Elastoplastic thick shell analysis by viscoplastic solid finite elements

Reprinted from International Journal for Numerical Methods in Engineering-- Volume 12, Issue 2, (1978

Semi-analytical modeling of a PWR lower head failure under severe accident conditions using an axisymetrical shell theory

The USNRC/SNL OLHF program was carried out within the framework of an OECD project. This program consisted of four one-fifth scale experiments of a reactor pressure vessel (RPV) lower head failure (LHF) under well controlled internal pressure and large throughwall temperature differentials; the objectives were to characterize the mode, timing and size of a possible PWR lower head failure in the event of a core meltdown accident. These experiments should also lead to a better understanding of the mechanical behavior of the reactor vessel lower head, which is of importance both in severe accident assessment and the definition of accident mitigation strategies. A well-characterized failure of the lower head is of prime importance for the evaluation of the quantity of core material that can escape into the containment, since this defines the initial conditions for all ex-vessel events. A large quantity of escaping corium may lead to direct heating of the containment or ex-vessel steam explosion. These are important issues due to their potential to cause early containment failure. The experiments also provide data for model development and validation. For our part, as one of the program partners, a 2D semi-analytical model has been developed and used to simulate these experiments. The aim of this effort is to develop a simplified but well predicting code that can be then implemented in European integral severe accident computer codes (ASTEC, ICARE/CATHARE). This paper presents the detailed mathematical formulation of this simplified method which is used to interpret the experimental results. The axi-symmetric shell theory under internal pressure proposed by Timoshenko has been utilised. The solution to the equilibrium equations is presented, with particular attention to the Rabotnov analytical formula. The radius and the polar angle of the deformed structure have been written as analytical expressions in order to take the large displacements and large strains into account using our mathematical formulation. The Norton type creep law and the Kachanov damage law have been used. Several failure criteria were used in the calculations and their effect on the numerical results is discussed. This 2D semi-analytical model gives very satisfactory results when compared, with the experimental and numerical results that were presented recently in the Benchmark calculations based on the first test of the OLHF program. The performance of this model is also illustrated by its capacity to accurately simulate the deformation of the lower head, including the variation of wall thickness. © 2004 Elsevier B.V. All rights reserved