A hybrid analysis procedure enabling elastic design rule assessment of monoblock-type divertor components
Introduction
The plasma facing component (PFC) used in the ITER divertor is based on the “monoblock” construction (Fig. 1) comprising tungsten armour block with through CuCrZr cooling pipe separated by a copper interlayer [6]. The CuCrZr pipe provides both the structural support and the means for cooling the armour layer. This type of PFC is also being considered for the divertor in DEMO (the demonstration fusion power plant), but because loading conditions are expected to be more onerous (with high levels of irradiation and particle flux) new monoblock designs are being investigated [1] (as part of the EUROfusion power plant physics and technology programme).
Preferably, before undergoing physical testing, new designs would be assessed using Design by Analysis (DBA) methods following a design code. This is usually achieved by subjecting the results of an elastic Finite Element Analysis (FEA) to a set of “elastic” code rules defining allowable stress for each anticipated failure mechanism. However even the most appropriate current code as used by ITER (SDC-IC [2]) is not ideally suited for assessing PFCs (such as monoblocks) as highlighted in [5] because it is based largely on existing codes for pressure vessels (e.g. ASME [3]) or conventional nuclear installations (RCCMR [4]). Such codes are aimed mainly at thin-walled single material structures, and so are not well suited to the analysis of the multi-material thick-walled construction of the monoblock. Furthermore, monoblock (and most PFC) materials have different coefficients of thermal expansion (CTEs) which cause considerable residual stress following manufacturing joining processes (e.g. when cooling from brazing temperatures). As will be shown in this paper, these stresses are through-thickness stresses and, as such, are not factored into existing elastic design-code methods.
ITER currently use both DBA and “design by experiment” methods to overcome the DBA shortfall in their divertor monoblock design assessments [6]. For DEMO, a new (DBA) assessment code is being created to be called the “DEMO Design Criterion” (DDC) based on elasto-plastic FEA methods tailored to PFCs [7]. However, this is not expected to be released in time for the new concepts currently being developed by EUROfusion [8]. To overcome the immediate shortfall, EUROfusion are supporting the development of a “preliminary” analysis procedure specifically for monoblocks (aspects of this procedure are expected to be integrated into the final DDC). This will not only give a design “performance” measure to use in design optimisation, but also create a common assessment approach to assess the relative performance of the various design concepts being developed.
This paper describes the first stage of this process in which a simplified monoblock elastic analysis procedure (MEAP) has been created. This procedure aims to give a simple but accurate assessment under steady state normal operating conditions and is based on the existing “elastic” code rules (rules to be used with elastic FE analysis), but in a revised form to suit the monoblock construction. The advantage of elastic rules is that they are simple to apply, are well proven and have considerable status. The disadvantage is that there is no explicit method in the associated elastic FE analysis to incorporate residual stress effects - potentially invalidating the resulting code assessment. In this paper, the validity of the elastic code rule methodology is assessed by making comparisons between an elastic code assessment FE model, and a more accurate full elasto-plastic model of the type devised by Li and You [22,23]. The latter allows residual stress to be calculated (approximately) which is then carried forward into the analysis of normal operating load steps to give the improved accuracy. From this comparison, a revised set of rules have been formed to create the MEAP.
Section snippets
Load cases
The divertor in both ITER and the proposed European DEMO fusion power plant, is required to withstand nominal steady state heat loads of the order of 10 MW/m2 during plasma pulses and 20 MW/m2 during occasional “slow transient” events (estimated to last several seconds) [30,31]. In both scenarios steady state heat distribution is achieved. Higher instantaneous heat loads are possible during fast transient major disruption events lasting a few milliseconds [30], but these events tend to affect
FEA models
Two types of model are used initially in this work: an elastic code assessment model, and a full elasto- plastic model with residual stress simulation. From these a hybrid model is created combining both elastic and elastoplastic methods as described below.
Analysis results and discussion
The results from the elastic model and the elasto plastic model are compared by two methods: comparison of stress value/distribution at each load step, and comparison of stress/strain history throughout all load steps.
The monoblock elastic analysis procedure (MEAP)
The monoblock elastic analysis procedure was based on the results of the above study. The procedure was formalised into a guideline document listing the recommended modelling method and the assessment rules to apply. The recommended modelling method is essentially as described above using the same quarter model simplification and the same boundary conditions, material definitions and mesh distribution.
The procedure is termed “elastic” because elastic code rules are applied. However, the finite
Discussion
The hybrid model employed in the MEAP shows the ability to capture the cyclic stress range of the more complex elastoplastic model allowing elastic code rules to be applied. To be more precise the stress range calculated is comparable only if elastic shakedown occurs. Nonetheless, this satisfies the needs of a code assessment model which needs only to accurately detect stress up to and including the 3Sm (elastic range) limit being assessed. The MEAP model does not claim to predict stress range
Conclusions
- 1
A simplified simulation of the manufacturing cycle of a typical monoblock design using elastoplastic modelling methods has shown that significant through thickness residual stress can be expected in the structural pipe component resulting from the differential contraction of the tungsten armour and CuCrZr pipe.
- 2
There is almost no correlation between the absolute pipe stress (magnitude and distribution) calculated by a purely elastic model (as used in design code assessment) and that calculated
Further work
The MEAP will be superseded by a procedure based on a fully elasto-plastic finite element modelling method similar to that described for the benchmark model above and the work of Li and You [10,22,23]. From this, rules for assessing the design performance using the elasto-plastic methods are to be developed; rules which it is intended can be applied to all components within the monoblock assembly and that are devised specifically to overcome the problems associated with all plasma facing
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 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.
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