Thermo-Mechanical Modelling of Pebble Beds in Fusion Blankets and its Implementation by a Return-Mapping Algorithm
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0981-JJ04-04
Thermo-Mechanical Modelling of Pebble Beds in Fusion Blankets and its Implementation by a Return-Mapping Algorithm Yixiang Gan, and Marc Kamlah IMF II, Forschungszentrum Karlsruhe, Postfach 3640, Karlsruhe, D-76021, Germany
ABSTRACT In this investigation, a thermo-mechanical model of pebble beds is adopted and developed based on experiments by Dr. Reimann at Forschungszentrum Karlsruhe (FZK). The framework of the present material model is composed of a non-linear elastic law, the DruckerPrager-Cap theory, and a modified creep law. Furthermore, the volumetric inelastic strain dependent thermal conductivity of beryllium pebble beds is taken into account and full thermomechanical coupling is considered. Investigation showed that the Drucker-Prager-Cap model implemented in ABAQUS can not fulfill the requirements of both the prediction of large creep strains and the hardening behaviour caused by creep, which are of importance with respect to the application of pebble beds in fusion blankets [1]. Therefore, UMAT (user defined material’s mechanical behaviour) and UMATHT (user defined material’s thermal behaviour) routines are used to re-implement the present thermo-mechanical model in ABAQUS. An elastic predictor radial return mapping algorithm is used to solve the non-associated plasticity iteratively, and a proper tangent stiffness matrix is obtained for cost-efficiency in the calculation. An explicit creep mechanism is adopted for the prediction of time-dependent behaviour in order to represent large creep strains in high temperature. Finally, the thermo-mechanical interactions are implemented in a UMATHT routine for the coupled analysis. The oedometric compression tests and creep tests of pebble beds at different temperatures are simulated with the help of the present UMAT and UMATHT routines, and the comparison between the simulation and the experiments is made. INTRODUCTION In the development of fusion technology, pebble beds are used in the helium-cooled pebble bed (HCPB) blanket. There are three main functions of the HCPB blanket: besides transformation of the neutron energy originating from the fusion reaction into usable heat and shielding of the superconducting magnets against neutron and gamma radiation, its main purpose is breeding of the fuel tritium by capturing neutrons in lithium [2, 3]. Two main types of pebble beds are used in the HCPB blanket: first ceramic pebble beds as breeder material, such as lithium orthosilicate (Li4SiO4) and lithium metatitanate (Li2TiO3); second beryllium pebble beds as neutron multiplier. The blanket is split into several modules filled in alternating sequence with breeder and neutron multiplier pebble beds. The pebble beds are composed of nearly spherical shaped pebbles, whose diameters range from 0.25mm to 2mm [4]. Due to the extreme working conditions in the fusion reactor, a deep understanding of the thermo-mechanical properties of these pebble beds is essential. Thus, a material model for describing their response to the
external excitation is needed, to
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