Journal of Materials Processing Technology 229 (2016) 703–712
Contents lists available at ScienceDirect
Journal of Materials Processing Technology
journal homepage: www.elsevier.com/locate/jmatprotec
A multiscale modeling approach for fast prediction of part distortion
in selective laser melting
C. Li a , C.H. Fu a , Y.B. Guo a,∗ , F.Z. Fang b
a
b
Dept of Mechanical Engineering, The University of Alabama, Tuscaloosa, AL 35487, USA
Center of MicroNano Manufacturing Technology, Tianjin University, 300072, China
a r t i c l e
i n f o
Article history:
Received 20 December 2014
Received in revised form 13 August 2015
Accepted 19 October 2015
Available online 26 October 2015
Keywords:
Selective laser melting
Distortion
Multiscale simulation
Residual stress
a b s t r a c t
Selective laser melting (SLM) is a powder bed based additive manufacturing process. It is widely used
to make functional parts in a layer upon layer fashion. The severe temperature gradients produce large
tensile residual stress which leads to part distortion and negatively affect product performance. Due to
the complex coupling multi-scale mechanisms, it is a great challenge to predict part distortion since
traditional modeling approaches demand an exceedingly long computational time. This study has developed a practical multi-scale modeling methodology for fast prediction of part distortion by integrating a
micro-scale laser scan model, a meso-scale layer hatch model, and a macro-scale part model. A concept
of equivalent heat source has been developed for the micro-scale laser scan model. Local residual stress
field was predicted in the meso-scale layer hatch model using the equivalent heat source. The residual
stress field was then imported to the macro-scale model to predict part distortion and residual stress.
The predicted part distortions were validated with the experimental data with four different scanning
strategies.
© 2015 Elsevier B.V. All rights reserved.
1. Introduction
Selective laser melting (SLM) is a powder bed based additive
manufacturing process. It can manufacture functional parts directly
from the CAD data in a layer upon layer fashion (Kruth et al., 1998).
Parts produced by SLM have near full density with mechanical
properties comparable to bulk material (Kruth et al., 2007). SLM
has wide application potentials in tool (Levy et al., 2003), aerospace
(Rochus et al., 2007), automotive (Clare et al., 2008), biomedical
(Vandenbroucke and Kruth, 2007), and energy industries (Wong
et al., 2007).
Meiners et al. (2001) have developed the SLM process in which a
fine powder delivering system is used to place a 20 mm to 100 ␮m
thick powder layer onto a substrate plate inside the chamber with
inert atmosphere. In order to achieve near full density, a laser is
used to fully melt the powder materials. During the melting process,
energy and mass transformation occur through various physical
phenomena, such as laser absorption and scattering, heat transfer,
and fluid flow within the melt pool. Shiomi et al. (2004) reported
that the high temperature gradients due to rapid heating and cooling generate high tensile residual stress leading to microcracks and
∗ Corresponding author. Fax: +1 205 348 6419.
E-mail address: yguo@eng.ua.edu (Y.B. Guo).
http://dx.doi.org/10.1016/j.jmatprotec.2015.10.022
0924-0136/© 2015 Elsevier B.V. All rights reserved.
part distortion. High viscosity of melt powder materials makes the
melt pool break apart into small balls, also known as balling effect,
which results in deteriorated surface finish and porosity (Tolochko
et al., 2004).
Part distortion due to high tensile residual stress is one of the
major defects of SLM parts. It reduces the part dimension accuracy
and detrimentally affects the performance of the end-use parts.
