Surface tension is an essential material property that defines many aspects of thermal processes involving liquids. Metal materials have high melting temperatures, and surface tension could often be measured around melting temperature and is, therefore, known for many pure materials and simple material systems. However, high-energy input during laser, electron beam, or plasma processes is known to increase the material temperatures far above the melting point. To build theoretical models, simulate processes, and increase process understanding, surface tension values at those high temperatures would be beneficial to know. However, it can be difficult to create stable circumstances and measure surface tension in those conditions. Therefore, it is suggested in this work to indirectly derive surface tension values from the pressure balance inside keyholes created during laser deep penetration processing. A variety of different keyhole shapes were created using dynamic beam shaping by means of coherent beam combining. From the observed keyhole shapes using inline x-ray observations, temperature distributions on the keyhole walls were calculated using ray tracing. The temperature defines the local recoil pressure that counteracts the surface tension pressure, which contains the surface tension value as the only unknown variable. At increasing temperatures above the boiling point, an increasing surface tension was observed.
INTRODUCTION
When processing liquid materials, in many cases, surface tension effects are involved. However, values and understanding of surface tension, in particular, at high temperatures of metals further above melting or close to boiling temperatures are not available. Increasing the knowledge about surface tension at higher temperatures would improve process understanding and support process development and simulation models.
Surface tension can be understood as a force acting between surface atoms or molecules.1 For most pure metals, surface tension decreases at increasing temperature.2 However, measurements were mainly conducted just slightly above the melting temperature of metals3 due to limitations of the typically used equipment. Different methods of surface tension measurement were developed and used for many materials. However, many of those are not directly applicable to high-temperature measurements of liquid metals. The high temperatures involved limit the use of contact methods, such as the maximum bubble pressure or sessile drop methods. Capillary waves can be recorded at no contact4 as well as levitated or falling drops.5–7 However, the creation of drops at a stable high temperature is challenging.
Since the challenge of surface tension measurements at high temperatures is the creation of an environment with reliable circumstances regarding surface tension without affecting the measurement equipment, one possibility was recently tested where surface tension is an influencing factor, namely, the keyhole (KH) or vapor channel occurring during laser deep penetration welding.8 KHs were observed with x-ray high-speed imaging and their shapes were extracted. Based on the pressure balance on the KH walls, the surface tension could be estimated. Typically, a linear decrease in surface tension at an increasing temperature is assumed (e.g. Ref. 9). A recent work has shown that a linear decrease in surface tension might not be sufficient to explain the complex phenomena at increasing temperature.10 The decrease was seen to be steeper below the boiling temperature and remaining at a certain value around the boiling temperature.
To create different and stable KHs, beam shaping can be used. Beam shaping has been shown in various cases to support stable welding processes with static refractive,11 diffractive12,13 optics, combined beams,14 or oscillation patterns.15–17 A new possibility of high-frequency beam shaping for high-power lasers by coherent beam combining and optical phase array was introduced by CIVAN.18 It was, for example, shown that using high frequencies (>10 kHz) enlarges the processing window to achieve stable welding in the case of aluminum overlap welding.19
In this work, the possibility of creating stable KHs using high-frequency beam shaping is evaluated for the extraction of KH shapes for surface tension derivation at temperatures above the boiling point.
METHODOLOGY
For the surface tension measurements, KHs during laser deep penetration were recorded using surface high-speed imaging (HSI) and x-ray observation. A CIVAN OPA6 laser (wavelength of 1064 nm and a beam parameter product of 5 mm mrad) was used for the experiments (Fig. 1). The laser beam was guided through a focusing optic of 1500 mm focal length onto the test specimen. The specimen (DOCOL 200 steel, SSAB) was 2 mm wide and 100 mm long, and a weld track of 60 mm length was produced.
Surface monitoring was done with a HSI camera (Photron SA5) at a frame rate of 50 000 Hz (exposure time 19.75 μs, 165 pixel/mm). Illumination was enabled using a pulsed Cavilux laser (50 000 Hz at 2 μs pulse duration). The x-ray system consisted of an x-ray tube (88 W at 140 kV acceleration voltage) and a recording setup. The image was projected onto a scintillator guided through an image intensifier to the camera.20 This HSI camera (Photron SA3) recorded the frames at a frame rate of 2000 Hz (exposure time 499 μs, 65 pixel/mm).
