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Design and life assessment of first wall components
ELSEVIER
Fusion Engineering and Design 27 (1995) 210-215
Fusion Engineering and Design
Design and life assessment of first wall components E. Diegele, D. Munz, G. Rizzi Association KfK-EURATOM, Kernforschungszentrum Karlsruhe, Institut fiir Materialforschung II, P.O. Box 3640, D-76021 Karlsruhe, Germany
Abstract
The first wall (FW) of a tokamak fusion reactor is subjected to periodically changing large heat fluxes. Water-cooled FW panels made from austenitic SS 316 L steel are analyzed. First, life predictions for initially defect-free components, obtained by applying design code rules, are compared with experimental results. It is shown that designing by code is very conservative under thermal fatigue. Secondly, a fracture mechanical analysis of the I T E R - C D A FW is presented using linear-elastic and elastic-plastic approaches. Fatigue growth of pre-existing cracks is considered. Problems of FW composite structures of dissimilar materials are addressed. The mismatch in the thermal expansion coefficients give rise to residual stresses during the joining process, and leads to a jump in the stress at the interface. Moreover, different elastic properties result in stress singularities at free boundaries or at interface corners.
1. Introduction
The first wall (FW) of a tokamak fusion reactor is subjected to periodically changing large heat fluxes. The severe loading conditions imply restrictions on FW concepts. The selection of candidate structural materials, of cooling media, of the range of operating temperatures of design implementations in geometry terms as well as the problems of protection tiles and/or limiters are strongly interrelated. In this paper, a predominantly low temperature concept (reference design during I T E R - C D A ) is investigated. Austenitic steel (SS 316 L) is used as the structural material for the component, which is actively cooled (cooling tubes in the FW) by water at low pressure and low temperatures of 60-100 °C. Also, on the plasma-facing surface, it is completely covered by protective graphite (CFC) tiles. Elsevier Science S.A. SSDI 0920-3796(94)00333-5
For structural analyses of 316 stainless steel, extensive material data and experience are available and documented in several design frameworks. Thus, transient thermomechanical calculations and "design by code analysis" of the bulk material can be performed in a straightforward manner. For lifetime assessment, the database is also quite good (such as fatigue curves under various conditions), and a lot of experience has been gained in material and damage modelling. Moreover, within the European Community (EC), there are several programmes on FW mock-ups to verify life assessment, as well as to develop and evaluate manufacturing processes. Hence, life evaluation of SS 316 makes sense. However, as a result of the lack of fatigue data at design-relevant strain levels and the lack of crack-growth measurements--as well as because of the uncertainty regarding the applicability of existing material data for vanadium alloys or C u - C r - Z r al-
E. Diegele et al./ Fusion Engineering and Design 27 (I995) 210-215
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211
dent (such as progressive accumulation of deformation, fatigue crack growth); (structural) analysis, including qualification of stress types. A schematic diagram demonstrating the interaction of design and life assessment is shown in Fig. 1. For the past 2 years, there have been several design approaches used for "shield blankets" or for "advanced blanket concepts", using different materials, different cooling media and different FW concepts (integrated or separated). In this paper, some of these concepts are analyzed. However, concepts will not be discussed on the basis of code rule assessment. Each design has to undergo a special optimization procedure (varying the sizes of radii of curvature, diameter and pitch of cooling tubes, thickness of layers, etc.). At present, the different approaches are at very different levels with respect to geometrical optimization, and varying some dimensions often results in a reduction in peak stresses by a factor of 2, which is one order of magnitude in terms of the fatigue life. In the following, the results of an International Atomic Energy Agency (IAEA) benchmark exercise using austenitic FW mock-ups is discussed. 2.1. I A E A benchmark exercise
Fig. 1. Schematic diagram of lifetime assessment.
loys--more detailed analyses for other blanket design options are not yet reasonable. As will be demonstrated, fatigue crack growth may be one of the most critical failure mechanisms of FW panels. Cracks originate from manufacturing processess or are likely to be generated during operational excursions, such as by plasma disruptions. The blanket concepts presently under discussion make use of layered structures. This raises questions currently not covered by code rules, such as over the characterization of stress fields in composite structures, and the effect of residual stresses after cooling down from the joining to the operational temperature.
