- Email: [email protected]
Stress and lifetime limitations of first-wall structural materials
Journal of Nuclear Materials 85 & 86 (1979) 0 North-Holland Publishing Company
153-l
57
STRESS AND LIFETIME LIMITATIONSOF FIRST-WALLSTRUCTURALMATERIALS* C.
K.
YOUNGDARL and D. L. SMITH
Argonne National Laboratory,Argonne, Illinois
60439, USA
Proceduresare demonstratedfor working backward from desired lifetime of a fusion reactor first-wallto trade-offswith surface heat flux and temperature,using failure criteria obtained from ASME Code Case 1592. The maximum surface heat flux on a stainless steel firstwall is predicted by the proceduresdevelopedhere for a range of design parametersappropriate to a tokamak fusion power reactor. The remainderof the paper will be divided into two parts: First, lifetime criteria based on the general primary membrane stress limit Smt and long-holdtimefatigue will be used for illustratingtrade-offsbetween heat flux, average temperature,and lifetime and for comparing candidate structuralmaterials. Second, ratchetingand creep criteria will be added using a modified Bree Diagram to refine the design point suggestedby the first step. For purposes of illustration,the first wall will be taken as a thin cylindricalsurface of radius R and thickness6, loaded by an internal coolant pressure p and a surface heat flux w. For this case, the volumetricheat generationis negligiblecompared to the energy depositedon the surface. This configuration is intended to representeither a tube or the front curved surface of a blanket module, Bending stresses caused by constraintof the first wall by its support structureor the remainder of the blanket module will be ignored in the present analysis. Since the bending stresses are design-dependent,they can be minimized by judicious engineering. The extent of these effects would have to be determined in a more detailed analysis of a specificwall design. A plasma burn cycle duration T of 0.5 hr is assumed in the present calculations.
1. INTRODUCTION High power output, high thermal efficiency, and long operating life are desirableattributes of a commercialtokamak reactor that place conflicting requirementson the design of the first wall and the selectionof structuralmaterials. Since the heat flux on the first wall varies directly with reactor power and thermal efficiency depends on operating temperature,realistic quantificationof the three-waytrade-off between heat flux, wall temperature,and lifetime Is important In comparingconfiguration and material options. The purpose of this paper is to demonstrate procedures for working backward from desired lifetime,based on various failure mechanisms, to restrictionson heating rate, average temperature, and wall thickness. This approach contrasts with the normal method of selectinga design configurationand operating conditions, and then calculatinglifetimes for various failure mechanisms,such as creep, fatigue, ratcheting,etc. Since the lifetimesobtained in this way are likely to vary widely, the design may be overly conservativein some respects and inadequatein others. It will be assumed here that a design which has the same lifetime for all the failure mechanisms considered Is in some sense an optimum design..
2.
The failure criteria and analysis procedures employed are based on ASME Code Case 1592 for Class 1 Components in Elevated Temperature Service [l] because the code covers the relevant failure mechanisms In a well-documented, systematicmanner. However, it should be recognized that more detailed analyses, specialized to the particularcase of a fusion reactor first wall,would give more realistic estimatesof lifetime and avoid some of the conservatisms built into the Code Case. The proceduresdiscussed here are intended to be useful in the comparisonof candidate structuralmaterials, in the quantificationof design parameter tradeoffs, and in the selectionof an initial design point for further development.
STRESS AND FATIGUE LIFE ANALYSIS
The primary membrane stress op in a thin curved wall is QP = pR/6
(1)
and the cyclic strain range cT produced by the surface heat flux is
(2) where a, k, and v are coefficientof thermal expansion,thermal conductivity,and Poisson's ratio, respectively. The associatedelastic thermal stress oT is aT
*
,
'EE
T
(3)
where E is the elastic modulus. The thermal stress is computed elasticallyfor code purposes even though Eq. (2) may give strains that are well into the plastic range. The
This work was supportedby the U.S. Department of Energy.
153
154
C. K. Youngdahl and D.L. Smith /Stress and lifetime limitations
material properties CL, k, E, and v are all functions of temperature T. The primary membrane stress must not exceed Smt, so that for a fixed value of pR, 6
min
*,5,
,
Tavif
,
900
900
“y”
12;o,
(4)
= pR/S,t
The primary membrane stress limit Smt is the lesser of the time-independent allowable stress limit S, and the time-dependent allowable stress limit St. The limit S, is a function of temperature, yield stress, and ultimate stress, and the limit St depends on design lifetime, temperature, and creep properties. The design lifetime for primary loads will be denoted by L . Long-holdtime fatigue curves such as Fig. TE1430 of Code Case 1592 relate strain range to number of allowable cycles Nd at Various temThe design cyclic lifetime L, is peratures. given by Lc = Nd'l .
