PSI - Issue 65

D.S. Bezverkhy et al. / Procedia Structural Integrity 65 (2024) 17–24 D. S. Bezverkhy and N. S. Kondratev / Structural Integrity Procedia 00 (2024) 000–000

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order of 0.8 – 0.9, then after compression the workpiece is rotated to a certain angle. During such processing, dynamic recrystallization occurs in the material.

Fig. 1. Scheme of multistage upsetting.

3. Mathematical formulation of problem

The finite element modeling software Abaqus and its built-in phenomenological model of plastic flow theory are used to simulate multistage upsetting. Within the framework of this theory, an additive decomposition of the strain rate into plastic and elastic components is used; Hooke’s law is used for the elastic component, and the associated law of plastic flow is used for the plastic component. The values of the strain rate tensor components D and temperature Θ of individual material points obtained in this way are then transmitted to a multilevel constitutive model (Bezverkhy D. S. & Kondratev N. S. ( in Print )) for a detailed study of the material structure state, taking into account the dynamic recrystallization process. During the simulation of the hot upsetting process, the initial workpiece configuration is a solid cylinder of radius R w = 0.2 m and height H w = 0.6 m preheated to temperature Θ = 1150 °C. Its finite element (elements of type C3D8R – hexahedrons) partition used in the calculations is shown in Fig. 2 along with pairs of parallel non deformable planes modeling the pressing tool. The orientations of these pairs relative to the X , Y , Z axes of the laboratory coordinate system were chosen in such a way as to effectively reproduce the physical rotation of the deformed workpiece between stages.

Fig. 2. Finite element model of the hot upsetting problem of a cylinder.

The mathematical formulation of the boundary value problem of determining the stress-strain state is given in (Trusov P. V. & Ostapovich K. V. (2023)). The mathematical formulation of the multilevel constitutive model of dynamic recrystallization is described in (Bezverkhy D. S. & Kondratev N. S. ( in Print )). The kinematics of the tool was specified by the speeds v Y , v Z , v X of approaching planes at successive stages, i.e. along Y , Z , X respectively. During these stages, each lasting T = 1 s, the indicated speeds had the values (m/s): v Y = 0.28, v Z = 0.20, v X = 0.25. During deformation, sources of energy dissipation leading to a temperature increase were not taken into account, i.e. the process was assumed to be isothermal with a uniformly distributed temperature over the workpiece under consideration.