Towards reliable design-by-analysis for divertor plasma facing components – Guidelines for inelastic assessment (part 1: Unirradiated)
Introduction
In ITER, the divertor is the component with the highest design steady state heat loads (Merola [25]) of circa 10 MW/m2 (with excursions to 20 MW/m2). While these loads are already demanding, in (EU)DEMO (the proposed European demonstration power plant) conditions are expected to be more arduous with longer pulse times and higher levels of irradiation (estimated at up to 10dpa (You [1]). To meet this expectation, EUROfusion are carrying out research and development on the next generation divertor components (as described by You [26,1]).
For this development, much guidance is drawn from the experiences of ITER divertor development both in design and qualification. A typical DEMO divertor PFC concept is similar to the ITER design comprising a tungsten armour block with through CuCrZr cooling pipe joined to the tungsten via a soft copper interlayer (see Fig. 1). Like ITER, assessment of DEMO designs is currently by high heat flux (HHF) testing (Greuner [36]), based again largely on the ITER specification (Morola [25]) of 5000 cycles at 10 MW/m2 and 300 cycles at 20 MW/m2. If a component fails, the predominant mode of failure in ITER and DEMO mock-ups is by cracking of the armour (as shown in Fig. 2), although failure of the heatsink cooling pipe and interlayer is also reported (Gavali [27]).
ITER have now demonstrated the required PFC performance using tests (Sun [31]) but is instructive to note that divertor component qualification tests have not historically been accompanied by extensive preceding analysis supporting the anticipated performance. Although discrete analysis studies have been published for DEMO (e.g. by Li Puma [6] and Crescenzi [28]) and failure modelling has been used to diagnose problems (Li [15]), for ITER at least it remains the case that it is mandatory to validate design “by experiments” (rather than analysis) (Hirai [24]). This begs the question about the perceived value of analysis as an accurate predictor of PFC structural integrity in HHF load conditions.
In this paper the case for analysis as a viable and necessary tool for assessing PFCs is presented. It is emphasised that analysis is particularly required for DEMO in its current state of development, and that despite the shortfalls in current analysis methods, these can be overcome, by a combination of new and existing alternative methods. To make the point the paper presents a detailed set of guidelines for the preferred method of assessing plasma facing components and this is demonstrated by an example analysis of an ITER-like component.
One reason why analysis is not relied upon to support current PFC qualification is that it fails to predict one of the dominant failure mechanisms experienced in HHF tests: the cracking of the armour. This is because current methods of assessment (which use standard elastic code rules) can only be applied to the nominal structural component i.e., the pipe. It follows then, for analysis to be successful, the scope of the structural integrity assessment process needs to be extended to include the armour. However, this is not straight-forward because, to the authors knowledge, there are no formally validated assessments methods relevant to brittle materials such as tungsten, so these methods need to be devised. Towards this end recent work by Li has suggested one potential mechanism for cracking which can be adopted in a design rule format. Nonetheless others are required.
Furthermore, even application of the existing code rules for assessing the ductile structural (sub)components in PFCs presents its own problems. This is partly because codes are derived from the analysis of pressure vessels (i.e., thin-walled axisymmetric structures) and hence are not ideally suited to the multi-material block-like construction of PFCs. This was demonstrated by Fursdon [2] who showed that stresses in the multi-material monoblock components bear little resemblance to the stress predicted by the conventional/common elastic code methodology.
The problem created by the multilateral construction of PFCs is mainly due to two factors. The first is the different coefficient of thermal expansion (CTE) of the subcomponent materials. This creates (at least in a monoblock) significant through-thickness residual stress developed during cooling in the joining processes (Fursdon [2]). The second is the difference in yield strength of these materials. This creates material dependant limits on the loads transferred between subcomponents.
