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Design and analysis of LMFBR structures
Nuclear Engineering and Design 69 (1982) 359-363 North-Holland Publishing Company
359
DESIGN AND ANALYSIS OF LMFBR STRUCTURES * J.L. P I C O U Novatorne Industries, 20 av. Edouard Herriot, F-92350 Le Plessis Robinson, France
In view of the imperatives concerning the LMFBR structure behaviour, the choice of operating conditions is quite limited. In this sense, some considerations regarding materials and manufacturing, stress analysis and design by test will be given. Much has been realized, but efforts are still necessary in order to attain the final goal.
1. Introduction The development of safe rules for the structural design at elevated temperature has required a huge amount of work. Understanding the right parameters governing the various damages, deriving appropriate criteria and determining the corresponding characteristics for each material, the effects of multiaxiality etc... have occupied a large number of laboratories and industrial organizations. The evolution that took place in the rules of analysis between the CC 1331.4 and the CC N 47.18 reflects the extensive work carried out by the ASME during the last fifteen years. However much remains to be done for a more comprehensive understanding; indeed the industrial implementation of such rules allows us to draw some lessons from their evolution, and can sensitize scientists and technicians to the problems still alive and to the necessary developments. It is not our intention to examine here all problems in detail, but certain general aspects specific to the NSSS components must at least be mentioned. I should like to apologize for giving preference during this presentation to my own experience of the French concept.
2. General data 2.1. Temperatures
It is worth-noting that all liquid metal fast breeder reactors operate under nearly the same thermal condi* Invited lecture of Division E, presented to the Plenary Session of SMiRT-6, Paris, France, August 19, 1981.
tions. In fact, from the main parameters, such as the nominal fuel cladding temperature, the steam characteristics, the steam generator tubing heat transfer efficiency, it can be shown, by optimizing the thermal conditions of the primary and secondary circuits, that the freedom is rather small. This is illustrated in table I, where are given, for the present main reactors, the core outlet temperature T~c and the temperature increase ATc through the core. Both of them are essential values because they condition the structural design and analysis process. These two values are in fact bound together by rules of the thermomechanical analysis, the first one by the creep/relaxation effects, the second one by the fatigue damage during scram; however, this binding is a complexe one, and it does not appear possible to answer, as far as the general behaviour of the structures is
Table I Core outlet temperatue (Tsc) and temperature increase through the core (ATc) for the present main reactors Reactor
Electrical power (MWe)
~c (°C)
AT~ (°C)
Phenix SPX Monju PFR CDFR Clinch river BN 600 BN 1600 SNR 300 SNR 2
250 1200 300 270 1200 380 600 1600 327 1460
560 545 529 562 540 535 550 550 546 540
160 150 132 162 170 147 170 200 169 150
0 0 2 9 - 5 4 9 3 / 8 2 / 0 0 0 0 - 0 0 0 0 / $ 0 2 . 7 5 © 1982 N o r t h - H o l l a n d
360
J.L. fiicou / Design and ana(v,~is q[ I.MFBR ,structure~"
concerned, whether modifying ~ . or A T~. is the preferable course of action. The answer is subordinate to the structure considered, to the choice of material, and to the organization of the fluid circulation, in particular for the pool concept. The situation is therefore such that acquired experience is of prime importance. Taking into account that, in other respects, we avail of limited modifications of the general operating conditions of the power plant, this experience leads to reduced design possibilities, and particularly those concerning the thermal conditions. 2.2. Materials and manufacturing
Because of the creep/relaxation effects, the material characteristics used in the structural analysis, are numerous and need quite a long time for their determination. French practice adds moreover to the data used in the CC N 47 rules, further data corresponding to rules, discussed in this SMiRT, related to a non-significant creep criterion, and to the verification of absence of ratchetting. Taking the admissible delay for the test into account, it is most often excluded to reproduce in the laboratory the strain and stress corresponding to the real structures; for instance, these structures are practically subjected to primary creep only. The extrapolation procedures have therefore to be established with care and adequate conservatism. On the other hand, the strains induced during fabrication can, if not removed, lead to a loss of ductility during operation at high temperature; they must be limited and controlled, and their influence on material characteristics have to be experimentally verified. The problems connected to welds are particularly important, because the size and shape of the structures are such that it is almost impossible to avoid that most of the welds undergo the same set of loadings as the basic material. In such a case, it is essential to verify the compatibility of the characteristics of the welds, as manufactured, and those of the basic material. Simply applying a criterion limiting the maximum strain as compared to that of the basic material does not seem sufficient (it can be noted that such a limit is in practice suitable only for use with non-linear analysis, because elastic analysis does not in general allow a precise estimation of strains). Further fundamental verifications must be performed, particularly connected with the fatigue or creep-fatigue damage, or with crack propagation. These tests are made complexe by the importance of the various parameters of the welding itself, such as
the weld geometry (weld surface, interface between weld and basic material) or the thermomechanical properties of molten material, heat affected zone, and basic material. Finally a correct alignment is necessary for satisfactory welding and stress distribution. Because of the thinness of the structures, this leads to severe manufacturing tolerances. Owing to limited possibilities of laboratories, the designer has little freedom in his choice of material, and once this choice is made, a strict application of verified manufacturing procedures, particularly for welding, is essential. Only small adjustments will be allowed, and in case of difficulty, it will be necessary to re-design the structure, or modify the operating conditions, without significant progress resulting from an important change of the material general data within a period compatible with a construction schedule.
