Abstract :
This paper presents a finite element method for studying continuous quenching processes
with emphasis on thermal and stress analyses of axisymmetric problems. Both the thermal and stress
problems involved in the quenching process are formulated in the Eulerian frame. The heat transfer
problem is solved with the Petrov-Galerkin method due to the convetion-diffusion nature of the
governing equation. For the thermal stress problem, since the acceleration term in the equation of
motion is small, it is neglected and the equilibrium equation is solved. The inelastic deformation
associated with the quenching process is modeled .with the visco-plastic type of constitutive laws.
To determine the inelastic deformation of the quenched body, the inelastic strain rates are integrated
along the quenched body with the Petrov-Galerkin formulation applied to the material derivatives
of the inelastic strain rates. An example problem for a continuous bar quenching process is studied
with the method presented in this paper. With the present method, computational time needed is
significantly less than that with Lagrangian approaches. © 1997 Elsevier Science Ltd.
