Study On Macro-micro Mechanical Model And Ductility Fracture Criterion Of Rolled AZ31B Magnesium Alloy

Ductile fracture often occurs during stamping,spinning and bending of magnesium(Mg)alloy sheet at room temperature due to weak formability.There is a progound significance for optimizing the forming process by establishing a ductile fracture criterion based on a finite element model for Mg alloy sheet under complex stress state.Taking AZ31 B Mg alloy sheet as the investigated object.At first,the macro-micro mechanical model is established by coupling the viscoplastic self-consistent model(VPSC)and elastic deformation into ABAQUS subroutine.Then,the mechanical behavior and texture evolution of AZ31 B Mg alloy sheet under uniaxial tension and compression were studied,and the material parameters of macro-micro mechanical model were determined by fitting the true stress-true strain curves and texture evolution.Further,the macro-micro mechanical model was used to simulate the mechanical behavior and texture evolution under shear deformation both in the plane and through thickness,and the simulation results are consistent with the experimental results.At the same time,different notched specimens were drawn up and carried out tensile tests.The stress triaxiality,Lode parameters and fracture equivalent plastic strains were output based on the macro-micro mechanical model simulated the different specimens to establish ductile fracture criteria.Finally,experimental study on the fracture behavior of prefabricated hole plane stress specimens,and the fracture behavior of the specimens was simulated based on the macro-micro mechanics model and the ductile fracture criterion.The accuracy of the model was verified by comparison between experimental results and simulation resultsThe macro-micro mechanical model was established by constructing local coordinate system at the finite element integration point.The elastic strain and plastic strain in the local coordinate system are solved by the ABAQUS subroutine.The elastic part is solved by the incremental stress method defined by the Jaumann rate and the plastic strain part is calculated by calling the VPSC model.The macro-micro mechanical model considering the micro-deformation mechanism of magnesium alloys was established,ie,the macro strain,strain hardening and deformation texture caused by basal slip,the prismatic slip,the pyramidal <c+a> slip and the tension twin of polycrystal.The stress-strain curves and texture evolution were obtained by uniaxial tensile and uniaxial compression tests of AZ31 B magnesium alloy sheet along the rolling(RD)and normal(ND)directions.The initial texture of the alloy sheet is a typical basal texture.The mechanical properties show typical anisotropy and tension-compression asymmetry.The yield strength of tension along RD is about 70 MPa higher than that of compression along the RD.The yield strength of compression along ND is about 58 MPa higher than that of tension along ND;the tensile yield strength along RD is about 27 MPa higher than that of compression along ND compression;the yield strength of compression along the RD is about 15 MPa higher than that of tension along the ND;the stress-strain curves of tension along RD and compression along ND appear as an "convex up" shape;while the stress-strain curves of compression along the RD and tension along the ND exhibit an "concave down" shape.The texture evolution is different due to the different loading paths.When compression along RD,the texture is deflected from the parallel along the ND to parallel along the RD;when tension along ND,the texture is deflected from the initial parallel along the ND to parallel along the TD;when tension along RD and compression along ND,no significant deflection of the texture occurred.The macro-micro mechanical model was used to perform simulation of uniaxial tensile and compressive deformation,and the material parameters of the macro-micro mechanical model were determined by compared with experimentally obtained stress-strain curves and textures.The initial critical resolved shear stresses(CRSS),steady state CRSS,initial hardening rate and the asymptotic hardening rate of basal slip is 28 MPa,22 MPa,235 MPa and 11 MPa,respectively.The initial CRSS,steady state CRSS,initial hardening rate and the asymptotic hardening rate of prismatic slip is 89 MPa,134 MPa,264 MPa and 62 MPa,respectively.The initial CRSS,steady state CRSS,initial hardening rate and the asymptotic hardening rate of pyramidal <c+a> slip are 112 MPa,220 MPa,4468 MPa and 71 MPa,respectively.The initial CRSS of tension twin is 48 MPa,and other parameter values of tension twin are zero.Mechanical behavior and texture evolution of magnesium alloy sheet under shear deformation are simulated by the macro-micro mechanical model based on determines the material parameters.The shear stress-strain curves and textures of the simulation results are similar to the experimental results,and it is verified that the macro-micro mechanical model is accurate under simple stress state.The ductile fracture criterion of AZ31 B magnesium alloy sheet was established by the notched specimen tension experiment and corresponding the macro-micro mechanical model simulation results.Rod-shaped and plane notched specimens were intended to study the mechanical behavior and fracture behavior under high stress triaxiality.Plane specimens containing shear deformation were intended to study the mechanical behavior and fracture behavior under low stress triaxiality.Round rod specimens with different height-to-diameter ratios for compression experiments to study the mechanical behavior under negative stress triaxiality.Through the fracture morphology analysis,it can be known that the fracture morphology contains many shear planes under low stress triaxiality;while the fracture morphology of the samples is dimple fracture under high stress triaxiality.The texture of the sample by the macro-micro mechanical model simulation shows that the texture does not deflect under high stress triaxiality,but the texture deflects under low and negative stress triaxiality.The stress triaxiality,Lode parameters,equivalent fracture strain of the different samples were simulated by the macro-micro mechanical model.The quadratic polynomial and the Johnson-Cook function were utilized to fit the relationship between the stress triaxiality and the fracture-equivalent plastic strain.Under the high stress triaxiality,the fracture-equivalent plastic strain decreases as the stress triaxiality increases;Under low stress triaxiality,with the increase of stress triaxiality,fracture-equivalent plastic strain increases;Under negative stress triaxiality,with the increase of stress triaxiality,fracture-equivalent plastic strain decreases.L-H model and L-H-M model were used to establish the three-dimensional relationship function between stress triaxiality,Lode parameters and fracture equivalent plastic strain.The particle swarm optimization algorithm is used to solve the minimum of the error function and the least squares fitting to determine the parameters of the L-H model and the L-H-M model.By comparing with the experimental results,it is found that solving the error function method by PSO is better than the least squares method of solving the results.Finally,using the particle swarm optimization algorithm to solve the error function to determine the material parameters of the L-H-M model as a ductile fracture criterion applied to the forming of magnesium alloy sheet.The loading path has a significant effect on the ductile fracture behavior of prefabricated hole plane stress specimen,and it is verified that the macro-micro mechanical model is accurate under under complex stress state.In the macroscopic fracture morphology,fracture mode of the in-plane specimens is neck-shrinkage fracture,while fracture mode of through the thickness specimen is shear-linking up fracture.The stress triaxiality and fracture equivalent plastic strain of the location nearby the hole in the sample cross-section direction and the location at the centre of two holes with a cross section of 45° is output by the macro-micro mechanical model simulation.By analyzing the relationship between the stress triaxiality and fracture equivalent plastic strain at different positions of the hole,it was found that the stress triaxiality at the center of two holes which the cross section with 45° was at a low stress triaxiality and the corresponding fracture equivalent plastic strain is smaller,and nearby the hole in the cross-sectional direction was at high stress triaxiality corresponds to a relatively large fracture equivalent plastic strain in the ductile fracture criterion.Through the ductile fracture criterion analysis,it can be concluded that the in-plane specimen fracture is mainly due to the neck of voids under high stress triaxiality,while the fracture in the thickness direction is due to shear-linking up of voids under low stress triaxiality.