3. Stress analysis 3.1. Non-significant creep
In fact, many structures of LMFBR are in contact with cold sodium at temperatures far below fhe temperature' limit where the effects of time dependance are significant, and exceed this limit only during very few events or hypothetical accidents. It is therefore useful to take this fact into account by a criterion which allows to apply customary rules, which could be seen as classical, for thermomechanical analysis where the effects of time are not considered. It is possible to formulate such a criterion as a summation of functions of strain, time, and temperature for each event. However, this kind of practice would not be very efficient, because the strain still has to be evaluated which could be a rather tricky job. If the number of events in the creep domain is small, which is usually the case, it is possible to eliminate the strain by deriving a criterion from a suitably over-estimated value of the creep strain, obtaining a function of the duration and temperature only. Thus, the condition is very easy to handle and considerably simplifies the thermomechanical analysis of a very important number of structures. Its drawback is that it is necessarily severe and has to be established for each alloy and product form. Such a criterion was set up by the CEA for materials used in the French design, and has been inserted into the French rules for LMFBR structure analysis. A similar option is given by the test 4 of CC N 47, which is a means to satisfy strain limits with the elastic analysis.
J.L. Picou / Design and ana(vsis of LMFBR structures 3.2. Primary stresses The LMFBR structures will in general be subjected to large thermal loading, particularly during scram, and their thickness has to be reduced as much as possible to minimize thermal stresses. This constraint balances the advantage of lack of pressure, specially during accidental events such as earthquake or sodium-water reaction. Finally, the structure thickness and stiffness wil be generally determined by the primary stress limits, considering all the levels of loadings, and not only level B events. The thermal loadings will be made acceptable by small design changes, by structural devices related to heat transfer such as thermal baffle or mixing device, or by adjustement of operating and controlling conditions. The use of the primary stress rules, as given by the CC N 47, to prevent creep-plastic tensile instability and gross deformation, presents no particular difficulties. It could be noted that the creep induced stress redistribution is not so complete as that due to perfect plasticity, and a correction, related to the relative importance of secondary stresses, can be made. Such a correction has been introduced in the French rules. However, two aspects must be pointed out: (1) On one hand, the determination of the primary part of the stress in a very hyperstatic structure as a large welded box, is not easy. The use of the reference stress method, related to the limit analysis, can sometimes be helpful for the demonstration. (2) On the other hand, the verification with respect to buckling is of prime importance for the LMFBR
361
structures. For instance, a circumferential defect of the order of the thickness on a few meters in a large vessel, can change very significantly the local shell curvature, and can even change its sign. It is then false to consider the behaviour of the reel structure as similar to the behaviour of a perfect structure. We are in fact dealing with another structure with a quite different buckling behaviour. This implies non only very severe geometry tolerances during fabrication and erection, but can require verification of the evolution of the creep or ratchetting deformations, during operation, in order to avoid a situation where the margin with respect to buckling damage would get out of control. Significant progress has been recently made in this field, for determining the loading, specially during earthquake taking the fluid-structure interaction into account, as well as for assessing the behaviour of. the component itself. Several communications related to this problem are given during the present SMiRT. Table2 gives some exemples of comparison between theoretical and test results on double curvature shell, which finally has been stiffened. Nevertheless, much has still to be done to reach a thorough understanding of this phenomenon and to elaborate simple methods for its treatment.
