1 Introduction

Laser welding is a non-contact process for joining both similar and dissimilar materials. This technique introduces the innovation needed to substitute the traditional tool wearing contact methods, such as mechanical clinching or friction stir welding, improving productivity using ultra-fast scanning devices. It has a good potential in micro-joining due to the high energy density, resulting in a very precise heat input control and high penetration/width ratio when compared to other fusion welding processes [1, 2]. Its versatility in the manufacturing of precision components ensures the required quality standards for electrical and mechanical connections without a filling material. Nevertheless, it is necessary to have a very accurate positioning [3, 4]. For a butt-joint configuration, for instance, the presence of a gap between the base materials is critical, being important to avoid that the beam passes through without interacting with the joining partners [5]. Therefore, a robust experimental setup is necessary to ensure repetitive and reliable results [6].

CW lasers can be applied in a wider range of material thicknesses due to their higher average power in comparison to PW lasers, which allows better productivity through faster processing speeds to minimise the heat input [7]. The deep penetration and good weld quality of CW mode are attributed to the stable heat conduction mechanism to the metal, since the peak power is always constant during the irradiation time, which does not happen in PW mode [8]. The most recent generation of PW fibre lasers have low operating and maintenance costs and the laser beam can be easily delivered to the workpiece due to its high optical quality (M2 ˂ 1.6). These lasers provide a cost-effective solution, being integrated into different industrial applications given the variety of temporal pulse shapes, also known as waveforms [9, 10]. Normally nanosecond lasers are used for material removal processes such as cutting [11], drilling [12], engraving and machining [13, 14] due to short pulse duration and high peak powers, but when operated at a high repetition rate, they can be used for precision welding [15], being able to minimise thermal damages, welding distortion and porosity formation [16]. However, in some applications, where higher fit-up tolerance and penetration depth are required, the CW lasers are often the best choice [17, 18].

The selection of different parameters in laser welding is complex as there are many variables to control for specific applications such as power, welding speed or beam diameter which affect the weld profile differently. Moreover, the material type and its application also affect the response to the laser energy. Laser welding of austenitic stainless steel is normally applied in nuclear structural fabrication, valve bodies and vessel internals because of the excellent mechanical properties achieved [19]. It is also used to precisely join small cylindrical cells and large cells with geometrical large interconnectors in automotive battery packs [20]. Kuryntsev et al. observed the benefits of tuning the beam diameter according to the laser application [21]. Using defocused beams, they increased the volume of the weld pool of stainless steel, reducing the requirement for preparation of edge and gap between workpieces [21]. In a different study, the volume of the weld pool was controlled by controlling the pulse shape [22]. Kumar et al. found that the fusion zone area and the penetration depth of stainless-steel welds decreased when the pulse width was increased beyond 5 ms. Nonetheless, the ultimate tensile strength of all the welded joints at different pulse widths was similar [22]. Modelling approaches have also been carried out to predict the required time for reaching melting temperature in each laser pulse [23], and the optimal process parameters for producing the expected welding bead profile [24].

In summary, PW lasers enable finer control of material interaction because the same pulse energy can be applied with different combinations of pulse width, peak power and pulse energy. For nanosecond PW lasers, these combinations of parameters can be selected through different waveforms which are characteristic of each laser system. Hence, it is difficult to understand which one is preferable for welding and how similar weld shapes can be achieved when other variables such as welding speed, pulse repetition frequency, average power and beam diameter are applied. For example, Sun et al. [16] observed that penetration depth increased for higher pulse frequency, owing to increasing overlapping factor and average power. In their research study, the data analysis was done in terms of system parameters, which prevented a direct process comparison with different PW laser systems. Therefore, the underpinning laser-material interaction in terms of power density and energy needs to be understood and correlated with the weld bead profiles.

The laser user typically wants to control the depth of penetration, weld width and distortion, and avoid defect formation. The power factor model, previously developed for low carbon steel [25] and then extended for aluminium [26], can select the optimum laser parameter settings for laser power and welding speed for a given beam diameter, to obtain a specific weld profile in CW macro laser welding. This study focuses on redefining the original formula to fit the characteristics of PW lasers. This research aims to create an analytical model which allows the choice of pulse width, peak power, pulse energy, welding speed, pulse repetition frequency and beam diameter to obtain the depth of penetration and weld width suitable for micro-joining applications, transferrable between various laser systems. Due to the considerable number of parameters used throughout this work, a list of abbreviations is presented in Table 1.

