Coupled FEM-DBEM method to assess crack growth in magnet system of Wendelstein 7-X

R Citarella,M Lepore,Victor Bykov,Felix Schauer,Joris Fellinger

doi:10.3221/igf-esis.26.10

Abstract

The fivefold symmetric modular stellarator Wendelstein 7-X (W7-X) is currently under construction in Greifswald, Germany. The superconducting coils of the magnet system are bolted onto a central support ring and interconnected with five so-called lateral support elements (LSEs) per half module. After welding of the LSE hollow boxes to the coil cases, cracks were found in the vicinity of the welds that could potentially limit the allowed number N of electromagnetic (EM) load cycles of the machine. In response to the appearance of first cracks during assembly, the Stress Intensity Factors (SIFs) were calculated and corresponding crack growth rates of theoretical semi-circular cracks of measured sizes in potentially critical position and orientation were predicted using Paris’ law, whose parameters were calibrated in fatigue tests at cryogenic temperature. In this paper the Dual Boundary Element Method (DBEM) is applied in a coupled FEM-DBEM approach to analyze the propagation of multiple cracks with different shapes. For this purpose, the crack path is assessed with the Minimum Strain Energy density criterion and SIFs are calculated by the Jintegral approach. The Finite Element Method (FEM) is adopted to model, using the commercial codes Ansys or Abaqus;, the overall component whereas the submodel analysis, in the volume surrounding the cracked area, is performed by FEM (“FEM-FEM approach”) or alternatively by DBEM (“FEM-DBEM approach”). The “FEM-FEM approach” considers a FEM submodel, that is extracted from the FEM global model; the latter provide the boundary conditions for the submodel. Such approach is affected by some restrictions in the crack propagation phase, whereas, with the “FEM-DBEM approach”, the crack propagation simulation is straightforward. In this case the submodel is created in a DBEM environment with boundary conditions provided by the global FEM analysis; then the crack is introduced and a crack propagation analysis has been performed to evaluate the effects of the crack shape and of the presence of nearby cracks on the allowed number of EM load cycles.

Highlights

The fivefold symmetric modular stellarator Wendelstein 7-X (W7-X) is currently under construction in Greifswald, Germany [1]
IFEM-Finite Element Method (FEM) vs. FEM-Dual Boundary Element Method (DBEM) approaches n Fig. 8 it is possible to compare the J-integral values calculated along the initial crack front with the 3 different approaches available: the FEM-DBEM approach provides two sets of results depending upon the software (Ansys or Abaqus) used for the global modelling, whereas the remaining set of results is related to the crack assessment done on the Abaqus submodel
As expected there is a non negligible discrepancy when considering the results coming from the Ansys global model but it is easy to find the reasons in the rough mesh and in the lack of a detailed geometric reproduction of the lateral support elements (LSEs); on the contrary a satisfactory correspondence is obtained between the results obtained by FEM and DBEM submodels when considering the Abaqus global model, apart from a non negligible discrepancy localised at the break through points that are more affected by extrapolation effects and mesh inaccuracy

Summary

Introduction

The fivefold symmetric modular stellarator Wendelstein 7-X (W7-X) is currently under construction in Greifswald, Germany [1]. The assessment is extended, for the most critical crack, using the DBEM [4,5,6,7,8,9,10,11] This most critical crack was located in LSE-D05 in the cast steel (Fig. 1). The method calculates the crack growth rate along the crack front rather than assuming a pure radial growth as done in [3] with a pure FEM approach. It enables the prediction of crack growth of non-circular cracks, differently from what imposed by the FEM sub-modelling approach, where only semicircular crack fronts are modelled [3].

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