Numerical modeling has been widely used to predict part residual stress and distortion. Traditional thermal-mechanical modeling
techniques demand exceedingly long computational time for a
practical macro-scale SLM part. There are several compelling reasons to develop a multi-scale simulation methodology to predict
part distortion and residual stress of a SLMed part. Firstly, the bulk
work in literature is limited to the single pass of micro-scale laser
scanning in SLM. The fabrication of a practical macro-scale part
requires millions of single micro-scale laser scan pass. The computational cost is prohibitively high to simulate the millions of laser
scan pass. In each laser scan, a very large number of element with
heat transfer and coupled thermal-mechanical analysis is required,
would needs a long computational time. Making a macro part
usually needs millions of laser scans. If every laser scan is to be simulated, the simulation cost will be exceedingly high and is beyond
the power of most computers. Secondly, different scanning strategies are often required to make different meso-scale sections of
a macro part to improve productivity, which further complicates
704
C. Li et al. / Journal of Materials Processing Technology 229 (2016) 703–712
Fig. 1. Multi-scale methodology for fast prediction of part distortion and residual
stress.
this issue. Thirdly, distortion and residual stress are critical structural integrity for a macro-scale SLMed part. Therefore, a novel
multi-scale simulation methodology is highly needed to predict
part distortion and residual stress with low computational cost.
2. Background on SLM modeling for part distortion
A few simulations have been tried to predict residual stress
and distortion of SLM parts on a micro-scale or meso-scale level.
Li et al. (2004) studied the local thermal stress distribution in the
melt pool and its implication on crack formation during laser melting of ceramic materials. Different thermal loads with and without
latent heat and fluid flow of the melt pool were used. Aggarangsi
and Beuth (2006) studied the residual stress reduction method
of a SLMed thin-wall structure. The powder material was locally
preheated by a secondary moving heat flux and then melted by a
primary moving heat flux. Hodge et al. (2013) studied the thermal
and mechanical history of SLM process on a meso-scale (12 layers of
powder). A volumetric moving flux was used to melt powder materials. Phase change during the process was considered and a coarse
mesh was used to reduce computational time. Dai and Shaw (2004)
studied the effect of powder-to-solid transition to investigate the
residual stress and distortion of metal and ceramic powders on a
small domain. Only two layers were built with a layer thickness
of 0.5 mm. It should be noted that the coupled thermal-mechanical
analysis for several layers at micrometer level with a fine mesh was
very time consuming. Thus, it is not practical to predict distortion
of a macro-scale SLM part using this method.
Some studies predicted residual stress and part distortion in SLM
on a macro-scale. Nickel et al. (2001) applied a constant heat flux
to heat an entire scan at same time. Different scanning patterns
were considered to predict the residual stress and distortion. Zaeh
and Branner (2010) applied a uniform thermal load adjusted from
experimental data to heat up 20 powder layers (meso-scale hatching zone) at the same time to predict the temperature and residual
stress distribution of a SLMed cantilever. Papadakis et al. (2013)
traced the temperature history of one specific point in the melt
pool, and then extended this temperature history to one powder
layer or multiple layers (hatching zone) to predict shape distortion
of a cantilever. These modeling approaches were all based on applying a uniform thermal load to one layer or multiple layers (hatching
layer) at one time. However, it should be noted that a uniform thermal load applied on one layer or multiple layers underestimates the
steep temperature gradients in a SLM process. Furthermore, scanning strategy plays an important role in temperature distribution,
part distortion, and cracks formation in SLM parts (Yasa et al., 2009).
However, little has been done to address the pressing problems.
Therefore, the objective of this study is to develop a practical
multi-scale methodology for fast prediction of distortion and residual stress of a SLMed part by: (a) developing a novel concept of
equivalent heat source that includes temperature gradient within
one layer in a micro-scale laser scan model; (b) calculating a local
residual stress field in a meso-scale hatch model; (c) mapping the
residual stress field into a macro-scale part model with four scanning strategies; to predict part distortion and residual stress field.
3. Multi-scale simulation methodology
3.1. Multi-scale modeling procedure
In order to develop an efficient method for fast prediction of the
distortion and residual stress field of SLM parts with reasonable
computational time, a multi-scale finite element model has been
developed. The procedures to develop the multi-scale simulation
model (Fig. 1) have three parts:
• Micro-scale laser scan model (Fig. 2): a moving heat flux was
applied on the surface of the powder material to determine an
equivalent heat source of a stabilized melt pool;
Fig. 2. Micro-scale laser scan model with 3D moving Gaussian heat flux.
C. Li et al. / Journal of Materials Processing Technology 229 (2016) 703–712
705
solid material, kr is the thermal conductivity portion of the powder
bed due to radiation among particles.