3.3. Cyclic loadings The complexity of the structural behaviour under cyclic loading in the creep domain is an obstacle to elaborate simplified methods based on the elastic analy-
Table 2 Buckling-tests on torispherical structure models Experimental results
Computed results *
Models: Unstiffened Ni A1 Stiffened Ni (annealed) Stiffened structure (part of the structure to scale) 304 SS
1
2
3
3000 mb ~ 850 mb
950 mb ~ 780 mb
530mb ~250mb 1350/1700mb
20/24 bar
9.5 bar
* 1 - Axisymetrical computation on the ideal structure 2 - Elastoplastic bifurcation computation with defects 3 - Elastoplastic large displacement computation with defects
6/8 bar
~570mb (uncertain) 250mb 1600mb
--6.5 bar (buckling not net)
362
J.L. Picou / Design and analysis of LMFBR structures
sis. It is already quite a feat to have set up the CC N 47 rules. However, application of such rule is not without problems. For instance, the proposed method to estimate the thermal ratchet, based on the BREE diagram, completed by the important work of O'DONNEL and POROWSKI, is not convenient in the case of three-dimensional structures. ROCHE has proposed a method, based on bi-axial experimental results, which seems particularly promising, because it allows an easy and industrial verification with respect to the progressive deformation. It is clear that the method for estimating the strain range in the creep-fatigue elastic analysis, based on the work of CAMPBELL, SEVERUD and HOUTMAN, permits, through a rather arduous procedure, a sufficient evaluation of the considered structure behaviour. Because of the relative importance of the thermal loading, the value of the strain range, calculated by this method, is often a very good approximation of the real range. The conservatism, often extensive, of the method, resides mainly in the establishment of the corresponding fatigue curves, which assure the saturation of the material behaviour and of the creep/relaxation effect between cycles. A more adequate definition of these curves would be appreciated. Because of the necessary conservatism, inherent in simplified methods, it might seem a solution to take refuge in non-linear analysis. But then other difficulties arise, essentialy related to the knowledge of adequat constitutive equations representing the material behaviour, and their good coherence with the behaviour of the welded joints. Besides the particular problems concerning the computational methods and the modelisation of large three-dimensional structures, for which an approximation using shell theory is quite inadequate at the boundaries, it is clear that kinematic bi-linear approximation does not predict the real behaviour of the structures. Then a few models among the large number proposed, must be chosen, their characteristic parameters defined from simple tests, after which computed results in complexe situations have to be compared with experimental results. This comparison is in most cases rather disappointing. Furthermore the dispersion in the behaviour of different samples of the same material is a difficulty for the generalization of a simpel model, based on a few characteristic parameters. In the field, the studies take a long time, and must be carefully organized and limited to a few types of material and to restricted loading conditions. The inelastic analysis must then be used with prudence, involving a certain conservatism, in a calculation procedure leading to ob-
viously overestimated strains or stresses, or in the criteria used for the comparison. Many studies are going on throughout the world on this subject, it is beyond doubt that we will succeed to correctly predict, by certainly complicated computations, the strain history of a complexe structure undergoing any loading. However, many tests on representative samples are necessary before general admittance of these methods. In view of the foreseeable difficulties for running this kind of approach during industrial study of power plant components, we dare hope that these methods will be only a step towards the development and finalizing of more accurate simplified methods based on linear analysis.
