Selection of parameters in nanosecond pulsed wave laser micro-welding

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.

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 (O_F), pulse energy (E_pulse), average peak power (P_peak), pulse duration (P_width) 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).

The overlap factor (O_F) 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]:

Interaction time (t_i) 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 (P_width) 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].

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

The average peak power density (q_{p, 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]:

The energy delivered to any specific point on the weld centreline is defined as the specific point energy (E_SP). 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 (E_{SP, pulse}), as given by Eq. (7):

In CW laser welding, q_p and E_SP 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 (P_{F, pulse}), which can be defined as the ratio of average peak power by the beam diameter, as given by Eq. (8):

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.

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 E_pulse, P_peak, v and PRF was described by q_{p, peak} and E_{SP, pulse}. In the first stage, q_{p, peak} was kept constant and E_{SP, pulse} was varied through different v, constant PRF, E_pulse and P_peak. In the second stage, E_{SP, pulse} was kept constant and q_{p, peak} was varied through different PRF, E_pulse and P_peak 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.

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 P_peak, E_pulse, v and PRF were used, resulting in a range of q_p from 1.60 to 10.4 MW/cm², q_{p, peak} from 32 to 81 MW/cm² and E_{SP, pulse} from 39 mJ to 1000 J. Since in CW mode it is possible to achieve the same penetration depth with high q_p and low E_SP 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.

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 P_{F, pulse} and t_i were used by varying P_peak, E_pulse, v and PRF. These combinations of system parameters resulted in a range of P_{F, pulse} from 4.5 to 57 MW/m and t_i 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 P_{F, pulse} of 22.4 and 11.2 MW/m were used for similar values of t_i, ranging from 0.05 to 0.5 ms. The processing parameters are shown in Tables 6 and Table 7.

This laser system allows the selection of thirty-one different waveforms [32]. Each waveform is characterised by a specific peak power, E_pulse and P_Width 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 P_{F, pulse} and t_i 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.

The effect of q_{p, peak} on the weld shape for constant q_p and E_{SP, pulse} is shown in Fig. 4. From Fig. 4a–b, the penetration depth increased from 0.35 to 0.50 mm by doubling q_{p, pulse} from 8 to 16 MW/cm² at constant q_p of 1.6 MW/cm² and E_{SP, 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 t_i 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 E_pulse and P_peak increase. Even though the average power is constant (100 W), an increase in P_peak is crucial to increase the material vaporisation rate through a higher q_{p, pulse}, which created a higher penetration depth in Fig. 4b in comparison to Fig. 4a. Thus, it is possible to conclude that q_{p, peak} controls the penetration depth in pulsed wave micro-seam welding for constant q_p and E_{SP, pulse}.

The effect of E_{SP, pulse} on the weld shape for a constant q_p and q_{p, pulse} is shown in Fig. 6. From Fig. 6a–c, the penetration depth increased by increasing E_{SP, pulse} at constant q_p of 1.6 MW/cm² and q_{p, 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 E_{SP, pulse} controls the penetration depth in pulsed wave micro-seam welding for constant q_p and q_{p, peak}.

The previous section showed that the penetration depth can be independently controlled by q_{p, peak} and E_SP, _pulse when q_p is kept constant by using constant beam diameter and average power. This section investigates the correlation between q_{p, peak} and E_SP, _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 E_SP, _pulse and q_{p, peak}, as shown in Fig. 7. The trend line corresponds to constant penetration depths from 0.5 to 1.7 mm. The q_{p, peak} needed to achieve a particular penetration decreases quadratically with E_{SP, 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 t_i and q_p have a direct influence on the maximum temperature of the thermal cycle [34], when E_{SP, pulse} increases through an increase in t_i for a constant q_{p, peak} (Eq. (7)), the material experiences a peak in temperature for a longer period, increasing the penetration depth as well.

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 E_SP, _pulse and q_{p, peak} from Fig. 8a–c. When the beam diameter increases, the duty cycle of the laser decreases to balance the reduction in q_{p, peak} with an increase in E_{SP, 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].

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 q_{p, peak} and E_SP, _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 P_{F, pulse} is shown in Fig. 9. Constant penetration depth curves can be obtained for different combinations of t_i and P_{F, pulse}, being the weld width proportional to t_i.

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 t_i and high P_{F, 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 t_i can either be achieved by fast welding speed, low overlapping factor or short pulse duration. Long t_i and low P_{F, pulse} (Fig. 10c), on the other hand, resulted in a wide weld profile similar to CW welding. Note that long t_i can be achieved by a high overlapping factor. Eventually, the weld profile will approach a typical CW weld profile with a further increase of t_i. 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.

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

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 P_{F, pulse} since t_i increased from 0.05 to 0.25 ms. In Fig. 14, on the other hand, the reduction of P_{F, pulse} from 22.4 to 11.2 MW/m at a constant t_i of 0.05 ms led to a reduction in the penetration depth. The variation of P_{F, pulse} at constant t_i and beam diameter influenced the penetration depth and the weld width, since PRF increased to compensate E_pulse and P_peak 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 P_{F, 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.

In Figs. 11 and 12, despite the increase in interaction time from 0.25 to 0.5 ms at constant P_{F, 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 t_i threshold, as shown in Fig. 15. For a beam diameter of 89 μm and constant P_{F, pulse} of 22.4 MW/m, the penetration depth increases until a t_i of 1 ms (Fig. 15b) and then drops. The energy delivered in Fig. 15c for a t_i 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 t_i and consequently higher E_{SP, 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 q_{p, peak} and E_{SP, 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 t_i for a maximum P_{F, 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 t_i of 0.25 ms and a maximum P_{F, pulse} of 22.4 MW/m, as previously shown in Fig. 11.

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 P_Width 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.

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 P_{F, pulse} is necessary to compensate the low t_i (Fig. 17a), whereas for longer pulses, a low P_{F, pulse} is compensated by a high t_i (Fig. 17c). From Fig. 17a–b, the P_Width increased 1.25×, from 280 to 350 ns. Consequently, the P_{F, pulse} was reduced 1.25×, whereas t_i was increased 1.25×. From Fig. 17a–c, the P_Width increased 1.8×, from 280 to 500 ns, and P_{F, pulse} and t_i 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 P_Width, the pulse power factor model cannot be applied. From Fig. 18a–b, P_Width increased 1.8× from 280 to 500 ns, but the duty cycle was reduced to half, which resulted in a constant t_i, higher P_{F, 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.

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 P_{F, pulse} and t_i due to a constant duty cycle of 5%. According to Table 9, this was possible by adjusting PRF to each P_Width. Hence, a constant combination of q_p, q_{p, peak} and E_{SP, 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.