Guide to a Deterministic Control of Laser Materials Processing with Dynamic Beam Shaping

1. Introduction

The processing of a wide range of materials using continuous-wave lasers is well established in industrial manufacturing. Key processes include hardening, where the material remains in the solid state; cutting, where the material is melted; and deep-penetration welding, where partial vaporization occurs. These processes enable a broad spectrum of industrial applications as is extensively described for example in [1].

In recent years, significant progress has been made in both laser technology and industrial applications. On the one hand, the average power of commercially available solid-state lasers has increased significantly - from a few kilowatts in 2005 to over 100 kW by 2022 [2]. On the other hand, the development of novel materials and enhanced processing techniques has paved the way for new applications. These include current progress in different industries like the use of high-strength alloys in crash boxes, aluminum-copper combinations for high-current applications such as in locomotives, and large-scale applications driven by the automotive industry's transition to e-mobility – such as welding large aluminum cooling plates and copper hairpins. Moreover, the trend toward mass individualization has led to a resurgence of laser-based additive manufacturing, ranging from powder- and wire-based material deposition (DED) to powder bed fusion by a laser beam (PBF-LB).

All these applications involve specific challenges regarding process stability and the resulting quality. Key issues include minimizing striations and dross, controlling kerf angles during the cutting of thick materials, and avoiding pores, spattering, humping, and the formation of hot cracks in the solidifying material during high-speed welding.

A promising approach to address these challenges is the active forming of the intensity distribution in the focused laser beam, usually referred to as beam shaping. The beam’s intensity profile has a key influence on the energy deposition in the workpiece and therefore on the entire process. The irradiance distribution resulting from the beam shape and the geometry of the interaction zone on the workpiece can be used to modify process features such as widening a weld seam, influencing the heat flow or enlarging a keyhole. Illustrative examples for deep-penetration laser welding are given in [3,4,5]. Theoretical modelling confirmed the influence of shaped beams on the shape of the welding keyhole [6,7]. As a result, various beam shaping methods have been developed and are successfully applied to improve different aspects of the laser welding process [8,9,10,11,12,13,14]. These beam shaping systems range from static configurations to dynamic systems operating at low modulation frequencies. Comprehensive overviews of beam shaping techniques can be found in [15,16].

Dynamic beam shaping is particularly comprehensive with lasers that enable very fast creation of arbitrary beam shapes. This can be implemented by means of actively controlled coherent beam combining. Current lasers based on this principle, referred to as “dynamic beam lasers” (DBLs), allow to create the time-averaged beam shapes by quickly scanning a single intensity peak to different positions in the focal plane at frequencies of up to 80 MHz. This method enables the generation of arbitrarily time-average beam shapes composed of a sequence of points on the workpiece surface that are scanned by an intensity peak in rapid succession, even at average powers exceeding 100 kW [17]. The time-average beam shapes themselves can be changed with frequencies in the order of MHz, offering unprecedented potential for influencing and controlling laser material processing, as first demonstrated in [18]. Offering such fast dynamic beam shaping, DBLs introduce additional time constants and frequencies into beam shaping, such as the dwell time of the intensity peak at a single position or refresh frequency of the time-average beam shape, which increases complexity but also opens a wide range of new possibilities for process control or process modifications.

Laser processing with dynamically modulated process parameters have revealed that characteristic modulation frequencies exist at which the influence on the process is particularly strong as e.g. seen in [19], where power modulation with about 300 Hz significantly improved welding of copper at the given process parameters. The knowledge of such characteristic frequencies is very helpful to allow deterministic process modification. At the present state of knowledge, it may be assumed that these characteristic frequencies are related to typical time constants and frequencies of the process.

The paper also proposes consistent naming of the possible types of beam shaping and process modifications and sets them in relation to characteristic time constants and frequencies. The characteristic frequencies allow to define three distinct process regimens, which can be related to successful process modifications such as the reducing of pores, giving hand to deterministic process development. An overview of typical time constants and frequencies associated with laser processes is given, to ease the determination of characteristic frequencies involved in beam shaping with DBLs.

