Parametric study of the laser energy absorption in high-power laser beam welding

High-power laser beam welding (LBW) is one of the widely utilized joining processes in many industries.¹ The most important feature of high-power LBW is the formation of an evaporation-induced cavity with a narrow and deep geometry, also known as a keyhole. The laser beam will be multiply reflected on the highly irregular and dynamically evolving keyhole wall. A certain amount of laser energy will be absorbed at every reflection, resulting in a high thermal efficiency (up to 90%) of the LBW process. The absorbed laser energy initiates all the relevant thermal, chemical, metallurgical, and mechanical phenomena in the welding process. Therefore, it is of great importance to obtain a clear physical insight into the laser absorption behavior during LBW.

To the best of the authorś knowledge, a direct experimental measurement of the spatial laser energy absorption inside the keyhole is still not available due to the nontransparency of the liquid metal and the dynamic evolution of the keyhole geometry. Nevertheless, some compromise strategies have been reported, in which characteristic keyhole forms are first reconstructed by using high-speed imaging² or x-ray transmission,^3,4 and then laser energy absorption is calculated by a post-ray-tracing algorithm. For instance, the 3D topology of the keyhole front wall was reconstructed in the work of Matti et al. based on the image grayscale and a cavity model.² It was found that 35%–43% of the total laser energy is absorbed by the illuminated keyhole front wall. Fetzer et al.³ and Allen et al.⁴ implemented an x-ray transmission technique to obtain a 3D reconstruction of the whole keyhole. The local energy distribution and the overall absorptivity were analyzed by a post-modeled ray-tracing calculation.

Recently, multiphysics modeling has been considered a promising approach to study the relevant physical phenomena in LBW. Coupled with a free surface tracking algorithm and a physics-based model of laser propagation, the model shows the capacity to reveal the correlation between the keyhole topology and the laser energy distribution. The commonly used methodologies describing laser propagation include the ray-tracing method,⁵ radiative transport equation,⁶ and electromagnetic wave equations.⁷ The calculated results suggest that the inclination angle of the keyhole front wall plays a critical role in the absorption of the laser energy.⁸ The irregularity of a vertical keyhole under low welding speed may lead to an irregular energy distribution. An inclined keyhole front wall, which is usually caused by a high welding speed, may produce a more uniform energy distribution. Further studies indicate strong absorption and reflection occur at the protrusions with micrometer size on the keyhole front wall, which is decisive for the transient energy distribution. The formation and movement of the small protrusions may initiate the fluctuation and collapse of the keyhole.^9,10 However, these simulation works confront similar limitations to experimental measurements mentioned above, i.e., the analysis only focuses on the energy distribution at a specific point in time. Since the welding process is usually conducted in a time scale of seconds, an instantaneous distribution of the laser energy can easily be influenced by subjective choice and may not guarantee statistical representativity.

In the authors' recent work, we proposed a statistical analysis of the time-averaged laser energy absorption and its influence on the keyhole dynamics using a 3D transient multiphysics model coupled with an advanced ray-tracing algorithm and the laser absorption model.¹¹ In the current study, the proposed model is further improved with a dynamic mesh adaption strategy so that the laser energy distribution can be more accurately characterized; meanwhile, the computational intensity remains at an affordable level. The influence of two important welding parameters, welding speed and focus position, on the laser energy distribution, is analyzed and discussed.

Bead-on-plate welding was performed on 1.4301 austenitic stainless steel plates (200 × 60 × 10 mm³) with a Trumpf disk laser system. A fixed laser power of 4 kW was used and the base metal surface was irradiated by a vertical laser beam. The parameters of interest were chosen as welding speed and focus position, which vary in a range of 1.5–3.0 m/min and −6 to +3 mm, respectively. The wavelength of the laser beam was 1030 nm, and the focal diameter was 0.42 mm. Mechanical cleaning was performed before the welding to minimize the formation of metallurgical porosity.

The cross sections were mechanically cut from the middle region of the specimens from different welding parameters and then ground, polished, and etched with a V2A etchant. Metallographic observation by an optical microscope was performed on the cross section to obtain the fusion zone profile as the validation data for the model.

Based on the previous works of the authors, a well-experimentally validated heat transfer and fluid flow model coupled with a volume-of-fluid (VOF) algorithm is employed to calculate the relevant physics in LBW, especially the keyhole evolution and the dynamic laser absorption on the keyhole wall.^11–13 A brief description of the theoretical framework with the nomenclature in Table I is given below.