Table 1 List of abbreviations
Full size table

2 Mathematical formulation of the model

2.1 Definition of the fundamental laser-material interaction parameters

The application of energy per unit length of the material is well defined for CW laser welding. However, the pulse shape can be electronically modulated in nanosecond pulsed lasers, as shown in Fig. 1. The power distribution is not constant during the entire duration of the pulse, the peak power being instantaneous. Consequently, the average peak power represents the average of the power distribution within a pulse, being lower than the peak power, but higher than the average power. The pulse energy is the integral of power over pulse duration, which can also be represented by the area in red of the pulse shape.

Fig. 1
figure 1

Differentiation of lasers in terms of temporal outputs in continuous wave and modulated pulsed wave modes

Full size image

The weld profile can be described by the fundamental laser-material interaction parameters (FLMIP) in CW mode, which include average power density, specific pulse energy and interaction time [27]. However, in PW processing, the same parameters can be applied with various temporal characteristics, such as overlap factor (OF), pulse energy (Epulse), average peak power (Ppeak), pulse duration (Pwidth) and pulse repetition frequency (PRF). Therefore, a new set of parameters is proposed and studied in this work for PW mode.

Several PRF can be selected for each waveform. According to Fig. 2, there is a specific frequency (PRF0) at which the laser operates with the highest pulse energy for a particular waveform. Below PRF0, the pulse energy remains constant, but the average power reduces proportionally to the frequency reduction. Above PRF0, the pulse energy decreases when the frequency increases [14], as given by Eq. (1). Since the peak power of each pulse is only instantaneous over the pulse duration, similarly to previous studies [28, 29], this work has also considered the average peak power over the entire pulse duration for the calculation of the pulse energy in Eq. (2).

Fig. 2
figure 2

Output characterization of the nanosecond PW laser [29]

Full size image
$$ {E}_{pulse}={P}_L/ PRF\ \left[\mathrm{J}\right] $$
(1)
$$ {P}_{peak}={E}_{pulse}/{P}_{width}\ \left[\mathrm{W}\right] $$
(2)

The overlap factor (OF) represents the percentage of overlap between the consecutive spots, which is dependent on the welding speed (v), beam diameter (d) and PRF, as given by Eq. (3) [30]:

$$ {O}_F=\left( 1-v/ dPRF\right)100\ \left[\%\right] $$
(3)

Interaction time (ti) defines the time in which a point is exposed to the laser beam in the weld centreline. Therefore, in PW mode, it is dependent on the duration of each pulse (Pwidth) and the overlap between them, as given by Eq. (4). At 0% overlap factor, the interaction time is equal to pulse duration and at 100%, the equation is not applicable, since the beam is stationary. Hence, Eq. (4) is only applicable below 100% of overlapping factor [28, 29].

$$ {t}_i=\left({P}_{Width}/\left( 1-{O}_F/100\right)\right)\ \left[\mathrm{ms}\right] $$
(4)

The average power density (qp) is defined as the ratio of the average output power (PL) to the area of the laser beam size on the surface (AS), which for a circular beam diameter is given by Eq. (5) [27]:

$$ {q}_p={P}_L/{A}_S\ \left[\mathrm{MW}/{\mathrm{cm}}^2\right] $$
(5)

The average peak power density (qp, peak) in PW processing is defined as the ratio of the average peak power by the area of the laser spot, as given by Eq. (6) [14]:

$$ {q}_{p, peak}={P}_{peak}/{A}_S\ \left[\mathrm{MW}/{\mathrm{cm}}^2\right] $$
(6)

The energy delivered to any specific point on the weld centreline is defined as the specific point energy (ESP). This definition was created for CW mode as the product of average power density, interaction time and the area of the laser spot on the surface [27]. However, due to the peak power effect on the weld shape for constant average power in PW mode [28, 29], the definition has been reformulated to specific pulse energy (ESP, pulse), as given by Eq. (7):

$$ {E}_{SP, pulse}={q}_{p, peak}{t}_i{A}_S={P}_{peak}{t}_i\ \left[\mathrm{J}\right] $$
(7)

