# Temporal and spatial determination of solidification rate during pulsed laser beam welding of hot-crack susceptible aluminum alloys by means of high-speed synchrotron X-ray imaging

M. Seibold, K. Schricker, L. Schmidt, D. Diegel, H. Friedmann, P. Hellwig, F.

Fröhlich, F. Nagel, P. Kallage, A. Rack, et al.

► To cite this version:

M. Seibold, K. Schricker, L. Schmidt, D. Diegel, H. Friedmann, et al., Temporal and spatial determination of solidification rate during pulsed laser beam welding of hot-crack susceptible aluminum alloys by means of high-speed synchrotron X-ray imaging. Journal of Advanced Joining Processes, 2024, 10, pp.100235. 10.1016/j.jajp.2024.100235. hal-05118231

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# Temporal and spatial determination of solidification rate during pulsed laser beam welding of hot-crack susceptible aluminum alloys by means of high-speed synchrotron X-ray imaging

M. Seibold<sup>a, *</sup>, K. Schricker<sup>a</sup>, L. Schmidt<sup>a</sup>, D. Diegel<sup>a</sup>, H. Friedmann<sup>a</sup>, P. Hellwig<sup>a</sup>, F. Fröhlich<sup>a</sup>, F. Nagel<sup>b</sup>, P. Kallage<sup>b</sup>, A. Rack<sup>c</sup>, H. Requardt<sup>c</sup>, Y. Chen<sup>c,d</sup>, J.P. Bergmann<sup>a</sup>

## ARTICLE INFO

### Keywords:

- Pulsed laser welding
- High-speed synchrotron X-ray imaging
- Solidification rate
- Hot cracks
- Aluminum alloys 6xxx group

## ABSTRACT

Pulsed laser beam welding is primarily used to join thin-walled components. The use of 6xxx group aluminum alloys is characterized by good mechanical properties but these alloys are prone to hot cracking during solidification, i.e., requirements regarding strength and tightness, as increasingly important for electromobility related applications, cannot be fulfilled. The solidification rate has been identified as dominant factor in pulsed conduction welding which can be adjusted by the pulse shape, i.e., by varying the beam power over time for a single pulse.

Pulse shapes with different, linear ramp-down slopes were studied to describe the interaction between beam power and resulting solidification rate for spot welds. Based on rotationally symmetric conditions of the spot welds, the solidification rate can be measured in radial and vertical directions. The welding process of EN AW 6082 alloy was examined by in situ high-speed synchrotron X-ray imaging at the European Synchrotron Radiation Facility (ESRF) for this reason. Frame rates up to 120,000 Hz and subsequent image analysis allowed in-depth analysis of the solidification processes, their dependence on different spatial directions, and the resulting effects on hot crack formation.

## Introduction

Pulsed laser beam welding has been a widely used technology for many years (Belforte, 1988). With the trend towards continuous high-power laser beam sources, pulsed welding processes have found their own niche and are used when thermal distortion needs to be minimized and tightness must be ensured, as in industries like battery manufacturing or medical technology (Medicaldevice; Cirtecmed). The pulsed laser welding of aluminum is of certain importance due to the low density and favorable mechanical properties, especially for alloys from the 6xxx group. However, welding these alloys is challenging due to their high tendency to hot crack formation (Ploshikhin et al., 2011). The periodic power input leads to melting during the pulse (typical pulse lengths: 2...20 ms (Chludzinski et al., 2022; Zhang et al., 2008)) and solidification during the pulse pause, i.e., high solidification rates and

temperature gradients occur. The interplay between temperature gradient, solidification rate and tensile stresses during solidification were identified as critical for hot crack formation (Gollnow and Kan-nengiesser, 2013; Quiroz et al., 2012). Therefore, various methods have been developed to prevent this issue addressing the named phenomena in pulsed laser beam welding.

