Finite Element Analysis of Cylindrical Inclusions in Polycrystalline Nickel Alloys

Inspired by nanotubes, a 3D finite element model was developed to simulate the influence of cylindrical inclusions on the polycrystalline mechanical behavior of Nickel alloys. A dislocation based strain hardening model, constructed in the so-called Kocks-Mecking framework, is used as the main strategy for the constitutive modeling of individual bulk grains. To determine the influence of the inclusions distribution, the direction of applied load and the size of the matrix phase on the inelastic stress-strain distribution, the digital microstructure code DREAM.3D was coupled to ABAQUS (C) finite element code through a MatLab (C) program. Four affordable computational representative volume elements (RVEs) meshes of two different edge sizes and two different inclusion distributions were tested to investigate the relation between micro and macro deformation and stress variables. The virtual specimens, subjected to continuous monotonic strain loading conditions, were constrained with random periodic boundary conditions. The difference in crystallographic orientation, which evolves in the process of straining, and the incompatibility of deformation between neighboring grains were accounted for by the introduction of single crystal averaged Taylor factors, single crystal Young's modulus, single phase elastic modulus and the evolution of geometrically necessary dislocation density. The effects of single crystal Young's modulus, inclusion distribution and direction of the applied load upon the aggregate local response are clearly observed. Results demonstrate a strong dependence of flow stress and plastic strain on phase type, Young's modulus values and direction of the applied load, but slightly on matrix grain size. The stress-strain curve extension and the variation in the elastic limit of the individual inclusions depend on the inclusion-matrix Young's modulus difference and applied load direction. The difference in curve extension and the difference in elastic limit decrease as the Young's modulus of the single crystal inclusion approach the Young's modulus of the matrix majoritary phase, while the resistance to flow increases when the applied load is perpendicular to the inclusion longitudinal axis.