Coupled FEM–DBEM approach on multiple crack growth in cryogenic magnet system of nuclear fusion experiment ‘Wendelstein 7-X’

At the Max Planck Institute for plasma physics in Greifswald, Germany, the world's largest nuclear fusion experiment of modular stellarator type Wendelstein 7-X has started plasma operation. The hot hydrogen plasma is confined in a plasma vessel by an electromagnetic field generated by 50 non-planar and 20 planar superconducting coils. The superconducting coils are encased in cast stainless steel housings. The coils are bolted onto a central support ring and welded together by so called lateral support elements (LSEs). In this paper, a procedure, based on a global–local finite element method (FEM)–dual boundary element method (DBEM) approach, is developed to simulate the propagation of multiple cracks detected in LSEs and undergoing a fatigue load spectrum. The global stress analysis on the superconducting coils is performed by FEM whereas the sub-modelling approach is adopted to solve the crack propagation in the DBEM environment. The boundary conditions applied on the DBEM submodel are the displacements calculated by the FEM global analysis, in correspondence of the cut surfaces (there are no body forces nor external loads applied on the submodel volume). Two cracks are simultaneously introduced, and a linear elastic fracture mechanics analysis is performed. Results in terms of cracks growth rates and evolving crack shapes are provided, and the residual life of the component is forecast.