A multi-scale MCCPFEM framework: Modeling of thermal interface grooving and deformation anisotropy of titanium alloy with lamellar colony

Abstract

Micro-scale thermal interface grooving (TIG), as an important breakdown mechanism of single lamella and the key to spheroidization of lamellar colony, does significant influence on the mechanical response and microstructural evolution of titanium alloy with lamellar colony during hot working. This influence may become remarkable by coupling with meso-scale deformation anisotropy of the colony. The coupled effect across different scales is crucial to the spheroidization of lamellar colony, while rare related research is reported due to the difficulty in experiment. In this work, a multi-scale MCCPFEM framework was proposed to model on the micro-scale TIG and meso-scale deformation anisotropy through the fully coupling of lattice kinetic Monte Carlo (MC) model and crystal plasticity finite element model (CPFEM). During the modeling, the modified MC algorithm was established based on the multiple-integral method (MIM) solution with Mullin's theory, which accounts for the TIG's microstructural evolution. In addition, the deformation anisotropy at different length scales including strain localization at lamella, and strain partitioning at colony was characterized by an explicit CPFEM which includes resistance anisotropy of slip systems, evolution of dislocations and high-fidelity representative lamellar colony. At the same time, geometrically necessary dislocation (GND) was also considered in the CPFEM by developing a new algorithm with mesh-free methodology and re-construct radial basic shape functions. The fully coupling of the multi-scale MCCPFEM was realized through the microstructure-based 2D grids acting as both finite elements and lattice sites. Moreover, re-set ‘zero’ of the deformation gradient of the TIG mesh was proposed to characterize the strain-free state of new TIG nucleation. Then, the TIG-induced changes in the dislocation density, lattice rotation, strain-free state and morphological characteristics were returned to MCCPFEM to determine the heterogeneous deformation and anisotropic mechanical response of the lamellar colony. With this multi-scale model, the coupled effect of the deformation anisotropy (strain localization in beta phase, stress relief in TIG and local internal stress concentration in alpha lamella) and TIG-induced microstructural evolution during the isothermal compression of the IMI834 alloy with lamellar colony is well captured and analyzed.