2.2 Definition of pulse power factor

In CW laser welding, qp and ESP control the depth of penetration and are both dependent on the area of the laser beam, being possible to achieve similar penetration depth with a combination of high power density and low specific point energy or vice versa [27]. The first parameter is the inverse square of the beam diameter, whereas the second is linearly dependent on the beam diameter. From this relationship, it was found that the depth of penetration is proportional to the ratio of average power to beam diameter and a new parameter was established, the power factor. It has been shown that the penetration depth in CW keyhole regime can be approximated by the power factor model, which enables the achievement of a particular depth of penetration independent of the beam diameter selected [25]. However, as previously shown in Fig. 1, the average power is the same as peak power and they cannot be independently varied in CW mode. On the other hand, in PW mode, the peak power is higher than the average power and both parameters can be independently varied, which affects the final weld shape [28, 29]. Hence, it is necessary to reformulate the definition of power factor for PW processing to take into consideration the effect of peak power in the weld shape when the average power is kept constant.

In this study, a new definition of power factor has been established and tested, the pulse power factor (PF, pulse), which can be defined as the ratio of average peak power by the beam diameter, as given by Eq. (8):

$$ {P}_{F, pulse}={P}_{peak}/d\ \left[\mathrm{MW}/\mathrm{m}\right] $$
(8)

3 Experimental setup

The welds were carried out in austenitic stainless steel 304L with the following dimensions: 40 × 70 × 2 mm (Width x Length x Depth). The chemical composition of this alloy is shown in Table 2.

Table 2 Chemical composition of the base materials [31]
Full size table

The experimental setup is shown in Fig. 3. A TRUMPF G4 nanosecond pulsed wave (Z-type) with an average output power of 100 W, maximum peak power of 10 kW, maximum pulse energy of 1 mJ and maximum pulse duration of 500 ns was used in these experiments. The temporal response of the laser radiation was measured using a high-speed photodetector (MenloSystems) connected to an oscilloscope (Tektronix) with 1 GHz bandwidth and a sampling capacity of 5 Giga samples per second (Gs/s). The laser beam was delivered through an optical fibre of 50-μm diameter connected to a galvo-scanner (RAYLASE Superscan) equipped with f-theta focusing lens with a focal length of 160 mm. An air knife was used with compressed gas to protect the lens from spatter and no shielding gas was applied on the substrate. The optical properties of the laser, such as beam diameter, focus position and depth of focus, were measured using a DataRay slit-scan beam profiler. The laser output power was measured by a Laserpoint power meter.

Fig. 3
figure 3

Experimental setup of PW fibre laser used for stainless-steel welding

Full size image

The samples were mechanically ground, polished and electrolytically etched with 10% of oxalic acid. Micrographs were taken with an Optiphot optical microscope with several magnifications. The weld width and depth of penetration were measured using a Carl Zeiss Axio Vision 4.8 image analysis software (https://www.zeiss.com/microscopy/int/products/microscopesoftware/axiovision.html). The experimental error was calculated based on the difference of the penetration depth measured between the first and second cross sections for the same welding parameters. The welds with an experimental error above 20% were excluded from this analysis.

4 Methodology

4.1 Experimental study rationale

It is known that in CW laser welding, the weld shape is controlled by both average power density and applied energy. High power density and high applied energy guarantee high vaporisation rate, and consequently, high aspect-ratio welds, whereas long laser-material interaction time creates large weld pools [27]. A specific penetration depth can be achieved through a trade-off between both parameters, which is the working base of the power factor model in CW mode [26].

A similar approach used in CW mode has been tested in PW mode to control the weld shape through a new set of three proposed parameters. First, the average peak power density should control the transition from conduction to keyhole mode. High aspect-ratio welds may be possible to achieve when high average peak power densities are applied through small beam diameters and high average peak powers at low pulse repetition frequencies. Second, the specific pulse energy may also control the penetration depth. High applied energy may lead to more heat accumulation to generate sufficient molten metal. It can be achieved through large beam diameters and high energy per pulse at low frequencies. Third, the interaction time may control the weld width. Large melt pools may be characteristic of low welding speeds at high pulse repetition frequencies.

