1. technology and computing

Procedia Manufacturing
Volume XXX, 2015, Pages 1–11
43rd Proceedings of the North American Manufacturing Research
Institution of SME http://www.sme.org/namrc
Finite Element Simulation and Experimental
Validation of Pulsed Laser Cutting of Nitinol
C.H. Fu1, M.P. Sealy1, Y.B. Guo1, X.T. Wei2
1
2
Dept. of Mechanical Engineering, The University of Alabama, Tuscaloosa, AL 35487, USA
School of Mechanical Engineering, Shandong University of Technology, Zibo 255049, China
Tel.: +1 205 348 2615; E-mail address: [email protected]
Abstract
Nitinol (NiTi) alloys are widely used in laser cutting of cardiovascular stents due to excellent
biomechanical properties. However, laser cutting induces thermal damage, such as heat affected zone
(HAZ), micro-cracks, and tensile residual stress, which detrimentally affect product performance. The
key process features such as temperature distribution, stress development, and HAZ formation are
difficult to measure experimentally due to the highly transient nature. In this study, a design-ofexperiment (DOE) based 3-dimensional (3D) finite element simulation was developed to shed light on
process mechanisms of laser cutting NiTi. The effects of cutting speed, peak pulse power, and pulse
width on kerf width, temperature, stress, and HAZ were investigated. A DFLUX user subroutine was
developed to model a moving volumetric (3D) heat flux of a pulsed laser. Also, a material user
subroutine was used that incorporated superelasticity and shape memory of NiTi.
Keywords: NiTi, Shape memory alloy, Laser cutting, FEA, Surface integrity
1 Introduction
Nitinol (NiTi), a nickel-titanium alloy of near equiatomic composition, is well known for its
outstanding properties such as superelasticity, shape memory, and good biocompatibility.
Superelasticity means NiTi can have a wider elastic region (up to 8%) compared to conventional
materials such as stainless steel. Shape memory describes the process in which NiTi returns to its
previously defined shape when heated above the transition temperature. Both of these properties are
based on a phase transformation process. There are two common phases at room temperature that are
involved in the phase transformation process: (1) martensite, which is stable at lower temperatures and
(2) austenite, which is stable at higher temperatures. The austenite to martensite transformation can be
triggered by applying stress or thermal loading (Guo et al., 2013).

Corresponding author
Tel.: 1-205-348-2615; fax: +1-205-348-6419. E-mail address: [email protected]
Selection and peer-review under responsibility of the Scientific Programme Committee of NAMRI/SME
c The Authors. Published by Elsevier B.V.
1
Pulsed Laser Cutting of Nitinol
C.H. Fu, M.P. Sealy, Y.B. Guo and X.T. Wei
Due to the excellent biomechanical properties, NiTi has received considerable attention since its
discovery in 1962 at the Naval Ordnance Laboratory. The excellent biomechanical properties refer to
similar mechanical behavior to human tissue, good biocompatibility, and non-toxicity. Many of the
early applications of NiTi focused on the shape memory effect. In recent years, a lot of attention has
been aimed towards the superelasticity of NiTi, with particular emphasis on biomedical
applications (Duerig et al., 1999). A typical example is cardiovascular stents. A stent is a cylindrical
medical device used to widen a narrow or stenosed lumen in order to maintain the patency of the
lumen. Currently, stents are being increasingly used in blood vessels and gastrointestinal, renal, and
biliary tracts (Chun et al., 2010). There are many materials such as stainless steel, cobalt-chromium,
and NiTi alloys used in making stents. NiTi is preferred because of its flexibility and ability to
maintain shape in a curved lumen. Moreover, the non-linear mechanical response of NiTi is similar to
natural material, such as hair, bone, and tendon.
The manufacturing process for stents is very complex. Traditionally, machining is done by laser
cutting due to the stent’s complex geometry and NiTi’s poor machinability. (Stoeckel et al., 2004)
reported that approximately half of the manufacturers use laser cutting for self-expanding NiTi stents.
