Fuel

I

The main mechanisms of failure in materials subjected to high-temperature environment usually consist of nucleation and growth of microscopic cavities due to creep fatigue damage. Such processes may ultimately lead to the coalescence of voids which usually merge to macroscopic cracks. In structural components made of nuclear reactor materials which can be found for example in fusion reactors or fast breeder reactors this process is significantly enhanced, especially the process of creep and creep damage in connection with the increased influence of neutron irradiation. Fuel claddings and first walls of the fusion reactors in particular are exposed to high temperature and fast neutron flux and are subjected to severe irradiation damage and irradiation induced inelastic deformation. Consequently, proper modeling of the effects of neutron irradiation on the process of inelastic deformation and damage is a prerequisite for the rational design, probability risk assessment, and life prediction analysis of different built-in components and nuclear structures as a whole. To consider and to evaluate the extent of irradiation damage of reactor steels and other components the need to develop constitutive models of irradiation creep, swelling, and irradiation creep damage based on the mechanisms of physical theories of neutron irradiation is of fundamental importance.

Quite recently, a class of new constitutive models to describe such behavior has been proposed in the literature. Basic assumption made in those models is that the irradiation creep can be decomposed into two major parts, namely the part due to irradiation-induced creep and the part due to irradiation-enhanced creep; the former is caused predominantly by irradiation and may occur even in cases under conditions of zero stress in the material, while the latter is attributed to ordinary thermal creep, but at the same time accelerated by irradiation. It has been shown experimentally that the overall stress dependence on irradiation-induced and irradiation-enhanced creep is nearly isotropic. This leads to the assumption that eventual anisotropy of material properties that may be caused by irradiation is negligibly small. From this a very powerful conclusion can be drawn. According to the tensor representation theorem frequently used in the theory of constitutive equations, bases of constitutive response functions can be chosen from a class of isotropic tensor functions. Consequently, using the fundamental principles of continuum mechanics intertwined with the description of the physical mechanisms of neutron irradiation from the perspective of materials science, the irradiation creep can be represented by an isotropic tensor function which accounts for the current state of stress within the material thus modeling stress-controlled thermal creep, isotropic tensor function with regard to neutron flux, as well as an isotropic tensor function of second rank accounting for the effects of neutron fluence. The volumetric part of the irradiation induced-creep is associated with volumetric swelling and dilatation, whereas the irradiation-enhanced creep is modeled by modified Kachanov-Rabotnov creep damage theory generalized in such a way to enable the incorporation of the effects of irradiation and also including effects of transient creep.

Most representative experimental data gathered for the 316 type of stainless steel are presented and certain qualitative and quantitative aspects of applicability of the proposed constitutive model are discussed in detail. Special attention is given to the investigation of the effects of neutron irradiation on creep deformation and creep damage.

Results obtained from the proposed constitutive model which is based predominantly on experimental observations are very promising even though they can be considered as semi-empirical since the evolution equations for irradiation-induced and irradiation-enhanced creep are not obtained as a result of rigorous thermodynamical derivation based on the use of the second law of thermodynamics or the Clausius-Duhem inequality. Results of such theory are still not known in terms of measure-observable internal variables. In spite of this, the evolution equations for irradiation-induced and irradiation-enhanced creep do not violate the principle of the second law of thermodynamics and the entropy inequality. They provide an efficient tool for analysis of very complicated phenomena at a reasonably moderate level of theoretical complexity.

The evolution equations are three-dimensional and can be incorporated in a straight forward manner in any open finite element code providing that the efficient algorithm is already available for the time integration of nonlinear systems of ordinary differential equations emerging from a standard finite element discretization procedure of the governing set of nonlinear partial differential equations describing the evolution of the creep induced damage of the material