3.2.2. Convection
It was stated that heat lost by convection between melt pool
and powder bed is significant in powder bed based additive manufacturing process (Dai and Shaw, 2004). Therefore, it is critical to
incorporate natural convection between the melt pool and its surrounding powder bed in the simulation. The heat loss due to this
convection is determined by
qc = hc (T − T0 )
Fig. 3. Dimension and boundary conditions in the meso-scale layer hatch model.
(3)
where T is melting pool temperature, T0 is the ambient temperature, and hc is the heat transfer coefficient, which is described by
hc =
Nu kf
L
(4)
where L is the characteristic length of the specimen, kf is the thermal conductivity of fluid, and Nu is the Nusselt number, which is
described by
⎡
Nu =
⎤1/6
⎢
Nu0 + ⎣ Gr Pr /300
1 + 0.5/Pr
9/16
⎥
16/9 ⎦
(5)
where Gr is the Grashof number and Pr is the Prandtl number. Gr
and Pr are given by Eqs. (6) and (7), respectively.
Fig. 4. Dimension and boundary conditions in the macro-scale part model.
Gr =
• Meso-scale layer hatch model (Fig. 3): the equivalent heat source
is imported to the meso-scale layer hatch model to obtain a local
residual stress field;
• Macro-scale part model (Fig. 4): the local residual stress field was
mapped to the macro-part model to predict part distortion and
residual stress field with four scanning strategies.
3.2. Heat transfer modeling
Heat dissipation between the melt pool and the environment is
through three mechanisms: conduction into powder bed and the
substrate, radiation and convection to the environment. Fig. 3 illustrates the three mechanisms of heat loss applied in the multiscale
modeling approach. The methods of heat transfer are detailed as
follows.
3.2.1. Conductivity
The heat loss through thermal conductivity from melt pool to the
powder bed and substrate during a SLM process can be described
as:
q = −k T
(1)
where k is the thermal conductivity coefficient, T is the temperature gradient between the two different materials. The effective
thermal conductivity of the powder bed k can be described as (Sih
and Barlow, 1995):
k
=
kf
+
1−
1−ϕ
1−ϕ
1+
2
1−
ϕ kr
kf
1
kf
ks
1−
kf
ks
ln
Pr =
s
kf
−1
kr
kf
Cp f
kf
(7)
3.2.3. Radiation
Radiation of the powder bed was also considered in this study.
Radiation into environment causes heat loss qr , which is determined by
qr = T 4 − T04
(8)
where is the Stefan-Boltzman constant, T0 is the ambient temperature, and is the emissivity of the powder bed, which is given
by
= AH H + (1 − AH ) s
(9)
where AH is the area fraction of the surface that is occupied by
the radiation-emitting holes, H is emissivity of the hole, and s is
the emissivity of the solid particle. AH and H are defined by Eqs.
(10) and (11), respectively.
0.908ϕ2
1.908ϕ2 − 2ϕ + 1
(10)
+
(6)
2f
where g is the gravitational acceleration, f is the fluid density, ˇf
is the thermal volumetric expansion (ˇf = 1/Tf , Tf = 0.5 (T + T0 )),
is the specific heat of the fluid, and is the viscosity of the melting
pool.
AH =
k gL3 f2 ˇf (T − T0 )
(2)
where ϕ is the fractional porosity of the powder bed, kf is the is the
thermal conductivity of air, ks is the thermal conductivity of the
H =
s 2 + 3.082( 1−ϕ
ϕ )
s 1 + 3.082( 1−ϕ
ϕ )
2
2
(11)
+1
where ϕ is the fractional porosity of the powder bed.
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C. Li et al. / Journal of Materials Processing Technology 229 (2016) 703–712
Fig. 5. Temperature field on the cross-section of melt pool during the micro-scale laser scan.
Table 1
SLM process parameters.