A common setup for laser cutting is to use a finely focused Nd:YAG laser beam that passes through a
coaxial gas jet to impinge the working surface of the tube while the linear and rotary velocity of the
tube is precisely controlled (Kathuria, 2005).
There have been numerous studies aimed at understanding laser cutting of NiTi. However, due to
the uniqueness of the NiTi material, the process mechanisms are poorly understood. Therefore, the
objective of this study is to develop a finite element simulation of laser cutting NiTi to shed light on:
(1) kerf width prediction and validation, (2) temperature distribution, (3) stress distribution, and (4)
HAZ prediction at different cutting conditions.
2 Heat Flux Modeling in Laser Cutting
Important process features in laser cutting such as temperature distribution, stress propagation, and
HAZ formation are directly related to cutting quality. However, they are difficult to measure
experimentally since laser cutting is a highly transient process. Therefore, finite element simulation
was used intensively to gain insight into the process. Simulations have been used to aid in determining
accurate thermal loading, verifying experimental data, and predicting temperature and residual stress
profiles.
An accurate thermal model is critical to simulate the laser cutting process. The most commonly
used heat flux model has the form of
( )
(1)
where I is the laser intensity, A is the laser absorption coefficient, P is the laser power, r0 is the spot
radius, B is the shape factor of the Gaussian distributed heat flux, and r is the distance to beam center.
Different geometrical shapes of heat flux were explored by many researchers (Lacki & Adamus,
2011; Yilbas et al., 2009; Li et al., 2004; Wang & Lin, 2007; Shuja et al., 2011; Luo et al., 2010; ZainUl-Abdein et al., 2010). It was shown that a volumetric (3D) heat flux has advantages over a surface
(2D) heat flux in predicting the thermal response of the material during laser processing. Therefore,
researchers proposed different forms of volumetric heat flux to simulate laser processing in different
applications. (Yilbas et al., 2009) simulated laser cutting of thick sheet metal using a volumetric
thermal model. The stress field and temperature field were predicted and found to be in agreement
with experimental observation. (Shuja et al., 2011) used a similar volumetric heat flux to simulate
laser heating of a moving slab. It was found that predicted melt thickness agreed with experimental
2
Pulsed Laser Cutting of Nitinol
C.H. Fu, M.P. Sealy, Y.B. Guo and X.T. Wei
measurements. (Lacki & Adamus, 2011) stated that the advantage of a conical volumetric heat flux
versus a surface heat flux was that it better captured the shape of the thermal field in deep welds
during laser melting. (Luo et al., 2010) and (Zain-Ul-Abdein et al., 2010) found that the use of a
conical shape heat flux better simulated the laser-material interaction with high penetration depth.
Pulsed laser operation is a key feature for current laser cutting processes. Different pulse durations
and repetition rates significantly affect surface roughness (Pfeifer et al., 2010; Muhammad et al.,
2012) and residual stress (Tönshoff & Emmelmann, 1989). Therefore, it is critical to incorporate the
pulsed laser operation in modeling of heat flux. A simulation using a 3D moving heat flux in pulsed
mode on NiTi is essential to improve the fundamental understanding of process mechanisms and the
influence of process parameters.
3 Simulation Procedure
3.1 Mesh
The mesh design is shown in Fig. 1. The dimensions of the workpiece were 6 mm (length) × 3 mm
(width) × 1 mm (thickness). The laser cutting direction was along the X-axis. Element size was biased
with a higher density of elements along the cutting direction (X-axis). Within the fine mesh in the
analysis zone, the element size was 50 µm × 50 µm × 10 µm. The boundary condition on the bottom
plane is fixed to provide proper constraint of the workpiece. Also, the model is symmetric with respect
to X-Z plane so that only half of the workpiece needs to be modeled to decrease the computational
time. The initial temperature was room temperature (20 oC).
