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@ARTICLE{VandenKerkhof:904081,
      author       = {Van den Kerkhof, S. and Blommaert, M. and Coenen, J. W. and
                      Baelmans, M.},
      title        = {{O}ptimized design of a tungsten–copper functionally
                      graded material monoblock for minimal von {M}ises stress
                      meeting the material operational temperature window},
      journal      = {Nuclear fusion},
      volume       = {61},
      number       = {4},
      issn         = {0029-5515},
      address      = {Vienna},
      publisher    = {IAEA},
      reportid     = {FZJ-2021-05651},
      pages        = {046050 -},
      year         = {2021},
      abstract     = {Functionally graded materials (FGMs) are a means to remove
                      discrete material interfaces which lead to high local stress
                      concentrations, such as the tungsten–copper (W–Cu)
                      interface of the current ITER monoblock design. This paper
                      employs adjoint-based optimization methods to identify the
                      highest potential reduction of stresses that could be
                      reached with these materials, while ensuring that the local
                      temperature does not exceed the material temperature
                      operational window. The cheap sensitivity evaluation
                      inherent to the adjoint approach enables the optimization of
                      the detailed 3D material distribution. Furthermore, a novel
                      optimization method based on an augmented Lagrangian
                      formulation is proposed that allows accurate treatment of
                      the material temperature window constraints. The temperature
                      and stresses are modelled by the steady heat conduction and
                      Navier's equation, respectively. We compare the results of
                      different optimization formulations, with cost functions
                      based on the von Mises stress and corresponding yield
                      criterion and considering different values of the stress
                      free temperature. To assess the performance under off-design
                      conditions, two optimized designs were chosen and compared
                      to the ITER and flat tile (FT) design, which consists of a
                      copper block protected by a tungsten layer on top. The
                      optimized designs lead to a factor 2–4 decrease in maximal
                      stress near the original W–Cu interface of the FT design
                      and a factor 10 decrease in yield criterion measure near the
                      cooling duct. Under off-design conditions, they realized a
                      factor 2–10 decrease in yield criterion in the upper part
                      of the monoblock. This confirms numerically that FGMs can
                      lead to significant design improvements. Finally, the
                      inclusion of the material temperature operation window
                      constraints leads to a decrease of 30–55 $vol\%$ W
                      compared to the unconstrained cases, thus profoundly
                      influencing the final design. The stress free temperature
                      was found to have a comparably weaker influence on the final
                      design with differences of 5–30 $vol\%$ W.},
      cin          = {IEK-4},
      ddc          = {620},
      cid          = {I:(DE-Juel1)IEK-4-20101013},
      pnm          = {1232 - Power-based Fuels and Chemicals (POF4-123) / 134 -
                      Plasma-Wand-Wechselwirkung (POF4-134)},
      pid          = {G:(DE-HGF)POF4-1232 / G:(DE-HGF)POF4-134},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000637348300001},
      doi          = {10.1088/1741-4326/abe7bb},
      url          = {https://juser.fz-juelich.de/record/904081},
}