See discussions, stats, and author profiles for this publication at: https://www.researchgate.

net/publication/252017073

Use of fundamental laser material interaction parameters in laser welding

Article · January 2011

CITATIONS READS

6 4,246

2 authors, including:

Wojciech Suder
Cranfield University
47 PUBLICATIONS   487 CITATIONS   

SEE PROFILE

Some of the authors of this publication are also working on these related projects:

Development of innovative laser welding for high strength aluminium structural alloys View project

New Wire Additive Manufacturing (NEWAM) View project

All content following this page was uploaded by Wojciech Suder on 22 August 2014.

The user has requested enhancement of the downloaded file.

JOURNAL OF LASER APPLICATIONS VOLUME 24, NUMBER 3 AUGUST 2012

Investigation of the effects of basic laser material interaction parameters

in laser welding
W. J. Suder and S. W. Williams
Welding Engineering and Laser Processing Centre, Cranfield University, MK43 0AL, United Kingdom
(Received 15 September 2011; accepted for publication 22 May 2012; published 15 June 2012)
The depth of penetration achieved in continuous wave (CW) laser welding results from a balance
of many complicated phenomena, which are linked with the characteristics of the heat source. In
this work, the laser welding process has been investigated in terms of basic laser material
interaction parameters: power density and interaction time. It has been shown that these two
parameters are insufficient to characterize the laser welding process. Thus, a third parameter,
specific point energy, has been introduced, which along with the power density and the interaction
time allowed the welding process to be uniquely defined. It has been shown that the depth of
penetration is mainly controlled by the power density and the specific point energy, whilst the weld
C 2012 Laser Institute of America.
width is controlled by the interaction time. V

Key words: laser welding, power density, interaction time

I. INTRODUCTION guished in terms of applied power density and interaction

time, as demonstrated by Steen.19 Ion20 has shown how to
Lasers are very flexible in terms of power density and
approximate the power density and the interaction time in
total energy delivered to a workpiece, which makes them
CW laser processing. Ashby and Easterling21 determined
attractive for many applications. The beam diameter has a
fundamental parameters which controlled the structure and
major effect in this energy flexibility, the importance of
the depth of hardened layer in laser hardening. One of the
which is commonly underestimated. In laser welding, the
key parameters in their analysis was the energy density. It
depth of penetration is a key parameter and laser users usu-
was also shown that bending rate in laser forming was de-
ally need to adjust it for the material being welded. The
pendent on the area energy and the interaction time.22 Jeb-
same depth of penetration can be achieved with different
bari et al.23 assumed the laser machining process to be a
combinations of system parameters, such as power and travel
periodical process, determined by the interaction time, which
speed, which makes the parameters selection complicated.
they further used to characterize the width of the thermal
Furthermore, it is not entirely clear which parameters deter-
affected zone during laser cutting. Fabbro and Chouf24
mine the depth of penetration despite this being a target of
developed a model, based on keyhole geometry. The depth
many research efforts. The leading themes of investigation
of penetration, according to this model, was a function of
include understanding of absorption conditions,1–3 absorp-
drilling velocity and interaction time, where the drilling ve-
tion of laser beam in the plume,4–6 and phenomena related to
locity was controlled by the absorbed power density.
the melt flow7–9 and keyhole formation.10–13
There is no case reported where a set of parameters, which
In most experimental work using continuous wave (CW)
uniquely define the characteristic of the heat source on the
lasers, the depth of penetration has been studied based on the
workpiece, were used experimentally in laser welding. In this
system parameters, such as the laser output power and the
work, a detailed study of the weld bead depth and width, in
travel speed. The system parameter approach makes the pro-
terms of power density, interaction time, and specific point
cess dependent on the particular laser system. When an
energy, has been carried out. This allowed some phenomeno-
experiment is carried out with respect to the system parame-
logical effects, such as the effect of beam diameter on weld
ters, some phenomena might be disguised by a simultaneous
profile to be studied. Also the parameters that control the depth
change of the fundamental parameters.
of penetration in CW laser welding have been identified.
To understand the parameters controlling the depth of
penetration in laser welding, independent of the laser system,
II. BASIC LASER MATERIAL INTERACTION
it is required to study the fundamental laser material interac-
PARAMETERS
tion parameters. It is commonly known from modelling14–16
that the power density or heat flux is the major parameter On the processing map shown in Fig. 1, various laser
defining the temperature distribution. Similarly, in pulsed processes can be distinguished according to the power den-
laser processing the fundamental pulse energy, power den- sity and the interaction time, the product of which is the
sity and duration time are naturally used to characterize the energy density. This figure, however, ignores the effect of
process.17,18 the size of the heat source.
Some authors tried to decompose laser processing into Interaction of a laser beam with a workpiece is deter-
basic parameters. In theory, every laser process can be distin- mined by the power density, time of irradiation, and the size

1042-346X/2012/24(3)/032009/10/$28.00 032009-1 C 2012 Laser Institute of America

V
032009-2 J. Laser Appl., Vol. 24, No. 3, August 2012 W. J. Suder and S. W. Williams

the interaction time, then the energy delivered to the laser

spot, denoted as the specific point energy ESP, is defined as
the integral of intensity and interaction time over the diame-
ter of the laser spot, given by
ðð
ESP ¼ Iðx; yÞsi dxdy: (3)