It was proven that the superposition of a pulsed laser welding process with a continuous diode laser enabled the oppression of hot crack formation (Bielenin et al., 2019). This was achieved by reducing of the solidification rate and temperature gradient as well as by inducing additional compressive stresses due to the temperature field of the diode laser (Bielenin et al., 2019). In addition, the temporal modulation of the laser beam power and therefore the realization of different pulse shapes affected hot crack formation (Matsunawa et al., 1992; Nakashiba et al., 2011; Bielenin, 2021). By using this approach, the solidification rate is

<footnote><sup>a</sup> Production Technology Group, Technische Universität Ilmenau, Ilmenau, Germany</footnote>

<footnote><sup>b</sup> Coherent, Hamburg, Germany</footnote>

<footnote><sup>c</sup> ESRF – The European Synchrotron Radiation Facility, Grenoble, France</footnote>

<footnote><sup>d</sup> RMIT University, School of Engineering, Australia</footnote>

<footnote>* Corresponding author.
E-mail address: marc.seibold@tu-ilmenau.de (M. Seibold).</footnote>
lowered while pulse duration is increased concurrently. The reduced solidification rate allows the molten material to remain in a fluid state for longer to filling the interdendritic cavities and minimizing the risk of hot cracking (Sheikhi et al., 2014; Rappaz et al., 1999). The adjustment of the solidification rate by pulse shaping was thereby identified as key parameter for minimizing hot crack formation (Seibold et al., 2022; Rappaz et al., 1999). Fig. 1 shows the dependency of hot crack length over the ramp down time of the pulse shape resulting in three segments based on (Seibold et al., 2022). This subdivision has already been demonstrated in previous works (Bielenin, 2021). Characteristic for segment 1 ($t_{RD}$ = 0...9 ms) is a noticeable formation of hot cracks and their reduction with increasing ramp down times. The following segment 2 covers a small interval of ramp-down times ($t_{RD}$ = 10...11 ms) in which no hot cracks were observed. Segment 3 is characterized by a rapid increase in hot cracking at a nearly constant level. This behavior is explained by a reduced solidification rate in segment 1 and 2 which correlates with an increase in the time required to fill the interdendritic cavities. In segment 3, however, a change in the solidification direction led to the occurrence of hot cracks independently from the ramp down time (Zhang et al., 2008).

A determination of the acting solidification rate depending the ramp down time can be carried out experimentally by high-speed recordings of the melt pool surface during solidification (von Witzendorff et al., 2015; Bielenin et al., 2019; Seibold et al., 2022) or based on numerical simulations (Bergmann et al., 2017; Herzog and Strelnikov, 2023; Sabbaghzadeh et al., 2008; Frewin and Scott, 1999). However, a comparison between thermal numerical simulations and experiments showed deviations due to simplifications of the model (Seibold et al., 2022). In addition, the changes in solidification direction with increasing ramp down times allow the conclusion that the dependence of the spatial direction can also have a decisive influence on hot cracking. A description of the underlying phenomena requires the consideration of processes in the melt pool under the surface of the melt pool itself that cannot be directly observed.

The determination of processes during laser beam and a sufficiently high spatial and temporal resolution can be achieved by utilizing high-energy, brilliant synchrotron radiation for X-ray imaging (Rack et al., 2018; Di Michiel et al., 2005). In situ studies of laser material processing have proven to obtain information on inner phenomena for different

materials, e.g., copper up to 20,000 Hz (Schricker et al., 2022; Kaufmann et al., 2023), titanium at 40,000 Hz (Chen et al., 2020), steel at 100,000 Hz (Schricker et al., 2023).

In this paper, pulsed laser beam welding of aluminum EN AW 6082 is studied based on in situ high-speed synchrotron X-ray imaging. Frame rates of up to 120,000 Hz and subsequent image analysis allowed a time-dependent analysis of the solidification processes, their dependence on different spatial directions and the resulting effects on hot crack formation. Based on rotationally symmetric conditions of spot welds, the solidification rate was determined in radial and vertical directions for pulse shapes with different, linear ramp-down slopes to manipulate the resulting solidification conditions. The results give a deep insight in the solidification behavior and the formation of hot cracks.

## Experimental setup

### Laser welding setup for in situ synchrotron X-ray imaging

The welding process was performed for spot welds in conduction mode using a COHERENT HighLight FL8000-ARM fiber laser with a Precitec YW52 stationary processing head. The laser beam source is a fiber laser that emits radiation with a wavelength of 1030 nm. To achieve a uniform power density, the set pulse power was distributed proportionally between the core and the ring. This means that 84 % of the total laser power was used for the ring beam and 16 % for the core beam. To maintain a tophat power distribution on the workpiece surface, the beam was defocused by 4 mm. With this focus position shift, it can be assumed that defocused welding does not negatively impact the welding result, as the process remains exclusively within the domain of conduction welding. The beam caustics, including the power distribution, were measured using the Primes (FocusMonitor 120) system. The following Fig. 2 shows the measured power distribution of a 4 mm defocused laser beam. The false color representation illustrates the intensity distribution. A core power of 72 W and a ring power of 378 W were set for the measurements. The beam caustic was measured using the D86 method.

