A comparative analysis of grain-scale stress and strain fields in two- and three-dimensional polycrystals

The results of a comparative analysis of the stress-strain patterns observed in two- and three-dimensional polycrystalline models under uniaxial tension are presented and discussed. The 3D polycrystalline structure is generated using a step-by-step packing method. Finite-difference calculations of uniaxial tension are carried out for the 3D model and some selected sections located at different depth below the surface. In the latter case, calculations are performed in terms of plane strain and plane stress. Stress and strain fields in 2D and 3D models are compared on the meso- and macroscales. It is found that the 2D approximations impose certain restrictions on the use and interpretation of the results obtained.