The specimen was moved with the processing speed of mainly 12 m/min, while the laser beam power was mainly set to 5.5 kW. Different beam shapes at different frequencies were applied (Fig. 2) to generate different round KHs. The frequency in the Civan system is defined as the number of times the pattern is performed per second and is varied between 1 and 50 kHz. The point duration varies according to the number of points in the pattern.
In the HSI frames of surface observations, the KH lengths and widths were extracted [Fig. 3(a)]. The x-ray frames gave the KH length and depth after flat-field correction and adapting the contrast [Fig. 3(b)]. Three measurements of every value were taken at different times and were averaged.
Surface tension coefficients were calculated based on the x-ray image of the KH (Fig. 4). For that, KHs were extracted from a black/white (b/w) frame. A 2D ray tracing was applied in MatLab (R2024a), while the single rays received the initial energy based on the local energy in the measured beam shape. Each ray was absorbed according to Fresnel's model (e.g., Ref. 21) when intersecting with the KH wall and, then, further reflected and absorbed inside the KH until exiting or a reduction in the ray energy to below 1% of its initial value. The KH was then virtually split into ten circular assumed segments,22 while in every segment, the absorbed energy was calculated. The temperature in each segment was calculated based on the total absorbed energy according to Ref. 23.
Extraction and calculation to derive surface tension values from laser-induced keyholes.
Extraction and calculation to derive surface tension values from laser-induced keyholes.
Assumed symmetrical deviations for the parameters in Eq. (2) including varying parameters.
| Parameter | Value | Deviation Δ | Ref./origin |
|---|---|---|---|
| Keyhole radius r (mm) | Measured | ±0.001 | Pixel resolution |
| Intensity Iv (W/cm2) | Calculated (ray tracing) | ±1.00 × 107 | Ray tracing and sectioning resolution |
| Latent heat of vaporization Lv (kJ/kg) | 6580 | — | 25 |
| Thermal diffusivity k (m/s2) | 6.0 × 10−6 | ±2.3 × 10−7 | 26 (at 1000 °C) |
| Molar gas constant R [J/(mol K)] | 8.314 471 | ±0.000 014 | 27 |
| Molar mass M (g/mol) | 55.845 | ±0.0005 | 28 |
| Keyhole temperature Ts (K) | Calculated (ray tracing) | ±10 | Measuring deviation |
| Parameter | Value | Deviation Δ | Ref./origin |
|---|---|---|---|
| Keyhole radius r (mm) | Measured | ±0.001 | Pixel resolution |
| Intensity Iv (W/cm2) | Calculated (ray tracing) | ±1.00 × 107 | Ray tracing and sectioning resolution |
| Latent heat of vaporization Lv (kJ/kg) | 6580 | — | 25 |
| Thermal diffusivity k (m/s2) | 6.0 × 10−6 | ±2.3 × 10−7 | 26 (at 1000 °C) |
| Molar gas constant R [J/(mol K)] | 8.314 471 | ±0.000 014 | 27 |
| Molar mass M (g/mol) | 55.845 | ±0.0005 | 28 |
| Keyhole temperature Ts (K) | Calculated (ray tracing) | ±10 | Measuring deviation |
RESULTS
Various keyholes were created with multiple beam shapes (Fig. 2), process parameters, and pattern frequencies. The resulting varying energy inputs led to different keyhole shapes. Figure 5 shows the keyhole opening dimensions measured in HSI videos and x-ray frames (Fig. 3). Due to keyhole dynamics, measurement values show variations. However, the measured dimensions of KH lengths in x-ray and high-speed images are in the same range. The general trend is that the measured KH width shows a slightly smaller value compared to its length, which can be related to the impact of the processing speed that elongates the KH.29,30 However, the KHs show a sufficiently circular shape to be used for estimating the KH shapes from the 2D x-ray images.
Measurements in the x-ray images were used to derive KH dimensions (Fig. 6). As expected, at higher energy input, the KH depth increases, which was achieved by higher laser power and reduced welding speed.
Each evaluated keyhole was split into ten sections, while the lowest section was disregarded due to the different circumstances regarding the impact of the keyhole tip melt curvatures affecting the surface tension. In the remaining sections, the pressure balance was calculated, and the surface tension values were derived (Fig. 7). The general trend shows an increase in surface tension above the boiling temperature, while the linear decreasing prediction (e.g., Ref. 9) seems to be not valid anymore at those high temperatures.
