fundamental and application of high precision laser micro bending

FUNDAMENTAL AND APPLICATION OF HIGH PRECISION LASER MICRO-BENDING



X. Richard Zhang and Xianfan Xu
*

School of Mechanical Engineering
Purdue University
West Lafayette, IN 47907-1288











*
To whom correspondence should be addressed. ; phone (765) 494-5639; fax (765) 494-0539
ABSTRACT
This paper presents the technique of high precision microscale
laser bending and the study of the thermomechanical phenomena
involved. The use of pulsed and CW lasers for microscale bending of
ceramics, silicon, and stainless steel is demonstrated. Experimental
studies are conducted to find out the relation between bending angles
and laser operation parameters. Bending results obtained by a pulsed

and a CW laser are compared. Changes of surface composition after
laser irradiation are analyzed. Numerical calculations based on
thermo-elasto-plastic theory are conducted and results are compared
with the experimental data. Examples of industrial applications of high
precision laser bending are given.

INTRODUCTION
Laser bending or laser forming is a newly developed, flexible
technique to modify the curvature of sheet metals or hard materials.
The schematic of a laser bending process is shown in Fig. 1. A target
is irradiated by a focused laser beam passing across its surface with a
certain speed. Heating and cooling cause plastic deformation in the
laser-heated area, thus change the curvature of the target permanently.
Bending mechanisms are determined by the specimen thickness, the
thermophysical properties of the specimen, and the temperature field,



Target
Clamped end Focused laser beam
Scanning line
Bending angle
z

y
x


Fig. 1 Schematic of the laser bending process

which in turn is determined by laser processing parameters. The
common laser bending mechanisms include the temperature gradient
mechanism and the buckling mechanism [1]. For the temperature
gradient mechanism, only surface layer is heated (thus there is a
temperature gradient with the highest temperature at the surface),
residual stress and strain will be concentrated in the near surface
region. Thus, the specimen will always bend toward the laser beam.
This type of heating and bending is preferred when a consistent
bending direction is required. If laser heating is uniform across its
thickness, the specimen will bend just like a beam under compression
(buckling); the bending direction depends on the pre-curvature and the
residual stress of the specimen.
Applications of laser bending include ship construction [2],
removing welding distortion and straightening car body parts [3],
forming in space [4,5], and rapid prototyping [6,7]. Recently, Chen et
al. [8] studied high precision laser bending for manufacturing
computer components. They achieved a bending precision of sub-
microradian, far exceeding those obtained using any other method.
Finite element methods have been used to model laser bending
[9-11]. Influence of laser operating parameters on bending can be
estimated from these calculations. While in most laser bending
researches a continuous wave (CW) laser is used, bending using a
pulsed laser for micro-scale bending and a 2-D finite element study on
the relation between bending angles and the pulsed laser parameters
were also reported [12]. Although a 3-D model is more appropriate for
predicting the actual pulsed laser bending process, the computation of
3-D pulsed laser bending is inhibited by the computer power. This is
because thousands of laser pulses are irradiated onto the target in
pulsed laser bending, therefore it is extremely time-consuming to
compute thermal and thermo-mechanical effects caused by all the

pulses. Zhang et al. [13] developed an efficient calculation method for
3-D finite element analysis of pulsed laser bending. In that method,
only a fraction of the total laser pulses instead of all the laser pulses

need to be calculated, thus reducing the computation time
considerably.
This paper presents high precision bending of ceramics, silicon,
and stainless steel specimens using a pulsed laser and a CW laser.
Laser beams are tightly focused onto the target surface to induce
localized residual stress and strain, thus to obtain high precision of
bending. The relation between bending angles and laser operating
parameters, such as laser power, laser scanning velocity, and number
of scanning lines are obtained experimentally. The dependence of
bending on optical and thermophysical properties of the target material
is illustrated. In order to understand the effects of laser irradiation,
surface composition before and after laser bending are analyzed using
electron probe microanalyser (EPMA). Results obtained by a pulsed
laser and a CW laser are compared. 3D numerical simulations of
stainless steel bending using a pulsed laser and a CW laser are
performed. Results of the simulations are compared with experimental
data.