To overcome both these complexities Fursdon [5] concludes elastoplastic analysis must be used. (i.e., where yielding is explicitly modelled). Although this adds an extra level of complexity and unfamiliarity in analysis, this does not mean that the method of formal structural integrity code assessment is in entirely “new territory”, since existing design codes already provide design rules for assessment using elastoplastic (and even inelastic) analysis methods (ASME [10], RCC-MR [33] and ITER SDC-IC [3]).
Even though these code methods have existed for some time, it is acknowledged that these rules seem rarely to be applied (to the author’s knowledge). Perhaps this is because in the design of existing conventional nuclear components, thin-wall single-material methods are deemed appropriate such that the severity of plasticity, if it occurs, can be estimated (e.g by a Neuber curve approach as described in [3]). However there also appears to be little application of elastoplastic rules in the fusion community either, where bulky components with multi-material construction are more prevalent. There may be a reluctance because of the increased analysis time and potential convergence issues, but it is suggested that these disadvantages are far outweighed by the significant increase in relevance of the results produced.
It is an aim of this paper to encourage and promote the use inelastic methods in the assessment of PFC components so that the much-needed reliable analysis data can be provided to support concept design proposals. This is not only to add the usual benefits of analysis as product development tool1, but also to address a particular need in DEMO that analysis seem best suited to satisfy.
Of the many benefits offered by analysis in component development the one that appears to stand out for DEMO is the potential for a greater understanding of the effects of irradiation. Degradation by neutron irradiation is expected to be particularly significant in DEMO (You et al [1]) and might create the limiting case when the resulting effect on component performance is determined. Although tests of irradiated components have been done [32], these pose many practical problems, and are not realistic in the concept development phase of development (i.e. the current DEMO status). It follows that in order to provide the necessary data on irradiated performance this will probably need to be supplied through analysis methods (albeit as an estimate).
The significance of the potential irradiation effect is emphasised by the scale of material property change possible. This is illustrated for example by the pre-post irradiation stress strain curve of copper as shown in Fig. 3 (with a fivefold increase in yield stress and complete loss of hardening), and the change in available elongation in CuCrZr as shown in Fig. 4. (with a drastic reduction of ductility at temperatures below 150 °C). Although these changes can be expected to significantly alter component stress/strain levels and material limits, with appropriate analysis, the effects of these factors can be assessed.
In the long term EUROfusion plan to produce a document known as the Demo Design Criterion (DDC) in 2025 [4] with recommended structural integrity assessment criterion for all DEMO plasma facing components. However, for the immediate needs of the divertor R&D (where design assessment of current concepts is required now), the EUROfusion’s divertor design group has created a set of preliminary guidelines known as the Inelastic Analysis Procedure (IAP). The IAP is the subject of this paper.
In the existing design codes (whether elastic or elastoplastic) many failure mechanisms are assessed. The minimum set covered by ASME [10], RCCMR [33] and SDC_IC [3] is plastic collapse, fatigue, ratcheting and creep. To these, SDC_IC and ASME add exhaustion of ductility and (SDC-IC) fast fracture. Much of the testing done to date suggests that failure by repeated cycling is the prime focus of failure assessment (e.g. failure by fatigue or perhaps ratcheting). However, if (as is argued) the irradiated “embrittled” condition is potentially the worst-case scenario, then it is possible that ductility or fast fracture becomes the limiting failure mode (i.e., from reduced allowable strain or from reduced fracture toughness). To this the potential for failure by creep must be added given the potential for high temperatures under high heat loads. No single code was found to be ideal for assessing all the above failure mechanisms in PFCs. Rather the IAP uses extracts from all the above codes to create the appropriate rule definitions. The details and rationale for the recommended rule created are detailed in Section 2 of this paper
It has already been highlighted that PFC assessment goes beyond normal structural integrity assessment convention by needing to include the assessment of the nominally non-structural armour material. There are also other particular features of PFCs that need special consideration.
To account for susceptibility of PFCs to potentially significant residual stress (discussed above) the recommended method of analysis includes an initial analysis step to simulate the manufacturing cycle as described for example by Li and You [15]. For PFCs with a CuCrZr pipe, the methods proposed in the IAP is to simulate the cooling from either the CuCrZr hardening temperature if a braze process is used (as in [34]), or the pressing temperature if hot radial pressing process is used (ref [35]). The method and rationale for this is detailed in previous work by the divertor group in reference [2].