4. Design by test It can happen that the way through the labryrinth of rules and computations does not succeed. A typical exemple is given by the verification of valve design; the complexity of the geometry, of the structure (because of the stelhting of some zones), and of the loadings, is particularly problematical for the stress-staff. Testing is then Often the more conclusive manner to prove the design adequacy. I should like to quote very briefly here the work done at INTERATOM by KASTL, R Z E Z O N K A and EBSEN on SNR 300 valves. The two-dimensional computations using elastic analysis having shown no capability to give conclusive results on fatigue damage, and a non-linear three-dimensional analysis seeming too difficult and not secure, it has been decided to test 6 valves with a sodium loop allowing thermal shocks between two temperature levels. Because of the limited possibilities of the loop, a preliminary study, conducted from simplified thermomechanical considerations, was made in order to define testing conditons, representative as far as possible, of the operating conditions of SNR 300. This preliminary study took into account, among other things, the difference between the heat exchange coefficients, related to the flow rate, and the temperature levels. This exercise led to define two sets of tests: (1) A first set corresponds to two types of loadings, different by the loading sequence, each one applied to two valves (twice two tests), and reproduces in the loop the real operating conditions in reactor, with a multiplying factor of 3 on the number of events, in accordance with ASME-code (Sec. III, Div. 1, Appendix 2), (2) A second set of two tests corresponds to extreme overloading conditions, in order to obtain an estimation
J.L. Picou / Design and analysis of LMFBR structures
of the ultimate behaviour of the valves. These extreme conditions gave a fatigue damage ratio of about 500, computed by the method previously used. The examination of the 4 valves of the first set of tests showed some weak surface crack indications, mainly at the corner of the seal and at the interface between stellite and housing. An overestimation of the depth of these cracks was 0.2 to 0.3 mm. It could be noted that the crack indications appeared for a number of events higher than the number corresponding to real operation in SNR 300, that is without the factor of 3, and that they influence neither the function nor the integrity of the valve. The most damaged valve of these four was subsequently tested using a dynamic hydraulic pressure up to 320 bar. The damage of the other two valves after overloading tests was obviously higher (deeper cracks), but the function and tightness were ensured at all times. It is evident that many lessons can be drawn from such tests for improving the design or computation methods. Testing is unfortunately feasible to scale for particular components only.
5. Conclusion Because of the importance of previous experience, and within a few fundamental constraints, the designer
363
disposes, in the design of LMFBR components, of a limited freedom on the load control as well as on the choice of materials and manufacturing procedures. The evolution of the basic choices, and of the general conception, is rather slow, governed by the progress in our knowledge of the data for the analysis, and by our capacity to foresee the overall behaviour of the structure, that is taking into account the manufacturing, welding, and analysis methods. This knowledge is growing, in the numerical methods and in the field of technology. However, the matter is difficult to handle since a theory is really valid only if it is extensively cross-checked by experimental results. This continous experimental verification, although long to implement, is essential. On the other hand, the methods become more and more sophisticated, and could become remote from industrial practice. In spite of the complexity of the phenomena, it is worth keeping in mind the development of simplified methods, even if they correspond to several procedures, each valid only within narrow, but well defined, limits. The road is hard, but it is only through this way that we will gain in cost, reliability, and safety. I have no doubt that these efforts will be crowned with success.
359
DESIGN AND ANALYSIS OF LMFBR STRUCTURES * J.L. P I C O U Novatorne Industries, 20 av. Edouard Herriot, F-92350 Le Plessis Robinson, France
In view of the imperatives concerning the LMFBR structure behaviour, the choice of operating conditions is quite limited. In this sense, some considerations regarding materials and manufacturing, stress analysis and design by test will be given. Much has been realized, but efforts are still necessary in order to attain the final goal.
1. Introduction The development of safe rules for the structural design at elevated temperature has required a huge amount of work. Understanding the right parameters governing the various damages, deriving appropriate criteria and determining the corresponding characteristics for each material, the effects of multiaxiality etc... have occupied a large number of laboratories and industrial organizations. The evolution that took place in the rules of analysis between the CC 1331.4 and the CC N 47.18 reflects the extensive work carried out by the ASME during the last fifteen years. However much remains to be done for a more comprehensive understanding; indeed the industrial implementation of such rules allows us to draw some lessons from their evolution, and can sensitize scientists and technicians to the problems still alive and to the necessary developments. It is not our intention to examine here all problems in detail, but certain general aspects specific to the NSSS components must at least be mentioned. I should like to apologize for giving preference during this presentation to my own experience of the French concept.
2. General data 2.1. Temperatures
It is worth-noting that all liquid metal fast breeder reactors operate under nearly the same thermal condi* Invited lecture of Division E, presented to the Plenary Session of SMiRT-6, Paris, France, August 19, 1981.
