Abstract

A closed-form analytical solution has been developed, using the known Green's function method, for the time-dependent temperature evolution inside an infinitely extended solid medium of finite thickness induced by a moving cylindrical laser beam with gaussian energy distribution. Physical properties were taken to be temperature independent and no phase changes are considered in this model. The domain geometry consists of a semi-infinite sheet of finite thickness. The laser is coupled to the surface by pure conductive heat transfer mechanism taken as a uniaxially moving non-linear boundary condition; heat loss by convection mechanism is also included at the latter boundary. At the bottom of the sheet total insulation is applied as the boundary condition. This model allows the estimation of process parameters (i.e. Fourier and Peclet numbers) during laser heat treatment of metal alloys such as laser annealing, bending and surface hardening. Due to the fact that the coordinate system is fixed to the laser beam axis and the time dependence is short lived, the model can be considered to behave in a quasi-static manner for practical purposes. Numerical results are presented for a 1 mm thick Al-Cu alloy sheet scanned at different velocities with a 250 W cw CO2 laser.