If the proposed new set of parameters controls the weld shape, the power factor model may also be applicable in PW mode. The common variables of average peak power density, specific pulse energy and interaction time are the beam diameter and the pulse repetition frequency. Therefore, the foundation of the pulse power factor model is built on the relationship between both: The combination of small beam diameters and low pulse repetition frequencies will lead to high values of pulse power factors and short interaction times. Consequently, a high vaporisation rate and high aspect-ratio welds may be achieved until a certain threshold to avoid drilling the material. On the other hand, large beam diameters and high pulse repetition frequencies will lead to low pulse power factor values and long interaction times, which may create enough heat accumulation to generate large weld pools, more suitable for applications where high fit-up tolerance is required. In both cases, similar penetration depths may be reached for different trade-offs between pulse power factor and interaction time, independently of the beam diameter and frequency selected.

The average laser output power was kept constant in this study. Therefore, the average power density can be disregarded from the analysis of the results. The laser temporal pulse shape selected dictates the maximum peak power and energy per pulse possible to achieve. Its effect on the material response was investigated for different pulse repetition frequencies and correlated with the model only in the last section.

4.2 Effect of average peak power density and specific pulse energy

This section investigates the effect of the proposed new set of parameters in the penetration depth of PW bead-on-plate welds using a fixed beam diameter, average power and pulse width. The joint effect of Epulse, Ppeak, v and PRF was described by qp, peak and ESP, pulse. In the first stage, qp, peak was kept constant and ESP, pulse was varied through different v, constant PRF, Epulse and Ppeak. In the second stage, ESP, pulse was kept constant and qp, peak was varied through different PRF, Epulse and Ppeak and a constant v. The set of parameters studied are shown in Table 3. The characteristics of the temporal pulse shape used are shown in Table 4.

Table 3 Set of parameters used for a constant beam diameter of 89 μm, pulse width of 500 ns and average power of 100 W
Full size table
Table 4 Characteristics of waveform 31 of PW laser
Full size table

4.3 Effect of beam diameter

To explore the applicability of the new parameters in different laser systems, a set of bead-on-plate welds with different beam diameters of 0.35, 0.59 and 0.89 μm, constant average power and pulse width were used. For each beam diameter, different combinations of Ppeak, Epulse, v and PRF were used, resulting in a range of qp from 1.60 to 10.4 MW/cm2, qp, peak from 32 to 81 MW/cm2 and ESP, pulse from 39 mJ to 1000 J. Since in CW mode it is possible to achieve the same penetration depth with high qp and low ESP or vice versa [27], this section intends to prove that the same dependence is also valid for PW mode when different beam diameters are applied. The set of parameters used is shown in Table 5.

Table 5 Set of parameters used for different beam diameters at constant pulse width of 500 ns and average power of 100 W
Full size table

4.4 Effect of pulse power factor and interaction time

The pulse power factor model was tested using a set of bead-on-plate welds achieved with different beam diameters of 0.35, 0.59 and 0.89 μm, constant average power and constant pulse width. The effect on the penetration depth and weld width was investigated in two stages: First, for each beam diameter, different combinations of PF, pulse and ti were used by varying Ppeak, Epulse, v and PRF. These combinations of system parameters resulted in a range of PF, pulse from 4.5 to 57 MW/m and ti from 0.05 and 5 ms. The penetration depths and weld widths were analysed for each combination and only four penetration depths (0.3, 0.7, 1.0 and 1.4 mm) were considered to simplify the representation of the results. In the second stage, to prove that similar weld shapes can be achieved independently of the beam diameter selected (35-89 μm), for each beam diameter, constant values of PF, pulse of 22.4 and 11.2 MW/m were used for similar values of ti, ranging from 0.05 to 0.5 ms. The processing parameters are shown in Tables 6 and Table 7.

Table 6 Set of system parameters used for different combinations of pulse power factor and interaction time at constant average power of 100 W and pulse width of 500 ns
Full size table
Table 7 Set of FLMIP used for different combinations of pulse power factor, interaction time and beam diameter at constant average power of 100 W and pulse width of 500 ns
Full size table

4.5 Effect of temporal pulse shape

This laser system allows the selection of thirty-one different waveforms [32]. Each waveform is characterised by a specific peak power, Epulse and PWidth and can be operated for a wide range of v and PRF. This section investigates the applicability of the pulse power factor model in controlling the weld shape when different laser temporal pulse shapes are used. A set of bead-on-plate welds with several combinations of PF, pulse and ti were applied in waveforms 0, 27 and 31 at constant beam diameter and average power. The intrinsic properties of each waveform are shown in Table 8 and the set of parameters used are shown in Tables 9 and 10.