The first, second, and third terms on the right-hand side of Eq. (6) are the recoil pressure, capillary pressure, and the Marangoni stress. The four terms on the right-hand side of Eq. (7) are laser energy input, thermal dissipation due to convection, radiation, and evaporation, respectively.

A physics-based model for the beam propagation and the laser-material interaction is implemented to provide a more accurate description of spatial laser energy absorption. A ray-tracing algorithm coupled with a computationally effective localized level-set method is used to calculate the propagation of the laser beam and the multiple reflections inside the keyhole.¹⁵ At every reflection point, a novel Fresnel absorption model is applied, in which the absorption coefficient is not only a function of the incident angle but also the temperature-dependent electrical conductivity,¹⁶ without requiring empirical parameter adaptions.

The simulation domain with dimensions of 12 × 9 × 11 mm³ is established to accommodate a solid steel phase with a thickness of 10 mm and a gaseous Ar phase with a thickness of 1 mm. The laser beam remains fixed during simulation and the welding speed is achieved by the movement of the materials. Initially, the central region of the domain (2 mm < X < 8 mm, −2 mm < Y < 2 mm) is uniformly meshed with 0.2 mm hexahedron cells. It is usually considered that this cell size can reach a compromised accuracy in the simulation of the keyhole dynamics and weld pool behavior in LBW.⁵ The cell size grows gradually from 0.2 to about 0.7 mm outside the central region. During the calculation, the cells for the region of interest, namely, the weld pool and the internal region of the keyhole, will be further refined with a multilevel mesh adaption technique (0.2 mm → 0.1 mm → 0.05 mm) so that a higher spatial resolution can be realized. The initial mesh of the simulation domain and an example of the refined mesh are shown in Fig. 1. The commercial software ANSYS Fluent 23.1 is used to solve the governing equations, with the convection-diffusion equations spatially discretized via the second-order upwind method. The Pressure implicit with splitting of operators algorithm was utilized for the pressure-velocity coupling. A more detailed description of the boundary conditions, numerical algorithms, and model parameters can be found in the authors' previous works.^11–13 

The time-varying spatial laser energy distribution together with the heat transfer, fluid flow, and keyhole dynamics can be calculated by the established numerical model. With certain mathematical operations, e.g., integration and time-averaging, the statistical analysis of the laser energy distribution can be achieved. The simulation cases with different welding speeds and focus positions are listed in Table II.

The proposed multiphysics model has been validated by various experimental measurements including the fusion line profile, weld pool shape from high-speed images, solid/liquid front geometry from metal/glass configuration observation, and X-ray fluorescence (XRF)-measured element distribution of the filler material.^11–13 A representative comparison between experimental and calculated penetration depth in the current welding parameter range is given in Fig. 2. An accurate prediction with a minor error of −11% to 5% can be achieved, which proves the feasibility of the model.

Figure 3 shows the influence of the welding speed on time-averaged laser energy absorption in the longitudinal section within 100 ms, in which the normalizations by the maximal value in each case are conducted. For a more intuitive description of relative positions, the keyhole profile at a certain time point is also visualized in the figure. A more intensive laser energy absorption can be found on the keyhole front wall for all welding speeds, which results from the first reflection of the laser beam. The keyhole rear wall also receives a certain amount of laser energy, especially at the upper region of the keyhole.

The time-averaged distribution of the total laser energy along the thickness direction is plotted in Fig. 4(a), which is calculated by dividing the integration of the absorbed laser energy with the same Z position (in W/m) with the welding speed (in m/min). A similarity in the distribution pattern can be found among the cases with different welding speeds. Three regions can be identified, including the top region where more laser energy is absorbed, the middle region where the laser energy shows a relatively uniform distribution and produces a stable penetration, and the bottom region where the laser can rarely reach from a statistical viewpoint, resulting in a dramatic drop of the absorbed laser energy. It should be pointed out that this distribution manner revealed by the 3D integration of the laser energy cannot be represented by the 2D distribution in Fig. 3.