tions. In fact, from the main parameters, such as the nominal fuel cladding temperature, the steam characteristics, the steam generator tubing heat transfer efficiency, it can be shown, by optimizing the thermal conditions of the primary and secondary circuits, that the freedom is rather small. This is illustrated in table I, where are given, for the present main reactors, the core outlet temperature T~c and the temperature increase ATc through the core. Both of them are essential values because they condition the structural design and analysis process. These two values are in fact bound together by rules of the thermomechanical analysis, the first one by the creep/relaxation effects, the second one by the fatigue damage during scram; however, this binding is a complexe one, and it does not appear possible to answer, as far as the general behaviour of the structures is
Table I Core outlet temperatue (Tsc) and temperature increase through the core (ATc) for the present main reactors Reactor
Electrical power (MWe)
~c (°C)
AT~ (°C)
Phenix SPX Monju PFR CDFR Clinch river BN 600 BN 1600 SNR 300 SNR 2
250 1200 300 270 1200 380 600 1600 327 1460
560 545 529 562 540 535 550 550 546 540
160 150 132 162 170 147 170 200 169 150
0 0 2 9 - 5 4 9 3 / 8 2 / 0 0 0 0 - 0 0 0 0 / $ 0 2 . 7 5 © 1982 N o r t h - H o l l a n d
360
J.L. fiicou / Design and ana(v,~is q[ I.MFBR ,structure~"
concerned, whether modifying ~ . or A T~. is the preferable course of action. The answer is subordinate to the structure considered, to the choice of material, and to the organization of the fluid circulation, in particular for the pool concept. The situation is therefore such that acquired experience is of prime importance. Taking into account that, in other respects, we avail of limited modifications of the general operating conditions of the power plant, this experience leads to reduced design possibilities, and particularly those concerning the thermal conditions. 2.2. Materials and manufacturing
Because of the creep/relaxation effects, the material characteristics used in the structural analysis, are numerous and need quite a long time for their determination. French practice adds moreover to the data used in the CC N 47 rules, further data corresponding to rules, discussed in this SMiRT, related to a non-significant creep criterion, and to the verification of absence of ratchetting. Taking the admissible delay for the test into account, it is most often excluded to reproduce in the laboratory the strain and stress corresponding to the real structures; for instance, these structures are practically subjected to primary creep only. The extrapolation procedures have therefore to be established with care and adequate conservatism. On the other hand, the strains induced during fabrication can, if not removed, lead to a loss of ductility during operation at high temperature; they must be limited and controlled, and their influence on material characteristics have to be experimentally verified. The problems connected to welds are particularly important, because the size and shape of the structures are such that it is almost impossible to avoid that most of the welds undergo the same set of loadings as the basic material. In such a case, it is essential to verify the compatibility of the characteristics of the welds, as manufactured, and those of the basic material. Simply applying a criterion limiting the maximum strain as compared to that of the basic material does not seem sufficient (it can be noted that such a limit is in practice suitable only for use with non-linear analysis, because elastic analysis does not in general allow a precise estimation of strains). Further fundamental verifications must be performed, particularly connected with the fatigue or creep-fatigue damage, or with crack propagation. These tests are made complexe by the importance of the various parameters of the welding itself, such as
the weld geometry (weld surface, interface between weld and basic material) or the thermomechanical properties of molten material, heat affected zone, and basic material. Finally a correct alignment is necessary for satisfactory welding and stress distribution. Because of the thinness of the structures, this leads to severe manufacturing tolerances. Owing to limited possibilities of laboratories, the designer has little freedom in his choice of material, and once this choice is made, a strict application of verified manufacturing procedures, particularly for welding, is essential. Only small adjustments will be allowed, and in case of difficulty, it will be necessary to re-design the structure, or modify the operating conditions, without significant progress resulting from an important change of the material general data within a period compatible with a construction schedule.
3. Stress analysis 3.1. Non-significant creep
In fact, many structures of LMFBR are in contact with cold sodium at temperatures far below fhe temperature' limit where the effects of time dependance are significant, and exceed this limit only during very few events or hypothetical accidents. It is therefore useful to take this fact into account by a criterion which allows to apply customary rules, which could be seen as classical, for thermomechanical analysis where the effects of time are not considered. It is possible to formulate such a criterion as a summation of functions of strain, time, and temperature for each event. However, this kind of practice would not be very efficient, because the strain still has to be evaluated which could be a rather tricky job. If the number of events in the creep domain is small, which is usually the case, it is possible to eliminate the strain by deriving a criterion from a suitably over-estimated value of the creep strain, obtaining a function of the duration and temperature only. Thus, the condition is very easy to handle and considerably simplifies the thermomechanical analysis of a very important number of structures. Its drawback is that it is necessarily severe and has to be established for each alloy and product form. Such a criterion was set up by the CEA for materials used in the French design, and has been inserted into the French rules for LMFBR structure analysis. A similar option is given by the test 4 of CC N 47, which is a means to satisfy strain limits with the elastic analysis.