2. Life assessment of defect-free components
Assessment of FW structures or blanket components includes the following: classification of operating conditions and load levels; classification of failure modes, either immediate (such as plastic instability, immediate fracture) or time depen-
At the IAEA meeting in 1985, the need was identified to compare and validate existing tools in lifetime analyses. This includes the utilization of different finite element (FE) computer codes and the application of different lifetime prediction rules, i.e. designing by code and designing by analyses. Therefore, a coordinated research program (CRP) on "Lifetime behaviour of the first wall of fusion machines" was initiated by the IAEA. The following are contributors to this benchmark analysis: The NET Team, Garching (NET); JAERI, Naka Fusion Research Establishment, Naka, Japan (JAERI); Russian Research Centre Kurchatov Institute, Moscow, Russia (KIAE); Joint Research Centre of the European Community, Ispra, Italy (JRC-Ispra); Karlsruhe Nuclear Research Centre, Karlsruhe, Germany (KfK). The results of the contributors have been published [1-5]. Three benchmark components (B1, B2 and B3) of a simple FW prototype geometry were manufactured (without any brazing or welding) and tested in thermomechanical fatigue. Components B2 and B3 are
212
E. Diegele et al. / Fusion Engineering and Design 27 (1995) 210-215
considered to be initally defect free. Lifetime assessment had to be performed "in advance". The number of cycles to failure was predicted by applying and intercomparing different codes, i.e. the ASME rules (U.S.A.), the French RCC rules and the Japanese "Monju" code rules. The experimental results and the lifetime estimates apply only to the bulk material SS 316 L; in particular, it is impossible to make any predictions with respect to the lifetimes of components, including flaws, generated during manufacturing or joining processes.
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The FE temperature analyses of all the participants are in excellent agreement. Moreover, the calculations agree fairly well with the experimental results. In mechanical analyses, the agreement is fairly good and acceptable. The following conclusions can be made: the main reasons for differences were the chosen boundary conditions (free or constrained bending); the predicted critical elastic stress ranges and inelastic strain ranges agreed within 5%-15% for the same boundary conditions. 2.3. Lifetime prediction
Designing by code within different frameworks and designing by analysis were performed, intercompared and related to the fatigue-induced damage observed in experiment~ The findings can be summarized as follows. (1) The allowable number of cycles, according to different nuclear design codes, was predicted to be 350-6500. Analysis using the elastic path of the design codes was shown generally to be more conservative. From inelastic analysis, 1230-7500 cycles were estimated. (2) Any component tested survived at least 32 000 load cycles. Hence, the lifetimes assessed by the codes are conservative--at least, they are on the safe side by a factor of 5. (3) A network of cracks originated from the heated surface. This is in excellent agreement with the predictions based on inelastic analysis, in which a point at the heated front was found to be subjected to the maximum strain, so that cracks are anticipated to initiate in the vicinity of this point. The statement also holds for the mechanical strain range calculated from linear-elastic analysis, by which (with one exception) the maximum was located at the same point.
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(4) The "realistic lifetime" for the more realistic free bending boundary conditions was estimated to be 50 000-74 000 cycles after the elimination of the safety factor. (5) At the end of the experiments (52 000 cycles), the largest crack detected was less than 1 mm in depth. If a distinction is made between the "crack initiation phase" (i.e. the time until the crack becomes visible) and the "crack propagation phase", then the crack initiation phase very often takes 70%-90% of the total life. Therefore, the fatigue life predicted agrees reasonably well with the stage of damage observed in the component tested for the longest time. (6) Nuclear design codes include various safety factors. They are more or less conservative, depending on the amount of stress under consideration. Examples of design curves and an intercomparison of lifetime prediction and experimental results are shown in Fig. 2.
3. Fracture mechanical evaluation
The I T E R - C D A reference F W was examined using various fracture mechanical approaches. The main results from the linear-elastic fracture mechanics (LEFM) approach are as follows. An initial defect (semi-elliptical surface crack of depth 0.5 mm and length 3 mm) will result in a anticipated life of 40 000-60 000 cycles. The most critical points are located at the cooling channel. No crack growth is predicted for the heated surface. The results from the elastic-plastic fracture mechanics (EPFM) approach are different. The most critical location was identified as being at the heated surface.