The simulation was performed using Abaqus/Standard since the moving heat flux subroutine
DFLUX can only be programed with the implicit solver. The advantage of using the implicit solver
was that the temporal discretization was more stable despite a certain reduction in computational
efficiency. In order to determine the temperature and stress distribution after laser cutting, a coupled
thermal-mechanical analysis was used. The laser cutting process was based on 3-D transient heat
transfer. The criterion to model material removal was based on whether nodal temperature exceeds the
melting temperature.
X
Y
Z
1 mm
Laser pulse
Optics
50 µm
Analysis zone
10 µm
Fig. 1 Simulation schematic of pulsed laser cutting.
3
Pulsed Laser Cutting of Nitinol
C.H. Fu, M.P. Sealy, Y.B. Guo and X.T. Wei
3.2 Modeling of moving volumetric (3D) heat flux of pulsed laser
In order to understand the laser cutting process from a theoretical perspective, a schematic of 3D
heat flux is shown in Fig. 2(a). The conical shape volumetric heat flux moves along the workpiece to
generate a cutting kerf and form a heat affected zone (HAZ) on both entrance and exit sides of the
kerf.
To simulate the characteristics of the heat flux of laser pulses, a DFLUX user subroutine of conical
shape volumetric heat flux was developed. The subroutine featured (1) a moving Gaussian heat flux
from laser, (2) a pulsed operation, and (3) a conical volumetric (3D) heat flux. The output of the
subroutine was the heat flux given by the following equation
(
)
(2)
where F is the applied heat flux, C is the energy absorption coefficient, P is the peak pulse power, R0
is the laser spot radius on the top surface, h is the sample thickness, f is the laser frequency, τ is the
pulse width, and r is the instantaneous radius of the heat flux, which for a conical shape is given by
(3)
where Rb is the heat flux radius on the bottom surface and h is the sample thickness. The schematic of
the conical shape volumetric heat flux is shown in Fig. 2(b).
is a function of both frequency and pulse width to simulate laser modulation. When a laser
pulse was used, the value of θ was set to 1. When there was no pulse within one laser pulse cycle
(1/f ), the heat flux was turned off by setting θ to zero.
{
pulse
no pulse
(4)
Gaussian distribution of heat flux
HAZ
Laser beam axis
R0
Entrance
X
z
h
r
Kerf
Y
Volumetric heat flux
Exit
Rb
Z
Fig. 2 (a) Schematic of laser cutting; (b) conical shaped volumetric heat flux.
4
Pulsed Laser Cutting of Nitinol
C.H. Fu, M.P. Sealy, Y.B. Guo and X.T. Wei
3.3 Simulation conditions
The simulation conditions are listed in Table 1. The design-of-experiment (DOE) simulation was a
sensitivity analysis to determine the effects of cutting speed (cases 1-3), peak pulse power (cases 4-6),
and pulse width (cases 7-9). The average power (P) and the pulse energy (E) were calculated by
(5)
(6)
where P is the average power, P0 is the peak pulse power, τ is the pulse width, f is the laser frequency,
and E is the pulse energy.
The laser frequency was 100 Hz, the laser spot radius on the top surface was 300 µm, and the topto-bottom ratio of the heat flux diameter was determined by the entry-to-exit kerf width ratio in the
experimental work (Pfeifer et al., 2010).
Case #
1
2
3
4
5
6
7
8
9
Peak pulse
power
(W)
1600
1600
1600
1000
1600
2000
800
1600
4000
Table 1 Simulation Conditions
Pulse
Cutting
Frequency
width
speed
(ms)
(Hz)
(mm/s)
0.5
100
2
0.5
100
5
0.5
100
8
0.5
100
5
0.5
100
5
0.5
100
5
1.0
100
1.7
0.5
100
1.7
0.2
100
1.7
Avg
power
(W)
80
80
80
50
80
100
80
80
80
Pulse
energy
(J)
0.8
0.8
0.8
0.5
0.8
1.0
0.8
0.8
0.8
3.4 Modeling of Nitinol Superelasticity and Shape Memory
The material parameters used to define the mechanical behavior is described in (Fu et al., 2014a).
