1. Introduction#

The fuel sheaths of pressurized water nuclear reactors are made of zirconium alloy. These alloys undergo metallurgical transformations between \(700°C\) and \(1000°C\), where they pass from a compact hexagonal structure phase to a cubic structure phase. In some cases of analysis such as heart accident scenarios due to loss of primary refrigerant (APRP), the jacket reaches temperatures of the order \(1000°C\) and then undergoes metallurgical transformations. To analyze the mechanical behavior of the sheath in these situations, it is necessary to take into account the influence of metallurgy on mechanics (modification of mechanical characteristics).

This document concerns the modeling of the structural transformations of Zircaloy during heating and cooling at a scale that, while remaining « reasonable » for the metallurgist, is easily usable by the mechanic.

Metallurgy calculations in code_aster are done either during the integration of the law of mechanical behavior, or with the dedicated operator CALC_META, in « post-processing » of a thermal evolution calculation. In this second case; the choice of the model is made with the keyword RELATION = “ZIRC” under COMPORTEMENT. This type of modeling is possible within the Code_Aster for all the elements (PLAN, AXIS, 3D) of the PHENOMENE « THERMIQUE ». To define the metallurgical behavior of Zircaloy, it is necessary to specify the keyword factor META_ZIRC under the command DEFI_MATERIAU [U4.43.01]. Finally, the definition of the initial metallurgical state is possible using the command CREA_CHAMP, under the keyword factor ETAT_INIT of the operator CALC_META.

The models implemented in Code_Aster to model the metallurgical transformations of Zircaloy are models developed by the CEA. These models were identified on the basis of dilatometry and calorimetry tests for sheath alloys (standard and new).

For mechanical behavior with the effect of structural transformations, there are several models to choose from:

  • or the same mechanical behavior relationships developed initially for 16 MND5 tank steel. These are all relationships declared in the STAT_NON_LINE operator under the COMPORTEMENT keyword of the type META_XX_XX. These are elastoplastic or elastoviscoplastic models, isotropic (linear or non-linear) or kinematic work hardening models, taking into account or not the phenomena of plasticity of transformation and restoration of work hardening of metallurgical origin (see R4.04.02 and R4.04.03).

  • or the law specific to Zircaloy. It is an elastoviscous model without threshold and anisotropic (Hill matrix). The key word under COMPORTEMENT is META_LEMA_ANI (cf. R4.04.05) in this case, the metallurgical phase is an internal variable of the law of behavior and is determined during the integration of the latter.