Quantitative Study On The Orientation Dependence Of Grain Boundary Strengthening In Hexagonal Close-packed Materials

Grain boundary strengthening constitutes one of the most important method to strengthen hexagonal close-packed（HCP）materials,and the strengthening effect could be well depicted by the Hall-Petch relation.Hall-Petch slope（k）is an important parameter reflecting the magnitude of strengthening due to grain refinement.A strong orientation dependence of grain boundary strengthening have been intensively reported for HCP materials,which is reflected by a highly changeable k with loading direction or texture.While the quantitative relation between orientation and k value is not clear.In this work,following studies were conducted to quantitatively study the mechanism for this orientation dependence of grain boundary strengthening for HCP-structured pure Ti and Mg alloys by combing the using of microstructure characterization,theoretical calculation and crystal plasticity finite element modeling（CPFEM）:（1）A new equation used to calculate Hall-Petch slope（k）based on the dislocation pile-up model was developed in this study.The validity of this new equation to calculate the orientation depence of k was tested through a comparison of the predicted k values with the experimental values of Mg alloys with different texture components.The results indicate that the new equation can achieve an accurate prediction for several previously reported texture effects on k.The reasons for this were analyzed and discussed.The strong deformation anisotropy for Mg alloys leads to a complex texture effect on k,including the effects from both external and internal stresses.Both effects are well expressed in the new equation.（2）A method by combining the Eshelby model and CPFEM to calculate the grain boundary strengthening effect for Mg alloys with different texture component was developed.Plastic deformation for AZ31 Mg alloys with different texture components are simulated using CPFEM,and the local stress near the grain boundary are carefully examined.The results shown that the simulated distributions of resolved shear stress near the grain boundary are consistent with that predicted by Eshelby model.The stress concentration factor representing the grain boundary strengthening effect for each boundary could be estimated by curve fitting the simulated stress profile with the Eshelby mode.The k values for Mg alloys with different texture component are well determined by estimating the stress concentration factor for each boundary,and results show that the calculated k values are similar to the experimentally determined ones.The relation between the barrier effect of each grain boundary and parameters that quantitatively describing the grain boundary strengthening effect,are systematically analyzed.（3）A strong orientation dependence of the k for pure Ti was reported in this study,that is,there is a much lower k for TD-tension of a Ti plate(188 MPaμm^1/2)than for RD-tension of the Ti plate(358 MPaμm^1/2),SD-tension(369 MPaμm^1/2)and SD-compression of a Ti rod(397 MPaμm^1/2)（where RD,TD,and SD refer to the rolling direction,transverse direction of the plate,and axial direction of the rod,respectively）.The mechanism behind this orientation effect is investigated by combining the use of CPFEM and Eshelby model.It is found that an orientation-mediated deformation transfer behavior is mainly responsible for this orientation effect.In this respect,for RD-tension,SD-tension,and SD-compression,a single slip system is predominant in most grains before deformation transfers into a neighboring grain,whereas additional slip systems are abundantly activated in individual grains for TD-tension.The activation of additional slip systems remarkably reduces the stress concentration intensity at grain boundaries and thus,leads to a much lower k.The reasons for the orientation-mediated deformation transfer behavior are also discussed.The results show that the activation of additional deformation modes is mainly determined by two factors:the difference in the Schmid factor（SF）between different slip systems in a grain,and the difference of activation stress（σ_d）between two neighboring grains.A smaller SF difference or a higherσ_d favor the activation of additional slip systems.There is often a smaller SF difference and a higherσ_d for TD-tension than that for other loading conditions,both of which contribute to the abundant activation of additional deformation modes in a grain under TD-tension.（4）Theoretical calculations and CPFEM were employed to disclose the mechanisms for the strong orientation dependence of grain boundary strengthening effect for HCP-structured metals.The results show that the effect of orientation on grain boundary strengthening can be ascribed to its effects on the ease of deformation transfer across grain boundaries and the activation of additional deformation modes in each grain.The results of theoretical calculations show that boundary misorientations often generate a much high activation stress difference and a poor geometrical condition for the deformation transfer in HCP materials,leading to a much more difficult deformation transfer in HCP materials.A harder deformation transfer will result in a higher grain boundary strengthening.It is found that the harder deformation transfer in HCP materials is related to the limited number of the easiest slip mode and the great difference of the critical resolved shear stress（CRSS）between easiest slip and harder deformation modes.Boundary misorientations will generate different activities of additional deformation modes in HCP materials.The results of CPFEM reveal that the activation of additional deformation modes will reduce the stress concentration factors at grain boundaries,and thus leads to a lower grain boundary strengthening.The fraction of grains with additional deformation modes for HCP materials is highly changeable with texture and CRSS ratio,a high activity of additional deformation modes will reduce the stress concentration at grain boundaries to a large extent,and thus decreases the grain boundary strengthening profoundly.