The material constants were based on a curve fitting process between a quasi-static stress strain curve
from Split-Hopkinson Pressure Bar tests and the given theoretical model (Fu et al., 2014b) under the
assumption that tension and compression curves were symmetric with each other. In previous
research, these material constants successfully captured the superelastic-plastic mechanical behavior
of NiTi (Fu et al., 2012).
4 Results and Discussions
4.1 The effect of cutting speed
Fig. 3 shows the representative predicted kerf geometry with transient temperature contour.
Elements that have temperatures above the melting point of Nitinol will be removed from the mesh to
form the kerf. To study the cutting speed effect, three levels of cutting speed were used at constant
peak pulse power, pulse width, and laser frequency.
5
Pulsed Laser Cutting of Nitinol
C.H. Fu, M.P. Sealy, Y.B. Guo and X.T. Wei
P = 1600 W
τ = 0.5 ms
f = 100 Hz
v = 2 mm/s
Temp. (°C)
Kerf
profile
HAZ
Exit
kerf
Entry
kerf
Taper
Fig. 3 Representative prediction of laser cut kerf.
Kerf width: The effect of cutting speed on kerf width is shown in Fig. 4(a). The predicted kerf
width agreed with experimental data on trend. As the cutting speed increased from 2 mm/s to 8 mm/s,
the kerf width decreased due to less heat input into the workpiece. The cause of discrepancy between
the simulated and experimental width may be contributed to several factors. For example, the energy
absorption coefficient C is not constant in laser cutting and could change at different cutting speeds.
Also, the influence of temperature on material properties could be another error source to contribute
the discrepancy.
Subsurface temperature: Temperature distribution in the subsurface is shown in Fig. 4(b). The
nodal temperature decreased dramatically from the laser beam’s center along the subsurface direction.
At a cutting speed of 2 mm/s, the temperature difference within 200 µm was smaller when compared
to other 2 simulation cases (5 mm/s and 8 mm/s). This was due to the fact that at a lower cutting speed
the thermal energy had more time to conduct into the subsurface.
Subsurface stress: Fig. 4(c) shows von Mises distribution in the subsurface. The maximum stress
occurred on the cut surface with a magnitude of 520 MPa, 440 MPa, and 400 MPa corresponding to
cutting speeds of 2 mm/s, 5 mm/s, and 8 mm/s. As the depth increased to 200 μm in the subsurface,
von Mises stress decreased approximately 35%. Slower cutting speeds led to higher stresses on the top
surface and in the subsurface. The slower cutting speeds allowed for more heat conduction which
generated more thermal expansion leading to higher stress. The maximum von Mises stress was
generated by the slowest cutting speed. The generated stress was still below the yield strength (2 GPa)
of NiTi. Thus, it can be claimed that there was no plastic distortion in these simulation cases. It was
shown that this thermal model is capable of predicting the stress distributions and can therefore be
used to select cutting parameters to minimize thermal stress and avoid thermal damage.
HAZ: It has been suggested that the prediction of HAZ can be based on a critical temperature. For
example, phase transformation temperature was used as the critical temperature for HAZ prediction in
laser-assisted machining (Singh et al., 2008). For NiTi, the phase transformation temperature from
martensite to austenite is close to ambient temperature (20 oC). Hence, it was not suitable to use this
temperature as the critical temperature. Based on a binary phase diagram given by (Frenzel et al.,
2004), the critical temperature used in this study was 1025 oC, which is the solidus temperature for
NiTi containing 50 at.% nickel. Fig. 4(d) shows the HAZ prediction based on this criterion. The HAZ
thickness was 70 µm, 20 µm, and 18 µm for cutting speeds 2 mm/s, 5 mm/s, and 8 mm/s, respectively.