Laser power Laser spot diameter Scan speed Scan spacing Layer thickness
W
300
␮m
600
mm/s
50
␮m
100
␮m
150
3.3. Simulation conditions
3.3.1. Process parameters
The laser source in this study was a continuous Nd:YAG laser
with a wavelength of 1.064 ␮m. The process parameters including
laser power, laser spot diameter, scan speed, scan spacing, and layer
thickness are listed in Table 1.
3.3.2. Material properties
This study aims to predict part distortion and compare with
the experimental data using lab-made iron-based powders (Kruth
et al., 2004). Due to the non-available property of the lab-made
Fe-based powder, very similar material properties of steel-based
commercial material DirectSteel® from EOS GmbH DirectSteel®
was used to approximate the iron-based powders. The comparison between the iron-based powder and DirectSteel® is listed in
Table 2. Temperature-independent mechanical and thermal material properties of DirectSteel® are listed in Table 3. The substrate
was a steel plate.
3.4. Micro-scale laser scan model
In the micro-scale laser single scan model, finite element analysis (FEA) package ABAQUS/Standard was used to conduct a thermal
analysis to predict temperature field in the melt pool. The mesh is
shown in Fig. 2. The model had two components: powder layer
and substrate. The dimensions of the powder layer were 5 mm
(length) × 0.6 mm (width) × 0.15 mm(thickness) and the dimensions of the substrate were 5 mm (length) × 0.6 mm (width) × 5 mm
(height). The powder layer had a fine mesh with an element size
of 50 ␮m (length) × 50 ␮m (width) × 37.5 ␮m (thickness). The heat
flux and melt pool are symmetrical with respect to the X-Z plane
to reduce the computational time. The initial temperature of powder and substrate was set to room temperature (20 ◦ C). A moving
Gaussian heat flux is applied to the top surface of the powder layer
as boundary condition. In the micro-scale laser scan model, conductivity dominates the heat transfer process due to the powder’s
short (in ms) exposure time to laser, convection and radiation of the
non-melting pool were incorporated as the coefficients of convection and radiation for the melting pool are difficult to determine.
It is assumed that energy loss of the melt pool through convection
Fig. 6. Temperature contour in the cross-section of the melt pool.
and radiation is small as the melt pool size is very small, which may
require a separate future study.
The size of melt pool is affected by process parameters and powder size, however, the average size of a melt pool is expected to
vary within a small range under the constant SLM conditions. In
this study, a continuum mechanics based finite element method
was used to predict the melt pool size. If the unstable melt pool
and non-equilibrium physical and chemical metallurgical problems
are focused, a separate method such as LBM (Lattice Boltzmann
Method) would be used for this purpose, which is beyond the scope
of this work. The nodal temperatures on the cross-section of the
melt pool were obtained, as shown in Fig. 5. The temperature contour on the cross section of the melt pool is shown in Fig. 6. It was
noted that the center of the melt pool has the highest temperature. Moving away from the pool center in both the depth and
width directions, the temperature dramatically decreases, which
indicates a severe temperature gradient.
Based on the fact that repeating laser scanning at same conditions will be performed many times, an equivalent heat input with
temperature gradient can be developed from the temperature field
and applied to the subsequent meso-scale hatch model to predict
local residual stress. Since every point on the cross-section along
C. Li et al. / Journal of Materials Processing Technology 229 (2016) 703–712
707
Table 2
Comparison of chemical composition between iron-based powder (Kruth et al., 2004) and DirectSteel® (Rombouts, 2006).
Powder material
Fe
wt.%
Ni
wt.%
Cu
wt.%
P
wt.%
Ref.
Iron-based powder
DirectSteel® Powder
62.66
59.3 ± 0.4
20
29.1 ± 1.4
15
9.6 ± 0.9
2.34
1.5 ± 0.1
(Kruth et al. (2004)
Rombouts (2006)
Table 3
Material properties of solid DirectSteel® (Eos GmbH, 2004).
