Statistical Evaluation of Local Stress and Strain of Three Dimensional Polycrystalline Material at Elevated Temperature

Abstract

The present paper presents results of numerical simulation for statistical evaluation of stress and strain at elevated temperature from view point of crystal plasticity level by employing a new Voronoi tessellation algorithm in the three dimensional geometry for general grain shape using first order tetrahedron element (four nodes). The elasticity tensors are assumed to include isotropic material and anisotropic material of FCC or BCC crystal using three material constant parameters. The employed finite element formulation is based on the updated Lagrange type expressed in the general form using trapezoidal integration rule in time domain, and the selective numerical integration scheme is used in the present analysis. The obtained numerical examples include the effects of employed finite elements, employed grain aggregate model, grain diameter size, and grain regularity on local stress. The statistical variation around mean value is investigated for the isotropic material and the anisotropic materials having different anisotropy ratio A in elastic range. The inelastic analysis at elevated temperature is also carried out for the anisotropic materials in order to investigate the statistical variation for the anisotropic materials in strain rate effect problem and creep strain program by introducing additional six cubic slip systems into the conventional 12 octahedral slip systems inelastic range.