A three-dimensional cellular automata-crystal plasticity finite element model for predicting the multiscale interaction among heterogeneous deformation, DRX microstructural evolution and mechanical responses in titanium alloys

Abstract

Dynamic recrystallization (DRX), heterogeneous deformation and mechanical responses at the levels of single grain and grains aggregate concurrently occur and interact with each other in hot-working processes of titanium alloys. The interaction has been partly taken into account in our previous work by creating a crystal plasticity finite element method (CPFEM) with DRX considered, but the morphological characteristics of DRX that are crucial to the performance of the formed part failed to be captured. In addition, the existing visualization approaches (e.g., cellular automata, CA) for modeling the morphology evolution treated DRX as a product of deformation and thus separated the interaction. To address these issues, combining the advantages of the above two methods, this work proposes a new concept by treating the morphological evolution of DRX as one intrinsic part of the constitutive behavior, which is realized by establishing a 3D CACPFEM model through the full coupling of CA and CPFEM. During the modeling, the CA algorithm accounting for the DRX evolution is built into the CPFEM framework that accounts for multiscale heterogeneous deformation. Based on the microstructure-based 3D grids acting as both finite elements and cells and the explicit consideration of grain boundary softening, the heterogeneous deformation and the induced non-uniform distribution of the dislocation density at the levels of the slip system, grain interior and boundary are calculated with CPFEM. The obtained results dominate the evolution of DRX synchronizing with the deformation, which is calculated with CA through a semi-probabilistic switch rule that considers the effects of the deformed grain morphology and misorientation between the adjacent matrix grain and recrystallized grain. The DRX-induced changes in the dislocation density, grain boundary, and grain size are returned to CPFEM to determine the slip resistance of the dislocations. Consequently, not only the mechanical response but also the subsequent plastic deformation is determined. With this model, the coupled effect of the heterogeneous deformation, mechanical response and DRX microstructural evolution during the isothermal compression of the TA15 alloy is well captured and analyzed, which is verified by experiments. It is shown that the framework of this model allows the integrated prediction of the macroscale forming, mesoscale deformation mechanism and microscale microstructural evolution of materials, and that it is capable of being extended and applied to other problems (e.g., phase transformation and lamellar spheroidization) in the hot-working processes of materials.