E. Diegele et al. / Fusion Engineering and Design 27 (1995) 210-215
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Crack growth analysis, using EPFM, is not a generally established procedure in the literature. There are only few experimental data. Therefore, one is forced to make some assumptions, such as on the amount of cracks opening during a complete cycle. Consequently, "realistic" (crack open during 80% of thermal cycle) and "conservative" (crack never closed during thermal cycle) approaches were analyzed. The study results in a predicted life of 27 500-60 000 cycles for the assumed standard crack size. The L E F M approach falls between both EPFM approaches. A summary of the results is depicted in Fig. 3.
4. Assessment of joints Within the F W designs currently discussed, there are a variety of solutions involving joints of dissimilar materials, i.e. materials that do not have the same mechanical properties: beryllium coatings several millimetres thick; brazed beryllium blocks acting as limiters; layered copper/steel structures intended to be bonded by explosion welding or to be hot isostatically pressed. Special attention must be paid to the design and analysis of these joints. The behaviour of composite structures, such as with respect to the strength of the joint and thermomechanical fatigue under cyclic temperature variation, needs to be qualified by rules. Code frameworks, however, tend to leave the justification of the problems addressed above to the designer. In operation, the interface of both materials is subjected to high stress gradients; in fact, there is a jump in stress. Therefore, the failure process at the interface may be governed by nucleation, growth and coalescence
-
failure criteria ?
Material 2
Fig. 4. Life assessment of composite structures.
of voids, resulting in cracking. Up to now, there has been no loading parameter by which failure can be described analytically on the basis of simple input data, such as the elastic material properties, shear stress or stress gradient. The following special features now will be addressed: structural analysis of a coated FW; characterization of stresses at the interface. 4.1. Structural analysis o f coated F W
There exist two limiting cases in the analysis of the thermomechanical behaviour of a joint of two materials: (1) high temperature gradients at a low temperature level (such as during the start-up phase); (2) high mean temperature and small temperature gradient. In the case of a plate, restraint from bending thermal and mechanical strains are given by the rise in temperature, and the stresses are approximately -
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where T is the mean temperature of the component. This leads to compressive stresses at the heated zones and tensile stresses at the cool part of the structure. For example, this is the main contribution to the stress field in an arc-like, thin-walled and thinly coated FW. In case (2), however, the stresses are dominated by the mismatch of thermal expansion coefficients of both materials. For a plate joined from two materials of thickness H a and //2 with t h e material parameters Ml = (El, Vl, (Xl,"~2.... ), a homogeneous rise in temperature of AT leads, in the case of suppressed bending, to stresses in material 1 and material 2 of
214
E. Diegele et al. / Fusion Engineering and Design 27 (1995) 210-215
Thermal analyses of first wall
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0"2~ --H22 0"1 If we take H~=4H2, M ~ = ( 1 2 0 0 0 0 MPa, 0.3, l0 x 10 6 K - l ) and Me = (240 000 MPa, 0.1, 15 x l 0 - 6 K -~) as an example, as homogeneous heating up of AT = 100 K leads to thermal stresses of 24 MPa and - 9 6 MPa in M1 and M~ respectively.
At 300 °C, the coefficient of thermal expansion of beryllium (about 17.5 x 10-6 K -l) is very close to that of austenitic steels or copper, but is different from that of vanadium alloys (about 10 x 10 6 K-l). As a result of this mismatch, when bonding beryllium to vanadium, additional thermal (and, consequently, mechanical) strains are induced. Considering a vanadium plate 4 mm thick coated by 1 mm of beryllium, the high compressive stresses in the beryllium layer have to be compensated for by the bulk material. This roughly doubles the tensile stresses as compared with an uncoated vanadium plate. Under operational conditions, there should be no problem with Be/Cu/steel composite structures. However, there is still a mismatch in the thermal expansion coefficients of the materials considered at higher temperatures. Hence, residual stresses are introduced during the cooling from the joining temperature to the operational temperature, and "stress-free temperature" of a joined structure is not very well defined. As an example, the stress distribution along a line of layered FW is shown in Fig. 5, where the component is considered as stress free, in one case at the cooling temperature and at a joining temperature of 500 °C in the other
case.
