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

Abstract

The fivefold symmetric modular stellarator Wendelstein 7-X (W7-X) is currently underconstruction in Greifswald, Germany. The superconducting coils of the magnet system are bolted onto a centralsupport ring and interconnected with five so-called lateral support elements (LSEs) per half module. Afterwelding of the LSE hollow boxes to the coil cases, cracks were found in the vicinity of the welds that couldpotentially limit the allowed number N of electromagnetic (EM) load cycles of the machine. In response to theappearance of first cracks during assembly, the Stress Intensity Factors (SIFs) were calculated andcorresponding crack growth rates of theoretical semi-circular cracks of measured sizes in potentially criticalposition and orientation were predicted using Paris’ law, whose parameters were calibrated in fatigue tests atcryogenic temperature. In this paper the Dual Boundary Element Method (DBEM) is applied in a coupledFEM-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 Jintegralapproach. The Finite Element Method (FEM) is adopted to model, using the commercial codes Ansysor 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 latterprovide the boundary conditions for the submodel. Such approach is affected by some restrictions in the crackpropagation phase, whereas, with the “FEM-DBEM approach”, the crack propagation simulation isstraightforward. In this case the submodel is created in a DBEM environment with boundary conditionsprovided by the global FEM analysis; then the crack is introduced and a crack propagation analysis has beenperformed to evaluate the effects of the crack shape and of the presence of nearby cracks on the allowednumber of EM load cycles