1 EXPERIMENTAL
For experiments, a 2 W Nd:VA nanosecond pulsed laser and a 9
W CW fiber laser are used. The operation parameters of these two
lasers are summarized in Table 1.

Table 1. Parameters of pulsed laser and CW laser
Pulsed laser CW laser

Laser wavelength 1.06 ?m 1.10 ?m
Laser pulse full width 120 ns
Laser pulse repetition 22 kHz
Laser maximum power 2.0 W 9.0 W
Laser beam diameter 50-60 ?m 40-80 ?m


The experimental setup for performing laser bending as well as
for measuring the bending angle has been discussed in previous work
[11,12]. Ceramics, silicon, and stainless steel (AISI 301) sheets are
used as test specimens. The parameters of the specimens are listed in
Table 2. The Al
2
O
3
/TiC ceramics is used in computer hard disks as the
material for the read/write head.

Table 2. Specimen parameters
Specimen material Ceramics Silicon Stainless steel
Length 10.0 mm 8.0 mm 10.0 mm
Width 1.25 mm 1.50 mm 1.00 mm
Thickness 0.35 mm 0.20 mm 0.10 mm


Before laser treatment, all the samples are polished and cleaned
with acetone. The elemental distribution maps of ceramic specimens
are recorded with EPMA before and after laser treatment. High
magnification photos of the surface topography and quantitative
composition analyses of the surface area irradiated by the lasers are

also obtained with EPMA.


2 EXPERIMENTAL RESULTS AND DISCUSSIONS
Bending angles of the ceramic specimens are obtained at various
laser processing conditions, as shown in Fig. 2–Fig. 5. The results of

0
10
20
30
40
50
0 1 2 3 4 5 6 7
Pulsed laser
CW laser
Bending angle ( ? rad)
Laser power (W)

Fig. 2 Bending angle of ceramics as a function of laser
power. (a) pulsed laser, 3.25 mm/s, (b) CW laser, 130 mm/s

5
10
15
20
25
30
35
40

0 5 10 15 20 25 30 35
0 100 200 300 400
Pulsed laser
CW laser
Pulsed laser scanning velocity (mm/s)
CW laser scanning velocity (mm/s)
Bending angle ( ? rad)

Fig. 3 Bending angle of ceramics as a function of scanning
velocity. (a) pulsed laser, 1.1 W, (b) CW laser, 5.0 W


pulsed laser and CW laser bending are compared. As expected, the
bending angle increases when the input laser power increases, and
decreases with an increase of the scanning velocity, as can be seen
from Fig. 2 and Fig. 3. It is found that the specimens always bend
toward the laser beam for pulsed laser bending, but they bend away
from the laser beam for CW laser bending when the scanning velocity
is reduced.
Figure 4 indicates that for both the pulsed laser and the CW laser,
scanning over the specimen surface repetitively would increase total
bending angle, but the amount of additional bending angle decreases
with the number of scanning lines. For the pulsed laser, the bending
angle obtained by the second laser scan drops to about 25% of the
angle obtained by the first scan, and no additional bending occurs after
four scans. For the CW laser, the bending angle of the second scan is
about 70% of the first scan, and no additional bending occurs after six
scans.

0

5
10
15
20
25
30
0 1 2 3 4 5 6 7
Pulsed laser
CW laser
Bending angle ( ? rad)
Number of scanning lines

Fig. 4 Additional ending angle of ceramics as a function of
number of laser scanning lines. (a) pulsed laser, 1.1 W, 3.25
mm/s, (b) CW laser, 5.0 W, 130 mm/s

0
5
10
15
20
25
30
35
40
0 50 100 150 200 250 300 350
Pulsed laser
CW laser
Bending angle ( ? rad)
Distance between scanning lines ( ?m)

Fig. 5 Bending angle of ceramics as a function of distance
between adjacent scanning lines. (a) pulsed laser, 1.1 W,
3.25 mm/s , (b) CW laser, 5.0 W, 130 mm/s