For a laser beam with a uniform intensity distribution and a

constant interaction time across the laser spot, the specific
point energy is equal to the product of power density qp,
interaction time si, and the area of laser spot on the surface
AS, which also corresponds to the product of laser output
power P and interaction time si and is given by

ESP ¼ qP  si  AS ¼ P  si ½J: (4)

FIG. 1. Processing map based on power density and interaction time [after
19 and 20]. Although the definition of specific point energy from Eq. (4)
in reality is only fulfilled in case of square or rectangular
of the heat source on the workpiece. The average power den- top-hat beams, however, this definition should be sufficient
sity qP is defined as the ratio of the laser power P to the area for relatively small beam diameters, which are commonly
of laser spot on the surface AS, which is given by used in laser welding.

P
qP ¼ ½W m2 : (1) III. EXPERIMENT
AS
The effect of interaction parameters on laser welding was
Interaction time defines the time, in which a particular point investigated on a set of autogenous bead-on-plate laser welds
on the workpiece is exposed to the laser beam, whilst the in 12 mm thick S355 low carbon steel. An IPG YLR-8000
beam is moving with a constant speed, as indicated in Fig. 2. CW fiber laser with a maximum power of 8 kW and a beam
This is similar to the pulse duration from pulsed laser weld- parameter product (BPP) of 16 mm mrad was used. The laser
ing. Considering a point in the weld centerline, the interac- beam was delivered through an optical fiber of 300 lm diam-
tion time si in case of a circular beam with a diameter d, eter, collimated with a 125 mm focal length lens, and focused
which travels with a welding speed v, is given by Eq. (2). using a set of focusing lenses with focal lengths ranging from
This definition defines the maximum interaction time in the 150 to 300 mm. The different focusing lenses were used to
weld centerline. In reality, the interaction time may vary ensure a top-hat intensity distribution, whilst the beam diame-
across the welding direction, due to the variation in beam ter was varied. The properties of the laser beam as well as the
length, unless a rectangular beam is used or in case of a spot beam diameters were measured by means of a Primes beam
welding with a stationary beam, profiler. The second order moment method25 was used for the
beam diameter evaluation. The set of focusing lenses gave
d the beam diameters at the focal points ranging from 0.38 to
si ¼ ½s: (2)
v 0.78 mm. All the welds were carried out at the focal point,
i.e., the laser beam being focused on the surface, unless other-
To uniquely characterize the laser processing, a third param- wise stated. In case of using out of focus conditions, the
eter is necessary. This is due to the fact that the same energy appropriate focus distance and the beam diameter were deter-
density (product of power density and interaction time) used mined using the beam profiler. The beam diameter in this
with different beam diameters on the surface will result in a study refers to the diameter of the laser beam projected on the
different energy delivered to the workpiece. If the laser surface. Pure shield argon was used as a shielding gas. All
welding is considered as a periodic process, whose period is welds were sectioned, polished, and examined under an opti-
cal microscope in order to measure the depth of penetration.
To evaluate the standard deviation of depth of penetration,
longitudinal cross sections were extracted from selected sam-
ples and the variation in depth of penetration was measured.
The welding parameters were chosen to ensure only the key-
hole mode to exclude the effect of changing the absorption,
which occurs in conduction welding.

A. Constant beam diameter

First, the effect of power density and interaction time
FIG. 2. Schematic of interaction of laser beam with workpiece. on the depth of penetration at a constant beam diameter on
J. Laser Appl., Vol. 24, No. 3, August 2012 W. J. Suder and S. W. Williams 032009-3

