A three-dimensional multi-scale polycrystalline plasticity model coupled with damage for pure Ti with harmonic structure design

In this paper, we developed, on the basis of the crystalline plasticity and homogenization method, a three-dimensional multi-scale numerical model to simulate the non-linear and damage behaviors of pure titanium with harmonic structure (HS). The theoretical approach couples a kinematic hardening law for slip systems in the Ti hexagonal crystals; the consideration of the grain size effect modulated by the Hall-Petch law; a special localization-homogenization procedure to allow transforming the microscopic hardening law into the macroscopic constitutive law and avoiding the microstructure meshing of the grains in a bimodal grain distribution; and finally, the Lemaître-Chaboche macroscopic ductile plastic damage model in order to describe the granular damage. This model was implemented into a finite element code by means of the User Defined Material files. The results of the numerical simulation show that the proposed model can predict the crystalline plasticity behavior efficiently for bimodal HS Ti. Moreover, the computing time is optimized and reduced to a very low level.