Subsequent Yield Behavior Of HRB400E Steel Under Tension-torsion Combined Loading And Anisotropic Yield Surface Model

The fracture of engineering structure is mostly caused by the failure of the metal.In order to ensure the safe service of metal structure,it is necessary to study the law of plastic deformation for members and structures under various complex loading conditions.The plastic deformation of the material is described by the evolution law of the subsequent yield surface,and the analysis of the yield surface is the most effective means to reveal the law of plastic deformation.A reasonable yield surface function is essential to investigate the plastic yield and flow behavior.The anisotropy induced by plastic deformation of metal materials dominated by the various preloading history,which is a scientific problem to be urgently solved.The subsequent yield characteristic and the plastic flow law of HRB400E steel under proportional and non-proportional tension-torsion combined loading have been studied by thin-walled circular tube specimens,and a new anisotropic yield surface theoretical model has been developed.The simulation of the subsequent yield surfaces for HRB400E steel,T2 pure copper and 45 steel has been performed to validate the capability of the proposed model.The main work and conclusions are summarized as follows:1.The cyclic softening and cyclic stability of HRB400E steel are studied by the axial symmetric cyclic experiments with eight strain amplitudes including 0.3%?0.4%?0.5%?0.6%?0.7%?0.8%?0.9%and 1%.The cyclic stability process of HRB400E steel under low strain amplitude loading is slow,and the cyclic stress-strain curve of HRB400E steel under high strain amplitude become stable after about ten cycles.The tensile elastic modulus of HRB400E steel decreased slightly after cyclic loading,and the tensile strength,fracture strain and tough fracture mode of HRB400E steel have not been affected by the 100-cycle loading.The yield limit of HRB400E steel decreases after the low strain amplitude cyclic loading,and the yield limit of HRB400E steel increases after the higher strain amplitude cyclic loading.2.The shapes of subsequent yield surfaces determined by different offset strains under pre-tension,pre-torsion and pre-tension-torsion proportional loading conditions are similar,and the size of yield surface increases gradually with the increase of offset strain.The yield surfaces determined by different offset strains are almost tangent in the preloading direction and expand mainly in the opposite direction of preloading.The shape of the subsequent yield surface is related to the preloading direction,presenting the characteristic of“flat at front and back,small in front and big in back"along the preloading direction.The subsequent yield surface under tension is relatively convex along the loading direction,and the yield surfaces under pre-torsion and pre-tension-torsion are slightly concave along the loading direction.3.The subsequent yield surfaces present the remarkable anisotropic deformation characteristic under six combined tension-torsion loading paths.The yield surfaces determined by different offset strains are almost tangent at the yield point along the preloading direction and expand similarly in the opposite direction of preloading with the increase of the offset strain,which shows the nonlinear hardening processes.The subsequent yield surface under pre-tension and then pre-tension-torsion indicates the characteristic of"the sharp point in pre-deformation direction and the relatively flat bottom at its opposite direction".The shapes of subsequent yield surfaces under other five kinds of bilinear tension-torsion combined preloading are like"pebble".4.There is a certain deviation between the experimental plastic strain:flow direction and the normal direction under the six bilinear tension-torsion preloading paths,and the size of the angle between the plastic strain flow direction and the orthogonal direction has certain dispersion at different yield points,and the angle decreases with the increase of the offset strain.5.Considering the loading history and hardening behavior of material during reloading,an anisotropic distortional yield surface constitutive model has been developed by introducing an anisotropic distortion yield function into the isotropic hardening term.The implicit integral algorithm and tangent stiffiness matrix of anisotropic constitutive model have been derived.The experimental data of subsequent yield surfaces for HRB400E steel,T2 pure copper and 45 steel under pre-proportional loading have been simulated by implementing the models into a numerical user defined material(UMAT)procedure based on the ABAQUS finite element package.The simulations demonstrate that the proposed model can well describe the anisotropic yield characteristic of the three metals under pre-proportional loading.Moreover,the cross-effect of subsequent yield surfaces for HRB400E steel,T2 pure copper and 45 steel and the evolution of anisotropic yield surfaces to isotropic yield surfaces under reloading can be captured,which verifies the reasonability and validity of the proposed model and lays a foundation for theoretical analysis of subsequent yield and hardening behavior of other metals.