Bending angles induced by the pulsed laser and the CW laser are
compared while keeping a same laser generated stress-affected zone.
The size of the stress-affected zone is determined in the experiments as
the separation distance above which any two adjacent laser scans do
not influence each other. The bending angle as a function of the
separation distance between two scans is measured. As shown in Fig. 5,
the stress affected zone is 100 ?m for the pulsed laser bending when
the scanning velocity is 3.25 mm/s and the power is 1.1 W. The same
stress affected zone is obtained for the CW laser when the scanning
velocity is 130 mm/s and the power is 5 W. However, the resulting
bending angles for the two lasers are different, the bending angle
obtained with the CW laser is about twice of that obtained from the
pulsed laser, which is due to the longer thermal diffusion length in the
CW laser heating.



(a)

(b)

Fig. 6 BSE images of ceramic specimen surface after (a)
pulsed laser bending, 1.1 W, 13 mm/s, (b) CW laser bending,
5 W, 130 mm/s

The backscattered electron (BSE) images of laser irradiated
Al
2
O
3
/TiC ceramic specimens obtained by EPMA are shown in Fig. 6.
The magnification is 2000X. TiC grains are white irregular “islands”
and alumina grains are the background “sea”. The bending angle
obtained is 9 ?rad for the pulsed laser and 30 ?rad for the CW laser.
After the pulsed laser irradiation, the surface becomes gray. In
addition, a few microcracks can be seen in Fig. 6a in the laser-
irradiated area. After the CW laser irradiation, an extensive gray color
region appears as shown in Fig. 6b. A 30 ?m wide band of new
homogeneous material replaces the original ceramic composite
material and a curved, 1 ?m wide microcrack is located at the center of
the scanning line, connected with several transverse microcracks.
Formation of the gray substance is possibly due to diffusion of TiC
into Al
2
O
3
, and/or oxidation of TiC to form TiO
2
or TiAl
2
O
5
.

Considering the microcracks produced after the laser irradiation, more
material damages are produced by the CW laser than the pulsed laser,
though a larger bending angle is obtained by the CW laser.


20

25

30
35

40
0 1 2 3 4 5
Al

Ti

The weight percent (%)

Number of scanning lines

(a)


10

20

30

40

50
0 1 2 3 4 5 6
Al

Ti

The weight percent (%)

Laser power (W)
(b)

Fig. 7 Al and Ti weight percent changes versus (a) number
of pulsed laser scanning lines, 1.1 W, 13 mm/s, (b) CW
laser, 130 mm/s


Al and Ti weight percentage changes are also obtained using
EPMA. Two sets of experiments are carried out. For the first set of
experiments, the pulsed laser is used with a power of 1.1 W and a
scanning velocity of 13 mm/s. The element weight percentage change
versus the number of scanning lines is given in Fig. 7a. It can be seen
that the weight percent of Al decreases slightly with an increase in the
number of lines scanning at the same location. For the second set of
data shown in Fig. 7b, the CW laser is used at a scanning velocity of
130 mm/s. It can be seen that there is almost no change in the weight
percent when the laser power is increased from 1 W to 5 W. The
weight percent of Ti increases slightly from 23.8% to 24.8% when the
laser power is increased from 1 W to 3 W, and then decreases

significantly to 17.0% at 5 W.
The behavior of the ceramics under laser irradiation shown in Fig.
6 and Fig. 7 can be qualitatively understood by analyzing the optical
and thermal properties of the ceramics. In the ceramics specimen, the
alumina grains are transparent to the laser irradiation, while the TiC
grains absorb the laser energy. Heating of alumina is through heat
conduction from the TiC grains to the alumina grains. On the other
hand, alumina has lower melting temperature (2345 K) and
vaporization temperature (3803 K) compared to those of TiC (3413 K
and 5093 K) [14]. During pulsed laser irradiation, a certain amount of
alumina grains are evaporated, and possibly some TiC grains as well.
TiO
2
and other oxides such as TiAl
2
O
5
can be produced due to
oxidation. TiC and its oxides form a gray pattern on the surface as
shown in Fig. 6a. Overall, the evaporation is weak because of the short
heating time; relatively less material is ablated, causing a small change
in the element weight percentages. For the CW laser irradiation, at low
laser powers (<3 W), the temperature reached in the TiC grains could
be lower than its vaporization temperature (5093 K) but it could be
higher than the vaporization temperature of alumina (3803 K) in the
alumina grains. Therefore, more alumina is evaporated and TiC and its
oxides