J.L. Picou / Design and ana(vsis of LMFBR structures 3.2. Primary stresses The LMFBR structures will in general be subjected to large thermal loading, particularly during scram, and their thickness has to be reduced as much as possible to minimize thermal stresses. This constraint balances the advantage of lack of pressure, specially during accidental events such as earthquake or sodium-water reaction. Finally, the structure thickness and stiffness wil be generally determined by the primary stress limits, considering all the levels of loadings, and not only level B events. The thermal loadings will be made acceptable by small design changes, by structural devices related to heat transfer such as thermal baffle or mixing device, or by adjustement of operating and controlling conditions. The use of the primary stress rules, as given by the CC N 47, to prevent creep-plastic tensile instability and gross deformation, presents no particular difficulties. It could be noted that the creep induced stress redistribution is not so complete as that due to perfect plasticity, and a correction, related to the relative importance of secondary stresses, can be made. Such a correction has been introduced in the French rules. However, two aspects must be pointed out: (1) On one hand, the determination of the primary part of the stress in a very hyperstatic structure as a large welded box, is not easy. The use of the reference stress method, related to the limit analysis, can sometimes be helpful for the demonstration. (2) On the other hand, the verification with respect to buckling is of prime importance for the LMFBR
361
structures. For instance, a circumferential defect of the order of the thickness on a few meters in a large vessel, can change very significantly the local shell curvature, and can even change its sign. It is then false to consider the behaviour of the reel structure as similar to the behaviour of a perfect structure. We are in fact dealing with another structure with a quite different buckling behaviour. This implies non only very severe geometry tolerances during fabrication and erection, but can require verification of the evolution of the creep or ratchetting deformations, during operation, in order to avoid a situation where the margin with respect to buckling damage would get out of control. Significant progress has been recently made in this field, for determining the loading, specially during earthquake taking the fluid-structure interaction into account, as well as for assessing the behaviour of. the component itself. Several communications related to this problem are given during the present SMiRT. Table2 gives some exemples of comparison between theoretical and test results on double curvature shell, which finally has been stiffened. Nevertheless, much has still to be done to reach a thorough understanding of this phenomenon and to elaborate simple methods for its treatment.
3.3. Cyclic loadings The complexity of the structural behaviour under cyclic loading in the creep domain is an obstacle to elaborate simplified methods based on the elastic analy-
Table 2 Buckling-tests on torispherical structure models Experimental results
Computed results *
Models: Unstiffened Ni A1 Stiffened Ni (annealed) Stiffened structure (part of the structure to scale) 304 SS
1
2
3
3000 mb ~ 850 mb
950 mb ~ 780 mb
530mb ~250mb 1350/1700mb
20/24 bar
9.5 bar
* 1 - Axisymetrical computation on the ideal structure 2 - Elastoplastic bifurcation computation with defects 3 - Elastoplastic large displacement computation with defects
6/8 bar
~570mb (uncertain) 250mb 1600mb
--6.5 bar (buckling not net)
362
J.L. Picou / Design and analysis of LMFBR structures
sis. It is already quite a feat to have set up the CC N 47 rules. However, application of such rule is not without problems. For instance, the proposed method to estimate the thermal ratchet, based on the BREE diagram, completed by the important work of O'DONNEL and POROWSKI, is not convenient in the case of three-dimensional structures. ROCHE has proposed a method, based on bi-axial experimental results, which seems particularly promising, because it allows an easy and industrial verification with respect to the progressive deformation. It is clear that the method for estimating the strain range in the creep-fatigue elastic analysis, based on the work of CAMPBELL, SEVERUD and HOUTMAN, permits, through a rather arduous procedure, a sufficient evaluation of the considered structure behaviour. Because of the relative importance of the thermal loading, the value of the strain range, calculated by this method, is often a very good approximation of the real range. The conservatism, often extensive, of the method, resides mainly in the establishment of the corresponding fatigue curves, which assure the saturation of the material behaviour and of the creep/relaxation effect between cycles. A more adequate definition of these curves would be appreciated. Because of the necessary conservatism, inherent in simplified methods, it might seem a solution to take refuge in non-linear analysis. But then other difficulties arise, essentialy related to the knowledge of adequat constitutive equations representing the material behaviour, and their good coherence with the behaviour of the welded joints. Besides the particular problems concerning the computational methods and the modelisation of large three-dimensional structures, for which an approximation using shell theory is quite inadequate at the boundaries, it is clear that kinematic bi-linear approximation does not predict the real behaviour of the structures. Then a few models among the large number proposed, must be chosen, their characteristic parameters defined from simple tests, after which computed results in complexe situations have to be compared with experimental results. This comparison is in most cases rather disappointing. Furthermore the dispersion in the behaviour of different samples of the same material is a difficulty for the generalization of a simpel model, based on a few characteristic parameters. In the field, the studies take a long time, and must be carefully organized and limited to a few types of material and to restricted loading conditions. The inelastic analysis must then be used with prudence, involving a certain conservatism, in a calculation procedure leading to ob-
viously overestimated strains or stresses, or in the criteria used for the comparison. Many studies are going on throughout the world on this subject, it is beyond doubt that we will succeed to correctly predict, by certainly complicated computations, the strain history of a complexe structure undergoing any loading. However, many tests on representative samples are necessary before general admittance of these methods. In view of the foreseeable difficulties for running this kind of approach during industrial study of power plant components, we dare hope that these methods will be only a step towards the development and finalizing of more accurate simplified methods based on linear analysis.
