Study Of Anisotropic Mechanical Behavior Of AZ31B Rolled Magnesium Alloy

The study of the mechanical behavior of metals has developed into a multi-level and cross-scale modeling approach in recent years.The methods can be broadly divided into macro-scale phenomenological and micro-scale constitutive models.Considering the computational efficiency and cost of engineering problems,macroscopic phenomenological is widely used in engineering applications.Establishing a constitutive model that accurately reflects the essential properties of materials is the basis for reliable analysis of engineering problems.AZ31B rolled magnesium alloy is widely used in industrial production due to its high specific strength and stiffness.The rolled AZ31B sheet has a significant anisotropic mechanical behavior due to the orientation of the grains.AZ31B sheet needs to be reworked and formed in practical engineering,so it is essential to study its anisotropy and strength differential to establish a constitutive model that can describe its mechanical behavior for the forming and application of magnesium alloy sheet.This paper summarizes the basic concepts of elastic-plastic model establishment,establishes the AZ31B elastic modulus matrix,summarizes the method of transforming isotropic invariants to anisotropic properties,and proposes the distortion-hardening model for describing the hardening behavior of AZ31B rolled magnesium alloy.The two flow rules are compared and the plastic potential function is established based on the Non-associated flow rule.The loading criterion and consistency conditions are summarized.To establish an elastic-plastic constitutive model and finite element model for AZ31B rolled magnesium alloy,the equivalent plastic strain and plastic multipliers based on different flow rules are derived.An applicable stress update algorithm is selected for the proposed constitutive model.Based on the characteristics of the AZ31B,the odd functional criterion that involves both invariants of the stress deviator is used and extended to orthotropy for describing plastic anisotropy and SD effects.The specimens of AZ31B rolled magnesium alloy with five orientations(0~°30~°,45~°,60~°and 90~°along the rolling direction)were subjected to uniaxial tensile,uniaxial compression,and shear loading.Deformations of the three types of experiments are captured by the DIC,and the true stress-true strain data are obtained by Match ID software.The strength anisotropy of AZ31B rolled magnesium alloy was analyzed by comparing true strain-true stress data of tension and compression with different directions.The appropriate models were selected to description hardening behavior by comparing the results of existing hardening model and improved model under different working conditions.Based on the plastic work equivalence principle,the plastic work is obtained by integrating the stress-plastic strain under various working conditions with different orientations.The true stress-equivalent plastic strain relationship,and plastic strain ratio-equivalent plastic strain relationship are obtained for different orientations and various stress states.The evolution of anisotropic parameters in the yield criterion and plastic potential function are described by interpolation and fitting.The yield surface and plastic potential surface characteristics at different strain levels are compared and analyzed.The anisotropic deformation hardening constitutive model with parameters evolution is established,and the material constitutive model is implemented into finite element simulation through Abaqus by VUMAT material subroutine.The availability of the proposed model is demonstrated by comparison with experimental results,which provides theoretical and technical support for the reliability in material processing and engineering applications.