines and Functions

Routine	Description
ALPHC	Mean thermal expansion coefficient of the cladding
ALPHF	Mean thermal expansion coefficient of the fuel
CAVITE	Molten cavity gas release and pressurization
CLADSW	Irradiation-induced cladding swelling
CLDFAL	Cladding failure fraction calculations
CRAKER	Volume fraction of cracks in fuel
CSIGMA	Thermal-elastic calculation in the cladding
DEFINI	Initial setup routine
DEFORM	Main mechanics driver routine
DFORM3	DEFORM-4 interface to SAS4A for transient calculation
ECLADF	Cladding modulus of elasticity function
EFUELF	Fuel modulus of elasticity function
EXPAND	Thermal-mechanical axial expansion routine
FAILUR	Determination of reaching failure criterion
FK	Fuel thermal conductivity function
FSIGMA	Thermal-elastic calculation in the fuel
FSWELL	Fission-gas bubble swelling/compaction routine
GRGROW	Grain growth in the fuel
HGAP	Fuel-cladding gap conductance function
KFUEL	Thermal conductivity of the fuel
MKDRIV	Thermal-elastic and interface pressure control routine when solid fuel is completely cracked
NABOND	Fuel-cladding gap conductance for sodium-bonded metal fuel
OUTPT3	Short form output routine
OUTPT4	Standard output routine
PORMIG	As-fabricated porosity migration routine
PRESPL	Plenum pressure calculation
RELAX	Stress relaxation in the fuel (not operational)
RELGAS	Fission gas release in the fuel
RHOF	Theoretical density of fuel, solid and liquid
RHOL	Density of liquid fuel (not currently used)
RHOS	Density of solid fuel (not currently used)
SOLID	Thermal-elastic and interface pressure iteration control routine
SIGFRA	Fracture strengths of the fuel
SSFUEL	DEFORM-4 interface to SAS4A for pre-transient irradiation
UTS	Ultimate tensile strength of the cladding
YLDCF	Yield point of the cladding

Table 8.6.2 DEFORM-4 Subroutines and Functions Associated with 15-15Ti Cladding

Routine	Description
InitCheckClad15Ti(cladthickness, NCHAN)	Checks for the errors and calls INITSCLAD15Ti in order to allocate the required derived data type for each channel. “cladthickness” is the thickness of the cladding and NCHAN is the total number of channels.
INITSCLAD15Ti(ICH)	Initializes a CLAD15 derived typed for channel ICH. Called from SSFUEL.
BEGINCLAD15Ti(j)	Used to preserve initial values of the variables at each time step. Sets the values of the target variables using dummy storage variables for each axial node j.
ENDCLAD15Ti(j)	Used to update the dummy storage variables using the computed values of the target variables at the end of each time step for each axial node j.
CDFNORMALDIST(j)	Computes the clad failure fraction as a function of logarithm of CDF at axial location j.
INPT_CLAD15TiReadDat(unit,ich)	Reads the relevant variables for the 1515Ti cladding for channel “ich” from the restart file with an assigned file number, “unit”. It also calls INITSCLAD15Ti in order to allocate the required derived data type for each channel.
INPT_CLAD15TiWriteDat(unit,ich)	Writes the relevant variables for the 1515Ti cladding for the channel “ich” to the restart file with an assigned file number, “unit”.
ET15TI(sigma, temp)	Computes clad thermal creep rate for a given applied stress (sigma) and temperature (temp).
EPSWC15TI(neutronflux, fluence, dosconversion, temp)	Computes and returns the linear clad irradiation induced void swelling rate for 15-15Ti cladding, given the fast neutron flux (neutronflux), fast neutron fluence (fluence), dose conversion factor (doseconversion) and temperature (temp).
EPSIR15TI(temp, neutronflux, stress, dosconversion)	Computes and returns the clad irradiation creep rate for 15-15Ti cladding, given the temperature (temp), fast neutron flux (neutronflux), applied stress (stress) and dose conversion factor (dosconversion).
CRUP15TI(sigma, temp, dose)	Computes the creep rupture time of the cladding given the applied stress (sigma), temperature (temp), and cladding dose (dose).