It was expected that the lowest cutting speed generated the thickest HAZ due to the excessive heat
input.
6
Pulsed Laser Cutting of Nitinol
C.H. Fu, M.P. Sealy, Y.B. Guo and X.T. Wei
1400
300
200
Sim_entrance
Exp_entrance
Sim_exit
Exp_exit
100
1000
600
200
0
(a)
2
4
6
8
10
Cutting speed (mm/s)
600
0
(b)
v = 2 mm/s
v = 5 mm/s
v = 8 mm/s
500
300
200
50
100
150
100
80
400
0
50
200
Sim_entrance
Sim_exit
60
40
20
0
2
200
Depth in the subsurface (µm)
150
Depth in the subsurface (µm)
HAZ thickness (µm)
von Mises stress (MPa)
800
400
0
(c)
v = 2 mm/s
v = 5 mm/s
v = 8 mm/s
1200
Temp. (°C)
Kerf width (µm)
400
(d)
5
8
Cutting speed (mm/s)
Fig. 4 Effect of cutting speed on width (a), temperature (b), stress (c), and HAZ thickness (d).
4.2 The effect of peak pulse power
To study the effect of peak pulse power, three levels of peak pulse power were used at constant
pulse width, laser frequency, and cutting speed.
Kerf width: Fig. 5(a) compares the calculated kerf width with the experimental data. The trends
between the predicted values agreed with experimental data. As the peak pulse power increased, the
kerf width increased due to more heat input. At the lowest peak pulse power, there was approximately
40% difference between the simulated and experimental width. This might be associated with the
change of energy absorption coefficient at different laser powers. At a lower laser power, the
temperature was lower on the workpiece surface and there was less energy loss due to radiation.
Therefore, the energy absorption could be higher than the assumed value of 0.8. It is suggested that the
energy absorption would be different at different laser powers.
Subsurface temperature: Temperature distribution in the subsurface is shown in Fig. 5(b). The
nodal temperature decreased with increased depth in the subsurface. In the subsurface zone of 50 µm,
the temperature distribution was similar for all the three simulation cases. Beyond 50 µm in the
subsurface, the temperature distribution was significantly different. It suggests that peak pulse power
influences the temperature distribution in the deep subsurface while having little or no effect near the
top surface. This is because higher peak pulse power penetrates deeper into the subsurface.
Subsurface stress: Fig. 5(c) shows von Mises stress in the subsurface at different peak pulse
powers. At the largest peak pulse power, the maximum stress occurred on the top surface with a
magnitude of 520 MPa. At the smallest peak pulse power of 1000 W, the maximum stress was
280 MPa and located 75 μm in the subsurface. The reason why the maximum residual stress was
7
Pulsed Laser Cutting of Nitinol
C.H. Fu, M.P. Sealy, Y.B. Guo and X.T. Wei
located in the subsurface was due to more thermal radiation into the air on the top surface. It is clear
that high peak pulse power produces higher temperature on the top surface and in the subsurface.
HAZ: Fig. 5(d) shows the predicted HAZ based on the critical temperature of 1025 oC. The
averaged HAZ thickness was 30 µm, 20 µm, and 20 µm for peak pulse powers of 1000 W, 1600 W,
and 2000 W, respectively. It is interesting to note that the HAZ at the exit side of the kerf was
generally wider than the entrance side even though the heat input was higher on the entrance side. It
suggests that the heat penetration on the exit side was deeper than on the entrance side. This was most
likely due conical heat flux being more concentrated on the exit side.