Table 8 Properties of waveforms 0, 27 and 31 at PRF0 and maximum average power of 100 W
Full size table
Table 9 Set of system parameters for different combinations of pulse power factor and interaction time applied in waveforms 0, 27 and 31 at constant beam diameter of 35 μm and average power of 100 W
Full size table
Table 10 Set of FLMIP for different combinations of pulse power factor and interaction time applied in waveforms 0, 27 and 31 at constant beam diameter of 35 μm and average power of 100 W
Full size table

5 Results and discussion

5.1 Effect of average peak power density and specific pulse energy

The effect of qp, peak on the weld shape for constant qp and ESP, pulse is shown in Fig. 4. From Fig. 4a–b, the penetration depth increased from 0.35 to 0.50 mm by doubling qp, pulse from 8 to 16 MW/cm2 at constant qp of 1.6 MW/cm2 and ESP, pulse of 125 mJ. The reduction of frequency at constant welding speed, beam diameter and pulse width led to a reduction of the overlap between pulses (Table 3), which resulted in fewer pulses applied per unit length and consequently, a reduction of ti from 0.250 ms in Fig. 4a to 0.125 ms in Fig. 4b. However, as shown in the temporal response of the laser in Fig. 5, when the frequency decreases, the pulse shape changes and Epulse and Ppeak increase. Even though the average power is constant (100 W), an increase in Ppeak is crucial to increase the material vaporisation rate through a higher qp, pulse, which created a higher penetration depth in Fig. 4b in comparison to Fig. 4a. Thus, it is possible to conclude that qp, peak controls the penetration depth in pulsed wave micro-seam welding for constant qp and ESP, pulse.

Fig. 4
figure 4

Micrographs of bead-on-plate welds made at different average peak power densities, similar average power density of 1.6 MW/cm2 and specific pulse energy of 125 mJ

Full size image
Fig. 5
figure 5

Pulse shapes of waveform 31 (pulse width of 500 ns) for different pulse repetition frequencies at constant average power of 100W

Full size image

The effect of ESP, pulse on the weld shape for a constant qp and qp, pulse is shown in Fig. 6. From Fig. 6a–c, the penetration depth increased by increasing ESP, pulse at constant qp of 1.6 MW/cm2 and qp, peak of 8 MW/cm2. Due to an increase of overlap between pulses at constant PRF and beam diameter, the welding speed decreased (Table 3), which is reflected in an increase in the number of pulses applied per unit length and a consequent increase of the laser-material interaction time from 0.05 in Fig. 6a to 5 ms in Fig. 6c. Consequently, the total energy delivered to the laser spot increased in the same ratio, from 25 to 2500 mJ, and the heat transfer rate from the hot surface to the cold bottom was much higher, being enough to build up the temperature of the material to a such level where a keyhole was formed. It can be concluded that ESP, pulse controls the penetration depth in pulsed wave micro-seam welding for constant qp and qp, peak.

Fig. 6
figure 6

Micrographs of bead-on-plate welds at different specific pulse energy, similar average peak power density of 8 MW/cm2 and average power of 1.6 MW/cm2

Full size image

5.2 Effect of beam diameter

The previous section showed that the penetration depth can be independently controlled by qp, peak and ESP, pulse when qp is kept constant by using constant beam diameter and average power. This section investigates the correlation between qp, peak and ESP, pulse and its effect on the penetration depth when different beam diameters of 35, 59 and 89 μm and constant average power of 100 W are used.

From a wide range of experiments, a few different cases with the same penetration depth were selected and plotted as a function of ESP, pulse and qp, peak, as shown in Fig. 7. The trend line corresponds to constant penetration depths from 0.5 to 1.7 mm. The qp, peak needed to achieve a particular penetration decreases quadratically with ESP, pulse. This means that similarly to CW welding [26], there is also a trade-off between both parameters through a constant rate of material vaporisation [33] in PW micro-seam welding. Since both ti and qp have a direct influence on the maximum temperature of the thermal cycle [34], when ESP, pulse increases through an increase in ti for a constant qp, peak (Eq. (7)), the material experiences a peak in temperature for a longer period, increasing the penetration depth as well.