8.6.2. Input Variables

Table 8.6.3 DEFORM‑4 Input Variables

Equation Variable	Reference Eq. Or Section No.	SAS4A Input Variable	Block	Location	Suggested Value	External Reference
		IPROPT	1	6	0
		IYLD	1	26	2
	8.3.7	IMELTV	1	28	1
		IXSTPC	1	32	0
		IXSTPF	1	33	0
		IMCVTY	1	34	0
		IAREXT	1	40	0
		POW	12	1
	8.3-166	BETADN	12	4-9
ρo	8.7-1	COEFDS(1)	13	1	11.08D+3	8-17
C1	8.7-1	COEFDS(2)	13	2	2.04D-5	8-17
C2	8.7-1	COEFDS(3)	13	3	8.70D-9	8-17
C1	8.7-13	COEFK(1)	13	4	2.10D+0	8-32
C2	8.7-13	COEFK(2)	13	5	2.88D-3	8-32
C3	8.7-13	COEFK(3)	13	6	2.52D-5	8-32
C4	8.7-13	COEFK(4)	13	7	5.83D-10	8-32
C5	8.7-14	COEFK(5)	13	8	5.75D-2	8-32
C6	8.7-14	COEFK(6)	13	9	5.03D-4	8-32
C7	8.7-14	COEFK(7)	13	10	2.91D-11	8-32
Tr	8.2-5	TR	13	419
MWfg	8.3-24	FGMM	13	600
fg	8.3-22	GATPF	13	601	0.246	8-17
Ef	8.3-23	ENPF	13	602
Req	8.3-7	RLEQ	13	603	0.6
Rueq	8.3-21	RUEQ	13	604	1.2
	8.3.1	PRSMIN	13	605	0.02
Ts	8.3-87	TFSOL	13	786-793
Tl	8.3-87	TFLIQ	13	794-801
Po	8.3-7	PRSTY	13	1073-1080
Not currently used		AC	13	1081
Not currently used		QSWL	13	1082
Ap	8.3-1	APORE	13	1083	20.704	8-6
Qp	8.3-1	QPORE	13	1084	4.5281D+5	8-6
A	8.3-1	ABC	13	1085	1.5	8-6
R		RGASSI	13	1086	8.31433
γ	8.3-45	GAMMA	13	1087	0.45	8-6
Apg	8.3-44	APG	13	1088	5.0D+4	8-6
Qpg	8.3-44	QPG	13	1089	56506.5	8-6
Gk	8.3-11	GK	13	1090	1.717D+10	8-11
Qv	8.3-11	QV	13	1091	3.87D+5	8-11
G	8.3-13	GK1	13	1092	1.4556D-8	8-12
Q	8.3-13	QV1	13	1093	2.67D+5	8-12
Gm	8.3-12	GRAINK	13	1094	2.23D-3	8-12
Qm	8.3-12	GRAINQ	13	1095	6.3375D+4	8-12
Cv	8.3-145	CVXE	13	1096	94.69	8-30
Cv	8.3-145	CVHE	13	1097	3.13D+3	8-30
δf	8.3-143	ROFF	13	1098	3.30D-06
δc	8.3-143	ROFC	13	1099	1.78D-06
Not currently used		AZEROX	13	1100
γ	8.3-145	GAMGS	13	1101	1.66	8-30
Not currently used		HARDNS	13	1102
Not currently used		ET	13	1103	1.0	8-30
ai	8.3-144	ACCHE	13	1104	0.15	8-19
ai	8.3-144	ACCXE	13	1105	0.85	8-19
Co	8.3-146	CZERO	13	1106	1.98	8-30
σ	8.3-135	STEBOL	13	1107	5.69D-8
εf	8.3-135	EMSF	13	1108	0.9	8-19
εc	8.3-135	EMSC	13	1109	0.8	8-19
QA1	8.3-42	QA1	13	1110	6.92D+3	8-16
QA2	8.3-42	QA2	13	1111	33.95	8-16
QA3	8.3-43	QA3	13	1112	0.338	8-16
QA4	8.3-43	QA4	13	1113	1.48D+4	8-16
QA5	8.3-43	QA5	13	1114	9.575	8-16
Aα	8.3-33	ALFSS	13	1115	2.0D-04
Qα/R	8.3-33	BETSS	13	1116	1.1D+04
vc	8.2	CNU	13	1117	0.3	8-17
vf	8.2	FNU	13	1118	0.3265	8-17
Not currently used		AM	13	1119
Not currently used		QLAX	13	1120
Not currently used		QLAX2	13	1121
Not currently used		DDX	13	1122
Not currently used		DDX2	13	1123
fgb	8.3-29	FIFNGB	13	1148	0.10
fm	8.3-81	FNMELT	13	1169	0.30
τg	8.3-107	CIRTFS	13	1170	16.67
C3	8.7-2	COEFDL(2)	13	1201	9.3D-5	8-17
