New Orthotropic Yield Theory Of Hexagonal Close Packed Metals

Hexagonal close packed(HCP)metals and alloys have been widely applied on the aspects of engineering structures,biomedical and defense industries and so on.Due to their huge application values,more and more studies are focused on the crystal structures of HCP metals and their physical and mechanical properties.It is shown that due to the low symmetry of their crystal structures the HCP metals present clearly the anisotropic plastic behaviors.Since the Hill48 criterion[1],numerous anisotropic yield criteria have been proposed for metals and verified numerically and experimentally,it is found however that they cannot describe the orthotropic behaviors of HCP sheet metals effectively.In 2006,Cazacu et al[1]established the CPB06 criterion,which can predict the plastic properties of a wide range of HCP metals(e.g.magnesium alloys,titanium alloys,and etc.)effectively.Because the CPB06 criterion is established in the principal stress space with the effects of shear stress components being ignored,its numerical implementation becomes tedious and complicated due to the involved partial derivatives of the principal stress components with respect to the general stress components.In order to overcome these shortcoming of the CPB06 criterion,a new orthotropic yield criterion described in the general stress space is presented,and is applied to characterize the orthotropic plastic behaviors of AZ31 magnesium alloy plates under different temperatures and loading rates on the basis of the experimental results of Khan et al[3].The following aspects have been conducted in the work:(1)Based on the consideration of the plastic deformation mechanisms of HCP metals,the present work is focused on the difference of the tensile and compressive yield strengths and the orthotropic yield characteristics of HCP sheet metals,and the main factors affecting the plastic behaviors of the HCP sheet metals are summarized.(2)On the basis of the CPB06 yield criterion proposed by Cazacu et al,a new orthotropic yield criterion described in the general deviatoric space of stress is formed.Then,from the new criterion,a series of specific yield functions are derived for multiple loading conditions(3)By comparing the yield curves drawn by using the new criterion and the Hill48 criterion,it is proved that the new yield criterion can characterize the difference of the tensile and compressive strengths and the anisotropic plastic behavior of HCP metals.(4)By using the mechanical properties of the AZ31 alloys at different temperatures and strain rates,the sensitivity coefficients of stain rate and temperature in different directions are calculated,and the effects of the two factors on the tensile and compressive properties of AZ31 are obtained.Further,the effectiveness of the new criteria is verified by comparing the yield curves predicted by it and the experimental results under different plastic strain levels.(5)From the experimental data under different temperatures and strain rates,the tensile and compressive hardening rate parameters in several directions are calculated.By using a finite element program,the stress-strain curves in different loading directions are simulated,and further compared with the experimental observation of Khan et al.[3],it is shown that numerical prediction of yield criterion is consistent with the experimental results,it can be concluded that the yield criterion,numerical algorithms and proceduresThe orthotropic yield criterion and the corresponding numerical program established in this thesis can circumvent the difficulties in the numerical implementation of CPB06,and sets a solid foundation for further theoretical and numerical analysis of HCP metal forming.