Identification of material parameters of a thermo-mechanical model for pebble beds in fusion blankets

In this paper, a thermo-mechanical model of pebble beds is adopted [D. Hofer, M. Kamlah, Drucker-Prager-Cap creep modelling of pebble beds in fusion blankets, Fusion Eng. Des. 73 (2005) 105–117] 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 [O. Coube, Modelling and numerical simulation of powder die compaction with consideration of cracking, PhD Thesis, University Pierre et Marie, Paris VI, 1998], the Drucker-Prager-Cap theory [ABAQUS, Analysis User's Manual, Version 6.5, 2004], a modified creep law [D. Hofer, M. Kamlah, Drucker-Prager-Cap creep modelling of pebble beds in fusion blankets, Fusion Eng. Des. 73 (2005) 105–117]. Furthermore, the volumetric inelastic strain dependent thermal conductivity of beryllium pebble beds [J. Reimann, G. Piazza, Z. Xu, A. Goraieb, H. Harsch, Measurements of the thermal conductivity of compressed beryllium pebble beds, FZKA 7096 (2005)] is taken into account and full thermo-mechanical coupling is considered.By analyzing the deformation mechanism of the oedometric experiments, a new method is developed to determine the set of material parameters, including the temperature dependent hardening law. With the new method, the material parameters can be derived directly from the empirical equations (the so-called “Reimann fits” for pebble beds) including the thermoplastic behaviour. All these thermo-mechanical constitutive laws are implemented in ABAQUS by user defined field (USDFLD) and CREEP subroutines. The oedometric compression tests and creep tests under different temperatures are simulated by the present model, and the results show that the model gives a good description of experimental results. The analysis on the precompaction procedure of pebble beds assembly (PBA) is applied to show the feasibility of the present material model.