Final work : Homogenization of single crystal nickel based super-alloys. An overview of the creep behavior

Abstract

An overview of the creep behavior of an aeronautical-type single crystal turbine blade is analyzed by means of two methodologies: a fully-optimized second order homogenization method and a Finite Element numerical approach. Micro-structure, i.e porosity level, is shown to have an important role in creep behaviour of porous FCC single crystals. The homogenization-based constitutive model developed by Ponte-Castaneda makes use of the fully optimized second order variational approach of (Ponte Castañeda, 2015), along with the iterated homogenization method of (Agoras and Ponte Castañeda, 2013) to define a constitutive model for the finite-strain macroscopic response of porous single crystal in the sense of visco-plasticity. For the computations (Song and Ponte Castañeda, 2017a), Song et al. implemented a numerical implementation in Fortran language. The numerical finite element calculations are carried out using a three dimensional Finite element code of a Unit Cell. The single crystal matrix is defined by a simple power law viscous crystal plasticity constitutive relation. The Unit Cell is initially cubic with a sphere or ellipsoid located in the center, constituting the inclusion phase. Fully periodic boundary conditions are imposed in the Unit Cell Finite element model by means of the MPC capability of ABAQUS and the "dummy node" technique. The effect of crystal orientation and loading conditions on the micro-structure evolution in a face center cubic (FCC) single crystal is analyzed. Two different initial crystal orientations are considered. The calculations are carried out for six different values of stress triaxiality and for three different Lode parameter. Additionally, the effect of an initial ellipsoidal void shape and the effect of the initial porosity level is addressed. Micro-structure evolution in an FCC single crystal may produce a softening or hardening effect related to the void growth or collapse, setting the base for further research in terms of enhancement of creep properties of FCC single crystals. Strain rates along deformation were analyzed allowing to understand the physics behind micro-structure evolution and its consequence in creep properties. Moreover, stress concentration around the inclusion phase depends highly on the crystal orientation and loading conditions.