1. Introduction

The integrity of nuclear power plant structures for all loading modes, normal or accidental, must be constantly ensured. In particular, for the most important structures such as the tank or the primary circuit, the aim is to evaluate the mechanical resistance from the design stage in relation to brittle and ductile failure.

From the point of view of maintenance in service, the aim is also to justify the mechanical strength of structures in the presence of a crack when defects have been detected during an inspection. This approach makes it possible to establish a schedule for the repair or replacement of components. Moreover, some components cannot be controlled, in which case it is necessary to demonstrate mechanical strength in the presence of hypothetical defects.

In this context, fracture mechanics provides the tools necessary for the analysis of cracked components. Its objective is to characterize the damage (crack, damage) in order to model each type of failure in order to be able to establish failure criteria to judge load margins under normal or accidental operating conditions [1].

From a physical point of view, we consider a metallic structure that is stressed thermomechanically. In this document, we are only interested in the fragile rupture of a structure, that is to say when the material breaks suddenly by cleavage.

The Beremin model, which is based on the knowledge of mechanical fields in the most stressed areas, is used to obtain a local failure criterion representative of the physical mechanisms involved (instability of cleavage microcracks).

1.1. Industrial context

From an engineering point of view, the resistance of a material to the propagation of a crack is measured using tenacity. Depending on the temperature and the rate of deformation, some steels (in particular ferritic REP vessel steels or carbon-manganese steel for secondary piping) have characteristics that are either fragile or ductile. At low temperatures, these steels break fragilely by cleavage, sometimes exhibiting intergranular decohesion, while at higher temperatures, ductile tear occurs. The transition between these two mechanisms is characterized by the fragile/ductile transition temperature. Resilience measurements make it possible to establish criteria, such as the transition temperature, to define the field of use of the material [2].

In the case of ferritic steels in tank REP under normal operating conditions, the material is stressed in the ductile domain. However, during its operation under the effect of neutron irradiation, the tank will « age » and may become fragile. In addition, very exceptional accidental conditions such as cold thermal shock (Pressurized Thermal Shock, PTS) under pressure in the event of loss of primary refrigerant (APRP) could cause stress on the component in the ductile-fragile transition domain. This is why it is important to determine the degree of embrittlement of the material using the ductile-brittle transition curve and to know precisely the tenacity of the material in the transition domain in order to prevent all risks of sudden rupture [3].

With regard to secondary circuit pipes, C-Mn steels that are used in the various emergency circuits (ASG, Emergency Power for Steam Generators, for example), are sensitive to aging under deformation (static) which induces a shift in their ductile-fragile transition to high temperatures [4]. In order to predict the fragile failure of these components in the presence of static aging, several previous studies have been carried out to model the mechanical behavior of the material taking into account aging under deformation [5, 6, 7].

This work has already shown that the probability of failure by cleavage can be correctly described in the fragile bearing by a local approach to failure as proposed by Beremin.

1.2. The value of the local approach

To justify the mechanical strength of nuclear power plant components, the global approach is often used. The global approach aims to describe the loading conditions of a cracked component leading to failure using a single parameter that depends on geometry and loading. The most commonly used parameter in the field of breakage by cleavage (linear elastic case) is the stress intensity factor in mode I, \({K}_{I}\). The ruin of the structure will be obtained when this parameter reaches a critical value, tenacity \({K}_{\mathit{Ic}}\). The safety analysis compares the stress intensity factor with minimum values of the toughness of the steel, which are established by numerous mechanical tests and gathered in the form of a reference curve RCC -M annex Z.G. Throughout the operating period of the tank, it is verified that the toughness properties, deduced from the operation of the monitoring program, are greater than those provided by the reference curve, indexed to a conventional transition temperature RTNDT (Reference Temperature for Nil Ductility Transition) [3].

The global approach is well validated and accepted by the Safety Authority, but it remains simple and conservative. It can therefore be too broad in certain particular cases, such as for example in the case of « small defect effect », « triaxiality effect », « hot preloading effect », or in the case of non-proportional loading. This is why in support of mechanical strength justification files, a finer local approach can be used that makes it possible to establish a link between the toughness of a material and the local breaking stress for a macroscopically homogeneous material.

An additional reason for using the Beremin-type local approach method is explained by the tenacity values, which are highly dispersed in the field of ductile-fragile transition. By introducing a statistical model, this approach makes it possible to explain and quantify the dispersion inherent in these tests, via the knowledge of local metallurgical parameters [2].