Elasto-Visco-Plastic Buckling of Thick Anisotropic Shells: Numerical Buckling Predictions and Experiments

Abstract

This work is focused on elasto-visco-plastic (EVP) buckling of thick shell structures. In particular we are interested in predicting accurately the buckling risk of stainless steel components of nuclear fast sodium reactor working under high pressure and at high temperature (around 180 bar and 500 °C). We follow a modeling/experimental approach to solve this problem. The set-up of relevant experiments at such high temperature being complex, we work with a representative material that shows similar EVP and buckling behavior at room temperature. The representative material is an alloy mostly composed of tin, silver and copper, commonly named Sn 3.0 Ag 0.5 Cu. The elasto-visco-plastic constitutive model of the material was first characterized using tensile tests on notched specimen at room temperature under various strain rates, and the model parameters identified using finite element model updating (FEMU). In a second step we performed in plane compressive buckling tests of thick plates for various displacement rates. Surface 3D displacements were acquired using three cameras and digital image correlation. It is well known for thick plates that linearized tangent moduli derived from Levy-Mises flow theory does not give accurate elasto-plastic buckling prediction. Linearized tangent moduli derived from Hencky’s deformation theory gives more accurate buckling prediction for thick plates. This numerical phenomenon known as buckling paradox was well correlated to experiments in the literature. This paradox is applied here to thick plates, with EVP constitutive model, in order to predict buckling. Finally, finite element (FE) modeling of the buckling experiments was performed. Plates are modeled using SHB8PS solid shell elements. Solid shell elements allow direct displacement correlation with experiments and accurate through the thickness behavior with a 3D material model. The numerical modeling includes real plate geometry obtained using post machining measurements, experimental boundary conditions derived from the DIC (Digital Image Correlation) results and the previously identified constitutive material law. Buckling risk is tested at each loading step of the incremental algorithm using the tangent operator derived with the Hencky’s deformation theory. Numerical results show a very good correlation with the experimental results on load and displacement history as well as buckling critical load and buckling mode.