The time-averaged laser energy intensity in the middle region, i.e., stable absorption region, has only a minor variation from 1.1 × 10⁷ to 1.4 × 10⁷ J/m² even if the linear energy is doubled. In contrast, more energy is absorbed in the upper region of the keyhole with the increase of the linear energy. It provides a direct explanation for a widely experimentally observed fact that the penetration depth will not increase proportionately with the increase of linear energy but will be saturated.¹⁷ It should be noted that the formation of the wineglass-shaped weld profile, which is defined as a significantly widened fusion zone at the top of the weld, is not dominated by the over-absorption of the laser energy at the upper region. Our recent study recognizes the importance of the secondary heating effect of the vapor plume in the formation of the wineglass-shaped form.¹⁸ 

The integration operation is also performed along the X direction (welding direction) so that the absorption ratio of the laser energy on the keyhole front wall can be calculated, see Fig. 4(b). It denotes that the time-averaged absorption ratio on the keyhole front wall has a negative correlation with welding speed. The absorption ratio varying between 30.5% and 37% corresponds well with experimental results from Matti and Kaplan.² More analysis of the absorption behavior on the keyhole rear wall should be performed since the majority of the laser absorption occurs thereon.

The normalized time-averaged laser energy distribution on the longitudinal section with different focus positions is given in Fig. 5. Compared with the welding speed, the variation of the focus position shows a more apparent influence on the distribution pattern of the laser energy, especially at the keyhole bottom region. Regardless of the same linear energy, the distinct energy distributions resulting from the shifting of the focus position lead to different penetration capacities.

As shown in Fig. 6(a), the time-averaged laser energy intensity, especially in the middle and bottom regions of the keyhole, is considerably influenced by the focus position. The focus position of −3 mm produces a stable absorption region until the bottom of the keyhole and correspondingly generates the deepest penetration. This stable absorption regime becomes less pronounced when a focus position of −6 mm is applied. Conversely, the absorbed laser energy shows a gradual decrease.

It is also noteworthy that a different distribution pattern can be observed for a zero or a positive focus position. Instead of a rapid decrease, the absorbed laser energy exhibits a certain increase at the keyhole bottom. It can be foreseen that this special energy distribution will impact the keyhole dynamics such as fluctuation or collapse at the bottom area. It may also correlate with some recently found phenomena, such as narrowing and bulging, in the weld pool and play a critical role in the formation/suppression of some weld defects (porosity and hot cracking).^13,19 Additionally, the variation of focus position from negative to positive leads to a monotonic increase of the absorption ratio on the keyhole front wall from 36.8% to 40.5%.

The influence of two important welding parameters, i.e., welding speed and focus position, on the laser energy distribution, is analyzed and discussed from a statistical aspect in a relatively long-time range, using a 3D transient multiphysics model. The main conclusions are drawn below.

1. The time-averaged laser energy distribution on the keyhole wall in high-power LBW can be, in principle, divided into three distinct regions: the top region with more pronounced absorption, the middle region with a relatively uniform laser energy intensity, producing a stable penetration, and the bottom region with a dramatic drop of the absorbed laser energy.

2. The laser energy distribution regime is slightly influenced by the welding speed in the studied parameter range (1.5–3.0 m/min). The focus position has a remarkable effect on the time-averaged laser energy distribution, especially the absorption at the keyhole bottom when applying a positive focus position.

3. The absorption ratio of the laser energy on the keyhole front wall varies between 30% and 40%. It decreases with increasing welding speed and increases with upward-moving focus positions

This work was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project Nos. 506270597 and 466939224.

The authors have no conflicts to disclose.

Xiangmeng Meng: Conceptualization (equal); Data curation (lead); Formal analysis (lead); Funding acquisition (supporting); Investigation (lead); Methodology (equal); Software (lead); Validation (lead); Visualization (lead); Writing – original draft (equal); Writing – review & editing (equal). Stephen Nugraha Putra: Software (equal); Validation (equal); Visualization (equal); Writing – original draft (supporting); Writing – review & editing (supporting). Marcel Bachmann: Conceptualization (equal); Formal analysis (supporting); Funding acquisition (lead); Investigation (equal); Methodology (equal); Project administration (lead); Supervision (lead); Validation (supporting); Visualization (supporting); Writing – original draft (equal); Writing – review & editing (equal). Michael Rethmeier: Funding acquisition (supporting); Supervision (equal); Writing – original draft (supporting); Writing – review & editing (supporting).