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

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


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.

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