(5)
The surface heat flux associated with given values of Lp and L, is therefore
0-
400 W i 9
Smt (T,L ) cT (T,L ) P C
and the design life would be and L,. From the dependence sT on L, it is apparent that mized for a specified design
450
500
(6)
the lesser of L of Smt on L an W will be m t: xi- z life if Lp = L,.
550
600
650
T ‘C PY9’
Fig. 1.
Figure 1 shows maximum surface heat flux as a function of temperature for various lifetimes, using Eq. (6) with Lp = L,. The lifetime data for Type 316 stainless steel were obtained from the Code Case. The product pR is taken to be 0.25 MPa-m; this corresponds to a 0.25 m radius, lithium-cooled duct at 1 MPa pressure or a tube of 0.05 m diameter cooled with pressurized water at 10 MPa.
Maximum surface heat flux as a function of temperature for various design lifetimes for first wall made of Type 316 stainless steel; pR = 0.25 MPa-m.
TW9. 800 6
I I
‘F
900
In00
II00
1200
1300
I
I
I
I
I
1400
7
Figure 2 shows a comparison of candidate structural materials for design lifetimes of 3 x lo4 hrs (c 3 yr) and lo5 hrs (* 10 yr). Materials properties data were obtained from various sources and are summarized elsewhere Although the completeness of the data 121. base varies from material to material and considerable extrapolation or interpretation is required for some of the needed properties, the trend of the results is clear. 3.
RATCHETING AND CREEP ANALYSIS
A convenient format for representing ratcheting information is the Bree Diagram [3] shown in Fig. 3. The vertical axis is the secondary and the horizontal axis is stress ratio the primary stress ratio up/S , with Sy being the temperature-dependent yie I d stress. Design points in region E correspond to purely elastic In regions SI and S2, shakedown to behavior. elastic behavior occurs in the first few cycles. Cyclic plastic strains occur in portions of the oT/sy,
Fig. 2.
Comparison of maximum surface heat fluxes for various structural materials; PR = 0.25 MPa-m.
C K. Youngdahl and D. L. Smith / Stress and lifetime limitations
minimum stress to rupture curvest and Nd and strain range CT are related through long holdtime fatigue curves.
3
2
UT 3
I
0 I
*F@F
Fig. 3.
155
Bree Diagram. Stress regimes on cyclic stress - primary stress plane.
cross-sectionfor design points tn region P; strain-hardeningeffects tend to prevent short term failure in this region, but the design must be checked for fatigue failure. Stress states in the rarchetingregions R1 and R produce incrementaIplastic growth in each c$cle and lead to short-termfailure. Code Case 1592 prescribesprocedures for elasticallycomputingan effective creep stress CJ~%which is shown on Fig. 3 for several values of the ratio o,fS . Long-term creep ratcheting etermined from isochronous strain, which is if stress-straincurves using a stress of 1.25 UC, is limited to an accumulationof 1% over the design lifetime L of the component. Proceduresand criteria for evaluationof creep-fatigueinteractionusing elastic analysis are also provided in the Code Case. The linear damage criterionappropriateto the simplified stress analysis used for the first wall is given by (7) where n is the number of applied cycles, N is the nuaher of design allowable cycles at t4e appropriatetemperatureand strain rate, t is the time duration of the loadfng, and td is the tima to creep rupture at an effective reference stress OR, The latter is given by (up + o&K' oR = smaller of
(8) 1.25 SylR
where K' depends on the material. The recommended value of K' for stainless steel is 0.9. The reference stress aR is related to td through
A useful diagram for the purposes of this study is a plot of surface heat flux W versus wall thickness6, showing the same stress regions as the Bree Diagram. To obtain this modified diagram, the product of coolant pressure and channel radius pR is taken as a fixed value,materialpropertiesare selected at a given temperature,and a design lifetime L is chosen to evaluate long-term failure criteria. Figure 4 shows the modified Bree Diagram for Type 316 stainless steel at 482'C (300'F) for pR = 0.25 MPa - m, correspondingto the reference vaLues of pressure and radius used in Figs. 1 and 2. To protect against short-term failure, the design point must be in the E, S, or P regions. Various long-term effects can be shown on the same diagram. A design lifetime of lo5 hrs was selected,correspondingto 2 x lo5 cycles at 0.5 hr/cycle. To avoid longterm failure from primary loads, the design point must be to the right of the vertical dashed Line, computed from Eq. (4). Using the long holdtime fatigue data of Code Case 1592 to find the allowable cyclic strain range ~~ for the desired cyclic life, Eq. (2) then gives an upper limit to the heat flux at a given wall thickness. The other dashed line on the diagram shows this fatigue limit. The intersectionof the dashed curves at A corresponds to the value shown in Figs. 1 and 