TABLE I. Parameters used for study of the effect of beam diameter on the diameter was varied. This means that the laser power and the
depth of penetration at constant power density and interaction time; (d— travel speed were adjusted with respect to the beam diame-
beam diameter on the surface, F—focal length of focusing lens, v—travel
speed, and P—laser power).
ter, according to Eqs. (1) and (4). The tests were carried out
at two levels of power density: 1.6 and 2.6 MW/cm2, respec-
d (mm) 0.38 0.5 0.63 0.78 tively, and a constant specific point energy of 60 J, as shown
in Table II.
F lens (mm) 150 200 250 300
P (kW) for 1.6 MW/cm2 1.82 3.2 5 7.6
v (m/min) for 38 ms 0.6 0.8 1 1.2 D. Depth of focus (DOF)
v (m/min) for 19 ms 1.2 1.6 2 2.45
To measure the experimental depth of focus, a focusing
v (m/min)for 7.6 ms 3 4 5 6.15
v (m/min) for 2.5 ms 9 12 15 18.6
lens with 250 mm focal length was used. All welds were car-
ried out at a constant laser power of 5 kW and three travel
speeds: 0.75, 2, and 5 m/min. The laser beam was defocused
the surface was studied. A focusing lens with a focal length up to 10 mm in negative and positive directions for all travel
of 250 mm, which provided a beam diameter of 0.63 mm on speeds. The positive and negative directions of defocusing
the surface, was used. The power density was varied by correspond to the focal point placed above and below the
changing the laser power in the range from 2 to 8 kW, surface, respectively. This distance resulted in a variation of
whilst the interaction time was varied by changing the beam diameter on the surface from 0.63 mm at the focal
travel speed from 0.3 to 15 m/min, according to Eqs. (1) point to 1.25 mm at the maximum out of focus plane.
and (2). Next, the experimental depth of focus was compared
with the Rayleigh length. One Rayleigh length corresponds
B. Effect of beam diameter to the drop of the power density by a factor of 2. The effect
of power density on the depth of penetration was examined
Second, the effect of beam diameter on the depth of pen-
by changing the power density by a factor of 2. Two differ-
etration at a constant power density of 1.6 MW/cm2 and dif-
ent cases were compared. In the first case, the power density
ferent interaction times in a range from 2.5 to 38 ms was
was changed by varying the laser power at constant beam
investigated. This was achieved by adjusting the laser power
diameter of 0.63 mm on the surface and travel speed of
and the travel speed to a given beam diameter on the surface
2 m/min. The power was changed from 1 to 8 kW with 1 kW
of the workpiece, according to Eqs. (1) and (2). Each combi-
intervals. In the second case, the power density was varied
nation of power density and interaction time was studied on
by defocusing the beam at constant power of 5 kW and travel
four different beam diameters on the surface as follows:
speed of 2 m/min. The laser beam was defocused by 10 mm
0.38, 0.5, 0.63, and 0.78 mm. The beam diameters were
in the positive and the negative directions, corresponding to
achieved using different focusing lenses with the following
the focal point being placed above and below the surface.
focal lengths: 150, 200, 250, and 300 mm. The parameters
are shown in Table I.
Furthermore, the effect was investigated at different lev- E. Effect of specific point energy on depth of focus
els of power density and a constant interaction time, using To investigate the influence of energy conditions on the
the same set of focusing lenses (F150, F200, F250, and achieved depth of penetration during defocusing of the laser
F300) to change the beam diameter on the workpiece. In this beam, the following experiment was carried out. An experi-
case, three power densities were used as follows: 1.6, 1, and mental depth of focus obtained by defocusing the laser beam
0.5 MW/cm2. To ensure the keyhole regime, a long interac- was compared with an estimated depth of focus from a varia-
tion time of 38 ms was used. tion of power density and specific point energy. In the
experiment, the laser beam was defocused by a distance of
C. Parameters controlling depth of penetration 10 mm in both directions at a constant laser power of 5 kW
Next, the effect of beam diameter on the depth of pene- and three travel speeds of 0.75, 2, and 5 m/min. The pre-
tration at a constant power density and specific point energy dicted depth of focus was achieved from a curve fit based
was investigated. In this case, the power density and the spe- on an arbitrary combination of parameters, as shown in
cific point energy were maintained constant, whilst the beam Table III. The parameters were selected to match the power
density at the focal point (1.6 MW/cm2) and at a distance of
TABLE II. Parameters used for study of the effect of specific point energy
and power density on the depth of penetration at constant power density and TABLE III. Parameters used to explain depth of focus (d—beam diameter
specific point energy (d—beam diameter on the surface, F—focal length of on the surface of the workpiece, F—focal length of focusing lens, v—travel
focusing lens, v—travel speed, and P—laser power). speed, and P—laser power).

1.6 MW/cm2 60 J 2.6 MW/cm2 60 J Power density 1.6 (MW/cm2) 0.4 (MW/cm2)

d (mm) 0.38 0.78 0.5 0.63 F lens (mm) 250 300

F lens (mm) 150 300 200 250 d (mm) 0.63 0.78
P (kW) 1.82 7.6 5 8 P (kW) 5 2
v (m/min) 0.68 5.9 2.5 5 v (m/min) 0.3–15 0.3–15
032009-4 J. Laser Appl., Vol. 24, No. 3, August 2012 W. J. Suder and S. W. Williams

TABLE IV. Parameters used to investigate the effect of intensity distribu-

tion on depth of penetration (F. position—focus position, d—beam diameter
on the surface, P—laser power, and v—travel speed).

Focusing lens F150 F300 F150

F. position (mm) 4 0 þ4
d (mm) 0.78 0.78 0.78
P (kW) 5 5 5
v (m/min) 2 2 2

10 mm out of focus (0.4 MW/cm2) from the defocused case.

The specific point energy was varied by changing the travel
speed in a range from 0.3 to 15 m/min in every case.
The data from this experiment were used to explain the
experimental depth of focus, which will be highlighted in
Sec. IV E. FIG. 4. Depth of penetration as a function of interaction time and power
density for a beam diameter of 0.63 mm.