A three-axis processing system was used for positioning the sample. Fig. 3 shows a schematic of the setup. The experiments were carried out at European Synchrotron Radiation Facility (ESRF, beamline: ID 19) for

<figure><img src="image_4.png" /><figcaption>**Fig. 1.** Relationship between hot crack occurrence and ramp down duration for single pulse laser beam welding (data and visualization based on (Seibold et al., 2022)).</figcaption></figure>
<figure><img src="image_5.png" /><figcaption>Fig. 2. Illustration of the measured power distribution of the ARM system with a 4 mm defocused laser beam. Below: Section through the center of the beam.</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>Fig. 3. a) Schematic of setup for high-speed synchrotron X-ray imaging. b) detailed view of the welding process and a single image after image processing.</figcaption></figure>

in situ high-speed synchrotron X-ray imaging. A Photron SA-Z high-speed camera was coupled to a scintillator (Crytur, Ce-doped Lu3Al5O12, thickness: 250 µm). The distance between sample and scintillator was 4.5 m to profit from propagation-based X-ray phase contrast, the mean X-ray photon energy 60 keV given by the filtered radiation of an u32 undulator (minimum gap) and the beam size 4 × 4 mm² enabling a recording frequency of 120,000 Hz at a resolution of 384 × 336 pixel².

Fig. 3 b) shows the detailed illustration of the T-beam geometry of the aluminum specimen (width: 2 mm, EN AW-6082 T6), which was separated from the material by wire cutting. The chosen width of the specimen allowed high acquisition rates in X-ray imaging. In addition, the geometry is designed to enable a large number of welds to be carried out on the same specimen under comparable conditions. Spot welds for single pulses with a spot diameter of 400 µm were performed on a T-beam shaped specimen (thickness: 0.5 mm) to achieve a geometry that is
comparable to a typical sheet. Each welding pulse was applied on a single flange of the T-beam to prevent mutual influence from heat conduction and thermally induced stresses. The welding position is located centrally on the flange of the T-beam geometry, maintaining a distance of 5 mm from both the edge and the web (see Fig. 3b).

A shielding gas nozzle was directed at the weld surface to prevent oxidation during welding. Argon 5.0 was used as the shielding gas with a volume flow of 4 l/min (nozzle diameter: 3 mm). The digital mass flow meter from Brockhorst, the EL-FLOW Prestige type FG-201CV-AGD-33-V-DA-000, ensured accurate control of the shielding gas flow rate.

In order to adjust the solidification rate during pulsed laser beam welding, different ramp-down times tRD were utilized resulting in different slopes in reducing the beam power over time. In all cases, the set beam power was kept constant at 900 W for 5 ms (tconst.) and subsequently ramped down linearly to 0 W. This ramp-down phase was varied based on different ramp down times tRD ranging from 0 ms to 20 ms in steps of 5 ms. The experiments thus address all three relevant segments of the ramp down times known from the state of the art (see section 1). The time-dependent beam power of each pulse shape was measured with a COHERENT PowerMax-HP Pro device at a frequency of 20,000 Hz.

## Image processing

The solidification rate is determined through image processing for the purpose of identifying the melt pool contour. Various techniques are used sequentially to improve the visibility of the melt pool contour. The

original image and a reference image are divided into three areas (see Fig. 4), separated by the sample in the middle. In this way, the image is split into three areas: the first one above the specimen, the second one in the specimen sheet, and the third one below it. An absolute difference is calculated from the image areas of the original video and the reference video, and it is added to the average gray value of the entire image area. This approach facilitates the removal of artefacts in the image area (1). An uneven gray value distribution of the image area may result from a varying X-ray beam intensity over time. To maximize image homogeneity, the reference image is first inverted by the average gray value and offset against the original image (2). The resulting image is then treated with image processing techniques such as Gaussian blurring and application of a Contrast Limited Adaptive Histogram Equalization (CLAHE) function to enhance the weld pool contour. The image can be further analyzed after binarization by using a Canny algorithm. This edge detection method is defined by two threshold values. Pixels with gray values between the two thresholds are represented as white (255) and all others as black (0). The corresponding threshold values are adjusted for each set of frames to accurately extract the contour with minimal artifacts.