4. Design by test It can happen that the way through the labryrinth of rules and computations does not succeed. A typical exemple is given by the verification of valve design; the complexity of the geometry, of the structure (because of the stelhting of some zones), and of the loadings, is particularly problematical for the stress-staff. Testing is then Often the more conclusive manner to prove the design adequacy. I should like to quote very briefly here the work done at INTERATOM by KASTL, R Z E Z O N K A and EBSEN on SNR 300 valves. The two-dimensional computations using elastic analysis having shown no capability to give conclusive results on fatigue damage, and a non-linear three-dimensional analysis seeming too difficult and not secure, it has been decided to test 6 valves with a sodium loop allowing thermal shocks between two temperature levels. Because of the limited possibilities of the loop, a preliminary study, conducted from simplified thermomechanical considerations, was made in order to define testing conditons, representative as far as possible, of the operating conditions of SNR 300. This preliminary study took into account, among other things, the difference between the heat exchange coefficients, related to the flow rate, and the temperature levels. This exercise led to define two sets of tests: (1) A first set corresponds to two types of loadings, different by the loading sequence, each one applied to two valves (twice two tests), and reproduces in the loop the real operating conditions in reactor, with a multiplying factor of 3 on the number of events, in accordance with ASME-code (Sec. III, Div. 1, Appendix 2), (2) A second set of two tests corresponds to extreme overloading conditions, in order to obtain an estimation
J.L. Picou / Design and analysis of LMFBR structures
of the ultimate behaviour of the valves. These extreme conditions gave a fatigue damage ratio of about 500, computed by the method previously used. The examination of the 4 valves of the first set of tests showed some weak surface crack indications, mainly at the corner of the seal and at the interface between stellite and housing. An overestimation of the depth of these cracks was 0.2 to 0.3 mm. It could be noted that the crack indications appeared for a number of events higher than the number corresponding to real operation in SNR 300, that is without the factor of 3, and that they influence neither the function nor the integrity of the valve. The most damaged valve of these four was subsequently tested using a dynamic hydraulic pressure up to 320 bar. The damage of the other two valves after overloading tests was obviously higher (deeper cracks), but the function and tightness were ensured at all times. It is evident that many lessons can be drawn from such tests for improving the design or computation methods. Testing is unfortunately feasible to scale for particular components only.
5. Conclusion Because of the importance of previous experience, and within a few fundamental constraints, the designer
363
disposes, in the design of LMFBR components, of a limited freedom on the load control as well as on the choice of materials and manufacturing procedures. The evolution of the basic choices, and of the general conception, is rather slow, governed by the progress in our knowledge of the data for the analysis, and by our capacity to foresee the overall behaviour of the structure, that is taking into account the manufacturing, welding, and analysis methods. This knowledge is growing, in the numerical methods and in the field of technology. However, the matter is difficult to handle since a theory is really valid only if it is extensively cross-checked by experimental results. This continous experimental verification, although long to implement, is essential. On the other hand, the methods become more and more sophisticated, and could become remote from industrial practice. In spite of the complexity of the phenomena, it is worth keeping in mind the development of simplified methods, even if they correspond to several procedures, each valid only within narrow, but well defined, limits. The road is hard, but it is only through this way that we will gain in cost, reliability, and safety. I have no doubt that these efforts will be crowned with success.