E. Diegele et al. / Fusion Engineering and Design 27 (1995) 210-215 4.2. Stress singularities in dissimilar joints
For compounds of different elastic materials, there is stress singularity at free edges as well as at interface comers. The singularity is caused by the difference in the elastic material constants. The near-term fields in polar coordinates (r, 0) read for any component of the stress tensor as K where co = o (E 1, E2, vl, v= joining angle) is the order of singularity, K = K(~l, cz2, El, E2, vl, v2) is the so-called stress intensity factor and f j is an angular function. The order of singularity for a given material combination is the same under any mechanical or thermal loading conditions. The assessment of this singularity is not yet taken into consideration within the framework of nuclear design codes. Structural analyses by means of FE modelling are necessary to determine the stress intensity factor K. Any single result of the analyses (e.g. peak stresses) is dependent on mesh refinement and, hence is not meaningful in qualifying the joint. The order of the singularity can be determined analytically. By solving an eigenvalue problem, o) is given as the solution of a set of non-linear equations [6]. In the case of a 90 °C/90 °C composite, there is a singularity if E 1 is different from E2. Within the compounds currently proposed for F W panels, the ratio of the Young's moduli ranges from about 1.5 (steel/copper) to 3 (beryllium/copper), resulting in singularities of the order 0.09-0.2. However, in the case of a 135 °C/45 °C composite, the stresses near the corner are bounded as long as the ratio E1/E2 is less than 0.86. The stress intensity K has to be determined numerically, such as from fitting of FE results [7].
5. Conclusions Some problems of life predictions have been addressed. Life prediction of thermally cycled, initially defectfree F W components using nuclear design code rules may be very conservative, A lifetime assessment of cracked components was performed for the I T E R - C D A reference FW. It was
215
shown that fatigue crack growth might be a severe problem. As a second step, within the IAEA, benchmark experiments on precracked components are under way. Life predictions from fatigue crack growth analyses by the participants are reported. Some items concerning structural analysis of joints of dissimilar materials were discussed. There is a need for fatigue experiments of composite structures, and tools for analytical characterization of joints have to be developed.
Acknowledgments This work was performed in the framework of Nuclear Fusion Project of the Kernforschungszentrum Karlsruhe and was supported by the European Communities within the European Fusion Technology Program. Part of the work was performed as an NET study contract (ERB 5000 CT 9100 72 NET) entitled "Crack growth of the NET first wall". The authors also want to thank the IAEA, Vienna, Austria, for its support.
References [1] R.R. Jakeman and H. Gorenflo, IAEA coordinated research programme on lifetime behaviour of first wall components under thermal fatigue, NET Rep. N/I/3310/9/A, 1991. [2] S. Suzuki, M. Araki and M. Akiba, Summary report for IAEA CRP on lifetime prediction for the first wall of a fusion machine, Rep. JAERI-M-93-049, JAERI, Naka, 1993. [3] A. Klishenko, Analysis of IAEA first wall thermal cycling benchmark problem, Kurchatov Rep. 40/6376, 1993. [4] M. Merola, Numerical analysis and nuclear standard code applications to thermal fatigue, EUR Rep. EUR14028, CEC, JRC, Ispra, 1991. [5] E. Diegele, D. Munz and G. Schweinfurther, Lifetime prediction for the first wall of a fusion machine, IAEA co-ordinated research programme, Second interim report: behaviour of first wall components under thermal fatiguestress analysis and life assessment, KfK Rep. 5283, 1993. [6] M.L. Williams, Stress singularities resulting from Various boundary conditions in angular corners of plates in extension, Trans. ASME, J. Appl. Mech., 74 (1952) 526-528. [7] O.T. Iancu, Berechnung yon thermischen Eigenspannungsfeldern in Keramik/Metall-Verbunden, Thesis, Fortschr. Berichte VDI, 18 (74) (1989) (in German).
Fusion Engineering and Design 27 (1995) 210-215
Fusion Engineering and Design
Design and life assessment of first wall components E. Diegele, D. Munz, G. Rizzi Association KfK-EURATOM, Kernforschungszentrum Karlsruhe, Institut fiir Materialforschung II, P.O. Box 3640, D-76021 Karlsruhe, Germany
Abstract
The first wall (FW) of a tokamak fusion reactor is subjected to periodically changing large heat fluxes. Water-cooled FW panels made from austenitic SS 316 L steel are analyzed. First, life predictions for initially defect-free components, obtained by applying design code rules, are compared with experimental results. It is shown that designing by code is very conservative under thermal fatigue. Secondly, a fracture mechanical analysis of the I T E R - C D A FW is presented using linear-elastic and elastic-plastic approaches. Fatigue growth of pre-existing cracks is considered. Problems of FW composite structures of dissimilar materials are addressed. The mismatch in the thermal expansion coefficients give rise to residual stresses during the joining process, and leads to a jump in the stress at the interface. Moreover, different elastic properties result in stress singularities at free boundaries or at interface corners.