Not currently used		QSTAR	13	1202
Not currently used		ABCPU	13	1203
Not currently used		QPU	13	1204
Not currently used		DPUO	13	1205
Not currently used		TMIDFG	13	1218
Not currently used		FGSPRD	13	1219
Not currently used		FGPORX	13	1220
Not currently used		FGMIN	13	1221
Not currently used		HECOND	13	1222	1.58D-3	8-38
Not currenty used		FGCOND	13	1223	7.2D-5	8-38
Not currently used		AKCOND	13	1224	0.75	8-38
Mn	8.3-140	HEMM	13	1225	4
sfp	8.3-62	EPSSFP	13	1226	2.46D-3	8-17
Not currently input		HEMASX	13	1227
Not currently input		ZSWFAC	13	1228
Af	8.2-57	FAXIAL	13	1258	1.0
εcw	8.3-62	FCLDWK	13	1259
Not currently used		FMELTD	13	1260
Not currently used		FSTRAN	13	1261
fH	8.5-1	FTMPCH	13	1262	0.6
fa	8.3-116	EXPCOF	13	1263	1.0
		PRTSTR	13	1264	0.0
		PRTDEL	13	1265	0.0
	8.4.3	FIRLIM	13	1266	0.80
	8.4.3	SECLIM	13	1267	0.95
	8.4.3	THRLIM	13	1268	0.98
	8.4.3	DTFAL1	13	1269	0.020
	8.4.3	DTFAL2	13	1270	0.010
	8.4.3	DTFAL3	13	1271	0.002
Not currently used		AKD	13	1272
Not currently used		CKD	13	1273
Not currently used		QKD	13	1274
	8.3.6	FGFI	13	1275
	8.7.4	IRHOK	51	3	3
N	8.3-27	NT	51	14	11
		IFUELV	51	15
		IFUELB	51	16
		ICLADV	51	17
	8.3.3	KTING	51	19	0
		NAXOP	51	20	25
		MSTEP	51	21
	8.3.5	ITAU	51	22	0	8-17
	8.3.5	IRATE	51	23	0	8-17
	8.3.8	IHGAP	51	24	1
Npps	8.3-166	NPIN	51	25
Nspc	8.3-166	NSUBAS	51	26
	8.1	MZUB	51	27
	8.1	MZLB	51	28
		IRELAX	51	30	0
n	8.3-11	NGRAIN	51	31	4	8-11
		ISSFUE	51	32	1
		NPLIN	51	37-44
		JPRNT1	51	46	0
		JPRNT2	51	47	0
		NNBUG1	51	48	0
		NNBUG2	51	49	0
		IDBUGF	51	50	0
		NSKIP	51	51-58
		MFAIL	51	86	3
		IFAIL	51	87	0
		JFAIL	51	88	0
	8.3.4.1	IPSIG	51	95	3
		IHTPRS	51	96	0
		IPRD	51	97	3
	8.1	IEQMAS	51	118	1
		ISSFU2	51	122	1
		IHEALC	51	123	2
		IAXTHF	51	124	1
A	8.3.9	AXHI	61	8-31
		PLENL	61	53
		RBR	61	54-77
		RER	61	78-101
		RBRPL	61	102
		RERPL	61	103
		RINFP	61	104-127
		ROUTFP	61	128-151
		RBR0	61	180
		RER0	61	181
		PSHAPE	62	6-29
S	8.3-27	PSHAPR	62	30-44
		PLIN	62	45-52
		TPLIN	62	53-60
		FLTPOW	62	61
	8.3.9	FUELRA	62	208-231
A	8.3-152	AHBPAR	63	2	0.0	8-22
B	8.3-152	BHBPAR	63	3	0.0	8-22
C	8.3-152	CHBPAR	63	4	0.0	8-22
	8.3.8	HBMAX	63	5	4.0D+4	8-22
	8.3.8	HBMIN	63	6	1.0D+2
H	8.3-152, 153	HBPAR	63	7	0.0
Do	8.3-21	DGO	63	26	1.0D-5
Pogas	8.3-6	P0GAS	63	27
		FCLOP	63	68
Ts1	8.5-2	TSEP1	63	69	2.2D+3
Ts2	8.5-2	TSEP2	63	70	1.0D-8
		BONDNA	63	71
		REFDEN	63	72
	8.4	FSPEC	65	1
	8.4	FMELTM	65	2	0.20
		IDEFOPT	INPCHN	497
		ICTYPE	INPCHN	225
	Eq. (8.7-52)	IDEFSTFAL	INPCHN	498
	Eq. (8.7-49)	CDOSECONV	PMATCH	149
	Section 8.7.17.5	COCOR	PMATCH	150
\(\mu\)	Eq. (8.7-52)	CDFMEAN	PMATCH	151
\(\sigma\)	Eq. (8.7-52)	CDFSIGMA	PMATCH	152