Image processing steps are performed on all high-speed images. To determine solidification rates in radial and z-direction, the melt pool contour was determined along two lines in the binarized video for each image. A horizontal line around two pixels (approx. 4.54 µm) below detected edge of the sheet surface to provide data on the width (x) of the melt pool (radial) while a vertical column at the center of the pool offers insight into its depth (y). These lines are then plotted along an axis

<figure><img src="image_7.png" /><figcaption>Fig. 4. Illustration of the methodical image preprocessing.</figcaption></figure>
for all images over time, delivering the time-dependent melt pool width (x) and depth (z) (Fig. 5).

The solidification rate can be determined by taking the time derivative of this plot (Fig. 5). The mathematical definition of this relationship is as follows Eq. (1) where $d_t$ for the melt pool diameter at a time t and $d_{t-1}$ corresponds to the melt pool diameter at the previous time step. Analogously, t corresponds to a discrete time point as well as like t-1 to the previous time point. It should be noted that the sign of the term is negative to obtain a positive solidification rate from the coordinate system used when the melt pool contour decreases. To calculate the radial solidification rate $R_R$, it is necessary to divide the melt pool width by two since this is a radial rate.

$$R_R(t) = -\frac{\frac{d_t}{2} - \frac{d_{t-1}}{2}}{t - (t-1)} \quad (1)$$

The solidification rate in z direction $R_Z$ can be determined by measuring the change in weld penetration depth ($z_t$) over time. The melt pool depth $z_t$ is measured at a time step t and at the preceding time step t-1, respectively. A positive solidification rate can be assumed as the melt pool decreases, i.e., the sign of this term is negative too.

$$R_Z(t) = -\frac{z_t - z_{t-1}}{t - (t-1)} \quad (2)$$

It should be noted that the image processing was unable to fully detect a melt pool contour for every individual image in the binarized melt pool contour and thus in the plot over time. In the case of smaller defects that occur primarily over time, these can be neglected due to the high frame rate of 120,000 Hz that allows a sufficiently determination of the solidification rate even if single data points are missing. If a larger defect occurs, it is minimized by adjusting the Canny algorithm of the image processing. Artifacts were also found in the binarized melt pool contour. These occur sporadically and are not relevant to solidification rate determination if they do not occur in the areas of interest, i.e., the lines along x- and z-direction. If the artifacts are outside the melt pool contour, they can be removed by using a mask. In most cases, however, this is not necessary or can be reduced by adjusting the Canny function.

With the steps shown for the determination of the liquidus isotherm, the calculation of the solidification rate for the two spatial directions is possible.

## Results and discussion

Based on the high-speed X-ray image, the melting process as well as the solidification process can be observed very well. Fig. 6 describes the pulsed laser welding process for a single pulse shape as an example, for the general behavior of the pulsed laser welding that can be transferred to the different pulse shapes used.

Fig. 6 is divided into two sections. The top section displays the plotted nominal and measured laser power against time. The pulse shape includes a range with lasting 5 ms ($t_{const}$) followed by a decreasing ramp of 20 ms duration ($t_{RD}$). The measured power is shown to exceed the nominal laser power, with the power falling constantly to 0 W with the linear power ramp. This behavior enables precise control of the solidification process. Selected frames of high-speed X-ray imaging are shown below. Laser power increases from 0 W to 900 W immediately after pulse initiation (1, $t = 0$ ms). At this stage, the aluminum specimen is still solid, and a melt pool is not yet detectable. After 1.33 ms, the increasing dimensions of the melt pool can be seen (2). The half elliptical geometry of the melt pool is remarkable. The melt pool that forms is significantly wider than the depth of the melt pool. The top of the workpiece is heated directly by the laser beam, causing the aluminum material to reach the melting temperature at this point first. The material underneath is then gradually melted by the heat conduction. At $t = 4.73$ ms (3) a darker central contour can be identified in the melt pool. A part of the inner area of the melt pool appears brighter than its surrounding melt, indicating a lower density within this contour. This suggests the presence of a pore in the melt, based on the behavior of this contour. The very short existence of this pore can be seen in the fourth image (4, $t = 4.825$ ms). Here, the size of the pore is already reduced, showing that it is slowly dissolving into the surrounding melt or atmosphere. After reaching the maximum dimensions, the pore disappears in approximately 300 µs as can also be recognised in the high-speed images. In the fifth image (5),