2 for stainless steel at the specified temperature and lifetime. The isochronousstress strain curves at 482'C (Fig. T-1800-B3 of Code Case 1592) show that an effectivecreep stress oc of 1.25 S produces less than 0.4% strain in lo5 hrs, go creep-ratchetingis not a factor in the determinationof a design point under these conditions. Similarly,creep is insignificant in creep-fatigueinteractioneffects, although it must be consideredat higher temperatures, as will be shown later. Consequently, the highest allowable heat flux, taking into account both short-termand long-termeffects, is point B on Fig. 4. In Fig. 5, the temperatureis increased to 538*C (1000'F)with the other parameters the same as in Fig. 4. The long hold-time fatigue curve for 316 SS is used as before in constructing the dashed fatigue limit curve on the diagram. Its intersectionat A with the Smt limit on primary stresses again gives the preliminarydesign point shown in Figs. 1 and 2. The creep-ratchatingcurve indicates those design points that correspondto an accumulation of 1% creep-ratchetingstrain in lo5 hrs; the isochronousstress-straindata of Code Case 1592 were used to determine the value of 1.25 ac needed to obtain this curve. The creep fatigue interactioncurve is computed from Eq. (7). Its intersectionwith the creep-ratcheting curve at B is the design point for the given input parameters;i.e., it correspondsto the
156
C.K. Youngdahl and D.L. Smith / Stress and lifetime limitations
the creep-fatigue curve gives the largest heat flux which corresponds to a design point that meets all the failure criteria considered here. 0.6
The maximum values of the design points (labeled B in Figs. 4-6) are plotted in Fig. 7 to show the variation with temperature. The curve shows a significant drop in allowable heat flux with increasing temperature for the range 450-6OO'C. As a point of reference, the surface heat load for a commercial tokamak
0
I
2
3
4
5
6
7
8
8,mm Fig. 4.
Modified Bree Diagram for first wall made of Type 316 stainless steel; T = 482'C, pR = 0.25 MPa-m, L = lo5 hrs. 2
4
5
6
7
6
8an
0.6
0 0
3
I
2
3
4
5
6
1
Fig. 6.
Modified Bree Diagram for first wall made of Type 316 stainless steel; T = 593'C, pR = 0.25 MPa-m, L = lo5 hrs.
Fig. 7.
Maximum surface heat flux based on modified Bree Diagram for first wall made of Type 316 stainless steel; pR = 0.25 MPa-m, L = lo5 hrs.
6
8. IllIll
Fig. 5.
Modified Bree Diagram for first wall made of Type 316 stainless steel; T = 538*C, pR - 0.25 MPa-m, L = lo5 hrs.
largest heat flux which satisfies all the failure criteria. Figure 6 shows results at the still higher temperature of 593'C (1100'F). The Smt curve is moved farther to the right as compared to the previous figure because Smt switches from S, to St in the temperature interval between 538'C and 593'C. The creep-ratcheting and creep-fatigue curves are lower because of the increasing influence of creep effects with temperature. Point B at the highest point of
reactor that operates without a divertor is expected to be 2, 0.3 to 0.6 MW/m2 [2]. Results in Fig. 7 indicate that these heat loads are acceptable for stainless steel at temperatures below Q 45O'C. However, it should again be emphasized that radiation effects have not been incorporated into these results. Only limited data on the effects of radiation on mechanical properties of stainless steel are
C. K. Youngdahl and D. L. Smith / Stress and lifetime limitations
available and they do not generally include the As a reeffects of high helium generation. sult, it is impossible to accurately determine a design life for irradiated material. One can, however, compare trends expected with the baseline data used in the present investigation. Since neutron radiation typically tends to increase both the yield and ultimate tensile strength of annealed stainless steel, the timeindependent allowable stress limit might be expected to increase. The effects of radiation on the time-dependent mechanical properties (creep) have not been sufficiently established to clearly define any variations from the baseline data. Post irradiation fatigue data at modest neutron fluences have indicated relatively small effects of fission reactor radiation on the fatigue life of stainless steel. From general observations of microstructural effects on fatigue behavior, one might predict better fatigue life for radiation hardened materials at low strain ranges. It may also be argued that other environmental effects, e.g., effects of lithium on fatigue properties, may be more detrimental than the radiation effects. In either case, the inherent conservatism incorporated into the code case may be sufficient to allow for these effects. The present analysis provides an estimate of allowable firstwall heat fluxes based on accepted criteria and provides a methodology for comparison of allowable heat fluxes for various candidate structural materials. 4.
