Mathematical modelling of striation formation in oxygen laser cutting of mild steel

Abstract

A physicomathematical model is proposed for the phenomenon of formation of periodic striations in oxygen laser cutting of mild steel sheets. The mechanism of roughness origination is assumed to be caused by a cyclic reaction of iron–oxygen oxidation. The mathematical description is based on solving the adjoint problems of heat and mass transfer in the liquid phase and in the solid metal with nonlinear moving interfaces between the substances and phase changes. The motion of the boundaries occurs owing to metal melting under the action of focused laser radiation and the heterogeneous chemical reaction of iron oxidation in oxygen. The main feature of iron oxidation is the loss of protective properties of its oxide film due to melting. The general statement of the problem for the nonlinear heat-conduction equation with variable coefficients is formulated by the type of the Stefan problem solved with the use of the difference method with smoothing coefficients at the melting point and the fictitious domain method, which allows obtaining of the solution without explicit identification of the cut boundary and the phase-transition front. Results of numerical simulations of the shape and linear size of roughness as functions of the cutting velocity, purity of oxygen and thickness of the film of the iron oxide being formed are presented.

Modeling of laser-induced combustion of iron in oxygen during gas-laser cutting

“…The indicated methods [20][21][22] allow calculations without explicitly distinguishing the moving boundaries Γ 0 , Γ 1 , and Γ 2 . Adaptation of the indicated methods to the problem considered above in the case of a two-dimensional formulation is described in detail in [10].…”

“…In a number of papers [3][4][5][6][7][8][9][10], the mechanisms of striation formation during oxygen gas-laser cutting of steel are treated using physical concepts based on the theory of cyclic oxidation of iron in oxygen [3]. Chemical oxidation reactions are initiated in the zone of thermal action of the laser beam and are accompanied by periodic cycles of ignition, combustion, and quenching.…”

“…Ermolaev [10] showed that the periodic combustion cycles initiated by the laser beam energy decay because of a decrease in the temperature of the front due to great heat transfer to the solid metal. The reaction rate increases with complete melting of the oxide film.…”

“…In [10], a two-dimensional formulation of the problem is proposed, and the temperature field is calculated ignoring heat transfer to the depth of the sheet; the flow of the liquid film was not considered. The cycles of ignition, combustion, and quenching were modeled without invoking artificial restrictions or experimental data.…”

“…In the present work, an attempt is made to extend the previously proposed model [10] to the threedimensional case.…”