Closed-form and numerical solutions to the laser heating process

Abstract

The laser processing of engineering materials requires an in-depth analysis of the applicable heating mechanism. The modelling of the laser heating process offers improved understanding of the machining mechanism. In the present study, a closed-form solution for a step input laser heating pulse is obtained and a numerical scheme solving a three-dimensional heat transfer equation is introduced. The numerical solution provides a comparison of temperature profiles with those obtained from the analytical approach. To validate the analytical and numerical solutions, an experiment is conducted to measure the surface temperature and evaporating front velocity during the Nd-YAG laser heating process. It is found that the temperature profiles resulting from both theory and experiment are in a good agreement. However, a small discrepancy in temperatures at the upper end of the profiles occurs. This may be due to the assumptions made in both the numerical and the analytical approaches. In addition, the equilibrium time, based on the energy balance among the internal energy gain, conduction losses and latent heat of fusion, is introduced.of evaporation (kJ/kg) I power intensity ( W/m2) I 0 peak power intensity ( W/m2) k thermal conductivity ( W/m K) 1 INTRODUCTION k B Boltzmann's constant m atomic weight (kg)The laser finds increasing commercial use as a machine p pressure (Pa) tool. However, for its use to be consolidated, it is necesp s recoil pressure (Pa) sary to explore the laser workpiece interaction mechanp z axial pressure (Pa) ism. Therefore, modelling the physical process can yield r radial distance (m) much insight into the complex phenomena occurring s, x distance from the surface (m) within the region activated by the laser beam. t time (s) Furthermore, modelling can substantially reduce the t eq equilibrium time (s) time required for process optimization, scale-up and T temperature ( K ) control. T s surface temperature ( K ) The modelling of temperature distribution induced by T sup superheat temperature ( K ) laser radiation in solids was previously investigated by V instantaneous velocity (m/s) several researchers (1-3) for stationary beam and for V liq liquid front velocity (m/s) moving beam interaction. In laser interaction mechan-V r evaporating surface velocity in the radial ism, the laser energy is absorbed at the surface by Fresnel direction (m/s) as well as surface plasma absorption (4). As the absorp-V vap vapour front velocity (m/s) tion is substantiated, the metal vapour reaches tempera-V z evaporating surface velocity in the axial tures much higher than the evaporation temperature, direction (m/s) resulting in strong ionization. The resulting plasma absorbs the laser radiation mainly by the effect of inverseThe MS was

Laser non-conduction limited heating and prediction of surface recession velocity in relation to drilling

“…They indicated that surfa ce temperatures and evaporating front velocities were in agreement with the experimental results. A closed-form solution for a step input laser heating pulse was presented by Yilbas et al [10]. They introduced the equilibrium time, which was based on the energy balance among the internal energy gain, conduction losses and latent heat of fusion.…”

Thermal Stresses in Micro- and Nanostructures

“…Equation [16] is the hyperbolic form of energy equation and to obtain a closed form solution for eqn [14], the following steps are introduced in line with the previous study (21).…”

“…Introducing the following equalities and dimensionless variables [16] to eqn [15] yields finally Introducing the following equalities and dimensionless variables [16] to eqn [15] yields finally…”

“…Considerable research studies were carried out to examine laser processing and thermal stress analysis (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20). The main focus of the previous studies is numerical modeling of thermal stresses during laser processing, which mainly deal with the uncoupled thermal analysis.…”

Laser shock processing of Ti-6Al-4V alloy

“…Yilbas et al [2] investigated the surface evaporation process and developed an analytical expression for the surface evaporation rate. Yilbas et al [3] carried out an analytical study on the high-power laser heating process while assuming a constant surface evaporation rate. This assumption gave limited accuracy compared with the actual case, since the surface evaporation rate is the function of the rise in surface temperature.…”