1400
200
Sim_entrance
Exp_entrance
Sim_exit
Exp_exit
100
500
von Mises stress (MPa)
(a)
1000
1500
2000
600
P = 1000 W
P = 1600 W
P = 2000 W
400
1000
800
600
400
200
0
2500
Peak pulse power (W)
500
Temp. (°C)
300
0
300
200
100
(b)
50
100
150
200
Depth in the subsurface (µm)
60
Sim_entrance
Sim_exit
50
40
30
20
10
0
0
0
(c)
P = 1000 W
P = 1600 W
P = 2000 W
1200
HAZ thickness (µm)
Kerf width (µm)
400
50
1000
100 150 200 250 300
Depth in the subsurface (µm)
(d)
1600
2000
Peak pulse power (W)
Fig. 5 Effect of peak pulse power on kef width (a), temperature (b), stress (c), and HAZ thickness (d).
4.3 The effect of pulse width
To study the pulse width effect, three levels of pulse width were used at constant laser frequency,
cutting speed, and average laser power.
Kerf width: Fig. 6(a) shows the comparison between the predicted kerf width and the experimental
results. It was found that even though the pulse width changed significantly, the kerf width did not
change. This suggests that changing pulse width does not have significant effect on kerf width. This is
because the average laser power does not change in the three cases, indicating that the level of average
power dominates the kerf width at these cutting conditions.
Subsurface temperature: Temperature distribution in the subsurface is shown in Fig. 6(b). The
nodal temperature decreased with increasing depth in the subsurface. Also, changing pulse width did
not have a significant impact on the temperature distribution in subsurface due to the same heat input.
8
Pulsed Laser Cutting of Nitinol
C.H. Fu, M.P. Sealy, Y.B. Guo and X.T. Wei
Subsurface stress: The results of pulse width effect on von Mises stress distribution in the
subsurface is shown in Fig. 6(c). The lowest pulse width generated the highest stress magnitude on the
surface. This was because the lowest pulse width corresponded to the highest peak pulse power. As a
result, the stress was concentrated in a localized area.
HAZ: Fig. 6(d) shows the predicted HAZ thickness. The averaged HAZ thickness was 50 µm,
45 µm, and 70 µm for a pulse width of 0.2 ms, 0.5 ms, and 1.0 ms, respectively. It is suggested that at
these conditions, decreasing the pulse width does not necessarily decrease the HAZ thickness.
1400
300
250
200
Sim_entrance
Exp_entrance
Sim_exit
150
1200
1000
100
800
0
0.2
0.4
0.6
0.8
1
1.2
Pulse width (ms)
(a)
0
600
500
400
300
100
150
200
80
HAZ thickness (µm)
von Mises stress (MPa)
Pulse width = 1.0 ms
Pulse width = 0.5 ms
Pulse width = 0.2 ms
50
Depth in the subsurface (µm)
(b)
700
60
Sim_entrance
Sim_exit
40
20
0
200
0
(c)
Pulse width = 1.0 ms
Pulse width = 0.5 ms
Pulse width = 0.2 ms
350
Temp. (°C)
Kerf width (µm)
400
50
100
150
Depth in the subsurface (µm)
0.2
200
(d)
0.5
1
Pulse width (ms)
Fig. 6 Effect of pulse width on kef width (a), temperature (b), stress (c), and HAZ thickness (d).
5 Conclusion
A 3D FEA model of laser cutting NiTi has been developed through user subroutines of moving
volumetric heat flux, superelasticity, and shape memory. The key findings are summarized as follows:
 The kerf width was predicted and verified by experimental data.
 Increasing cutting speed decreases kerf width, stress magnitudes in the subsurface, and HAZ
thickness, while the influence of peak pulse power is on the contrary.
 Pulse width does not have significant influence on kerf width, temperature distribution, and
HAZ thickness. However, it will affect the stress distribution.
 Peak pulse power dominates stress formation and average power dominates kerf generation.
9
Pulsed Laser Cutting of Nitinol
C.H. Fu, M.P. Sealy, Y.B. Guo and X.T. Wei
6 Acknowledgements
Dr. Wei would like to thank NSFC (Grant # 51375284) and Taishan Scholar Program for financial
support of the collaborative research.
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