STEADY-STATE THERMOMECHANICAL ANALYSIS OF CONTINUOUSLY QUENCHED MATERIALS

摘要

This paper presents a methodology for thermomechanical analysis of a continuously quenched material at steady state. The heat transfer associated with the quenching process is governed by a convection-diffusion equation, and the thermal stress evolution is governed by the equation of motion and the constitutive equations. To formulate the thermomechanical problem, the Petrove-Galerkin finite element method is used for the heat transfer problem, while the virtual work principle with the finite element method is applied to the thermal stress problem. Both the thermal and stress problems are solved in the Eulerian frame with the inelastic strain rate systematically integrated along the quenched material. To integrate the inelastic strain rate, a weak formulation is applied to the material derivative of the constitutive equation for inelastic deformation, where the Petrove-Galerkin approach is also employed. In a test problem with a classical viscoplastic constitutive model, numerical results are compared with analytical solutions and good agreement is achieved. An example for Aluminum plate quenching is provided to demonstrate the capability of this method. The results obtained with the present steady-state method agree well with the transient solutions, but the steady-state method requires significantly less computational time than the transient method.