F. Effect of intensity distribution profile

observed in Fig. 3 with the slope dependent on the interaction
To investigate the effect of intensity distribution profile time. In contrast, there is a logarithmic dependence on the
on the depth of penetration and weld shape, a series of bead- interaction time, which is shown in Fig. 4, suggesting different
on-plate welds with two different focusing lenses were carried effects in different operating regimes. Initially, the slope of
out. Two focusing lenses were used in a way to achieve the the curve is very high, indicating that the interaction time has
same beam diameter on the surface. A focusing lens with a a strong effect on the depth of penetration. When the interac-
focal length of 150 mm was defocused by 4 mm in both direc- tion time is high, its effect is smaller with depth of penetration
tions to achieve a beam diameter of 0.78 mm on the surface. being primarily dependent on the power density.
This was compared with a focusing lens with a focal length of The fact that the interaction time has more effect on the
300 mm being used at the focal point. In both cases, the weld- depth at shorter interaction times than at longer interaction
ing parameters were the same, as shown in Table IV. times indicates complex utilization of energy. For a given
power density, there is a minimum interaction time that will
IV. RESULTS AND DISCUSSION produce a keyhole, corresponding to a threshold energy den-
sity (product of power density and interaction time). This is
A. Interaction parameters at constant beam diameter the energy density needed to bring matter to the boiling point
The effect of power density and interaction time on the and to increase the vaporization rate to a level sufficient to
depth of penetration at a constant beam diameter is shown in generate a keyhole. Thus, a certain part of the energy density
Figs. 3 and 4, as the analogy to the laser power and travel is first utilized to initiate the keyhole, and only the remaining
speed. The power density and the interaction time were varied part, if there are no further losses, is available for an increase
by changing the laser power and the travel speed at a constant of depth of penetration. Therefore, the resultant depth of pen-
beam diameter, as described in Sec. III A. A linear depend- etration is determined by the amount of energy density that
ence of the power density on the depth of penetration can be is applied in relation to the threshold value.
At short interaction times, the process conditions are
more likely to be nearer the threshold energy density. Thus,
at this range, any small variation of laser parameters can
have a significant effect on depth of penetration, as shown in
Fig. 4. At long interaction times, in contrast, the keyhole is
relatively stable due to the high energy density, thus any fur-
ther increase of the interaction time has only a small effect
on the depth of keyhole.

B. Effect of beam diameter

The effect of beam diameter on the depth of penetration
at a power density of 1.6 MW/cm2 and different interaction
times is shown in Fig. 5. In this case, the laser power and the
travel speed were adjusted for a given beam diameter on the
surface to maintain the power density and the interaction
time, as showed in Table I in Sec. III B. It can be seen in
FIG. 3. Depth of penetration as a function of power density and interaction Fig. 5 that the depth of penetration increases with increasing
time for a beam diameter of 0.63 mm. beam diameter on the surface, which is opposite to that
J. Laser Appl., Vol. 24, No. 3, August 2012 W. J. Suder and S. W. Williams 032009-5

FIG. 5. Effect of specific point energy on depth of penetration at different FIG. 7. Depth of penetration as a function of specific point energy at a con-
interaction times and a constant power density of 1.6 MW cm2. stant power density of 1.6 MW cm2 (the data from Fig. 5 presented as a
function of specific point energy).

observed when changing the beam diameter at a constant

power and travel speed.26,27 In addition, there is a depend- energy results in the increase of depth of penetration, as
ency of the rate of increase of depth of penetration on the observed in Fig. 5.
interaction time. The longer the interaction time the higher All the interaction parameters are dependent on the
the rate of increase of depth of penetration. beam diameter. This means that there is only one beam di-
A relationship between the beam diameter on the surface ameter which can give a particular combination of power
and the depth of penetration, at a constant interaction time density, interaction time, and specific point energy. Further-
of 38 ms and three levels of power density, is presented in more, constant power density and interaction time do not
Fig. 6. In all cases, the depth of penetration increases steadily provide a constant depth of penetration when varying the
with increasing beam diameter. This underlines the impor- beam diameter, due to the change of specific point energy.
tance of interaction time on the rate of increase of depth of However, a closer analysis of Fig. 5 reveals that some points
penetration observed in Fig. 5. on this graph have similar depths of penetration, as indicated
The data shown in Figs. 5 and 6 suggest that constant by a horizontal dashed line, despite a significant difference
power density and interaction time do not provide a constant in the interaction times between the points. It was found that
depth of penetration when the beam diameter changes. The all the points with similar depths of penetration also had sim-
phenomenon of increasing of depth of penetration with ilar specific point energies. Since the power density in Fig. 5
increasing beam diameter on the workpiece can be attributed was also constant, the effect of specific point energy has
to the effect of specific point energy. When the beam diame- been investigated further. This can be better understood by
ter is increased, at a given power density and interaction plotting all the data from Fig. 5 as a function of specific point
time, the energy delivered to the workpiece also increases, as energy, as shown in Fig. 7.
indicated by Eq. (4). This increase of the specific point It can be seen that at a constant power density the depth
of penetration is indeed proportional to the specific point
energy and independent of the interaction time down to a
minimum level.
The results from Fig. 7 indicate that almost in the entire
range of interaction times the depth of penetration is depend-
ent on the power density and the specific point energy. How-
ever, the trend changed at very short interaction times.
Namely, all welds obtained with an interaction time of
2.5 ms in Fig. 7 exhibit significantly lower depths of penetra-
tion, despite the specific process energy being comparable.
This is also visible in Fig. 5 where the slope for 2.5 ms inter-
action time is almost zero. This indicates that at some condi-
tions the specific point energy cannot be utilized efficiently
for extending the keyhole depth if the process is carried out
below a certain threshold interaction time, which is attrib-
uted to the threshold energy density (product of power den-
sity and interaction time) for the keyhole regime. Therefore,
FIG. 6. Effect of beam diameter on depth of penetration at different levels at very short interaction times or low power densities, the
of power density and a constant interaction time of 38 ms. process may respond differently to the applied conditions.
032009-6 J. Laser Appl., Vol. 24, No. 3, August 2012 W. J. Suder and S. W. Williams

FIG. 8. Macrographs at constant power density of 1.6 MW cm2 and point energy of 60 J: (a) interaction time of 38 ms (1.8 kW, 0.68 m/min, beam diameter
0.38 mm); (b) interaction time of 8 ms (7.6 kW, 5.9 m/min, beam diameter 0.78 mm).