CONCLUSIONS
In summary, long holdtime fatigue data and the primary stress limit S can be used to obtain trade-offs between sur "E ace heat flux, temperature, and lifetime, as in Figs. 1 and 2. Based on this information and considerations such as cost, surface properties, compatibility with the coolant, etc., a suitable structural material can be selected and a preliminary design point chosen. Additional failure criteria can then be included in the modified Bree Diagram to derive an improved design point for further, more detailed analysis. The criteria for creep and ratcheting failure used here are based on elastic analysis and are presumably more conservative than an inelastic analysis would require. Consequently, a more detailed analysis should bring point B closer to point A in Figs. 4-6. On the other hand, constraints imposed by the first wall support structure will produce bending stresses to be added to the membrane stress and thus necessitate a larger wall thickness and lower heat flux for a given wall life, The modified version of the Bree diagram proposed here can then be used with improved models of creep, fatigue, ratcheting, and radiation effects to obtain a realistic choice of design parameters.
157
REFERENCES 1.
Code Case 1592 - Class I Components in Elevated Temperature Service, Section III ASME Boiler and Pressure Vessel Code.
2.
D. L. Smith and C. Trachsel, et al., "Fusion Reactor Blanket/Shield Design Study," Argonne National Laboratory and McDonnell Douglas Company, ANL/FPP/79-1 (1979).
3.
J. Bree, J. Strain Analysis, p. 226.
2 (1967)
153-l
57
STRESS AND LIFETIME LIMITATIONSOF FIRST-WALLSTRUCTURALMATERIALS* C.
K.
YOUNGDARL and D. L. SMITH
Argonne National Laboratory,Argonne, Illinois
60439, USA
Proceduresare demonstratedfor working backward from desired lifetime of a fusion reactor first-wallto trade-offswith surface heat flux and temperature,using failure criteria obtained from ASME Code Case 1592. The maximum surface heat flux on a stainless steel firstwall is predicted by the proceduresdevelopedhere for a range of design parametersappropriate to a tokamak fusion power reactor. The remainderof the paper will be divided into two parts: First, lifetime criteria based on the general primary membrane stress limit Smt and long-holdtimefatigue will be used for illustratingtrade-offsbetween heat flux, average temperature,and lifetime and for comparing candidate structuralmaterials. Second, ratchetingand creep criteria will be added using a modified Bree Diagram to refine the design point suggestedby the first step. For purposes of illustration,the first wall will be taken as a thin cylindricalsurface of radius R and thickness6, loaded by an internal coolant pressure p and a surface heat flux w. For this case, the volumetricheat generationis negligiblecompared to the energy depositedon the surface. This configuration is intended to representeither a tube or the front curved surface of a blanket module, Bending stresses caused by constraintof the first wall by its support structureor the remainder of the blanket module will be ignored in the present analysis. Since the bending stresses are design-dependent,they can be minimized by judicious engineering. The extent of these effects would have to be determined in a more detailed analysis of a specificwall design. A plasma burn cycle duration T of 0.5 hr is assumed in the present calculations.