Fig. 7
figure 7

Specific pulse energy versus average peak power density for depths of penetration of 0.5, 1.3 and 1.7 mm at a constant average power of 100 W and pulse width of 500 ns

Full size image

The corresponding micrographs from Fig. 7 are shown in Fig. 8 for a constant penetration depth of 0.5 mm. The duty cycle also needs to be considered in the trade-off between ESP, pulse and qp, peak from Fig. 8a–c. When the beam diameter increases, the duty cycle of the laser decreases to balance the reduction in qp, peak with an increase in ESP, pulse in the same proportion. For higher duty cycles, the substrate is subjected to high thermal load since the period between pulses is shorter [35]. Consequently, there is a reduction of energy loss between pulses, keeping the penetration depth constant. This is even more evident when the pulse overlapping is high, creating a cumulative energy effect of the laser radiation through several pulses [14].

Fig. 8
figure 8

Different combinations of average power density, average peak power density and specific pulse energy for a constant weld depth of 0.5 mm

Full size image

5.3 Effect of pulse power factor and interaction time for PW welding

As previously shown in Section 5.2, it is possible to achieve constant penetration depth with different beam diameters by varying processing parameters in such a controlled way to reach a particular combination of qp, peak and ESP, pulse. The problem with such an approach is that both parameters are dependent on beam diameter and pulse repetition frequency. This can be simplified to a single parameter, the pulse power factor. An example of random data plotted as a function of PF, pulse is shown in Fig. 9. Constant penetration depth curves can be obtained for different combinations of ti and PF, pulse, being the weld width proportional to ti.

Fig. 9
figure 9

Pulse power factor for depths of penetration of 0.3, 0.7, 1 and 1.4 mm as a function of interaction time for beam diameters of 35, 59 and 89 μm

Full size image

Three micrographs were taken from the constant trend line of a penetration depth of 0.7 mm from Fig. 9 and presented in Fig. 10. At short ti and high PF, pulse (Fig. 10a), spiky weld profiles are achieved, which is a characteristic of a short interaction between the laser and the material, leading to rapid keyhole development and solidification. Short ti can either be achieved by fast welding speed, low overlapping factor or short pulse duration. Long ti and low PF, pulse (Fig. 10c), on the other hand, resulted in a wide weld profile similar to CW welding. Note that long ti can be achieved by a high overlapping factor. Eventually, the weld profile will approach a typical CW weld profile with a further increase of ti. However, this model is not necessarily a good theory, especially for the same penetration depth due to fit-up problems [5]. Similar trend lines observed in PW micro-seam welding in Fig. 9 using the new definition of power factor (Eq. (8)) have also been demonstrated in CW macro welding of low carbon steel [25] and aluminium [26] using the standard definition of the model.

Fig. 10
figure 10

Constant depth of penetration of 0.7 mm achieved with different combinations of pulse power factor and interaction time for beam diameters of 35 μm, 59 μm and 89 μm

Full size image

In Figs. 11 and 12, depth of penetration is presented as a function of PF, pulse and ti using different beam diameters. Constant penetration is demonstrated for constant ti but only for certain spot sizes. For a beam diameter of 35 μm at ti of 0.5 ms, there is a higher variation in the depth of penetration when compared to larger beams of 59 and 89 μm.

Fig. 11
figure 11

Effect of the beam diameter on the depth of penetration at different interaction times and a constant pulse power factor of 22.4 MW/m

Full size image
Fig. 12
figure 12

Effect of the beam diameter on the depth of penetration at different interaction times and a constant pulse power factor of 11.2 MW/m

Full size image

The weld profiles from Figs. 11 and 12 are shown in Figs. 13 and 14. Comparing Fig. 13a–c with Fig. 13d–f, the penetration depth increased at constant PF, pulse since ti increased from 0.05 to 0.25 ms. In Fig. 14, on the other hand, the reduction of PF, pulse from 22.4 to 11.2 MW/m at a constant ti of 0.05 ms led to a reduction in the penetration depth. The variation of PF, pulse at constant ti and beam diameter influenced the penetration depth and the weld width, since PRF increased to compensate Epulse and Ppeak reduction. Consequently, it is likely the reduction of the laser’s drilling force, being the energy delivered through more pulses, enlarging the weld pool. Therefore, constant PF, pulse applied with a small beam diameter and high PRF does not have the same effect on the weld width as the combination of a larger beam and lower PRF.

