A. Yu. Chirkov

Elastoplastic Fracture Resistance Analysis of NPP Primary Circuit Equipment Elements

Ñurrent calculation analysis approaches to the fracture resistance assessment for main equipment elements of the WWER NPP primary circuit are considered. It is noted that the solution of the problems of justifying safe operation, assessment of the integrity and extension of the lifetime of the reactor pressure vessel is essentially dependent on the results of calculations of the kinetics of the stress strain state, a proper consideration of the residual welding stress and strain fields, reliable evaluation of non-linear fracture mechanics parameters. A general methodology is developed for a calculated analysis of the fracture resistance of WWER reactor pressure vessels in the simulation of emergency cooling conditions. The main statements in the elastoplastic calculation of the kinetics of the stress strain state for reactor pressure vessels are formulated with consideration of the residual welding stress and strain fields, and the calculation procedure for determining the fracture parameters of the postulated crack is presented. Using the calculation methods and software product developed, a significant influence of such factors as consideration of the thermomechanical loading history and elastoplastic deformation of the metal in the vicinity of the postulated crack front, different ways of taking into consideration the residual welding stress level, the regularity and density of the finite element mesh in the vicinity of the calculated crack front, the procedure for calculating the elastoplastic fracture parameters in discrete finite element method models on the calculated fracture resistance assessment of WWER-1000 reactor pressure vessels is shown. It is found that the neglect of the loading history and residual stress level after heat treatment results in a non-conservative assessment of the fracture resistance for the collector-to-nozzle welded joint in the PGV-1000 steam generator in the simulation of the operating cycle of loading.

Construction of two-level integration schemes for the equations of plasticity in the theory of deformation along the paths of small curvature

The construction of a set of two-level integration ω-schemes for the equations of the flow theory of plasticity, describing anisothermic loading processes along the deformation paths of small curvature, is described. In this case, a stress-strain state is dependent on thermomechanical loading history, and inelastic deformation should be followed over the whole examined time interval in step solving the boundary problem. Basic concepts of the phenomenological model are built upon the Prandtl– Reuss equations of plasticity and the Huber–Mises yield condition. The loading process is divided into several time steps. The equations of plasticity are integrated in a loading step. The general procedure of transformations to construct a set of two-level integration ω-schemes for the equations of plasticity is proposed. The conditions for the agreement between the considered equations of plasticity and the principle of work irreversibility with plastic strain increments and Drucker’s hardening postulate are formulated. As an example, illustrating the properties of these equations, the deformation problem is solved for a thin-walled round pipe subject to axial tension and torsional moment. Results of solving the model problem, obtained with different two-level integration schemes, are presented. Practical recommendations as to the choice of the parameter ω are given.

Stress-Strain State of the Coolant Collector-to-Nozzle Welded Joint in the PGV-1000M Steam Generator Under the Operating Loads with Consideration of Residual Manufacturing Stresses

Results are presented for both the calculated assessment of the residual manufacturing stress fields in the simulation of the heat treatment in the vicinity of welded joint No. 111, and the calculation analysis of operating stresses and the fracture resistance of the collector-to-nozzle welded joint in the PGV-1000M steam generator in the simulation of the operating loading cycle.

Mixed Approximation Scheme of the Finite-Element Method for the Solution of Two-Dimensional Problems of the Elasticity Theory

For the solution of two-dimensional boundary-value problems of the elasticity theory, a triangular finite element, ensuring stability and convergence of mixed approximation, is proposed. The system of resolving equations of the mixed method is derived with account of strict satisfaction of static boundary conditions at the surface. To solve matrix equations of the mixed method, various algorithms of the conjugate-gradient method with the pre-conditional matrix have been considered. Numerical data on convergence and accuracy of the solution for a number of test problems of the elasticity theory and fracture mechanics are given. The results obtained by the conventional and mixed finite-element method approaches are compared.

MIXED PROJECTION-MESH SCHEME OF THE FINITE-ELEMENT METHOD FOR THE SOLUTION OF PROBLEMS OF THE ELASTICITY THEORY

A mixed projection-mesh scheme for solving the boundary-value problems of the elasticity theory has been formulated. Correctness and convergence of the mixed approximations for strains and displacements are studied. Application of the numerical integration has been analyzed, and the obtained results are given. The theory of generalized functions and the functional analysis methods have been used for the convergence and accuracy estimates. Iteration algorithms for solving the discrete problems have been proposed.