1. Introduction
The first wall (FW) of a tokamak fusion reactor is subjected to periodically changing large heat fluxes. The severe loading conditions imply restrictions on FW concepts. The selection of candidate structural materials, of cooling media, of the range of operating temperatures of design implementations in geometry terms as well as the problems of protection tiles and/or limiters are strongly interrelated. In this paper, a predominantly low temperature concept (reference design during I T E R - C D A ) is investigated. Austenitic steel (SS 316 L) is used as the structural material for the component, which is actively cooled (cooling tubes in the FW) by water at low pressure and low temperatures of 60-100 °C. Also, on the plasma-facing surface, it is completely covered by protective graphite (CFC) tiles. Elsevier Science S.A. SSDI 0920-3796(94)00333-5
For structural analyses of 316 stainless steel, extensive material data and experience are available and documented in several design frameworks. Thus, transient thermomechanical calculations and "design by code analysis" of the bulk material can be performed in a straightforward manner. For lifetime assessment, the database is also quite good (such as fatigue curves under various conditions), and a lot of experience has been gained in material and damage modelling. Moreover, within the European Community (EC), there are several programmes on FW mock-ups to verify life assessment, as well as to develop and evaluate manufacturing processes. Hence, life evaluation of SS 316 makes sense. However, as a result of the lack of fatigue data at design-relevant strain levels and the lack of crack-growth measurements--as well as because of the uncertainty regarding the applicability of existing material data for vanadium alloys or C u - C r - Z r al-
E. Diegele et al./ Fusion Engineering and Design 27 (I995) 210-215
J IComponent Design I....... IServWce Ioadingl I •--1 I I "1, t J
~~
[Choose material]
J
Preliminary assessment
I Mechanica[ properties I
J
(Elastic)
s.tress analysis (Design by code)
Second step DetaTIled
1.Re-DesTgn 2.Use different materiel 3.Modffy Loading
assessment
Material characterisatlon Inelastic time dependent irradiation properties
nO
211
dent (such as progressive accumulation of deformation, fatigue crack growth); (structural) analysis, including qualification of stress types. A schematic diagram demonstrating the interaction of design and life assessment is shown in Fig. 1. For the past 2 years, there have been several design approaches used for "shield blankets" or for "advanced blanket concepts", using different materials, different cooling media and different FW concepts (integrated or separated). In this paper, some of these concepts are analyzed. However, concepts will not be discussed on the basis of code rule assessment. Each design has to undergo a special optimization procedure (varying the sizes of radii of curvature, diameter and pitch of cooling tubes, thickness of layers, etc.). At present, the different approaches are at very different levels with respect to geometrical optimization, and varying some dimensions often results in a reduction in peak stresses by a factor of 2, which is one order of magnitude in terms of the fatigue life. In the following, the results of an International Atomic Energy Agency (IAEA) benchmark exercise using austenitic FW mock-ups is discussed. 2.1. I A E A benchmark exercise
Fig. 1. Schematic diagram of lifetime assessment.
loys--more detailed analyses for other blanket design options are not yet reasonable. As will be demonstrated, fatigue crack growth may be one of the most critical failure mechanisms of FW panels. Cracks originate from manufacturing processess or are likely to be generated during operational excursions, such as by plasma disruptions. The blanket concepts presently under discussion make use of layered structures. This raises questions currently not covered by code rules, such as over the characterization of stress fields in composite structures, and the effect of residual stresses after cooling down from the joining to the operational temperature.
