The mechanism for an orientation dependence of grain boundary strengthening in pure titanium

The Hall-Petch slope k represents the magnitude of grain boundary strengthening. For the first time, a strong orientation dependence of the k for pure titanium (Ti) is reported in the present study, namely, a much lower k for the TD-tension of a Ti plate (188 MPa μm1/2) than the k values for the RD-tension of the Ti plate (358 MPa μm1/2), SD-tension (369 MPa μm1/2) and SD-compression (397 MPa μm1/2) of a Ti rod. Here, the RD and TD are respectively the rolling direction and transverse direction of the plate, and SD is the axial direction of the rod, while tension and compression stand for uniaxial tension and compression, respectively. It is found that the mechanisms reported previously cannot explain the orientation dependence of k experimentally observed in the present study. A new mechanism is proposed by combining crystal plasticity finite element modeling and the Eshelby model for the stress concentration at grain boundaries. The results indicate that an orientation-mediated deformation-transfer is the main contributor to this orientation effect on k. More specifically, for the RD-tension, SD-tension and SD-compression, a single slip system is predominant in most grains when plastic deformation-transfer occurs. In contrast, multiple slip systems are activated in the majority of grains in the TD-tension. The activation of additional slip systems remarkably reduces the stress concentration at grain boundaries, leading to a lower k. Afterward, the reasons for the orientation-mediated deformation transfer behavior are discussed.