C. Parameters controlling depth of penetration to the saturation of depth of penetration with decreasing
beam diameter below a certain threshold value.
To confirm that the depth of keyhole in laser welding is
determined by the power density and the specific point
D. Depth of focus
energy, an experiment, where these two parameters were
kept constant whilst varying the beam diameter on the sur- A large depth of focus is observed in many CW laser
face, was carried out, as shown in Table II in Sec. III C. welding situations. This observed depth of focus is usually
Macrographs for a power density of 1.6 MW/cm2 are shown much greater than that might be expected from the variation
in Fig. 8. They reveal that the depths of penetration are very of power density with the beam diameter on the workpiece.
similar. Furthermore, in Fig. 9, macrographs for a specific Therefore, in order to investigate this effect, in terms of laser
point energy of 60 J and a power density of 2.6 MW/cm2 also material interaction parameters, the experiment with a defo-
show equal depths of penetration. Note the large variation of cused beam was carried out, as described in Sec. III D. This
power and travel speed in the example is shown in Fig. 8. experimental depth of focus was compared with the optical
The weld width, on the other hand, is controlled by the one. The Rayleigh length is commonly used as a definition
interaction time and thermal properties of the material and is of depth of focus and is equal to a distance from the focal
independent of the beam diameter on the workpiece, as point to a position at which the beam diameter increases by
shown in Figs. 8 and 9. In both examples, short interaction the root square of two. This was analyzed in terms of power
times resulted in narrow weld beads, irrespective of the density.
beam diameters. The experimental depth of focus for the optical set-up
The fact that the depth of penetration is dependent not with a focusing lens F250 mm is shown in Fig. 10. The Ray-
only on the power density but also on the specific point leigh length for this optics, measured by a beam profiler was
energy means that increasing the laser power is more benefi- 65.6 mm. It can be seen in Fig. 10 that if the beam is defo-
cial for the depth of penetration than reducing the beam di- cused by approximately one Rayleigh length, in case of a
ameter. This could explain the plateau of the depth of travel speed of 2 m/min, the depth of penetration decreases
penetration when the beam diameter is reduced below a cer- by 10%, as compared to the focal point. This depth of focus
tain value, at a constant laser power, which was reported in is indicated by a dashed line in Fig. 10. In laser macroweld-
some studies.28,29 The decreased specific point energy, as a ing applications, a practical depth of focus is often defined
result of decreasing beam diameter on the workpiece, domi- by a maximum acceptable variation of depth of penetration.
nates the energy balance, and the depth of penetration does If we assume this 10% reduction of depth of penetration, as
not increase, despite high power density. This further leads being the experimental depth of focus, other values of depth

FIG. 9. Macrographs at constant power density of 2.6 MW cm2 and point energy of 60 J: (a) interaction time of 12 ms (5 kW, 2.5 m/min, beam diameter
0.5 mm); (b) interaction time of 7.6 ms (8 kW, 5 m/min, beam diameter 0.63 mm).
J. Laser Appl., Vol. 24, No. 3, August 2012 W. J. Suder and S. W. Williams 032009-7

FIG. 10. Comparison of experimental depth of focus with theoretically pre- FIG. 11. Effect of reduction of power density on depth of penetration in
dicted from variation of power density and specific point energy for F250 fo- case of defocused beam (constant power and travel speed) and at a constant
cusing lens. beam diameter (variation of power).

of focus for the remaining travel speeds in Fig. 10 will

be 68 mm for 0.75 m/min and 64 mm for 5 m/min, as shown other parameters, i.e., whether the beam diameter or the laser
in Table V. power is varied.
The polynomials in Fig. 10 are predicted values of depth All results from the evaluation of depth of focus are com-
of focus based on the variation of power density and specific pared in Table V. It can be seen that the experimental depth of
point energy with the beam diameter, which will be high- focus varies with the travel speed. Only, at a travel speed of
lighted later. 2 m/min, the experimental depth of focus matches the Ray-
In Fig. 11, the experimental depth of focus for 2 m/min leigh length. Furthermore, in all presented cases, the experi-
travel speed from Fig. 10 is plotted as a function of power mental depth of focus is much greater than the expected depth
density. Note that in this case the power density was varied of focus from the variation of power density only.
by changing the beam diameter on the surface (defocusing) The situation is clarified when the other laser material
at a constant laser power of 5 kW. Also in the same figure, interaction parameters are taken into account. According to
the depth of penetration as a function of power density for a the Eqs. (1), (2), and (4), all the interaction parameters
constant beam diameter on the surface is compared. This change simultaneously with the beam diameter. This would
time the power density was changed by varying the laser mean that when a laser beam is defocused at a constant
power at a constant beam diameter of 0.63 mm, as described power and travel speed, two competing effects occur: on one
in Sec. III D. It can be seen in Fig. 11 that a reduction of hand, the power density decreases, but, on the other hand,
power density by a factor of 2 (one Rayleigh length), in the the specific point energy increases. It was shown previously
case of defocused beam, results in a decrease of depth of that the depth of penetration is controlled by these two pa-
penetration by only 10%. In contrast, the same change of rameters, thus the increase of specific point energy compen-
power density at a constant beam diameter results in a sates for the drop of power density during defocusing. Thus,
decrease of depth of penetration by a factor of 2. Thus, in the depth of penetration reduces less rapidly with defocusing,
order to achieve the 10% reduction of depth of penetration, as was shown in Fig. 11.
in this case, the power density can only decrease by 0.2 MW/
cm2. For this optical set-up, this would correspond to a
change of focus position by 2 mm. Thus, the effect of power
density on the depth penetration is strongly dependent on