2. Life assessment of defect-free components
Assessment of FW structures or blanket components includes the following: classification of operating conditions and load levels; classification of failure modes, either immediate (such as plastic instability, immediate fracture) or time depen-
At the IAEA meeting in 1985, the need was identified to compare and validate existing tools in lifetime analyses. This includes the utilization of different finite element (FE) computer codes and the application of different lifetime prediction rules, i.e. designing by code and designing by analyses. Therefore, a coordinated research program (CRP) on "Lifetime behaviour of the first wall of fusion machines" was initiated by the IAEA. The following are contributors to this benchmark analysis: The NET Team, Garching (NET); JAERI, Naka Fusion Research Establishment, Naka, Japan (JAERI); Russian Research Centre Kurchatov Institute, Moscow, Russia (KIAE); Joint Research Centre of the European Community, Ispra, Italy (JRC-Ispra); Karlsruhe Nuclear Research Centre, Karlsruhe, Germany (KfK). The results of the contributors have been published [1-5]. Three benchmark components (B1, B2 and B3) of a simple FW prototype geometry were manufactured (without any brazing or welding) and tested in thermomechanical fatigue. Components B2 and B3 are
212
E. Diegele et al. / Fusion Engineering and Design 27 (1995) 210-215
considered to be initally defect free. Lifetime assessment had to be performed "in advance". The number of cycles to failure was predicted by applying and intercomparing different codes, i.e. the ASME rules (U.S.A.), the French RCC rules and the Japanese "Monju" code rules. The experimental results and the lifetime estimates apply only to the bulk material SS 316 L; in particular, it is impossible to make any predictions with respect to the lifetimes of components, including flaws, generated during manufacturing or joining processes.
1,O00TS2 900C~
500-
-
700-
g ~ w
600-
L
m
• ~'~.
: : : : "l]'fe"p~e'dict]on"::L "'"'"' ........ "~~
500-
The FE temperature analyses of all the participants are in excellent agreement. Moreover, the calculations agree fairly well with the experimental results. In mechanical analyses, the agreement is fairly good and acceptable. The following conclusions can be made: the main reasons for differences were the chosen boundary conditions (free or constrained bending); the predicted critical elastic stress ranges and inelastic strain ranges agreed within 5%-15% for the same boundary conditions. 2.3. Lifetime prediction
Designing by code within different frameworks and designing by analysis were performed, intercompared and related to the fatigue-induced damage observed in experiment~ The findings can be summarized as follows. (1) The allowable number of cycles, according to different nuclear design codes, was predicted to be 350-6500. Analysis using the elastic path of the design codes was shown generally to be more conservative. From inelastic analysis, 1230-7500 cycles were estimated. (2) Any component tested survived at least 32 000 load cycles. Hence, the lifetimes assessed by the codes are conservative--at least, they are on the safe side by a factor of 5. (3) A network of cracks originated from the heated surface. This is in excellent agreement with the predictions based on inelastic analysis, in which a point at the heated front was found to be subjected to the maximum strain, so that cracks are anticipated to initiate in the vicinity of this point. The statement also holds for the mechanical strain range calculated from linear-elastic analysis, by which (with one exception) the maximum was located at the same point.
IAFJ~-Benchrrlark " 1~ Crack depth 0.6 mm
"..~~
--at
otk]n
surface
200
,E+o~
2.2. F E results
~ "~"
;
;
' iE;o,
;
;
' 'lE;Os
Number of ellowoble cycles, N
Fig. 2. Intercomparison of life predictions with experimental results, showing lifetime of SS 316 L FW mock-ups.
(4) The "realistic lifetime" for the more realistic free bending boundary conditions was estimated to be 50 000-74 000 cycles after the elimination of the safety factor. (5) At the end of the experiments (52 000 cycles), the largest crack detected was less than 1 mm in depth. If a distinction is made between the "crack initiation phase" (i.e. the time until the crack becomes visible) and the "crack propagation phase", then the crack initiation phase very often takes 70%-90% of the total life. Therefore, the fatigue life predicted agrees reasonably well with the stage of damage observed in the component tested for the longest time. (6) Nuclear design codes include various safety factors. They are more or less conservative, depending on the amount of stress under consideration. Examples of design curves and an intercomparison of lifetime prediction and experimental results are shown in Fig. 2.
3. Fracture mechanical evaluation
The I T E R - C D A reference F W was examined using various fracture mechanical approaches. The main results from the linear-elastic fracture mechanics (LEFM) approach are as follows. An initial defect (semi-elliptical surface crack of depth 0.5 mm and length 3 mm) will result in a anticipated life of 40 000-60 000 cycles. The most critical points are located at the cooling channel. No crack growth is predicted for the heated surface. The results from the elastic-plastic fracture mechanics (EPFM) approach are different. The most critical location was identified as being at the heated surface.
E. Diegele et al. / Fusion Engineering and Design 27 (1995) 210-215
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.'"'"1 1.80
Crack depth a, mm Fig. 3. Results of fracture mechanical evaluation of FW, showing life assessment under various approaches.