<figure><img src="image_8.png" /><figcaption>Fig. 5. Extraction of melt pool diameter (d) and melt pool depth (z) from the binarized high-speed images.</figcaption></figure>
<figure><img src="image_9.png" /><figcaption>Fig. 6. Comparison of the measured pulse shape with a ramp duration of 20 ms and the individual images of the corresponding high-speed X-ray images.</figcaption></figure>

the pore is no longer present. The time of 5 ms corresponds to the point where the laser power starts being linearly decreased. By comparing the melt pool in image (5) with that at 11.3 ms (6), it is evident that the melt pool size has further increased. Therefore, despite the power decrease of the linear ramp, there is no immediate reduction of the melt pool size. The solidification starts delayed compared to the ramp down at t = 13.70 ms in radial direction (7) and from the bottom even at a later point in time (t = 15.125 ms). The solidification progresses (8, t = 18.70 ms) until the full weld is solidified completely at t = 25.6 ms (9). At this point, the melt has solidified entirely, showing a crater where the previous melt pool was located. Because of the very slow cooling due to the low power decrease of the pulse shape, the end of the pulse and the time of complete solidification coincide. The continuous power input during the decreasing power ramp allows the low-melting phases existing in the melt sufficient time to accumulate in the center of the seam during solidification. This creates the possibility of maintaining a balance between the remaining melt and the process power throughout the solidification process.

The recordings enable the temporal and spatial determination of

relevant parameters, as illustrated by the following example of the melt pool diameter as a function of time.

Fig. 7 displays the growth of the melt pool diameter in response to a pulse with a constant power of 5 ms (t<sub>const.</sub>) and a ramp down time of 5 ms. The melt pool diameter is depicted in black over time. The figure shows that the melt pool begins to form with a slight delay after the pulse starts at 0 ms. This latency shows how long the laser power must be applied to obtain a measurable melt pool. The diameter of the melt pool shows a significant increase, particularly in the initial few microseconds (0.48 ms ... 0,8 ms), which then declines until the maximum width of the melt pool is achieved at 7.89 ms. From this point onwards, a clear reduction in the diameter of the melt pool is observable. This corresponds to the growth rate of the melt pool. The diameter of the weld pool then decreases. It can be seen that the melt pool decreases significantly more with increasing time. The melt pool is almost completely solidified at the time t = 11.8 ms, making it no longer measurable. The growth of the melt pool is graphed in gray, representing a time-dependent observation of the changes in the melt pool diameter. It is evident that the maximum growth of the melt pool occurs in the initial time range. As the
<figure><img src="image_10.png" /><figcaption>Fig. 7. Time resolved diagram of the melt pool diameter as well as the change over time of the melt pool for a pulse shape with a ramp down time of $t_{RD}$ = 5 ms and a constant area of $t_{const.}$ = 5 ms.</figcaption></figure>

width of the melt pool expands, the melt pool growth rate slows down. Simultaneously, at the point where the maximum melt pool width is reached at 7.89 ms, the melt pool growth experiences a zero crossing. As the melt pool width decreases, its growth rate also diminishes. The minimal growth rate is observed during the last stage of solidification, as

negative values. Isolated peaks can be seen in the measurement in the area of the maximum melt pool size. These peaks result from the pixel resolution of the images, which is why the measured contour in this area changes several times between a view pixel values. The comparison between the melt pool size and the melt pool growth rate at the times of

<figure><img src="image_11.png" /><figcaption>Fig. 8. Radial solidification rate for different pulse shapes with increasing ramp down time. Sorted at the last time of solidification.</figcaption></figure>
the peaks shows, that this has no significant influence on the melt pool growth rate.

Below the figure, the radial solidification rate calculated this way is depicted for different pulse shapes.

Fig. 8 shows the measured radial solidification rates on the left side, while the right side shows the corresponding pulse shapes. On the left side, the solidification rates are plotted on top of each other, and all possess the same scale. For comparing the effect of different ramp down durations, all velocities were set to the time of the respective maximum solidification rate. The solidification rate for the rectangular pulse shows that the solidification rate starts at approx. 5 ms and increases continuously from this point onwards. As the ramp down duration increases, so the duration of solidification process increases. This can be identified in the diagram by an earlier measurable solidification rate. The maximal solidification rate first declines with increasing ramp duration, then increases again at a ramp duration of 15 ms. It is particularly noticeable that the maximum solidification rate can basically be measured at the end of the solidification. It can be assumed that due to the large time span of power reduction, the separation of the melt into different phases can progress significantly. In addition, the time of solidification is strongly influenced. From the beginning of solidification to the point of maximum solidification rate, the solidification rate generally increases. Additionally, due to the increasing solidification durations, it is evident that a larger amount of melt has already solidified during the decreasing

pulse power. Thus, the remaining melt that solidifies in the final time period is small in volume and consisting of low-melting phases. Moreover, with longer pulse ramps, a change in the solidification directions can be observed, which is discussed in more detail in Figs. 9 and 10 and has already been demonstrated by Bielenin (2021).