Elastic modulus
Poisson’s ratio
Tensile strength
Yield strength
GPa
15.3
Melting point
◦
C
1330
–
0.41
Coefficient of thermal expansion
10−6 /K
9
MPa
600
Thermal conductivity
W/m K
13
MPa
400
Specific heat
J/kg K
375
Multiple scans with the fixed scan spacing were performed
simultaneously by applying the equivalent heat input on the powder layer. Fig. 7 shows the temperature profile at the top surface
of the powder layer. Then, the powder and substrate were cooled
down to a uniformly room temperature (around 20 ◦ C). Three cooling mechanisms are incorporated, namely, heat conduction to the
substrate, heat convection to the powder bed and surrounding
atmosphere, and heat radiation to the surrounding atmosphere.
The temperature distribution in the hatch layer before and after
cooling is shown in Fig. 8. The temperature history of the top surface of the hatch layer is shown in Fig. 9. Temperature dropped from
4900 ◦ C to 400 ◦ C in less than 0.1 s, which confirms the rapid cooling nature during the SLM process. The predicted residual stress
field in the meso-scale hatch model was imported to the subsequent macro-scale part model as a patch unit for predicting part
distortion and residual stress.
Fig. 7. Temperature profile at the top surface of the hatch layer.
the scanning path experiences a similar temperature history, it is
reasonable to apply the temperature field of the melt pool crosssection to the whole scan pass. Although the assumption of layer
equivalent model for various scan patterns may slightly increase
inaccuracy in residual stress prediction, the inaccuracy can be justified by the significantly shortened computational time upon the
prediction accuracy is acceptable.
In this study, since only one layer was deposited on the substrate in the experiment, there was no previous layer preheating
effect. But, there could be a certain heat accumulation between
neighboring hatches in the mesoscale hatch model. However, the
influence of the heat accumulation between neighboring hatches
could be small, which is indicated in another study (Zach, 2010) of
SLM process.
3.5. Meso-scale layer hatch model
In the meso-scale hatch model, a coupled thermal-mechanical
analysis was conducted to predict the local residual stress distribution of the scanned layer. The model dimensions with boundary
conditions are shown in Fig. 3. The powder layer had a dimension of 5 mm (length) × 5 mm (width) × 0.15 mm (thickness). Same
mesh density and mesh size were used in the powder layer
as the scan model. The powder layer was placed on a 5 mm
(length) × 5 mm (width) × 1 mm (thickness) substrate with constrained bottom.
3.6. Macro-scale part model
In SLM process, melt pool experiences a comparable mechanical
history; therefore, it is feasible to fast predict the distortion of a
macro-scale part by importing local residual stress field from the
meso-scale hatch model.
The mesh design of the macro part model is shown in Fig. 6.
The dimensions of the powder layer were 35 mm (length) × 15 mm
(width) × 0.15 mm (thickness). The powder layer was placed on top
of a steel plate that had a dimension of 45 mm (length) × 22 mm
(width) × 1 mm (thickness). Within the fine mesh in the powder
layer, the element size was 150 ␮m × 150 ␮m × 50 ␮m.Four different scanning strategies (Fig. 10) were studied for the macro
part model, namely, (a) horizontal sequential pattern, (b) vertical
sequential pattern, (c) successive pattern, and (d) “least” heat influence (LHI) pattern. For the successive and LHI patterns, the scanning
area was divided into 21 scan patches (5 mm × 5 mm). The number
inside each patch in Fig. 10 represents the hatching order.
The successive patches were laser scanned based on scanning
sequence, the initial residual stress tensor residual from the mesoscale layer hatch model was applied to each corresponding patch.
⎡
⎤
S11
S12
S13
residual = ⎣ S21
S22
S23 ⎦
S31
S32
S33
⎢
⎥
(12)
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C. Li et al. / Journal of Materials Processing Technology 229 (2016) 703–712
Fig. 8. Temperature field in hatch layer in the meso-scale layer hatch model ((a): before cooling, (b): after cooling).
4. Model validation and discussions
4.1. Deflection in the layer hatch model
Fig. 9. Temperature history of the top surface in the meso-scale layer hatch model.
The deflection predicted by the meso-scale hatch model is
shown in Fig. 11. At first, the expansion of the heated layer was
restricted by the surrounding material during laser scanning; therefore, a compressive stress was generated on the top surface. When
the yield stress of the material was reached, plastic bending occurs.