Crack growth analysis, using EPFM, is not a generally established procedure in the literature. There are only few experimental data. Therefore, one is forced to make some assumptions, such as on the amount of cracks opening during a complete cycle. Consequently, "realistic" (crack open during 80% of thermal cycle) and "conservative" (crack never closed during thermal cycle) approaches were analyzed. The study results in a predicted life of 27 500-60 000 cycles for the assumed standard crack size. The L E F M approach falls between both EPFM approaches. A summary of the results is depicted in Fig. 3.
4. Assessment of joints Within the F W designs currently discussed, there are a variety of solutions involving joints of dissimilar materials, i.e. materials that do not have the same mechanical properties: beryllium coatings several millimetres thick; brazed beryllium blocks acting as limiters; layered copper/steel structures intended to be bonded by explosion welding or to be hot isostatically pressed. Special attention must be paid to the design and analysis of these joints. The behaviour of composite structures, such as with respect to the strength of the joint and thermomechanical fatigue under cyclic temperature variation, needs to be qualified by rules. Code frameworks, however, tend to leave the justification of the problems addressed above to the designer. In operation, the interface of both materials is subjected to high stress gradients; in fact, there is a jump in stress. Therefore, the failure process at the interface may be governed by nucleation, growth and coalescence
-
failure criteria ?
Material 2
Fig. 4. Life assessment of composite structures.
of voids, resulting in cracking. Up to now, there has been no loading parameter by which failure can be described analytically on the basis of simple input data, such as the elastic material properties, shear stress or stress gradient. The following special features now will be addressed: structural analysis of a coated FW; characterization of stresses at the interface. 4.1. Structural analysis o f coated F W
There exist two limiting cases in the analysis of the thermomechanical behaviour of a joint of two materials: (1) high temperature gradients at a low temperature level (such as during the start-up phase); (2) high mean temperature and small temperature gradient. In the case of a plate, restraint from bending thermal and mechanical strains are given by the rise in temperature, and the stresses are approximately -
eE(T- -
T)
2(1 - v)
where T is the mean temperature of the component. This leads to compressive stresses at the heated zones and tensile stresses at the cool part of the structure. For example, this is the main contribution to the stress field in an arc-like, thin-walled and thinly coated FW. In case (2), however, the stresses are dominated by the mismatch of thermal expansion coefficients of both materials. For a plate joined from two materials of thickness H a and //2 with t h e material parameters Ml = (El, Vl, (Xl,"~2.... ), a homogeneous rise in temperature of AT leads, in the case of suppressed bending, to stresses in material 1 and material 2 of
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E. Diegele et al. / Fusion Engineering and Design 27 (1995) 210-215
Thermal analyses of first wall
IS+eeq cu t Be I aoot.
1
6
5
Option:
"..
z
100 "
~
........................~ Thloknees,mm """
2i
steel-copperberyllium compound
.
.......... °
2(]( L°°°°°.°.,**°°***°,,°oo
1Ill
ThJgknesl=,mm)
or
--100]
**********************
@
150+
'°°t \ s:I ;, -50
b
Option: including residual stress
Thl~-kne... mm
°-......,.,.
""°"°'°"',,.,11
Option: steel-coppercompound
Fig. 51 Stress distribution in a composite structure under different options.
~-
~
>
material 1 material 2
a,=-
~E 2oo-
~ 1.sok. loo 50 i
o!
Coordinate (r/L)
Fig. 6. Stress singularity at the surface of a composite structure, i.e. same under mechanical or thermal load.
(~2 -- 7q)ATE1 0-1 = (1 - vl) + (1 - v2)HIEI/(H2E2) H1
0"2~ --H22 0"1 If we take H~=4H2, M ~ = ( 1 2 0 0 0 0 MPa, 0.3, l0 x 10 6 K - l ) and Me = (240 000 MPa, 0.1, 15 x l 0 - 6 K -~) as an example, as homogeneous heating up of AT = 100 K leads to thermal stresses of 24 MPa and - 9 6 MPa in M1 and M~ respectively.