The pulse shape with a ramp down duration of 10 ms is an exception here. With this pulse shape, a local maximum as well as minimum can be recognized in the radial solidification rate.

These results allow the calculation of solidification rate over time. The figure below illustrates the solidification rates obtained for two pulse shapes with a constant laser power over time (t<sub>const.</sub>) and an added ramp down time of 10 ms.

In Fig. 9, the measured laser power of the two pulse shapes is shown in black. A nominal maximum power of 900 W is reached in the first 5 ms. In Fig. 9 a), the laser power then drops immediately to 0 W. In contrast, the laser power in Fig. 9 b) is reduced to 0 W during 10 ms. It should be noted that the displayed pulse shape a) corresponds with that in Fig. 3 of the first segment and Figure b) of the second segment. The gray colors illustrate the solidification rates in the respective spatial direction. In light gray, the solidification rate is plotted starting from the base material R<sub>Z</sub>. The radial solidification rate R<sub>R</sub> is plotted in dark gray. In Fig. 9 a) it can be observed that the solidification begins after 5 ms. The start of solidification rate therefore followed with the end of the laser pulse; thus, the shape of the pulse no longer influences the

<figure><img src="image_12.png" /><figcaption>Fig. 9. The solidification rates in both spatial directions for two pulse shapes are shown. a) rectangle pulse shape. b) ramp down pulse shape with a constant area of 5 ms and a ramp down time with a duration of 10 ms.</figcaption></figure>
<figure><img src="image_13.png" /><figcaption>**Fig. 10.** Application of the maximum solidification rates over the different maximum ramp down times. In addition, the segments from Fig. 3 and comparable single pulse welds based on (Seibold et al., 2022).</figcaption></figure>

solidification rate. The courses of both solidification rates $R_R$ and $R_Z$ increase exponentially, so that the maximum solidification rate occurs just before the weld is completely solidified. From the point of view that the solidification rate can see as the dominant parameter for hot cracking, the selected pulse shape must continue to be applied at the last moment of solidification and thus have an influence on the solidification process. This influence is more pronounced in the Fig. 9 b). In comparing with Fig. 9 a), a delayed occurrence of the solidification rate can be observed. Whereas solidification begins directly after the end of the pulse at 5 ms with a rectangular pulse, solidification starts at 10 ms in this case. It should be noted that solidification in the radial direction at the top side $R_R$ begins earlier than $R_Z$. This behavior was previously mentioned when analyzing the single frames of the high-speed X-ray images (Fig. 6, images 6 and 7, time interval $t = 15.125$ ms ... 18.7 ms). The solidification process in z-direction is initiated at 12 ms and shows a qualitatively similar behavior compared to the radial solidification rate. What characterizes the behavior at these solidification rates is the occurrence of a local maxima of the solidification rate. This maximum occurs for both solidification directions measured close at 12.5 ms. This means that the solidification is slowed down at this point but continues to progress ($t \approx 13.45$ ms). In Fig. 9 b) the local maximum occurs due to undercooling of the melt. Lowering the laser power gradually enlarges the mushy zone. For the used aluminum alloy of the main group 6xxx, this mushy zone occurs in the range of 585 °C to 650 °C (Seibold et al.,

2022), which leads to an increase in the low-melting areas, however, further investigations are still necessary. The solidification rate increases rapidly after this local drop until the residual melt is fully solidified. Here, the solidification rates reach their global maximum of $R_{max} = 0.129$ m/s. Furthermore, it is evident that the highest solidification rates for both spatial directions are nearly identical. It should be noted that for both pulse shapes the solidification rate starts with a radial solidification. In addition, as shown in Fig. 8, the solidification rate basically increases during the solidification process. This means that for all pulse shapes, the maximum solidification rate occurs at the end of the solidification process, which is why these maximum values are used for the following figure.