are left on the surface. Evaporation is rather weak and the
element percentage changes are small. On the other hand, at high laser

powers (>3 W), a higher peak temperature is reached on the surface of
the TiC grains, causing stronger evaporation and stronger oxidation.
However, it is noticed that the slight increase in Al does not offset the
large decrease in Ti, indicating other compounds are formed such as
oxides. Forming of TiO
2
from TiC would reduce the weight
percentage of the Ti element. Thus, it can be concluded that more
oxides are formed with a high laser power, resulting in reduced C and
Ti concentrations.
0
5
10
15
20
0 1 2 3 4 5 6 7 8
Pulsed laser
CW laser
Bending angle ( ? rad)
Laser power (W)

Fig. 8 Bending angle of silicon as a function of laser power
at scanning velocity 3.25 mm/s for (a) pulsed laser, (b) CW
laser


Figure 8 shows the bending angle of silicon specimens as a
function of the power of the pulsed laser and the CW laser,
respectively. The thermal diffusivity ??of silicon is much larger than
that of ceramics. For pulsed laser bending, the larger ? value of silicon

does not cause much difference in the bending angle since the pulse
duration is very small (120 ns), and the heat diffusion depth is much
smaller than the thickness of the specimen. However, for the CW laser,
the temperature gradient in the silicon specimen is not as steep as that
in the ceramic specimen because of the larger ? value and a relatively
long heating time. Another factor that affects the temperature profile in
the thickness direction is the optical absorption depth of materials. The
optical absorption depth of silicon is about 0.5 mm and that of
ceramics is less than 100 nm. The longer optical absorption depth of
silicon results in a more uniform heating but a lower peak temperature.

Using the CW laser and a scanning velocity of 3.25 mm/s, the ratio of
the heat diffusion depth to the silicon specimen thickness is on the
order of 10, thus, bending could be caused by the buckling mechanism.
It can be seen from Fig. 8 that, for the CW laser, the bending angles of
the silicon specimen are less than half of the bending angles of the
ceramics specimen at most power levels, even the scanning velocity of
the latter is 40 times faster than the former.
0
5
10
15
20
0
0.001
0.002
0.003
0.004
0.005
0 0.5 1 1.5 2 2.5

Pulsed laser
CW laser
Laser power (W)
Pulsed laser bending angle ( ? rad)
CW laser bending angle (rad)

Fig. 9 Bending angle of stainless steel as a function of
laser power (a) pulsed laser, at scanning velocity 195 mm/s,
(b) CW laser, at scanning velocity 8 mm/s, laser beam
diameter 40 ?m


Figure 9 shows the bending angle of the stainless steel as a
function of the power of the pulsed laser and the CW laser. The laser
beam diameter of the CW laser is 40 ?m. At these laser powers,
melting does not occur. Compared with the pulsed laser bending of
ceramics and silicon, it is found that comparable bending angles can
be obtained for steel when the scanning velocity is about 60 times
higher and with only half of the laser power. This is because steel is
much more ductile, and the steel specimen used is thinner than other
two materials.


