Modification Of The M-K Model For The Forming Limits Prediction Of Sheet Metal And Its Experimental Verification And Application

The plastic forming technology of sheet metals has been widely used in the manufacturing fields for aerospace,automobile,ship,food packings,household appliance and so on.The FLCs(Forming Limit Curves)is an effective method to estimate the plastic forming performance of sheet metal,which has significant guidance in determining the forming process parameters and improving material utilization.As one of the theoretical FLCs prediction models,the Marciniak-Kuczynski(M-K)model has been widely applied for its simple calculation form and high accuracy.However,the FLCs prediction accuracy under complex stress state of the original M-K model is extremely limited because the normal stress and friction condition are not considered.Besides,the empirical failure criterion(based on the difference of equivalent strain increment inside and outside the groove)is usually used in the current M-K models to identify the necking occurance,which cannot accurately predict the forming limits of materials that do not have obvious necking phenomenon before fracture.Therefore,the original M-K model is modified in this work for expanding its application ranges and improving its prediction accuracy of FLCs.The main research work and conclusions are listed as below(1)Firstly,the normal stress expression is established through analyzing the stress state of specimens in the Nakazima test and considering the stress gradient along the sheet thickness direction,and the friction stress expression is set up by analyzing the friction condition on the contact surface between the specimen and the punch.Secondly the normal stress in the M-K model is equivalent to the plane stress components based on the hypothesis that the spherical stress tensor induced by the hydrostatic pressure does not affect the plastic deformation of material,and the friction stress is added to the major stress direction considering the influence of friction force on the material deformation.On this basis,the modified M-K model that simultaneously integrates the normal stress and the friction stress is established.Compared with other M-K models reported in the literatures,the modified M-K model established in this work is verified to have higher prediction accuracy of FLCs.Finally,the influence of the model parameters and the material parameters on the predicted FLCs of sheet metal are systemically investigated.(2)The yield points of the Al-Mg-Li alloy sheet with significant anisotropy are determined through uniaxial and cruciform biaxial tension tests.The Hills's 48 and Yld2000-2d yield criteria are employed to describe the theoretical yield locus of this sheet,and results show that the yield locus predicted by the Yld2000-2d yield criterion which includes more material anisotropy parameters is much close to the experimental yield points.On this basis,the Yld2000-2d yield criterion is introduced into the modified M-K model established in this work to predict the FLCs of the Al-Mg-Li alloy sheet.Within the whole range of strain paths,the forming limits of the Al-Mg-Li alloy sheet could be accurately predicted by the combination of the modified M-K model and the Yld2000-2d yield criterion.(3)The true stess-true strain relationship of the Al-Mg-Li alloy sheet within different ranges of temperatures(25?-450?)and strain rates(0.00025s-1?0.01s-1)is determined and sectionally described by the improved Johnson-Cook constitutive model.Then,the improved Johnson-Cook constitutive model is introduced into the modified M-K model to predict the FLCs of the Al-Mg-Li alloy sheet under different temperatures.Results show that at 25? and 150?,the predicted FLCs of the modified M-K model and the improved Johnson-Cook constitutive model are very close to the forming limits determined by the Nakazima test,but under 250? the predicted values are obviously lower than the experimental results.(4)The Gurson-Tvergaard-Needleman(GTN)meso-damage model is introduced into the modified M-K model for describing the nucleation and growth of voids inside the materials during the deformation process.The critical value of void volume fraction in the groove area is taken as the material failure criterion,and the 3D M-K-GTN model is established in this work.Compared with other M-K model employing the empirical failure criterion in the literatures,the 3D M-K-GTN model that applies the damage failure criterion has higher FLCs prediction accuracy for the AA6016 sheet,and solves the problem that the right hand of the predicted FLCs is obviously higher than the actual forming limits of material.