As the hatch layer cools down to room temperature, the contraction
of the top layer was then constrained by the surrounding material,
which leads to tensile residual stress on the top surface. Also, the
cooling induced shrinkage shortens the top surface compared to the
subsurface, thus, the layer was deflected towards the laser beam.
The predicted phenomenon agrees well with the temperature gradient mechanism (Kruth et al., 2004).
4.2. Distortion in the macro-scale part model
If there is a rotation of laser scanning vector between two successive patches, the residual stress tensor was applied by using the
transformation matrix:
⎡
cos Rz () = ⎣ − sin 0
sin cos 0
0
⎤
0⎦
(13)
1
where is the angle of rotation measured from the X-axis with
respect to Z axis (Fig. 10c). The residual stress tensor after rotation
can be calculated by:
residual = Rz () residual Rz ()
T
(14)
During the SLM experiment, one iron-based powder layer was
deposited on a 1 mm thickness steel plate. However, this is not
the scenario of a SLM production, for actual SLM production of
metal parts, a substrate with only 1 mm thickness would not be
used, instead a much thick substrate will be usually used. Four
different scanning strategies were used, then the deflections for
different scanning strategies were measured from the bottom surface of the substrate and compared. Since this study is limited to
the prediction of the effect of different scanning strategies on distortion and correlation with the experimental data. As one layer
was deposited on the substrate, if a thick substrate was used the
deflection of the deposited layer would be too small to measure. The
use of a thin substrate in the SLM experiment will produce a relative large deflection for easy measurement. The sequential scanning
pattern was favored according to the measurement. The normal-
C. Li et al. / Journal of Materials Processing Technology 229 (2016) 703–712
709
Fig. 10. Four scanning strategies: (a) horizontal sequential, (b) vertical sequential, (c) successive, and (d) “least” heat influence (LHI).
Fig. 11. Deflection in the meso-scale layer hatch model (half-hatch due to symmetric).
Fig. 12. Comparison between the predicted distortion and the measured data.
ized deflection is defined as the ratio of deflection at each point to
the maximum deflection. The normalized distance is defined as the
ratio of each point’s distance to the part edge to the part length. The
distortion was measured by recording the deflection of measuring
points located on the bottom surface of the substrate.
4.2.1. Longitudinal distortion of sequential pattern vs.
experimental result
The distortion along the longitudinal direction (X) (Fig. 12) was
retrieved and compared to the experimental data. Similar bending
Fig. 13. Distortion along the longitudinal (X) direction for different scanning strategies.
trend and magnitude are observed for both the prediction and the
measured data. This trend is attributed to the thermal history of
the part during laser scanning. More specifically, the top layer was
expanded at first due to the heat input. The plastic strain in the
top surface became smaller than the bottom surface after cooling
down. Therefore a convex distortion towards the laser source side
gradually formed.
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C. Li et al. / Journal of Materials Processing Technology 229 (2016) 703–712
in longitudinal distortion was observed between the successive
pattern and the LHI pattern. The distortion for the successive pattern is only slightly smaller than the LHI pattern. The possible
reason for this difference is that a higher temperature gradient
exists in the LHI scanning process than that in the successive scanning process.
4.2.3. Crosswise distortions at different scanning strategies
Distortions along the crosswise direction (Y) for the four scanning strategies are shown in Fig. 14. It can be found that the
horizontal sequential pattern produced the biggest crosswise distortion, while the vertical sequential pattern resulted in the
smallest crosswise distortion. For the successive and LHI patterns,
almost same crosswise distortions were produced. The predicted
distortions along the longitudinal (X) and crosswise (Y) directions
for four scanning strategies were consistent with the experimental
data (Kruth et al., 2004).
Fig. 14. Distortion along the crosswise (Y) direction for different scanning strategies.