3 NUMERICAL SIMULATIONS
The CW and pulsed laser bending induced by the temperature
gradient mechanism is simulated using 3-D finite element models.
Thermal analysis and stress analysis are needed in the simulation. The
two analyses are treated as uncoupled since the heat dissipation due to
deformation is negligible compared with the heat provided by the
lasers. In an uncoupled thermo-mechanical model, a transient

temperature field is obtained first in the thermal analysis, and is then
used as a thermal loading in the subsequent stress analysis to obtain
transient stress, strain, and displacement distributions.
For the CW laser bending simulation, the laser beam is
considered as a constant heat source moving at a constant velocity.
The time step in the calculation must be small enough so that the
continuously moving laser flux can be accurately approximated.
Hence, the CW laser bending can be simulated using a 3-D model
directly. For the pulsed laser bending, direct simulation using a 3-D
model is impractical in terms of the computer power, since there are
too many pulses along a single laser scanning line. An efficient
method for simulating pulsed laser bending has recently developed by
Zhang et al. [13]. In most pulsed laser bending processes, constant
stress and strain fields along the laser scanning direction are obtained.
Although a single laser pulse generates non-uniform stress and strain
distributions, in practice, laser pulses with the same pulse energy,
separated by a very small distance compared with the laser beam
diameter are used. Thus, the laser-induced stress and strain vary little
along the scanning direction. Also, the stress and strain fields induced
by a laser pulse are contained within a short distance from the laser-
irradiated area. With these in mind, it is only necessary to calculate
several laser pulses until the stress and strain fields in an x-z cross-
section area are not changed by a new laser pulse. Then, the residual
strain field in this cross-section can be imposed onto the whole domain
to calculation the deformation distribution. In other words, a strain
field {?
r
}, which can be used to calculate displacements of the target
after pulsed laser scanning, is generated by calculating only a fraction
of the total pulses. Details of calculating displacements from a strain

field were provided elsewhere [13].
The non-linear finite element solver, ABAQUS is employed for
both CW and pulsed laser bending simulations. Only bending of the
stainless steel is simulated since more property data of stainless steel
are available compared with the other two materials. The maximum
temperatures obtained in all simulations are lower than the melting
point of steel (1650 K). Properties of stainless steel 301 [15] used in
the calculation are considered as temperature dependent.


3.1 MESH GENERATION
For both CW and pulsed laser calculations, a dense mesh is used
around the laser path and a coarse mesh is used outside the primary
processing region. Transition elements are created to connect the
dense mesh and the coarse mesh. The Eight-node linear brick elements
are used. The mesh used for the CW laser bending simulation is shown
in Fig. 10. The Cartesian coordinate system is attached to the
computational domain and the center of laser beam moves along the y-
axis at x = 0. The computational domain is the same as the dimensions
of the steel sheet used in the experiments, 10 mm x 1 mm x 0.1 mm.
The total element number is 20,790. The mesh for the pulsed laser
bending simulation is similar except a different element size is used
and the total element number is 99,440. Mesh refinement tests are
performed by increasing the mesh density until calculations are
independent of the mesh density. For each case, the same mesh is used
for both thermal and stress analyses.


o
x

y
z

Fig. 10 Mesh for the 3D simulation of CW laser bending


3.2 THERMAL AND STRESS ANALYSES
The thermal analysis is based on solving the 3D heat conduction
equation. The initial condition is that the whole specimen is at the
room temperature (300 K). The laser flux is handled as a volumetric
heat source absorbed by the target. Using the transient temperature
data obtained from the thermal analysis as thermal load, the transient
stress, strain, and displacement distributions are obtained by solving
the quasi-static force equilibrium equations. The material is assumed
to be linearly elastic-perfectly plastic. The Von Mises yield criterion is
used to model the onset of plasticity. The left edge is completely
constrained, and all other boundaries are force free.
Material properties including density, yield stress, and Young’s
modulus are considered as temperature dependent. The strain rate
enhancement effect is neglected since temperature dependent data are
unavailable. Due to the same reason, a constant Poisson’s ratio of 0.3
is used. Effects of unknown material properties on the computational
results have been discussed by Chen and Xu [12]. Creep is neglected
due to very short laser pulse duration.