TABLE V. Comparison of experimental depth of focus (Exp. DOF) with

Rayleigh length (Rayleigh DOF) and evaluated from variation of power
density with beam diameter in Fig. 11 (qPDOF).

Travel
speed Rayleigh Experimental Power density
(m/min) DOF (mm) DOF (mm) DOF (mm)

0.75 65.6 68 62

2 65.6 66 62
FIG. 12. A simultaneous variation of power density and specific point
5 65.6 64 62 energy with beam diameter at constant travel speed of 2 m/min and power of
5 kW.
032009-8 J. Laser Appl., Vol. 24, No. 3, August 2012 W. J. Suder and S. W. Williams

achieved depths of penetration were plotted as a function of

specific point energy, as shown in Fig. 13. This figure can be
used to investigate the effect of specific point energy and
power density on the depth of penetration from the previous
focus study (5 kW of power and 2 m/min travel speed).
Figure 13 shows a dependency of depth of penetration on
the specific point energy for two levels of power density,
which correspond to the power density in the focus position
and 10 mm out of focus from the previous case. It can be seen
that a decrease of power density from 1.6 to 0.4 MW/cm2, due
to defocusing, will result in a decrease of depth of penetration
from point 1 to point 2 in Fig. 13. At the same time, an
increase of specific point energy from 94 to 187 J will increase
the depth of penetration from point 2 to point 3. Thus, as a net
result, the depth of penetration will only decrease from point 1
to point 3 due to the compensating effect of specific point
FIG. 13. Effect of specific point energy on depth of penetration at two levels
of power density: 1.6 MW/cm2 (5 kW at 0.63 mm) and 0.4 MW/cm2 (2 kW energy for the drop in power density. This explains the large
at 0.78 mm). depth of focus observed experimentally.
Note that Fig. 13 was obtained by varying the travel
speed. Macrographs in Fig. 14 show that the same weld
E. Effect of specific point energy on depth of focus
depth, as in a defocused case, can be obtained by any combi-
The variation of interaction parameters with the beam nation of the system parameters, as long as the power density
diameter shown in Fig. 12 corresponds to the focus study and the specific point energy are the same. This is quite strik-
with a travel speed of 2 m/min from Fig. 10. It can be seen ing because it shows that during defocusing or any other
that an increase of beam diameter from 0.63 to 1.25 mm, due case when the beam diameter is changed the behaviors
to defocusing by a distance of 10 mm from the focal point, occurring are not a lot more complex than during changing
induces a simultaneous decrease of power density from 1.6 the laser power or the travel speed with respect to the power
to 0.4 MW/cm2 and an increase of specific point energy from density and the specific point energy.
94 to 187 J. The consequences of such variations of the inter- The experimental curves from Fig. 13 can be represented
action parameters can be evaluated. by Eq. (5). This equation was used to predict the depth of
To prove the compensating effect of specific point focus for other levels of specific point energy,
energy on the depth of focus, an additional experiment was
carried out. As shown in Fig. 12 when the laser beam with PD ¼ A  B  lnðESP þ CÞ; (5)
this particular optical set-up (F250 mm focusing lens) was
defocused by 10 mm, the power density decreased from 1.6 where A, B, C are constant dependent on the power density.
to 0.4 MW/cm2, as compared to the focal point. To match For a power density of 1.6 MW/cm2, A ¼ 5.54, B ¼ 2.31,
these two levels of power density, two combinations of laser and C ¼ 2.69; whereas for a power density of 0.4 MW/cm2,
power and beam diameter were used, as described in Table A ¼ 6.7, B ¼ 1.98, and C ¼ 24.8.
III in Sec. III E. To achieve a power density of 1.6 MW/cm2, The difference in the response of depth of penetration to
a laser power of 5 kW and a beam diameter 0.63 mm were the applied power density from Fig. 11 can be clarified using
used, whilst to achieve a power density of 0.4 MW/cm2, a Fig. 13 and Eq. (5). Both cases are shown in Fig. 15. When
laser power of 2 kW and a beam diameter of 0.78 mm were the power density is decreased by reducing the laser power
used. In both cases, the specific point energy was changed by at a constant beam diameter on the workpiece, not only the
using a range of travel speeds from 0.3 to 15 m/min. The power density reduces but also the specific point energy