The presence of multiple dissimilar metal joints in PFCs creates ongoing analysis challenges. Such joints risk the creation of stress/strain singularities in analysis as highlighted by Kelly [8] (with theoretically infinite values in peak stress or strain) which invalidate structural integrity assessment. A method proposed in the IAP to overcome this issue is by use of the hot spot method (for example as described EN 13445 [7]). However, this method requires prior test information on similar style joints and is currently only applied to fatigue evaluation. Alternatively, since stress singularities are an indication of a severe stress concentration, it is suggested that the design, rather than the assessment method should be modified (for example, by the methods outlined by Kelly [8] and illustrated in the example analysis described below in Section 3).
Special methodologies are also required to account for the changing properties of PFC material due to high levels of irradiation as demonstrated in Fig. 3. This is achieved by using material property change commands within the assessment analysis, so that strain usage before and during irradiation can be accumulated appropriately. The change in allowable strain is accounted for by use of usage fraction as detailed in Section 2.1.2.
Finally, as described in previous work [6], assessment of water cooled PFCs requires an assessment of the cooling water critical heat flux limit (the limit of nucleate boiling heat transfer). In the IAP this is achieved using the method described in reference [2] and is not discussed further here.
This paper gives a detailed description of the elasto-plastic rules used in the guidelines under conditions (temperatures) where creep is expected to be negligible (termed here “low temperature” rules). A negligible creep curve defining allowable time at temperature for a valid “low temperature” assessment will be presented in part #3 of this paper. To support the rule description an example assessment of an unirradiated ITER like monoblock is presented in which examples of specific methodologies are shown. In follow-up papers, methods and data collection for estimating PFC performance in their irradiated condition are described as well as rules for assessing creep damage when the negligible creep criterion is not met.
The guidelines focus on the structural integrity assessment under nominally normal 10 MW/m2 heat flux operating conditions and “slow transient” excursions to 20 MW/m2. Confirmation of assessment methods for fast transient load cases (such as ELM loading and disruption electromagnetic loading) and plastic collapse rules is ongoing.
The development of armour assessment rules is also under development and only preliminary armour rules are presented here. Further rules are anticipated as test data experience is accumulated.
While focussing on the design of divertor components made from CuCrZr, copper and Tungsten, it is the intention that the IAP can be applied to all multi-material plasma facing components including the use of materials such as Eurofer or variants (e.g. for target designs as described in [37]). Within the example analyses presented, a simple example assessment of ratcheting for a steel piped monoblock is given to suggest this wider applicability.
Section snippets
Rule definitions
The following section details the IAP rules, the rationale for their selection, and where appropriate, a recommended assessment methodology.
Example analysis and results
The application of the above rules is demonstrated by an example assessment carried out of an ITER-like monoblock divertor component made from CuCrZr Copper and Tungsten (as illustrated in Fig. 1) using ANSYS 18.2 workbench. The assessment includes a static thermal analysis and an elastoplastic static structural analysis (the former to define the temperature distributions used as inputs for the latter). The defined requirement for this example component is 5000 normal operation pulses of 2 h
Overview
This paper presents guidelines (known as the Inelastic Analysis Procedure-IAP) for the recommended method of assessing by analysis the structural integrity of PFCs under high heat flux loads. The objective is to be able to justify the merits a proposed DEMO concept design without complete reliance on testing.
The use of analysis to provide such a justification is particularly important when considering the irradiated case. In DEMO, the effects of irradiation are potentially very significant and
Acknowledgements
This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement No 633053, and from the RCUK Energy Programme [grant number EP/I501045]. To obtain further information on the data and models underlying this paper please contact [email protected]. The views and opinions expressed herein do not necessarily reflect those of the European Commission.
The
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