Cyclic Constitutive Model Of High-Speed Railway Train Axle Steel EA4t And Finite Element Implementation

Axle is one of the key mechanical components of high-speed railway bogie.When high-speed railway train starts,brakes and runs in harsh working environment and extreme conditions,the axle will often bear the effects of torsional alternating load,bending alternating load and axial tension compression alternating load.In this case,the axle is easy to produce local plastic accumulation.Even the axle will produce bending,wear,cracks and other faults in the design fatigue life,which brings challenges to safety of high-speed railway train.Therefore,the study of cyclic deformation mechanism of axle steel EA4 T has become an urgent scientific problem.In this paper,the cyclic deformation of high-speed railway train axle steel EA4 T is studied by experiments and theory.The main research work is as follows :(1)At room temperature,the cyclic softening and hardening characteristics and ratcheting behavior of high-speed railway train axle steel EA4 T were studied by considering uniaxial and non-proportional multiaxial loading paths.The experimental contents are as follows: Firstly,at different strain rates,the monotonic tensile stressstrain characteristic curves of axle steel EA4 T are studied,and it is found that the axle steel EA4 T has obvious viscous characteristics.Secondly,under symmetrical strain controlled cyclic loading,the dependence of cyclic softening/hardening behavior of high-speed train axle steel EA4 T on strain amplitude,strain rate and non-proportional multiaxial loading paths is discussed.Finally,under asymmetric stress controlled cyclic loading,the dependence of ratcheting behavior on stress level,stress rate and multiaxial loading paths and its evolution with cycle number were studied.The relevant experimental research results have laid a foundation for the development of more advanced macro cyclic constitutive model theory.(2)In the framework of elastic-plastic theory,A cyclic elasto-plastic constitutive model based on dissipative plastic energy is proposed.The specific idea is that dissipative plastic energy(instead of cumulative plastic strain)and dissipative plastic energy rate(instead of cumulative plastic strain rate)are introduced into the ratche tting parameter evolution equation and isotropic evolution rule respectively as internal variables.From the viewpoint of energy,the evolution rule of unclosed hysteresis loops under strain controlled or stress controlled cyclic is described.By comparing the numerical simulation with the experiment,it is verified that the model can effectively predict the rate independent cyclic softening characteristics and the rate independent ratcheting behavior of axle steel EA4 T.(3)In the framework of visco-plastic theory,based on the Ohno-Abdel-Karim nonlinear kinematic hardening rule,A unified cyclic visco-plastic constitutive model of moving back stress critical interface is proposed.Specifically,it is considered that the threshold of dynamic recovery term in the Ohno Abdel Karim model is not a constant,but changes with the evolution of cumulative plastic strain rate,which can indirectly weaken the effect of dynamic recovery term in back stress evolution equation and reasonably describe the ratcheting behavior of axle steel EA4 T.By comparing the numerical simulation with the experiment,it is verified that th is model has good prediction ability in describing the rate dependent behavior of axle steel EA4 T.(4)In the framework of elastic-plastic theory,based on the historical memory effect of fractional derivative,a fractional time-dependent cyclic constitutive model is proposed.Specifically,it is assumed that the viscosity function is defined as the fractional differential form of cumulative plastic strain,and t he fractional order can control the viscosity and change with the increase of plastic strain accumulation time.Moreover,in the numerical implementation,Radial return method with moving back stress critical interface is still used.It is found that fractional derivative is a flexible mathematical tool in describing the viscous properties of materials.(5)In the aspect of finite element implementation of cyclic constitutive model,the cyclic elasto-plastic constitutive model based on dissipated plastic energy is implemented into finite element code by using user material subroutine interface(UMAT).In this process,the consistent tangent stiffness matrix about the model is derived again to ensure the iterative convergence of the finite element n umerical calculation.An element body C3D8(simulating uniaxial tension compression cyclic deformation)and a hollow thin-walled cylinder(simulating multiaxial tension compression torsion cyclic deformation)are established as examples to verify the correctness of the finite element implementation of the model.