8.6.3. Output Specific to DEFORM-4

Figure 8.6.1 through Figure 8.6.13 show a sample of the output generated by DEFORM‑4. This sample is for a section of pre‑transient output, but the same output is generated in the transient case. What follows is a very brief discussion of the output format for each page.

Figure 8.6.1 SAS4A Steady-state Coolant Condition Output

The standard SAS4A coolant temperature/pressure summary.

Figure 8.6.2 SAS4A Fuel Temperature and Node Location Map

Fuel node boundary locations and cell temperatures. Radial and axial node numbers are shown. Under “IZ” is the node number of the first non‑molten cell. Under “IETA” is the node number of the last solid, i.e., un-cracked, cell. Therefore, IZ to IETA defines the extent of the solid annular fuel region.

Figure 8.6.3 SAS4A Fuel-pin Condition Summary Output

Fuel/cladding summary information is presented. The titles are self-explanatory except for the third one in the bottom section. This column shows the ratio of the calculated gap conductance to that used for the next time step thermal calculation. Since there is no iteration between the DEFORM‑4 mechanics calculation and the SAS4A thermal calculation, a scheme has been employed to avoid gross oscillations in the gap conductance and temperatures. This is to use the average of the calculated and previously used gap conductance for the next time step. In order to determine how close the values are to those calculated, this ratio is printed.

Figure 8.6.4 DEFORM-4 Radial Stress Map

The radial stress at each fuel and cladding node. Also printed is the fuel‑cladding gap, GAP, the fuel‑cladding interface pressure, PFCI, and the coolant pressure, PEXT. All stresses and pressures are in Pascal and the gap is in meters.

Figure 8.6.5 DEFORM-4 Circumferential Stress Map

The circumferential stress at each fuel and clad node boundary, in pascals.

Figure 8.6.6 DEFORM-4 Axial Stress Map

The axial stress at each fuel and clad node boundary in pascals.

Figure 8.6.7 DEFORM-4 Fission-gas Retention Fraction Map

The fission‑gas retention fraction in each fuel cell. The column titled ‘FG RET (KG)’ is the retained fission‑gas total in kg, ‘FG PRD (KG)’ is the total kg of fission gas produced, ‘M‑FG/M‑FUEL’ is the kg of fission gas retained divided by the mass of fuel, ‘FRAC RELS’ is the fractional release, and ‘NUET/M2’ is the fluence, for each axial segment.

Figure 8.6.8 DEFORM-4 Total Porosity Fraction Map

The total porosity fraction in the fuel cells, i.e., retained fission-gas porosity plus remaining as‑fabricated porosity.

Figure 8.6.9 DEFORM-4 Fission-gas induced Porosity Fraction Map

The fission‑gas‑induced porosity in each fuel cell.

Figure 8.6.10 DEFORM-4 Fuel Grain Size Map

The grain size in each fuel cell, in meters.

Figure 8.6.11 DEFORM-4 Fuel Crack Volume Fraction Map

The crack volume fraction in each fuel cell.

Figure 8.6.12 DEFORM-4 Radial Node Locations

Mesh points in the fuel and the inner and outer clad dimensions. Also shown are the boundaries between the unrestructured and equiaxed region, IUNEQA, and between the equiaxed and columnar regions, IEQCOL.

Figure 8.6.13 DEFORM-4 Short Form Pin Summary Output

Short summary output from DEFORM‑4 showing the values calculated for various failure parameters. The hoop stress values are a simple average based on the inner and outer pressures and thickness of the clad.

If a failure criterion has a value greater than 1.0, then that criterion predicts failure. Currently, only the MFAIL parameters are used to automatically initiate failure of the pin.

The amount of output can be controlled through the use of NSKIP and IPRD in block 51 of the input. In the transient state the output from DEFORM‑4 is printed at the end of a heat‑transfer time step, as controlled by IPO and IPOBOI.