3.3 NUMERICAL RESULTS AND COMPARISON WITH
EXPERIMENTAL DATA
Figure 11 and Figure 12 are the off-plane displacement and
residual stress ?

xx
profile along the x direction. Only half of the
computational domain is calculated because of the symmetry. For
pulsed laser bending as shown in Fig. 11, a “V” shape off-plane
displacement is obtained after laser scanning, with the valley located at
around 10 ?m from the center of the scanning line. The positive off-
plane displacement near the center of the scanning line is produced by
thermal expansion along the positive z-direction. The stress ?
xx
is
tensile and its value is around 1.1 GPa in the region within 15 ?m
from the pulse center. This agrees with the theoretical prediction that
the tensile residual stress will be obtained near the center of the laser-
irradiated area due to the thermal shrinkage during cooling. The tensile
stress drops quickly to zero at about 25 ?m from the center of the laser
beam. For CW laser bending as shown in Fig. 12, the off-plane
displacement has a similar profile but a much larger (hundreds times)
magnitude. However, the peak tensile residual stress, about 700 MPa,
is smaller than that induced by a pulsed laser.
For the pulsed laser energy of 4.4 ?J, 5.4 ?J and 6.4 ?J, bending
angles obtained by simulations are compared with experimental results,
as shown in Fig. 13. It is seen that the experimental results agree with
the calculated values within the experimental uncertainty. Both the
experiment and simulation results show the bending angle increases
almost linearly with the pulse energy.
Figure 14 compares the measured and calculated bending angles
obtained by a 2W CW laser with a fixed beam diameter of 80 µm, but
at different scanning velocities. Increasing the scanning velocity
decreases the bending angle because of the decrease of the energy
input. The calculated bending angles are about 20% lower than the

experimental data.

0
0.5
1
1.5
2
0
200
400
600
800
1000
1200
0 50 100 150 200
Displacement
Residual stress
Off-plane displacement w (nm)
x (? m)
Residual stress ?
xx
(MPa)

Fig. 11 Simulation results of pulsed laser (a) off-plane
displacement, (b) residual stress ?
xx
distributions (Laser
pulse energy 5.4 ?J, scanning velocity 195 mm/s)
0
0.1

0.2
0.3
0.4
0.5
0
200
400
600
800
0 500 1000 1500 2000 2500 3000
Displacement
Residual stress
Off-plane displacement w ( ? m)
x (? m)
Residual stress ?
xx
(MPa)

Fig. 12 Simulation results of CW laser (a) off-plane
displacement, (b) residual stress ?
xx
distributions (Laser
power 2 W, scanning velocity 8 mm/s, laser beam diameter
80 ?m)
0
2
4
6
8
10

12
0.09 0.1 0.11 0.11 0.12 0.13 0.14 0.14 0.15
0.2 0.25 0.3 0.35
Experimental
Simulation
Bending angle (
?
rad)
Laser fluence (J/cm
2
)
Laser power (W)

Fig. 13 Comparison of experimental and numerical results
of bending angles versus laser power (Pulsed laser,
scanning velocity 195 mm/s)


200
400
600
800
1000
5 10 15 20 25 30
Experimental
Simulation
Bending angle (
?
rad)
Scanning velocity (mm/s)

Fig. 14 Comparison of experimental and numerical results
of bending angles versus scanning velocity (CW laser,
laser power 2 W, laser beam diameter 80 ?m)


4 CONCLUSIONS
This work demonstrated using pulsed and CW lasers for
microscale bending of ceramic, silicon, and stainless steel samples.
Experimental studies were conducted to find out relations between
bending angles and laser operation parameters. Bending results
obtained by a pulsed and a CW lasers were compared. It was found
that when the laser generated stress-affected zone was kept the same,
the CW laser produced more bending than the pulsed laser did.
However, the pulsed laser caused much less surface composition
change and thermomechanical damage to the specimens. Numerical
calculations using the thermo-elasto-plastic theory were conducted and
the results of the calculations agreed with the experimental data.


ACKNOWLEDGMENTS
Support of this work by the National Science Foundation is
acknowledged. The authors are most grateful to Dr. Andrew C. Tam of
IBM Almaden Research Center for his contribution to this work. The
authors also thank SDL, Inc. for providing the CW fiber laser system,
and Mr. Carl Hager (EAS Department, Purdue University) for his help
on the EMPA measurements.


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