If we now consider the maximum solidification rates as a function of the ramp down duration, we obtain a ratio that is comparable to the range shown in Fig. 10.

As it can be seen from both pulse shapes in Fig. 9, the different maximum solidification rates are a function of ramp duration. Here, the maximum solidification rates of the two spatial directions show a comparable behavior as in Fig. 3. The three segments can also be found in the solidification rates. This has already been demonstrated in previous studies (Bielenin, 2021). To better illustrate the cracking behavior, cross-sections of the sample surface as well as individual X-ray images at the time of complete solidification for the used pulse shapes are included. The phase contrast of the X-ray image makes it possible to
visualize the remaining cracks and pores. The first segment also shows a linear decreasing behavior with increasing ramp down duration, comparable to Fig. 3. Thereby, the difference between the solidification rates of the two spatial directions is constantly small and approx. 4.04 %. The lowest solidification rates ($R_{max} = 0,129$ m/s) are determined in the second segment. In comparison with the hot crack ratio from Fig. 3, this is the area in which the weld does not show any hot cracks. This is followed by the third segment. In contrast to the first two segments, the solidification rate does not decrease further. The solidification rate also increases with increasing ramp duration. A linear behavior as in segment one cannot be determined here. In particular, the difference between the radial solidification rate $R_R$ and the solidification rate starting from the bottom of the melt pool $R_z$ is significantly different in this segment. The solidification rate starting from the underside of the melt pool shows higher maximum solidification rates here. It can therefore be concluded that, in addition to a low maximum solidification rate, another aspect is necessary to achieve hot crack-free single pulse welds. The solidification rates in both spatial directions must also be nearly identical. With a large deviation in the maximum solidification rate, the growth direction of the dendrites changes, which in turn affects the feeding.

## Conclusion

Precise knowledge of the solidification rate, which originates from the base material, is only possible through the use of X-ray transmission tests and could not previously be determined experimentally. Due to the high recording rate of 120,000 Hz, the process course could be resolved in time. By using image processing, the melt pool contour can be recognized very well from the images and extracted for a calculation of the solidification rate for the entire solidification process. In this work, the image processing and the methodology used to extract the solidification rate were presented. For tests with different ramp durations, it could be shown that the solidification starts at different times for the two spatial directions. In principle, the solidification rate in the radial direction sets in. First, the maximum solidification rate decreases with increasing ramp duration. After exceeding a ramp duration of 10 ms, a linear relationship can no longer be determined. When comparing the hot crack length over the ramp duration with the solidification speed over the ramp duration, it was possible to show that the same segments can also be identified here. In summary, the method presented in this article makes it possible to build a better understanding of the pulsed heat conduction welding process.

## Outlook

In the existing publication, it was demonstrated that the solidification rate is a decisive factor in hot crack formation. One aspect that primarily occurs in the third segment and was already suggested in previous works is the solidification rate in relation to the spatial direction. Future investigations should examine the influence on the microstructure and the consequent impact on feeding. Additionally, the stresses and strains occurring in this context, which are relevant to hot crack formation, need to be examined in future works.

## CRediT authorship contribution statement

**M. Seibold:** Writing – original draft, Investigation, Data curation, Conceptualization.
**K. Schricker:** Investigation, Conceptualization.
**L. Schmidt:** Investigation, Conceptualization.
**D. Diegel:** Investigation, Conceptualization.
**H. Friedmann:** Methodology, Investigation, Conceptualization.
**P. Hellwig:** Investigation, Conceptualization.
**F. Fröhlich:** Investigation, Conceptualization.
**F. Nagel:** Investigation, Conceptualization.
**P. Kallage:** Investigation, Conceptualization.
**A. Rack:** H. Requardt: Resources, Investigation, Conceptualization.
**Y. Chen:** Software, Resources, Methodology, Investigation, Conceptualization.
**J.P. Bergmann:** Resources, Methodology, Investigation,

Conceptualization.

## Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Acknowledgements

We acknowledge the European Synchrotron Radiation Facility (ESRF) for provision of synchrotron radiation facilities. The authors thank the German Welding Society (DVS) for their support and the AiF for funding the project (20.826 BR) within the program Industrial Collective Research (IGF) of the German Federal Ministry of Economic Affairs and Climate Action based on an enactment of the German Parliament. The authors thank the Free State of Thuringia for funding the project "Leistungszentrum InSignA" (2021 FGI 0010) that allowed carrying out the experiments at ESRF.

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