Listing 8.6.1 Sample DEFORM-4 Output using 15-15Ti Model (IDEFOPT > 0 and ICTYPE = 4)

 AXIAL  AXIAL    BURNUP   CLAD     CLAD         CLAD       CLAD      CLAD       CLAD       FUEL PINS
 FUEL   ELEV     ATOM     DOSE     OUTER       SWELLING  IRRADIATION THERMAL    FAILURE    FAILURE
 NODE    (M)     (%)     (DPA)   CORROSION(M)   (%)       CREEP(%)   CREEP(%)   MARGIN     FRACTION
  24   1.1940   0.0566   0.4579  0.000E+00    0.000E+00  0.388E-03   0.127E-02  0.100E-05  0.000E+00
  23   1.1840   0.0566   0.4579  0.000E+00    0.000E+00  0.388E-03   0.127E-02  0.100E-05  0.000E+00
  22   1.1551   2.2660  18.1978  0.000E+00    0.000E+00  0.151E-01   0.136E-02  0.100E-05  0.000E+00
  21   1.1069   6.8080  53.7328  0.000E+00    0.000E+00  0.438E-01   0.152E-02  0.100E-05  0.000E+00
  20   1.0582   7.8651  61.9464  0.000E+00    0.000E+00  0.514E-01   0.138E-02  0.100E-05  0.000E+00
  19   1.0094   8.8115  69.3621  0.000E+00    0.000E+00  0.581E-01   0.123E-02  0.100E-05  0.000E+00
  18   0.9607   9.7293  76.5560  0.000E+00    0.682E+00  0.636E-01   0.111E-02  0.100E-05  0.000E+00
  17   0.9118  10.4418  82.1941  0.000E+00    0.127E+01  0.654E-01   0.990E-03  0.100E-05  0.000E+00
  16   0.8629  11.0819  87.1732  0.000E+00    0.178E+01  0.707E-01   0.917E-03  0.100E-05  0.000E+00
  15   0.8140  11.4866  90.2900  0.000E+00    0.234E+01  0.990E-01   0.953E-03  0.100E-05  0.000E+00
  14   0.7651  11.7833  92.7017  0.000E+00    0.280E+01  0.138E+00   0.877E-03  0.100E-05  0.000E+00
  13   0.7163  11.9357  94.0680  0.000E+00    0.308E+01  0.194E+00   0.840E-03  0.100E-05  0.000E+00
  12   0.6676  11.9144  93.6432  0.000E+00    0.329E+01  0.286E+00   0.105E-02  0.100E-05  0.000E+00
  11   0.6188  11.7873  92.6803  0.000E+00    0.386E+01  0.369E+00   0.121E-02  0.100E-05  0.000E+00
  10   0.5699  11.4915  90.4318  0.000E+00    0.413E+01  0.408E+00   0.117E-02  0.100E-05  0.000E+00
   9   0.5210  11.1543  87.7450  0.000E+00    0.447E+01  0.477E+00   0.150E-02  0.100E-05  0.000E+00
   8   0.4721  10.5050  82.6725  0.000E+00    0.378E+01  0.514E+00   0.201E-02  0.100E-05  0.000E+00
   7   0.4230   9.8220  77.2449  0.000E+00    0.303E+01  0.733E+00   0.159E+00  0.100E-05  0.000E+00
   6   0.3740   9.0097  70.9643  0.000E+00    0.190E+01  0.489E+00   0.418E-02  0.100E-05  0.000E+00
   5   0.3252   8.0608  63.5630  0.000E+00    0.103E+01  0.456E+00   0.645E-02  0.100E-05  0.000E+00
   4   0.2633   0.0076   0.0612  0.000E+00    0.000E+00  0.459E-03   0.198E-01  0.100E-05  0.000E+00
   3   0.1880   0.0076   0.0612  0.000E+00    0.000E+00  0.459E-03   0.198E-01  0.100E-05  0.000E+00
   2   0.1128   0.0076   0.0612  0.000E+00    0.000E+00  0.459E-03   0.199E-01  0.100E-05  0.000E+00
   1   0.0376   0.0076   0.0612  0.000E+00    0.000E+00  0.459E-03   0.199E-01  0.100E-05  0.000E+00

Listing 8.6.1 shows an example output from a fuel performance with 15-15Ti cladding in a fuel channel. Columns show the axial node number, the axial elevation (m), fuel burnup (at%), clad dose (dpa), clad outer corrosion thickness (m), which is controlled by COCOR input, irradiation induced volumetric clad swelling (%), clad irradiation and thermal creep hoop strain (%), clad failure margin due to thermal creep rupture, which is the computed Clad Damage Fraction value (CDF) and fuel pin failure fraction (or probability) computed if stochastic clad damage evaluation module is switched ON (IDEFSTFAL > 0 and IDEFOPT > 0). Irradiation creep, thermal creep, void swelling, and clad creep rupture and clad failure fractions are computed by EPSIR15Ti, ET15Ti, EPSWC15Ti, CRUP15Ti, and CDFNORMALDIST routines, respectively. This output can be printed together with the DEFORM-4 output for normal operation and transient simulations at user specified steps.