FIG. 14. Macrographs at constant power density of 0.4 MW/cm2 and specific point energy of 187 J: (a) F250, 2 m/min, 5 kW, þ10 mm defocused beam,
1.25 mm diameter beam; (b) F300, 0.5 m/min, 2 kW, focused on the surface, 0.78 mm diameter beam; (c) F250, 2 m/min, 5 kW, 10 mm defocused beam,
1.25 mm diameter beam.
J. Laser Appl., Vol. 24, No. 3, August 2012 W. J. Suder and S. W. Williams 032009-9

for all travel speeds confirms that the large depth of focus
occurs due to the simultaneous increase of specific point
energy and a decrease of power density when the beam diam-
eter increases. Thus, the dependency of depth of focus on the
travel speed is related to the rate of increase of specific point
energy with the interaction time, which is greater at longer
interaction times. There is a small discrepancy at a travel
speed of 5 m/min in Fig. 10. This is due to the change of the
welding regime from keyhole to conduction at the maximum
out of focus position in the experiment. The specific point
energy in this case over predicted the depth of penetration.

F. Effect of intensity distribution profile

Since the results presented in this paper relayed on the
assumption of top-hat intensity distribution profile, accord-
FIG. 15. Predicted depth of focus from variation of different interaction ing to Eq. (4), the influence of intensity distribution on the
parameters with beam diameter during defocusing and compared with the depth of penetration had to be evaluated. Two different fo-
experimental depth of focus from Fig. 10. cusing lenses, one at the focal point and another out of
focus, were used to achieve the same beam diameter on the
workpiece, as described in Table IV in Sec. III F. It can be
drops at the same time. This caused a rapid drop of depth of seen in Fig. 16 that the depth of penetrations and weld pro-
penetration in Fig. 11. It can be seen in Fig. 15 that this case files are very similar, regardless if a top-hat or a nontop-hat
does not match the experimental results. On the other hand, beam was used. This justifies the use of simplified defini-
when the power density is reduced by defocusing at a con- tion of specific point energy, according to Eq. (4). The in-
stant laser power, an increase of specific point energy com- tensity distribution profile, however, might affect the
pensates for a reduction of power density. It is apparent from achieved depth when using lasers with high peak inten-
Fig. 15 that when the compensation effect of specific point sities, such as in case of single mode lasers. It is also worth
energy is taken into account, based on the logic from Fig. 13, mentioning that the lens with a shorter focal length required
the predicted curve matches the experimental results in much more attention during the experiment to achieve the
Fig. 15 very well. Note that both curves in this figure are fit- required beam diameter on the workpiece, due to the
ted parabolas based on predicted depths of penetration in shorter depth of focus. Therefore, in some cases, the same
three points: focal point, 10 mm negative defocusing, and energy density and specific point energy applied on differ-
10 mm positive defocusing, calculated from Eq. (5). ent lasers with various optical set-ups may lead to some
In the same way, Eq. (5) was used to determine the pre- differences, particularly when the depth of focus is very
dicted depths of focus in Fig. 10. These curves were also small. Also the same combination of interaction parameters
achieved by fitting parabolas, based on predicted depths of applied on laser with different wavelengths will interact
penetration in three points (focal point, 10 mm positive, and slightly differently with the material, due to differences in
10 mm negative defocusing), using Eq. (5). A good agreement absorption or plasma interaction.

FIG. 16. Effect of intensity distribution profile on weld shape at constant welding parameters and beam diameter: (a) F150 lens defocused by 4 mm below the
surface; (b) F300 lens focused on the surface; (c) F150 lens defocused by 4 mm above the surface.
032009-10 J. Laser Appl., Vol. 24, No. 3, August 2012 W. J. Suder and S. W. Williams

