Subsequent Yield Of Orthotropic Sheet Metal

Sheet metals generally exhibit anisotropic properties after the rolling and annealing processes,which strongly affect the formability and final performance of products,and also brings great difficulties to the development of forming process.In recent years,scholars at home and abroad have made great progress in the study of anisotropic behavior of sheet metals,and established various forms of anisotropic yield models to describe the anisotropic properties under different conditions.With the help of finite element analysis software,the cost caused by trial and error is effectively reduced,and the development efficiency of new products is significantly improved.However,the prediction accuracy of finite element software highly depends on the accuracy of yield model in describing the mechanical behavior of materials.Therefore,establishing a constitutive model that can accurately predict the anisotropic behavior of materials has always been one of the key and difficult problems in the field of plastic forming.On the one hand,the descriptive ability of anisotropic yield model depends on the equation form,on the other hand,it is directly related to the initial yield and subsequent yield test data used to calibrate anisotropic parameters,including uniaxial tensile stress,anisotropic coefficient and biaxial tensile stress.Therefore,the subsequent yield deformation behaviors of orthotropic metal sheet are studied in this paper.In the research of anisotropic coefficient r-value,firstly,the application conditions and limitations of three existing methods for solving variable r-value are compared and analyzed.On this basis,a reverse model for solving variable r-value is proposed.By analyzing the fitting error,the reliability of the inverse method is verified.Based on standard uniaxial tensile test and digital image correlation(DIC),the evolutions of r-value in the uniform deformation stage and the large deformation are studied,which lays a foundation for the establishment of subsequent yield model considering r-value evolution.The evolution of diffuse necking region and the distribution of stress and strain on the narrowest cross section of uniaxial tensile specimen are analyzed by the combination of DIC and numerical simulation.A hardening model for solving the stress and strain of anisotropic sheet metal in the diffuse necking stage of uniaxial tension is established.The reliability of the model is verified by the uniaxial tensile test of four kinds of low carbon steel plates and three typical anisotropic directions.These work not only reveal the deformation mechanism of diffuse necking in uniaxial tension for anisotropic sheet metal,but also provide a simpler and reliable method to obtain the stress-strain relationship of large deformation.Based on the above research methods,the distortional hardening and the evolution of yield locus in subsequent yield are analyzed.By constructing the stress error function and taking r-value as the constraint condition,a method for determining the anisotropic parameters of coupling distortional hardening and r value evolution is proposed.And then,an evolving non-associated Hill48 model considering the anisotropic evolution in subsequent yield is established.Through tensor coordinate transformation,the theoretical yield loci under different stress principal axis directions are given,and the diversity of yield locus caused by different stress principal axis directions is verified based on cruciform tensile tests in different directions in the plane.Based on the mathematical analysis of yield equation,the limitations of Hill48 yield model in predicting uniaxial tensile yield stress and r-value are studied.Taking various types of materials as the research object,the effects of parameters determination methods and test data on the prediction results under different stress states are explored.The necessary and sufficient conditions for judging the applicability of Hill48 yield model to different materials are established.The results show that due to the limitations of the equation,no matter what parameter determination method is used,it cannot simultaneously predict the anisotropic behavior under different stress states.For this,without changing the form of Hill48 quadratic function,the direction of stress principal axis is introduced into the anisotropic parameters,and a modified Hill48 model suitable for plane stress state is established.The theoretical prediction results show that the modified model can accurately predict the uniaxial tensile yield stress,r-value,yield locus and their evolution in subsequent yield for low carbon steel,high strength steel and some aluminum alloys based on the associated flow criterion.