New Characterization Of Orthotropic Yield Behavior Of HCP Metals

Hexagonal close packed(HCP)metals and alloys play an important role in modern society.They have been widely used in many fields such as aviation,aerospace,trans-portation,electronic products and so on,and their huge values in application have drawn the attentions of materials and mechanics researchers,the research on their anisotropic plastic behaviors and the theories in their applications have been substantially conducted.Since the orthotropic yield criterion[1]proposed by Hill in 1948,various forms of or-thotropic yield criteria have been proposed and used to describe the orthotropic plastic behaviors of sheet metals.However,the early orthotropic yield criteria are not suitable for describing the orthotropic behavior of HCP metals.The yield criterion CPB06[2]established by Cazacu et al.in 2006 for the orthotropic behaviors of HCP metals is a yield function expressed by the deviatoric tensor of principal stress,and can be more accurately in line with the experimental observations on several HCP metals.However,its mathematical form described in the space of the deviatoric tensor of principal stress causes a difficulty in its FEM implementaiton.Based on the analysis of the plastic deformation mechanisms of HCP metals(such as titanium alloys and magnesium alloys,etc.),the present work is focused on the yield strength difference and the orthotropic yield characteristics of HCP sheet metals.On the basis of the yield criterion established by Cazacu et al[2],the mathematical form of CPB06 described in the deviatoric space of principal stress is extended to the deviatoric space of stress,and a new orthotropic yield criterion has been established.From the new yield criterion,the expressions of the material parameters under different experimental conditions have been derived.By using the experimental data obtained from literatures,the material parameters in the criterion are determined.These works set a foundation for the numerical implementation of the new criterion.In order to well suit the application of the yield criterion at finite deformations,the criterion is formulated in the local polar corotational(i.e.R-corotatonal)coordinate systems.By using the convex property of the yield function,the inequality of internal dissipation under the polar corotational condition and the maximum plasticity dissipa-tion theory,the theoretical framework at finite elastoplastic deformations has been con-structed.In the aspects of numerical implementation,the stress update algorithm and the consistent tangent modula of the algorithm have been deduced.A UMAT subroutine embedded in the general finite element program ABAQUS has been coded.Further,the subroutine has been used for the numerical predictions of the experimental results ob-served by Gilles et al[3]and Khan et al[4].The results show that the numerical prediction of the yield criterion are well consistent with the experimental observations,therefore,it can be drawn that the yield criterion,the algorithm and the subroutine are effective in describing the orthotropic yield behaviors of the HCP sheet metals.The orthotropic yield criterion and the corresponding numerical algorithm con-structed in this thesis can circumvent the difficulties in the numerical implementation of CPB06,and sets a solid foundation for further theoretical and numerical analyses of HCP metal forming.