1. INTRODUCTION High power output, high thermal efficiency, and long operating life are desirableattributes of a commercialtokamak reactor that place conflicting requirementson the design of the first wall and the selectionof structuralmaterials. Since the heat flux on the first wall varies directly with reactor power and thermal efficiency depends on operating temperature,realistic quantificationof the three-waytrade-off between heat flux, wall temperature,and lifetime Is important In comparingconfiguration and material options. The purpose of this paper is to demonstrate procedures for working backward from desired lifetime,based on various failure mechanisms, to restrictionson heating rate, average temperature, and wall thickness. This approach contrasts with the normal method of selectinga design configurationand operating conditions, and then calculatinglifetimes for various failure mechanisms,such as creep, fatigue, ratcheting,etc. Since the lifetimesobtained in this way are likely to vary widely, the design may be overly conservativein some respects and inadequatein others. It will be assumed here that a design which has the same lifetime for all the failure mechanisms considered Is in some sense an optimum design..
2.
The failure criteria and analysis procedures employed are based on ASME Code Case 1592 for Class 1 Components in Elevated Temperature Service [l] because the code covers the relevant failure mechanisms In a well-documented, systematicmanner. However, it should be recognized that more detailed analyses, specialized to the particularcase of a fusion reactor first wall,would give more realistic estimatesof lifetime and avoid some of the conservatisms built into the Code Case. The proceduresdiscussed here are intended to be useful in the comparisonof candidate structuralmaterials, in the quantificationof design parameter tradeoffs, and in the selectionof an initial design point for further development.
STRESS AND FATIGUE LIFE ANALYSIS
The primary membrane stress op in a thin curved wall is QP = pR/6
(1)
and the cyclic strain range cT produced by the surface heat flux is
(2) where a, k, and v are coefficientof thermal expansion,thermal conductivity,and Poisson's ratio, respectively. The associatedelastic thermal stress oT is aT
*
,
'EE
T
(3)
where E is the elastic modulus. The thermal stress is computed elasticallyfor code purposes even though Eq. (2) may give strains that are well into the plastic range. The
This work was supportedby the U.S. Department of Energy.
153
154
C. K. Youngdahl and D.L. Smith /Stress and lifetime limitations
material properties CL, k, E, and v are all functions of temperature T. The primary membrane stress must not exceed Smt, so that for a fixed value of pR, 6
min
*,5,
,
Tavif
,
900
900
“y”
12;o,
(4)
= pR/S,t
The primary membrane stress limit Smt is the lesser of the time-independent allowable stress limit S, and the time-dependent allowable stress limit St. The limit S, is a function of temperature, yield stress, and ultimate stress, and the limit St depends on design lifetime, temperature, and creep properties. The design lifetime for primary loads will be denoted by L . Long-holdtime fatigue curves such as Fig. TE1430 of Code Case 1592 relate strain range to number of allowable cycles Nd at Various temThe design cyclic lifetime L, is peratures. given by Lc = Nd'l .
(5)
The surface heat flux associated with given values of Lp and L, is therefore
0-
400 W i 9
Smt (T,L ) cT (T,L ) P C
and the design life would be and L,. From the dependence sT on L, it is apparent that mized for a specified design
450
500
(6)
the lesser of L of Smt on L an W will be m t: xi- z life if Lp = L,.
550
600
650
T ‘C PY9’
Fig. 1.
Figure 1 shows maximum surface heat flux as a function of temperature for various lifetimes, using Eq. (6) with Lp = L,. The lifetime data for Type 316 stainless steel were obtained from the Code Case. The product pR is taken to be 0.25 MPa-m; this corresponds to a 0.25 m radius, lithium-cooled duct at 1 MPa pressure or a tube of 0.05 m diameter cooled with pressurized water at 10 MPa.
Maximum surface heat flux as a function of temperature for various design lifetimes for first wall made of Type 316 stainless steel; pR = 0.25 MPa-m.
TW9. 800 6
I I
‘F
900
In00
II00
1200
1300
I
I
I
I
I
1400
7
Figure 2 shows a comparison of candidate structural materials for design lifetimes of 3 x lo4 hrs (c 3 yr) and lo5 hrs (* 10 yr). Materials properties data were obtained from various sources and are summarized elsewhere Although the completeness of the data 121. base varies from material to material and considerable extrapolation or interpretation is required for some of the needed properties, the trend of the results is clear. 3.
RATCHETING AND CREEP ANALYSIS
A convenient format for representing ratcheting information is the Bree Diagram [3] shown in Fig. 3. The vertical axis is the secondary and the horizontal axis is stress ratio the primary stress ratio up/S , with Sy being the temperature-dependent yie I d stress. Design points in region E correspond to purely elastic In regions SI and S2, shakedown to behavior. elastic behavior occurs in the first few cycles. Cyclic plastic strains occur in portions of the oT/sy,
Fig. 2.
