Three-dimensional thermal simulation of nanosecond laser ablation for semitransparent material

Highlights

• Heat source model for laser processing of semitransparent material is proposed.

• Both reflection and transmission of laser are considered in the model.

• The effects of the material shape and transparency were simulated.

• The model is readily applicable for three-dimensional laser processing simulation.

• The experimental result shows a good agreement with the simulation by the model.

Abstract

A numerical study of nanosecond laser ablation process for semitransparent material was performed. A heat source model using ray tracing is suggested for three-dimensional simulations of laser material processing based on the volume-of-fluid (VOF) method. The model is capable to describe both the ray transmission into the material and the reflections from the material surface. In the computational implementation of the model, a stochastic approach was introduced to avoid the recursive branching of an incident ray into transmitted and reflected rays. Since the ray tracing highly depends on the shape of the target material, proper surface reconstruction method is also considered. For the spatially continuous representation of the free surface of the material, the piecewise linear surface of the VOF method was converted into the level set surface reconstructed by the interpolation of the signed distance function. The applicability of the model was validated by example simulations and experiments on polyimide workpiece with nanosecond laser.

Introduction

When laser is irradiated onto the free surface of a material, it is partially reflected and partially absorbed. The reflected portion of the incident laser beam has not always been considered in the calculation of the laser energy transfer in laser material processing simulations. This is acceptable when the reflected laser beam does not contact the free surface again or the reflectance of the material is sufficiently low. However, in laser material processing, a deep keyhole is typically formed, requiring the reflections inside the keyhole to be carefully considered. It is clear that the effect of reflections is significantly more important for highly reflective materials. However, the Fresnel reflection theory predicts that even a “nonreflecting” material will reflect almost 100% of an incident laser beam at grazing incidence. Ray tracing techniques have been implemented to calculate the effect of reflections [1], [2], [3], [4], [5], [6]. In these techniques, a laser beam consists of a number of rays. Each ray is traced in the simulation domain, and consequently, the total absorbed energy is summed over the entire domain to obtain the energy redistribution of the laser beam.

The refracted portion of the incident laser beam is transmitted into the material and eventually absorbed. If the material can be assumed to be perfectly opaque, it is not transmitted into the material and fully absorbed at the free surface. In this case, it is considered as the surface energy flux boundary condition at the free surface. Although a real material is partially transparent to some degree, the assumption is valid when the penetration depth of the laser beam into the material is sufficiently small. Metals usually satisfy this assumption. However, the absorption of the laser beam energy is not limited to the free surface and volumetric absorption occurs inside a semitransparent material such as polymer. Although a few numerical models describing volumetric absorption in polymer could be found in the literature [7], [8], the authors used predefined volumetric absorption models that do not correctly consider the time-varying shape of the laser-processed region.

Ray tracing highly depends on the geometry of a free surface. Several methods are available for the reconstruction of the free surface in numerical simulations. The level set (LS) method and the volume-of-fluid (VOF) method are the most prominent. The prime advantage of the VOF method over the LS method is its accuracy of the mass calculation, which is important to estimate the amount of material removal in the numerical simulation of laser material processing. The LS method gives smoother representation of the free surface, which is indispensable for the calculation of the reflected/refracted ray direction. Because the VOF and the LS methods are complementary to each other, some methods that couple them have been suggested [9], [10], [11], [12]. However, they are complicated because both the LS advection equation and VOF advection equation need to be solved together. Sun and Tao [13] suggested a simpler method in which only the VOF advection equation needs to be solved. The LS function which is needed for the free surface reconstruction is calculated by geometric operation of the volume fraction data of VOF.

It is difficult to find an integrated 3D simulation model including both the reflection and the volumetric absorption of the transmitted laser beam. Only one of the two is considered in most simulation models. Despite the frequent use of ray tracing in laser energy transfer models, an in-depth discussion of the ray tracing method itself is rarely given. In this study, an integrated model was established for the numerical simulation of laser material processing of a semitransparent material. Both the reflection and the volumetric absorption are considered by means of a ray tracing technique. The discretized signed distance function, a kind of LS function, is applied for ray/surface intersection detection and calculation of the reflected/refracted directions of rays.