STEADY-STATE THERMOMECHANICAL ANALYSIS OF CONTINUOUSLY QUENCHED MATERIALS

This paper presents a methodology for thermomechanical analysis of a c ontinuously quenched material at steady state. The heat transfer assoc iated with the quenching process is governed by a convection-diffusion equation, and the thermal stress evolution is governed by the equatio n of motion and the constitutive equations. To formulate the thermomec hanical problem, the Petrove-Galerkin finite element method is used fo r 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 emp loyed. In a test problem with a classical viscoplastic constitutive mo del, numerical results are compared with analytical solutions and good agreement is achieved. An example for Aluminum plate quenching is pro vided to demonstrate the capability of this method. The results obtain ed with the present steady-state method agree well with the transient solutions, but the steady-state method requires significantly less com putational time than the transient method.