The knowledge of the process regimes provides the basis for a guide to systematically assess suitable beam shaping parameters for specific dynamic process modifications to e.g. control issues such as pores, spiking, or spattering. An example demonstrating the reduction of process pores confirming these propositions is included.

2. Typical Time Constants and Frequencies in Laser Processes

Duration for Spreading the Heat

The depth of hardening or the thickness of the liquid layer between the welding keyhole and the solid material is given by the location or the distance between the respective isotherms. The thermal diffusion length

(1)

is commonly considered as a measure of the spatial extent of the temperature increase [1], where ${\kappa }_D={\mathsf{\lambda }}_{th}/(\rho ·c_p)$ is the thermal diffusion constant, ${\mathsf{\lambda }}_{th}$ the heat conductivity, ρ the mass density and c_p the specific heat capacity at constant pressure for the phase considered, and t_H is the duration of heating. A few values for κ_D for a selection of common metals can be found in [22,23] and are summarized in Error! Reference source not found. in the Appendix A. Solving for t_H gives the time

(2)

it takes until the temperature increase of about 9%^.T_max reaches the extent ℓ_D, where T_max is the maximum temperature reached after the duration $t_H$ on the surface, which is heated by the laser radiation.

Example: In solid iron, with κ_D,Fe = 2.3^.10^-5 m²/s, the time for reaching about 9%^.T_max at the distance of 0.5 mm below the irradiated surface is about 2.8 ms, whereas in solid aluminum, with κ_D,Alu = 9.8^.10^-5 m²/s, this time is only about 640 µs.

If the influence of heat conduction should be neglectable, the thermal diffusion length must be smaller than any critical extent ℓ_C of heat affected zones, such as melt layers, length of cracks or extents of hardened areas, i.e. ℓ_D < ℓ_C which means that the heating duration t_D must fulfil the condition

(3)

Duration for Reaching a Specific Temperature

The time required to heat the material to its melting or boiling temperature using a laser beam is of interest in every laser process. A convenient analytical approximation to estimate the temperature increase $\Delta T=T-T_0$, where $T_0$ is the initial temperature, can be found e.g. in [1] with the assumptions of heating the surface of a semi-infinite body. For short heating times t_H and hence one-dimensional heat flow induced by a Gaussian beam at normal incidence, the temperature increase on the surface is given by

$$\Delta T={\displaystyle \frac{8\cdot A}{{\pi }^{3/2}\cdot \sqrt{{\kappa }_T}}}\cdot {\displaystyle \frac{P_L\sqrt{t_H}}{d_w^2}},$$

(4)

where 𝜅_T = 𝜌 · c_p · λ_th, $d_w$ is the beam diameter on the workpiece surface, $P_L$ the laser power and $A$ the absorptivity of the material at the wavelength of the laser beam. A few values for κ_H for a selection of common metals are summarized in Error! Reference source not found..

The duration t_H for reaching a target temperature $T$ when starting from a given initial temperature $T_0$ on the surface of a material is therefore given by

(5)

Examples: In aluminum in liquid state at the melting temperature of T₀ = 660°C, with κ_H = 2.9^.10⁸ J²/m⁴/s/K², (material values are taken for the liquid phase), the time for reaching evaporation temperature of T =T_v = 2520°C on the surface when heating with a laser beam of 0.5 mm diameter, an average laser power of 10 kW and taking an absorptivity of A = 6% is about 167 µs. In contrast, in iron with κ_H = 2.3^.10^-5 m²/s and A = 40% the time is about 0.9 µs which is about 185x faster.

Propagation of Acoustic Excitations

The time for an acoustic excitation in the liquid metal to travel the distance $d_w$ of the laser beam diameter on the workpiece is given by

$$t_S=d_w/c_S,$$

(6)

where $c_S$ is the velocity of sound, the values of which in liquid metals can be found in [24]. A few values for a selection of frequently used metals are summarized in Table 5.

