A constitutive model for the thermo-mechanical behaviour of fusion-relevant pebble beds and its application to the simulation of HELICA mock-up experimental results

Status of ceramic breeder pebble bed thermo-mechanics R&D and impact on breeder material mechanical strength

“…One being Karlsruhe Institute of Technology, formerly FZK and referred to as such throughout this paper, and the other being ENEA-Brasimone with the Department of Nuclear Engineering at the University of Palermo, referred to as DIN throughout this paper. These two institutions have published a great deal of detail in regards to the specific details of their modeling techniques and the reader is referred to these publications for the fine points of the models [12,13,19,10]. The discussion here calls attention to differences between models and attempts to serve as a reference basis for future modeling efforts.…”

“…It should be noted that in the model's current form, it is incapable of directly capturing the creep behavior of pebble beds. However, the model was designed such that a future creep law could readily be implemented [12,13,19].…”

“…These models deduce a set of constitutive equations to be implemented in the framework of a finite element code. There are two major variants of phenomenological modeling approaches developed among institutions, including: (1) a non-linear elastic model and a modified Drucker-Prager-Cap theory for plastic strain [10,11]; and (2) a hyperporous non-linear elastic model and a Gurson model for plastic model [12][13][14]. The readers are referred to the additional efforts used in a third method [11] which employed two different elasticity laws for the loading and unloading branches but will not be discussed here.…”

“…Exemplary results of the DIN benchmarking with HELICA: temperature variations with time during a loading cycle at 100 mm from FW[12].…”

Thermal transient and the temperature profile in a HELICA mock-up simulated by a new finite element homogenous model

“…The pebble bed temperature gradient is controlled by two external helium-cooled plates and provided with square cooling channels. The operating conditions of coolant are: helium at nominal flow rate of 8 g/s, inlet pressure of 1.5 MPa and inlet temperature of 250 • C. Inside the pebble bed a helium flow rate (purge gas) was regulated at 0.002 g/s (witch means to have velocity inside the bed lower than 0.01 m/s); the inlet pressure is equal to 0.05-0.1 MPa and the inlet temperature 50 • C [6][7][8][9].…”