Comparison of maximum surface heat fluxes for various structural materials; PR = 0.25 MPa-m.
C K. Youngdahl and D. L. Smith / Stress and lifetime limitations
minimum stress to rupture curvest and Nd and strain range CT are related through long holdtime fatigue curves.
3
2
UT 3
I
0 I
*F@F
Fig. 3.
155
Bree Diagram. Stress regimes on cyclic stress - primary stress plane.
cross-sectionfor design points tn region P; strain-hardeningeffects tend to prevent short term failure in this region, but the design must be checked for fatigue failure. Stress states in the rarchetingregions R1 and R produce incrementaIplastic growth in each c$cle and lead to short-termfailure. Code Case 1592 prescribesprocedures for elasticallycomputingan effective creep stress CJ~%which is shown on Fig. 3 for several values of the ratio o,fS . Long-term creep ratcheting etermined from isochronous strain, which is if stress-straincurves using a stress of 1.25 UC, is limited to an accumulationof 1% over the design lifetime L of the component. Proceduresand criteria for evaluationof creep-fatigueinteractionusing elastic analysis are also provided in the Code Case. The linear damage criterionappropriateto the simplified stress analysis used for the first wall is given by (7) where n is the number of applied cycles, N is the nuaher of design allowable cycles at t4e appropriatetemperatureand strain rate, t is the time duration of the loadfng, and td is the tima to creep rupture at an effective reference stress OR, The latter is given by (up + o&K' oR = smaller of
(8) 1.25 SylR
where K' depends on the material. The recommended value of K' for stainless steel is 0.9. The reference stress aR is related to td through
A useful diagram for the purposes of this study is a plot of surface heat flux W versus wall thickness6, showing the same stress regions as the Bree Diagram. To obtain this modified diagram, the product of coolant pressure and channel radius pR is taken as a fixed value,materialpropertiesare selected at a given temperature,and a design lifetime L is chosen to evaluate long-term failure criteria. Figure 4 shows the modified Bree Diagram for Type 316 stainless steel at 482'C (300'F) for pR = 0.25 MPa - m, correspondingto the reference vaLues of pressure and radius used in Figs. 1 and 2. To protect against short-term failure, the design point must be in the E, S, or P regions. Various long-term effects can be shown on the same diagram. A design lifetime of lo5 hrs was selected,correspondingto 2 x lo5 cycles at 0.5 hr/cycle. To avoid longterm failure from primary loads, the design point must be to the right of the vertical dashed Line, computed from Eq. (4). Using the long holdtime fatigue data of Code Case 1592 to find the allowable cyclic strain range ~~ for the desired cyclic life, Eq. (2) then gives an upper limit to the heat flux at a given wall thickness. The other dashed line on the diagram shows this fatigue limit. The intersectionof the dashed curves at A corresponds to the value shown in Figs. 1 and 2 for stainless steel at the specified temperature and lifetime. The isochronousstress strain curves at 482'C (Fig. T-1800-B3 of Code Case 1592) show that an effectivecreep stress oc of 1.25 S produces less than 0.4% strain in lo5 hrs, go creep-ratchetingis not a factor in the determinationof a design point under these conditions. Similarly,creep is insignificant in creep-fatigueinteractioneffects, although it must be consideredat higher temperatures, as will be shown later. Consequently, the highest allowable heat flux, taking into account both short-termand long-termeffects, is point B on Fig. 4. In Fig. 5, the temperatureis increased to 538*C (1000'F)with the other parameters the same as in Fig. 4. The long hold-time fatigue curve for 316 SS is used as before in constructing the dashed fatigue limit curve on the diagram. Its intersectionat A with the Smt limit on primary stresses again gives the preliminarydesign point shown in Figs. 1 and 2. The creep-ratchatingcurve indicates those design points that correspondto an accumulation of 1% creep-ratchetingstrain in lo5 hrs; the isochronousstress-straindata of Code Case 1592 were used to determine the value of 1.25 ac needed to obtain this curve. The creep fatigue interactioncurve is computed from Eq. (7). Its intersectionwith the creep-ratcheting curve at B is the design point for the given input parameters;i.e., it correspondsto the
156
C.K. Youngdahl and D.L. Smith / Stress and lifetime limitations
the creep-fatigue curve gives the largest heat flux which corresponds to a design point that meets all the failure criteria considered here. 0.6
The maximum values of the design points (labeled B in Figs. 4-6) are plotted in Fig. 7 to show the variation with temperature. The curve shows a significant drop in allowable heat flux with increasing temperature for the range 450-6OO'C. As a point of reference, the surface heat load for a commercial tokamak
0
I
2
3
4
5
6
7
8
8,mm Fig. 4.