At 300 °C, the coefficient of thermal expansion of beryllium (about 17.5 x 10-6 K -l) is very close to that of austenitic steels or copper, but is different from that of vanadium alloys (about 10 x 10 6 K-l). As a result of this mismatch, when bonding beryllium to vanadium, additional thermal (and, consequently, mechanical) strains are induced. Considering a vanadium plate 4 mm thick coated by 1 mm of beryllium, the high compressive stresses in the beryllium layer have to be compensated for by the bulk material. This roughly doubles the tensile stresses as compared with an uncoated vanadium plate. Under operational conditions, there should be no problem with Be/Cu/steel composite structures. However, there is still a mismatch in the thermal expansion coefficients of the materials considered at higher temperatures. Hence, residual stresses are introduced during the cooling from the joining temperature to the operational temperature, and "stress-free temperature" of a joined structure is not very well defined. As an example, the stress distribution along a line of layered FW is shown in Fig. 5, where the component is considered as stress free, in one case at the cooling temperature and at a joining temperature of 500 °C in the other
case.
E. Diegele et al. / Fusion Engineering and Design 27 (1995) 210-215 4.2. Stress singularities in dissimilar joints
For compounds of different elastic materials, there is stress singularity at free edges as well as at interface comers. The singularity is caused by the difference in the elastic material constants. The near-term fields in polar coordinates (r, 0) read for any component of the stress tensor as K where co = o (E 1, E2, vl, v= joining angle) is the order of singularity, K = K(~l, cz2, El, E2, vl, v2) is the so-called stress intensity factor and f j is an angular function. The order of singularity for a given material combination is the same under any mechanical or thermal loading conditions. The assessment of this singularity is not yet taken into consideration within the framework of nuclear design codes. Structural analyses by means of FE modelling are necessary to determine the stress intensity factor K. Any single result of the analyses (e.g. peak stresses) is dependent on mesh refinement and, hence is not meaningful in qualifying the joint. The order of the singularity can be determined analytically. By solving an eigenvalue problem, o) is given as the solution of a set of non-linear equations [6]. In the case of a 90 °C/90 °C composite, there is a singularity if E 1 is different from E2. Within the compounds currently proposed for F W panels, the ratio of the Young's moduli ranges from about 1.5 (steel/copper) to 3 (beryllium/copper), resulting in singularities of the order 0.09-0.2. However, in the case of a 135 °C/45 °C composite, the stresses near the corner are bounded as long as the ratio E1/E2 is less than 0.86. The stress intensity K has to be determined numerically, such as from fitting of FE results [7].
5. Conclusions Some problems of life predictions have been addressed. Life prediction of thermally cycled, initially defectfree F W components using nuclear design code rules may be very conservative, A lifetime assessment of cracked components was performed for the I T E R - C D A reference FW. It was
215
shown that fatigue crack growth might be a severe problem. As a second step, within the IAEA, benchmark experiments on precracked components are under way. Life predictions from fatigue crack growth analyses by the participants are reported. Some items concerning structural analysis of joints of dissimilar materials were discussed. There is a need for fatigue experiments of composite structures, and tools for analytical characterization of joints have to be developed.
Acknowledgments This work was performed in the framework of Nuclear Fusion Project of the Kernforschungszentrum Karlsruhe and was supported by the European Communities within the European Fusion Technology Program. Part of the work was performed as an NET study contract (ERB 5000 CT 9100 72 NET) entitled "Crack growth of the NET first wall". The authors also want to thank the IAEA, Vienna, Austria, for its support.
References [1] R.R. Jakeman and H. Gorenflo, IAEA coordinated research programme on lifetime behaviour of first wall components under thermal fatigue, NET Rep. N/I/3310/9/A, 1991. [2] S. Suzuki, M. Araki and M. Akiba, Summary report for IAEA CRP on lifetime prediction for the first wall of a fusion machine, Rep. JAERI-M-93-049, JAERI, Naka, 1993. [3] A. Klishenko, Analysis of IAEA first wall thermal cycling benchmark problem, Kurchatov Rep. 40/6376, 1993. [4] M. Merola, Numerical analysis and nuclear standard code applications to thermal fatigue, EUR Rep. EUR14028, CEC, JRC, Ispra, 1991. [5] E. Diegele, D. Munz and G. Schweinfurther, Lifetime prediction for the first wall of a fusion machine, IAEA co-ordinated research programme, Second interim report: behaviour of first wall components under thermal fatiguestress analysis and life assessment, KfK Rep. 5283, 1993. [6] M.L. Williams, Stress singularities resulting from Various boundary conditions in angular corners of plates in extension, Trans. ASME, J. Appl. Mech., 74 (1952) 526-528. [7] O.T. Iancu, Berechnung yon thermischen Eigenspannungsfeldern in Keramik/Metall-Verbunden, Thesis, Fortschr. Berichte VDI, 18 (74) (1989) (in German).