DISCUSSION
The roundness of the created KHs was seen to be sufficient (Fig. 5), although variations due to process dynamics occurred. KH widths and lengths remain in the same range independent of the beam shape, pattern frequency, and even laser power and processing speed in the observed ranges. Only the KH depths show the known impacts of energy input variations showing larger depths at increased energy input.
Investigation of the pattern frequency was performed to gain insight into a possible threshold, above which the pattern frequency is high enough to maintain a KH and establish a quasi-static condition. Due to the high pattern frequencies used, melt cooling and possible KH opening collapse were not observed. Only the lowest frequency used (1 kHz) shows a slightly lower KH depth. From the related HSI video, it is visible that the KH opening starts closing the KH before the next energy input occurs and opens the KH in this section again. This effect induces additional dynamics of the KH and can be a reason for the limited transfer of energy to the KH tip and the related reduced KH depth.
The hypothesis that an increased energy input into the central part of the beam shape increases the KH depth could not be seen. It was expected that beam shapes D and E with increased numbers of illumination points within the beam shape pattern in the beam shape center lead to a more efficient energy transfer to the KH tip. However, the measured depths were similar to, e.g., beam shape F that had a focus on illuminating the circumference of the KH. This shows the complexity of beam shaping to alter the KH dimensions. Several further factors need to be considered, such as multiple reflections based on KH wall inclinations31,32 and vapor effects.33,34 KH dimensions can be extracted from x-ray imaging that enables the application of ray tracing methods to calculate energy input (e.g., Ref. 35).
Surface tension is known to decrease with increasing temperature.2 However, above the boiling temperature, additional effects seem to appear that alter that general trend.10,36 In the KH, the temperatures can be high37 and even exceed the boiling temperature,38 while it is still unclear how the surface boiling39 affects the surface tension. The results in this work indicate that surface tension can show higher values again. The uncertainties of the current measurement are relatively high due to the measuring method, but a general trend can be identified. An effect of the weakness of the 2D ray tracing method can be seen in the calculation of very high temperatures in some KH sections that might not be completely physical. Therefore, also the temperature values must be taken with care.
In a KH section with low energy input, a small recoil pressure can be expected acting on the KH wall. At the same time, surface tension should be high, which would lead to a small KH radius. High temperatures should lead to a high recoil pressure, low surface tension, and a related KH radius increase. However, the opposite is observed in the KH observations and calculations, similar to the previous observations.8 In the KH sections where most energy is absorbed, the KH radii are comparably small. This means that at a high recoil pressure, the melt surface tension must be higher again to be able to counteract the expanding recoil pressure. One possible reason for this effect might be an increased surface area due to the locally exiting atoms from the surface layers and the related higher surface forces.
CONCLUSION
Using advanced dynamic beam shaping, different keyholes were produced during deep penetration welding of steel. The pattern frequency showed a minor impact on the keyhole dimensions; only 1 kHz was too slow to permanently keep the keyhole open.
Using ray tracing on circular-shaped keyholes extracted from high-speed x-ray imaging, surface tension values at different temperatures could be extracted showing an increasing trend above the boiling temperature. It is suspected that the vaporization of surface atoms can increase the surface area and forces.
ACKNOWLEDGMENTS
The authors kindly acknowledge the funding of SMART—Surface tension of Metals Above vapoRization Temperature (Vetenskapsrådet—The Swedish Research Council, 2020-04250). The work was partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under No. 503306266. The collaboration expenses were supported by the InnovationCampus Future Mobility funded by the Baden-Württemberg Ministry of Science, Research and the Arts. The provision of the OPA6 laser system by CIVAN is highly acknowledged.
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Joerg Volpp: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Funding acquisition (equal); Investigation (equal); Methodology (equal); Project administration (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal). Felix Zaiss: Conceptualization (equal); Funding acquisition (equal); Methodology (equal); Project administration (equal); Validation (equal); Writing – review & editing (equal). Christian Hagenlocher: Conceptualization (equal); Funding acquisition (equal); Supervision (equal); Writing – review & editing (equal). Thomas Graf: Funding acquisition (equal); Supervision (equal); Writing – review & editing (equal).