4.2.2. Longitudinal distortions at different scanning strategies
Distortions along the longitudinal direction (X) for the four
scanning strategies are shown in Fig. 13. It can be seen that the
horizontal sequential pattern produced the smallest longitudinal
distortion, while the vertical sequential pattern resulted in the
biggest longitudinal distortion. Moreover, no significant difference
4.3. Residual stress in the micro-scale part model
Fig. 15(a) shows the residual stress S11 (longitudinal direction) of
the substrate along the depth (Z) direction for four scanning strategies. Within the top layers of the substrate, S11 was compressive. At
approximately 0.6 mm, the residual stress transitioned from compressive to tensile. The residual stress is compressive for top layers
while it is tensile for the bottom layers, which caused the substrate
Fig. 15. Residual stress profiles of substrate (Z direction) for four scanning strategies.
Fig. 16. Residual stress contours for four scanning strategies: (a) horizontal sequential, (b) vertical sequential, (c) successive, and (d) LHI.
C. Li et al. / Journal of Materials Processing Technology 229 (2016) 703–712
711
Fig. 17. Residual stress profiles on the part top surface.
Fig. 18. Residual stress profiles of the part along the depth (Z) direction.
bend up.Vertical sequential pattern generated the biggest residual
stress along X direction, while the horizontal sequential pattern
generates the smallest residual stress. In addition, no significant
difference was observed between residual stress generated by the
successive and LHI patterns. Fig. 15(b) shows residual stress S22
(crosswise direction) of the substrate along the depth (Z) direction for four scanning strategies. The horizontal sequential pattern
generated the biggest residual stress along Y direction, while the
vertical sequential pattern generated the smallest residual stress.
Also, there is no significant difference between residual stresses
generated by successive and LHI patterns.
Residual stress contours (von Mises stress, S11 , and S22 ) for the
part and the substrate at four scanning strategies are shown in
Fig. 16. No compressive residual stress was observed in the part.
Residual stress S11 and S22 profiles on the part surface for four
scanning strategies along the longitudinal (X) direction are shown
in Fig. 17. It can be observed that both horizontal sequential and
vertical sequential patterns generated a relatively stable and uniform tensile residual stress in X and Y directions compared to other
two scanning patterns. On the top surface of the part, the vertical
sequential pattern generated the biggest residual stress in X direction and the smallest residual stress in Y direction. The successive
and LHI patterns generated residual stresses along X direction varied from patch to patch, which led to stress oscillation. Fig. 18 shows
the residual stress profiles for four scanning strategies along the
depth (Z) direction. Both S11 and S22 increased as depth increases
for all scanning strategies. Moreover, horizontal sequential pattern
generated the smallest longitudinal residual stress (S11 ) and the
largest crosswise residual stress (S22 ).
This study provides a multiscale method to test the feasibility
of part deflection and residual stress by SLM using the regular laser
scan patterns. As the melt pool temperature field can be obtained
from the micro-scan model, the method can be extended to hatch
layers with irregular shapes as long as the nodal set for the uneven
length hatch vectors can be created. This versatile approach could
be applied to a complex scanning case in SLM. However, it should
be pointed out that the study was restricted to a simple enough case
for which the scan vectors remain of equal length and would not
interfere between physical layers, the layer equivalent model may
still capture the residual stress field. However, for a complex SLM
part with varying scan vectors not laid in 0-90-0 or 0-0-0 fashion
between layers, it would be very difficult for the method to capture
the residual stress field as residual stress produced in each physical
layer and their interferences between layers will be very complex
to predict precisely.
5. Conclusions
A multi-scale finite element simulation method has been developed for fast prediction of part distortion of SLMed parts. The
predicted distortions in four different scanning strategies were
investigated and verified by the experimental data. The key findings
are summarized as follows:
• A concept of equivalent heat source has been developed for the
micro-scale laser scan model and imported to the meso-scale
hatch model to predict local residual stress, which can be mapped
into the macro-scale part model to predict part distortion.
• For the sequential scanning pattern, the smallest deflection
occurs along the laser scanning direction. The successive scanning
strategy with the LHI pattern is preferred in terms of minimizing
part distortion.
• Both horizontal and vertical sequential patterns generated a relatively uniform tensile residual stress, while the successive and
LHI patterns generated oscillating tensile residual stress in the
part. Moreover, residual stresses became more tensile as depth
increased in the part for the concerned four scanning strategies.
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