Coupled cellular automata-crystal plasticity modeling of microstructure-sensitive damage and fracture behaviors in deformation of α-titanium sheets affected by grain size

Abstract

Concerning the micro-scale deformation of titanium metal sheets, the number of grains in the sheet thickness direction decreases, and their formability exhibits a strong grain size sensitivity. Meanwhile, the twinning-induced dynamic recrystallization (TDRX) associated with grain size significantly affects the fracture behavior in the microforming of titanium sheets. Therefore, an accurate prediction of formability to improve manufacturing reliability remains challenging in the microforming of miniaturized titanium components. To address this issue, an in-depth understanding of the grain size-dependent TDRX behavior and its role in damage and fracture development in the microforming of α-titanium sheets is critical, and a coupled cellular automata-crystal plasticity (CA-CP) modeling framework was thus developed as an approach providing efficient solutions and insightful comprehensions of the issue. For the proposed modeling framework, a kinematic model for TDRX was established and integrated into the CP model by the CA algorithm. As a result, the microstructure evolution caused by TDRX was regarded as an intrinsic part of the constitutive behavior to connect heterogeneous plastic deformation and damage evolution through data transmission between the CP model and the CA algorithm. Additionally, the coupled CA-CP modeling framework was validated with the internal defect morphologies and deformation microstructures characterized by X-ray computed tomography (X-CT) and electron backscattered diffraction (EBSD). Experiment and simulation results demonstrated that the fine recrystallized (DRXed) grains were generated after the twin fragmentation when the dislocation density at twin boundaries reached a threshold of 9.2 × 10¹³ /m². After TDRX, the dislocation density and the stress concentration intensity in recrystallization regions were revealed to decrease, accounting for the ductility improvement. Nevertheless, the dislocation density at twin boundaries was determined to decrease with the increase of grain size, leading to less twin fragmentation and the absence of TDRX. The uncoordinated deformation between fine DRXed grains motivated defects to grow spherically into microvoids, thereby preventing premature intergranular cracks along twins/grain boundaries. Ultimately, the deformation microstructures resulting from TDRX with the decrease of grain size were confirmed to control the brittle to ductile fracture transition of α-titanium sheets. The presented modeling framework and simulation procedure were validated to be able to predict the material integrity affected by crystalline microstructure in the deformation of titanium metal sheets.