Material Microstructure Scale Effect on Brittle Fracture Resistance of WWER-1000 Reactor Pressure Vessel Steel

Using the Toupin–Mindlin gradient theory of elasticity equations, the material microstructure scale effect on the brittle fracture resistance of the WWER-1000 reactor vessel steel was experimentally assessed. The results of determining the temperature dependence of the stress intensity factor (SIF) at the tip of postulated cracks under the reactor core’s emergency cooling condition are presented. The calculations were performed based on the mixed finite element method in an axisymmetric formulation using two types of postulated annular cracks located in the cylindrical part of the reactor vessel at the level of weld No. 4. Data were obtained to determine the SIF for a 22 mm deep surface crack beneath the cladding vessel inner surface and a 15 mm deep subsurface crack below the cladding-base metal interface. The SIF values were calculated using the formula used in linear fracture mechanics and methodological documents to assess the strength of reactor pressure vessels using the elastic energy release rate at the crack tip. To calculate the energy release rate under virtual crack advancement, the concept of energy balance is adopted, in which the increase in the potential energy of an elastic body is determined, taking into account the additional contribution from strain and stress gradients. The temperature dependences of the stress intensity coefficient for the surface and sub-surface cracks at different scaling parameter values associated with the material microstructure’s linear size are plotted. The main feature of the results obtained, which consider the influence of microstructure according to the equations of the gradient theory of elasticity, is a decrease in the calculated SIF values compared to solutions based on the classical theory of elasticity, which is the basis of linear fracture mechanics. For a subsurface crack, the microstructure scale effect is more significant than that of a surface one. Therefore, the strengthening effects from the strain gradient lead to a less conservative assessment of the resistance to brittle fracture. This allows justifying an additional safety margin for the reactor vessel.