Fig. 13
figure 13

Constant combinations of pulse power factor of 22.4 MW/m and interaction times of 0.05 ms and 0.25 ms for different beam diameters of 35, 59 and 89 μm

Full size image
Fig. 14
figure 14

Constant combinations of pulse power factors of 22.4 MW/m and 11.2 MW/ms and interaction time of 0.5 ms for different beam diameters of 35, 59 and 89 μm

Full size image

In Figs. 11 and 12, despite the increase in interaction time from 0.25 to 0.5 ms at constant PF, pulse and constant beam diameter of 35 μm, the penetration depth remained almost unchanged, which shows the limitation of the model in small beam diameters. However, this limitation is also visible for larger beam diameters from a certain ti threshold, as shown in Fig. 15. For a beam diameter of 89 μm and constant PF, pulse of 22.4 MW/m, the penetration depth increases until a ti of 1 ms (Fig. 15b) and then drops. The energy delivered in Fig. 15c for a ti of 5 ms is extremely high, being the thermal losses also higher for a constant average peak power which is not able to create more material vaporisation, leading to a reduction in penetration depth. Thus, it can be concluded that, in pulsed wave welding, higher ti and consequently higher ESP, pulse give the necessary cumulative heating effect to generate more material melting and increase the penetration depth, counteracting the high energy dissipation between pulses that the small heat source is subjected in comparison to the bulk material [14]. However, there is a limit in the trade-off between qp, peak and ESP, pulse to increase the penetration depth for a certain beam diameter and this limit is reached sooner for smaller beam diameters. Similar results were observed in laser machining using a similar nanosecond pulsed laser where the ablation rate increased with the power density until a certain point and then dropped from a certain limit [14]. The limit of this trade-off can be translated in the combination of maximum allowed ti for a maximum PF, pulse. Therefore, in this study, for the range of beam diameters tested from 35 to 89 μm, similar penetration depths can only be guaranteed until the combination of a maximum ti of 0.25 ms and a maximum PF, pulse of 22.4 MW/m, as previously shown in Fig. 11.

Fig. 15
figure 15

Bead-on-plate welds at different interaction times, constant pulse power factor of 22.4 MW/m, pulse duration of 500 ns, beam diameter of 89 μm, an average power of 100 W and duty cycle of 5%

Full size image

5.4 Effect of temporal pulse shape

In the previous sections, the pulse power factor model was applied for a single pulse duration of 500 ns. In this section, the model is used for different PWidth of 280, 350 and 500 ns at a constant beam diameter of 35 μm and average power of 100 W. The correspondent laser temporal response was measured and shown in Fig. 16 for a constant PRF of 100 kHz. The highest peak power of 10 kW is achieved for the shortest pulse duration (wfm 0), whereas for longer pulses of 280 ns (wfm 27) and 500 ns (wfm 31), similar peak powers of 7 kW are achieved. However, at similar PRF, all waveforms have the same pulse energy (Table 8), but the longer the pulse duration, the higher the laser duty cycle.

Fig. 16
figure 16

Pulse shapes of waveform 0, 27 and 31 for a pulse repetition frequency of 100 kHz at an average power of 100W

Full size image

In Fig. 17, a constant penetration depth of 1.3 mm was achieved independently of the waveform selected. For a short pulse duration, a high PF, pulse is necessary to compensate the low ti (Fig. 17a), whereas for longer pulses, a low PF, pulse is compensated by a high ti (Fig. 17c). From Fig. 17a–b, the PWidth increased 1.25×, from 280 to 350 ns. Consequently, the PF, pulse was reduced 1.25×, whereas ti was increased 1.25×. From Fig. 17a–c, the PWidth increased 1.8×, from 280 to 500 ns, and PF, pulse and ti changed in the same proposition. In all cases, the penetration depth was kept constant since the duty cycle of the laser compensated the difference in pulse duration and peak power verified in all waveforms in Fig. 16, allowing constant thermal losses between pulses. However, as observed in Fig. 18, if the duty cycle is not adjusted in the same proportion as PWidth, the pulse power factor model cannot be applied. From Fig. 18a–b, PWidth increased 1.8× from 280 to 500 ns, but the duty cycle was reduced to half, which resulted in a constant ti, higher PF, pulse and consequently, an increase in the penetration depth. Therefore, it can be concluded that the duty cycle is a critical parameter to consider in this model when different laser temporal modes are used.