Modified Bree Diagram for first wall made of Type 316 stainless steel; T = 482'C, pR = 0.25 MPa-m, L = lo5 hrs. 2
4
5
6
7
6
8an
0.6
0 0
3
I
2
3
4
5
6
1
Fig. 6.
Modified Bree Diagram for first wall made of Type 316 stainless steel; T = 593'C, pR = 0.25 MPa-m, L = lo5 hrs.
Fig. 7.
Maximum surface heat flux based on modified Bree Diagram for first wall made of Type 316 stainless steel; pR = 0.25 MPa-m, L = lo5 hrs.
6
8. IllIll
Fig. 5.
Modified Bree Diagram for first wall made of Type 316 stainless steel; T = 538*C, pR - 0.25 MPa-m, L = lo5 hrs.
largest heat flux which satisfies all the failure criteria. Figure 6 shows results at the still higher temperature of 593'C (1100'F). The Smt curve is moved farther to the right as compared to the previous figure because Smt switches from S, to St in the temperature interval between 538'C and 593'C. The creep-ratcheting and creep-fatigue curves are lower because of the increasing influence of creep effects with temperature. Point B at the highest point of
reactor that operates without a divertor is expected to be 2, 0.3 to 0.6 MW/m2 [2]. Results in Fig. 7 indicate that these heat loads are acceptable for stainless steel at temperatures below Q 45O'C. However, it should again be emphasized that radiation effects have not been incorporated into these results. Only limited data on the effects of radiation on mechanical properties of stainless steel are
C. K. Youngdahl and D. L. Smith / Stress and lifetime limitations
available and they do not generally include the As a reeffects of high helium generation. sult, it is impossible to accurately determine a design life for irradiated material. One can, however, compare trends expected with the baseline data used in the present investigation. Since neutron radiation typically tends to increase both the yield and ultimate tensile strength of annealed stainless steel, the timeindependent allowable stress limit might be expected to increase. The effects of radiation on the time-dependent mechanical properties (creep) have not been sufficiently established to clearly define any variations from the baseline data. Post irradiation fatigue data at modest neutron fluences have indicated relatively small effects of fission reactor radiation on the fatigue life of stainless steel. From general observations of microstructural effects on fatigue behavior, one might predict better fatigue life for radiation hardened materials at low strain ranges. It may also be argued that other environmental effects, e.g., effects of lithium on fatigue properties, may be more detrimental than the radiation effects. In either case, the inherent conservatism incorporated into the code case may be sufficient to allow for these effects. The present analysis provides an estimate of allowable firstwall heat fluxes based on accepted criteria and provides a methodology for comparison of allowable heat fluxes for various candidate structural materials. 4.
CONCLUSIONS
In summary, long holdtime fatigue data and the primary stress limit S can be used to obtain trade-offs between sur "E ace heat flux, temperature, and lifetime, as in Figs. 1 and 2. Based on this information and considerations such as cost, surface properties, compatibility with the coolant, etc., a suitable structural material can be selected and a preliminary design point chosen. Additional failure criteria can then be included in the modified Bree Diagram to derive an improved design point for further, more detailed analysis. The criteria for creep and ratcheting failure used here are based on elastic analysis and are presumably more conservative than an inelastic analysis would require. Consequently, a more detailed analysis should bring point B closer to point A in Figs. 4-6. On the other hand, constraints imposed by the first wall support structure will produce bending stresses to be added to the membrane stress and thus necessitate a larger wall thickness and lower heat flux for a given wall life, The modified version of the Bree diagram proposed here can then be used with improved models of creep, fatigue, ratcheting, and radiation effects to obtain a realistic choice of design parameters.
157
REFERENCES 1.
Code Case 1592 - Class I Components in Elevated Temperature Service, Section III ASME Boiler and Pressure Vessel Code.
2.
D. L. Smith and C. Trachsel, et al., "Fusion Reactor Blanket/Shield Design Study," Argonne National Laboratory and McDonnell Douglas Company, ANL/FPP/79-1 (1979).
3.
J. Bree, J. Strain Analysis, p. 226.
2 (1967)