THERMAL-STRESS EVOLUTION IN CONTINUOUSLY QUENCHED CIRCULAR BARS

This paper presents a finite element method for studying continuous qu enching processes with emphasis on thermal and stress analyses of axis ymmetric problems. Both the thermal and stress problems involved in th e quenching process are formulated in the Eulerian frame. The heat tra nsfer problem is solved with the Petrov-Galerkin method due to the con vetion-diffusion nature of the governing equation. For the thermal str ess problem, since the acceleration term in the equation of motion is small, it is neglected and the equilibrium equation is solved. The ine lastic deformation associated with the quenching process is modeled wi th the visco-plastic type of constitutive laws. To determine the inela stic deformation of the quenched body, the inelastic strain rates are integrated along the quenched body with the Petrov-Galerkin formulatio n applied to the material derivatives of the inelastic strain rates. A n example problem for a continuous bar quenching process is studied wi th the method presented in this paper. With the present method, comput ational time needed is significantly less than that with Lagrangian ap proaches. (C) 1997 Elsevier Science Ltd.