8
V. CONCLUSIONS J. Kroos, U. Gratzke, M. Vicanek, and G. Simon, “Towards a self-
consistent model of the keyhole in penetration laser beam welding,”
From the ongoing experiment, the following conclusions J. Phys. D 26, 481–486 (1993).
9
could be drawn: R. Fabbro, “Melt pool and keyhole behaviour analysis for deep penetration
laser welding,” J. Phys. D 43, 1–9 (2010).
10
• The depth of penetration is mainly controlled by two pa- J. Dowden, N. Postacioglu, M. Davis, and P. Kapadia, “A keyhole model
in penetration welding with a laser,” J. Phys. D 20, 36–44 (1987).
rameters, the power density and the specific point energy. 11
X. Jin, L. Li, and Y. Zhang, “A study on fresnel absorption and reflections
The weld width is controlled by the interaction time. in the keyhole in deep penetration laser welding,” J. Phys. D 35,
• A large observed depth of focus in CW welding occurs 2304–2310 (2002).
12
due to the compensating effect of specific point energy for S. Fujinaga, H. Takenaka, T. Narikiyo, S. Katayama, and A. Matsunawa,
“Direct observation of keyhole behaviour during pulse modulated high-
the reduction of power density when increasing beam power Nd:YAG laser irradiation,” J. Phys. D. 33, 492–497 (2000).
diameter on the workpiece. 13
P. Solana and G. Negro, “A study of the effect of multiple reflections on
• At slower welding speeds, the depth focus is larger due to the shape of the keyhole in the laser processing of materials,” J. Phys. D
the higher rate of increase of specific point energy with 30, 3216–3222 (1997).
14
T. W. Eagar and N. S. Tsai, “Temperature fields produced by traveling dis-
longer interaction times. tributed heat sources,” Weld. J. (Miami, FL, U.S.) 62, 346–355 (1983).
• This means that by using a longer interaction time either 15
J. Goldak, A. Chakravarti, and M. Bibby, “A new finite element model for
by using larger beam diameters or lower travel speeds will welding heat sources,” Metall. Trans. B 15, 299–305 (1984).
16
result in a larger depth of focus. J. Mazumder and W. M. Steen, “Heat transfer model for cw laser material
processing,” J. Appl. Phys. 51, 941–947 (1980).
• Applying extremely small beam diameters does not pro- 17
P. W. Fuerschbach and G. R. Eisler, “Effect of laser spot weld energy and
vide a deep penetration if the specific point energy is duration on melting and absorption,” Sci. Technol. Weld. Joining 7,
insufficient. 18
241–246 (2002).
Y. F. Tzeng, “Process characterization of pulsed Nd:YAG laser seam
welding,” Int. J. Adv. Manuf. Technol. 16, 10–18 (2000).
19
ACKNOWLEDGMENTS W. M. Steen, “Laser material processing - An overview,” J. Opt. A, Pure
Appl. Opt. 5, S3–S7 (2003).
20
This project was supported by Tata Steel and EPSRC C. J. Ion, “Laser processing diagrams,” in Laser Processing of Engineer-
Council through Cranfield IMRC. Authors would also like to ing Materials (Elsevier, Oxford, 2005), pp. 178–187.
21
M. F. Ashby and K. E. Easterling, “The transformation hardening of steel
thank Dr. Paul Colegrove for his valuable comments. surfaces by laser beams-I. Hypo-eutectoid steels, doi not available,” Acta
Metall. 32, 1935–1937, (1984); ibid. 32, 1939–1937 (1984).
1 22
P. W. Fuerschbach, “Measurement and prediction of energy transfer effi- R. McBride, F. Bardin, M. Gross, D. P. Hand, J. D. C. Jones, and A. J.
ciency in laser beam welding,” Weld. J. (Miami, FL, U.S.) 75, 24-s–34-s Moore, “Modelling and calibration of bending strains for iterative laser
(1996). forming,” J. Phys. D 38, 4027–4036 (2005).
2 23
M. Schneider, L. Berthe, R. Fabbro, and M. Muller, “Measurement of laser N. Jebbari, M. M. Jebari, F. Saadallah, A. Tarrats-Saugnac, R. Bennaceur,
absorptivity for operating parameters characteristic of laser drilling and J. P. Longuemard, “Thermal affected zone obtained in machining steel
regime,” J. Phys. D 41, 1–6 (2008). XC42 by high-power continuous CO2 laser,” Opt. Laser Technol. 40,
3
J. T. Norris, C. V. Robino, M. J. Perricone, and D. A. Hirschfeld, 864–873 (2008).
24
“Development of a time-resolved energy absorption measurement tech- R. Fabbro and K. Chouf, “Dynamical description of the keyhole in deep
nique for laser beam spot welds,” Weld. J. (Miami, FL, U.S.) 89, 75s–81s penetration laser welding,” J. Laser Appl. 12, 142–148 (2000).
25
(2010). “Lasers and laser related equipment - Test methods and beam properties
4
R. Fabbro, S. Slimani, I. Doudet, F. Coste, and F. Briand, “Experimental ratios - Part 1: Stigmatic and simple astigmatic beams,” ISO11146-1:2005.
26
study of the dynamical coupling between the induced vapour plume and S. Katayama and Y. Kawahito, and Z. Jiguang, “Interpretation of laser
the melt pool for Nd-Yag CW laser welding,” J. Phys. D 39, 394–400 weld penetration and welding phenomena,” Chin. J. Lasers 36, 3160–3166
(2006). (2009).
5 27
Y. Kawahito, K. Kinoshita, N. Matsumoto, M. Mizutani, and S. Katayama, E. Beyer, B. Brenner, and L. Morgenthal, in XVI Symposium on Gas Flow,
“Effect of weakly ionised plasma on penetration of stainless steel weld Chemical Lasers and High Power Lasers, Gmunden, 2006 (SPIE—The Inter-
produced with ultra high power density fibre laser,” Sci. Technol. Weld. national Society for Optical Engineering, Bellingham, WA, 2007), Vol. 6346.
28
Joining 13, 749–753 (2008). G. Verhaeghe and P. Hilton, in Proceedings of 24th International Congress
6
D. Lacroix, G. Jeandel, and C. Boudot, “Spectroscopic characterization of on Applications of Lasers and Electro-Optics, ICALEO 2005 (Laser Insti-
laser-induced plasma created during welding with a pulsed Nd:YAG tute of America, Miami, FL, 2005), pp. 264–271.
29
laser,” J. Appl. Phys. 81, 6599–6606 (1997). J. Weberpals, A. Russ, F. Dausinger, and H. Hugel, in Proceedings of the
7
V. V. Semak, J. A. Hopkins, M. H. McCay, and T. D. McCay, “Melt pool 3rd International WLT Conference on Lasers in Manufacturing (The Ger-
dynamics during laser welding,” J. Phys. D 28, 2443–2450 (1995). man Academic Society of Laser Technology, Munich, 2005), pp. 39–42.

View publication stats