Some Aspects of Inclusion of Loading History in the Fracture Strength Analysis of Reactor Pressure Vessels Under Thermal Shock Conditions

The paper addresses some aspects of inclusion of loading history in the fracture strength analysis of reactor pressure vessels under thermal shock conditions. The strength assessment of a reactor pressure vessel and its lifetime extension are shown to essentially depend on reliability of results of elastic-plastic modeling of stress-strain kinetics and determination of design values of the fracture mechanics parameters. The present findings of the finite-element analysis demonstrate that the loading history must be taken into account in the determination of the temperature dependence of stress intensity factor for a postulated specified crack. It is shown that, in the fracture toughness analysis of a reactor pressure vessel, the temperature dependence of the stress intensity factor has to be derived from the results of the analysis of kinetics and mode of loading of metal at the crack tip under thermal shock conditions. For construction of the above dependence, we proposed approach, which accounts for the active loading and unloading processes occurring in the metal in the crack front vicinity. Incorporation of the loading history into the analysis of the temperature dependence of the stress intensity factor using the proposed approach forcan permit revealing some additional margin of strength during the substantiation of lifetime extension for a reactor pressure vessel under thermal shock conditions.

Peculiarities of the Fracture Strength Design of the Branch Pipe Zone of the Nuclear Reactor Vessel

The main methodological principles and the procedure of the refined calculation of the stress-strain state and fracture strength of the branch pipe zone of the reactor vessel under thermal shock have been formulated. A mixed scheme of the finite element method was taken as a basis of finite element analysis; it ensures continuous approximation both for displacements and for stresses and strains, which allows the fracture mechanics parameters to be determined with a high degree of accuracy. The paper presents the results of an elastic-plastic analysis of the fracture strength of the inlet branch pipe zone with an underpad crack in the simulation of the typical emergency core cooling conditions of a WWER-1000 reactor. The location and orientation of the postulated crack are substantiated to obtain the most conservative estimate of the fracture strength of the branch pipe. The calculations were performed with including the postulated crack in the finite element model of a fragment of the inlet branch pipe zone using the procedure of successive mesh thickening in the crack region. To determine the allowable critical temperature of brittleness of the branch pipe base metal, the tangent point, thermal crimping and descending branch approaches were used. According to the obtained results, the elastoplastic deformation of the metal and stress history affect the calculated estimate of the fracture strength of the branch pipe zone of the reactor vessel. It has been shown that the traditional linear elastic calculation, which is used to evaluate the fracture strength of the branch pipe, does not have sufficient degree of conservatism, which results in an exaggerated estimate of its strength.

Improving the Computational Analysis of Stress-Strain State and Fracture Resistance of Welded Joints Between Coolant Headers and PGV-1000M Steam Generator Vessel of Nuclear Power Station

The authors have outlined methodological principles and a procedure of performing the updated analysis of stress-strain state and fracture resistance of welded joints between coolant headers and PGV-1000M steam generator vessel. The paper gives the results of the elastic-plastic fracture resistance analysis of a welded joint containing variously shaped surface defects, in modeling a design operation cycle and an accident situation. According to the data obtained, the deformation loading history, residual technological stresses, and inclusion of surface damages have a significant effect on the design assessment of fracture resistance of a welding joint. It has been shown that the conventional linearly elastic calculation of fracture resistance of welded joints has an inadequate degree of conservatism and thus overestimates strength of the joints.

Calculation analysis of the stress-strain state of the collector-to-nozzle weld in the steam generator under seismic loading

The authors present the calculation results for the stress-strain state of the weldment of the “hot”collector to the nozzle in the PGV-1000 steam generator in the area of welded joint No. 111 in the simulation of the seismic loading specified using the response spectra for the vertical and horizontal vibrations. The calculation of seismic stresses is performed based on the linear-spectral analysis using the three-dimensional model of the WWER-1000/338 reactor plant.

Consideration of hydrostatic stress in problems of the deformation theory of plasticity

The conditions ensuring the single-value solution of elastoplastic edge problems that take into account hydrostatic stress under proportional loading are established.