When discussing the elasticity and plasticity of materials, it is considered that under a certain external load, the relationship between stress and strain in the object is constant, regardless of the duration of the load action. This assumption is reliable in the case where the forming temperature is not high, the duration of the external load is not long, and the unloading speed is not high. However, when the deformation temperature is high and the deformation speed has a significant influence on the yield of the material, the viscoplastic finite element must be used.
Since the temperature change is a major factor in the stress change of the workpiece during the heat treatment. Therefore, to accurately analyze the temperature and stress changes during the deformation process, it is necessary to calculate the two different field quantities of temperature and deformation, that is, to deal with two different field equations of heat balance and force balance.
The incremental finite element expressions for the elastoplastic analysis described by the updated Lagrangian method are as follows: 11 For large workpieces with a volume of V, a density of, and a boundary of S, the energy conservation equation is:
VvivitdV VtUdV=V(Q bivi)dV S(Pivi-H)dS where vi is the velocity field; U is the internal energy; Q is the volumetric heat flow; bi is the fixed volume force; Pi is the boundary force per unit area; The heat flow intensity per unit area on the boundary S. Establish the integral equilibrium force equation: V(bi-vit)dV=SPidS where Pi is an applied load and introduce the Cauchy stress component ij, which can be expressed as: Pi=njij can be obtained by introducing the force balance equation into the energy equation. - Force-coupling energy conservation equation; V(Q-Ut ijvixjdV=SHdS according to the principle of virtual work, there are: VijuixidV=VbiuidV-VvituidV because the heat treatment process analysis is quasi-static analysis, the influence of the inertia term can be ignored, the second right end of the formula The term can be omitted. The finite element solution is: at the beginning of each incremental step, the region V and the boundary S are corrected by the current displacement increment, and then the force balance and mass conservation equations are alternately iterated in the incremental step.
The calculation model gear shaft heat treatment model is an axisymmetric model. In order to improve the calculation efficiency, this study only discretizes its 1/2 part, and adopts a four-node quadrilateral unit. The parameters used in the calculation are as shown in 1. The simulation results show the equivalent strain distribution cloud diagram of the 12Cr gear shaft when the cooling time is 0s, 150s, 300s and 600s respectively.
The strain in the cooling process is mainly concentrated at the steps and forms a distinct transition zone. This is because the change of the external dimensions of the workpiece leads to the difference of the cooling speed at different radii, which causes the internal stress generated by the phase transformation to produce obvious stress at the step during the transformation of austenite to pearlite and martensite. Concentrated phenomenon. This has been verified in actual observations.
It can be seen that the cooling speed of the gear shaft core portion is slow, and the end portion cooling speed is fast. Properly increasing the cooling rate or extending the cooling time can improve the microstructure of the core. Due to the large difference in the size of the end and the core, the method of segmental cooling may have a better effect on this 12Cr gear shaft.
Clearly shows the transformation of the gear shaft during the cooling process of martensite. Combined with the temperature field distribution, it can be said that the transformation of martensite is mainly concentrated at a lower temperature, and some unconverted pearlite or austenite remains.
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