Fig. 17
figure 17

Constant penetration depth of 1.3 mm achieved with different combinations of pulse power factors and interaction times in waveforms 0, 27 and 31 at constant average power of 100 W and beam diameter of 35 μm

Full size image
Fig. 18
figure 18

Different penetration depths achieved in waveforms 0 and 31 for different pulse power factors and constant interaction time of 0.1 ms, average power of 100 W and beam diameter of 35 μm

Full size image

There is an alternative to applying the model in different temporal pulse shapes. As observed in Fig. 19, a constant penetration depth of 1.3 mm was achieved in different waveforms for a constant PF, pulse and ti due to a constant duty cycle of 5%. According to Table 9, this was possible by adjusting PRF to each PWidth. Hence, a constant combination of qp, qp, peak and ESP, pulse was possible to achieve for the three different waveforms (Table 10). Consequently, the substrate was subjected to a constant thermal cycle since the period between successive pulses was constant, keeping the surface temperature and the penetration depth constant [35]. As previously concluded from Fig. 17 and confirmed once again in Fig. 19, the duty cycle is a critical parameter to consider in the pulse power factor model to achieve similar penetration depths in different waveforms. Similar results have been observed for laser scoring using a nanosecond pulsed laser [14], which means that the applicability of the pulse power factor model can be extended to other applications rather than just micro-joining.

Fig. 19
figure 19

Constant penetration depth of 1.3 mm achieved in waveforms 0, 27 and 31 at a constant pulse power factor of 57.1 MW/m, interaction time of 0.1 ms, a duty cycle of 5%, an average power of 100 W and beam diameter of 35 μm

Full size image

6 Conclusions

The standard formulation of the power factor model in CW processing was redesigned and exploited in PW seam welding. The new definition, the pulse power factor, correlates the peak power rather than the average power with the beam diameter. The following conclusions have been taken:

  • Average peak power density and specific pulse energy control the material vaporisation rate and heat accumulation, whereas the interaction time controls the weld width. The combination of these parameters simplifies the selection of pulse width, peak power, pulse energy, welding speed, pulse repetition frequency and beam diameter through the application of a new phenomenological model;

  • The pulse power factor model allows the laser user to select a weld profile in stainless steel which meets certain quality and productivity requirements independent of the laser system: High aspect-ratio and productive welds can be achieved for high values of pulse power factor and short interaction times, whereas wider melt pools suitable for higher fit-up tolerance and less productive applications can be achieved for lower pulse power factors and longer interaction times;

  • Constant penetration depth curves against interaction time and pulse power factor were achieved in stainless steel: A certain combination between high pulse power factor and short interaction time or vice versa will lead to similar penetration depths but different weld widths. The higher the penetration depth required, the higher the pulse power factor needed for similar interaction time;

  • For each beam diameter, there is a threshold in the maximum interaction time for a certain pulse power factor, creating limitations on the applicability of the model due to unpredictable variations of the penetration depth. This limit is reached sooner for smaller beams than larger beams due to the difference in high energy losses caused by the ratio of the heat source to the bulk material;

  • For a constant average power and beam diameter, the duty cycle is a critical parameter to calculate the pulse power factor and interaction time values needed to achieve similar weld shape in different laser temporal modes: For shorter pulse durations, the laser duty cycle is reduced to compensate in the same proportion the increase in peak power, keeping constant the trade-off between pulse power factor and interaction time.

  • The high vaporisation rate applied through high peak power creates high aspect-ratio welds. This may be not suitable for other materials with different physical properties, such as melting point and thermal conductivity. For those circumstances, the model may show several limitations or may need to be optimised to guarantee a working envelope where the drilling regime is avoided and only melting in keyhole mode is possible.