Examples: The time for an acoustic excitation to travel the distance of the diameter of the laser beam is about the same in aluminum and iron t_S = 0.1 ms. It is noted that, for example in deep-penetration laser welding, the melt pool is much longer in steel than in aluminum and strongly depends on the processing parameters and beam shapes. Therefore, the time for an acoustic excitation to reach the solidification region must be calculated for each process parameter set.

Maximum Flow Speed Around a Keyhole

If a keyhole exists e.g. during laser welding, the melt created in front of the keyhole must flow around the keyhole. The maximum velocity of this melt flow is one of the important quantities defining the quality of the weld as was described in the introduction. The speed of the flow of the liquid metal around the keyhole was described in the PhD-work of Beck at the IFSW [23]. A comprehensive summary of the work can be found in [1] p. 325ff. For a cylindrical keyhole with a diameter of the diameter $d_w$ of the laser beam and assuming that the velocity of the liquid metal v_L increases linearly from the border of the melt pool to the border of the keyhole, the maximum flow velocity v_L,max can be approximated by [23]

(7)

where v_F is the feed rate, $T_L$ the melting temperature, $T_V$ the vaporization temperature, and $T_0$ the initial temperature. It is seen that for low feed rates and small beam diameters ${v_{L,max}\approx v}_{Feed}$, whereas for very high feed rates, the maximum flow velocity scales with about $v_{L,max}\propto v_{Feed}^{7/4}$. However, as the width of the liquid layer in eq. (7) is purely determined by heat conduction, it is possible to influence the maximum flow speed by increasing the difference between the lateral width of the melt pool and the lateral keyhole width, e.g. with modified laser beam profiles or beam wobbling.

The time for the liquid to pass the keyhole, within which it is possible to influence the melt flow with the laser beam, can be calculated with

$$t_{KH}={\displaystyle \frac{d_w}{v_{L,max}}}.$$

(8)

Figure 1 shows for example the minimum liquid-keyhole-passing-time as a function of the feed rate for aluminum (blue) and iron (orange) for a beam diameter of 0.5 mm and the material values κ_T,Al = 9.8^.10^-5 m²/s and κ_T,Fe = 2.3^.10^-5 m²/s.

At the feed rate of 6 m/min the keyhole-passing-time for aluminum is about 10 ms and for steel 3 ms. At the feed rate of 60 m/min the keyhole-passing-time for aluminum is reduced to about 200 µs and for steel to 80 µs.

Keyhole Collapse, Pore Formation and Spiking

Partial or complete keyhole collapse is the origin of several issues such as blow outs, pore formation or spiking at the tip of the keyhole [1]. The keyhole collapse shows typical time constants t_c and quasi-periodicity with the frequency f_c = 1/t_c which depends on the process parameters and the processed material. The time constants of the process are determined by convection and surface tension and rates of vaporization inside the keyhole which determine how long it takes to open or close a capillary. Convenient analytical solutions do not exist to the best of our knowledge. However, recent publications allow estimations of the time constants involved: Opening and closing time of a keyhole in steel was seen is in the order of t_c = 1 ms [18]. In [18] it was observed in deep-penetration welding of steel that the tip of the capillary could clearly follow the movement of a laser beam up to frequencies of f_c = 100 Hz, i.e., within about t_c = 10 ms, while no clear correlation to the excitation was found for frequencies of f_Proc = 1 kHz and higher. In [26] it was measured in Ti that the collapse at the tip of the keyhole, which might result in the formation of a pore, happened in about t_c = 4 µs.

Summary of the Examples for Typical Time Constants and Frequencies

Table 1 shows a summary of a few typical process time constants for the physical quantities given above for a feed rate of 1 m/s and an average laser power of 10 kW. For the corresponding frequencies, a periodic repetition of the effect was assumed.

A thermal diffusion length of ℓ_D = 0.5 mm and a width of the laser beam on the surface of d_W =0.5 mm were taken as typical values for the example. It is seen that the frequency range spreads over more than three orders of magnitude, from the lowest frequencies in the range of 1 kHz up to the highest frequency of 1 MHz. It can be assumed that characteristic frequencies of beam shaping are expected in this range. However, due to the strong dependence on the processing parameters and on the material properties, the values must be determined for each specific configuration.