Residual stresses in select ive laser sintering
and selective laser melting
Peter Mercelis and Jean-Pierre Kruth
Division PMA, Department of Mechanical Engineering, University of Leuven, Leuven, Belgium
Abstract
Purpose – This paper presents an investigation into residual stresses in selective laser sintering (SLS) and selective laser melting (SLM), aiming at a
better understanding of this phenomenon.
Design/methodology/approach – First, the origin of residual stresses is explored and a simple theoretical model is developed to predict residual
stress distributions. Next, experimental methods are used to measure the residual stress profiles in a set of test samples produced with different process
parameters.
Findings – Residual stresses are found to be very large in SLM parts. In general, the residual stress profile consists of two zones of large tensile
stresses at the top and bottom of the part, and a large zone of intermediate compressive stress in between. The most important parameters determining
the magnitude and shape of the residual stress profiles are the material properties, the sample and substrate height, the laser scanning strategy and the
heating conditions.
Research limitations/implications – All experiments were conducted on parts produced from stainless steel powder (316L) and quantitative results
cannot be simply extrapolated to other materials. However, most qualitative results can still be generalized.
Originality/value – This paper can serve as an aid in understanding the importance of residual stresses in SLS/SLM and other additive manufacturing
processes involving a localized heat input. Some of the conclusions can be used to avoid problems associated with residual stresses.
Keywords Sintering, Lasers, Stress (materials)
Paper type Research paper
Introduction
Selective laser sintering (SLS) and selective laser melting
(SLM) are two production technolog ies offer ing great
advantages and opportunities compared to traditional
material removal techniques ( Kruth et al., 2003, 2004).
However, the residual stresses that arise in the parts being
produced impose some serious limitations to the practical use,
since they introduce part deformations and/or micro cracks.
Moreover, large residual stresses can limit the load resistance of
the parts compared to a stress free state.
In the field of Laser Engineered Net Shaping, a lot of effort
has been done to measure, predict and control residual
stresses (Vasinonta et al., 2000; Aggarangsi and Beuth, 2003).
Whereas researchers mainly focussed on the stresses in the
growth-direction at the substrate-part connection, the current
research will focus on the stresses perpendicular to the build
direction, and their variation along the build direction.
In order to investigate the residual stresses, the origin of the
stresses is firstly explained. Next, a simple theoretical model is
presented to predict the basic residual stress distribution.
Using an experimental procedure, residual stress profiles are
then measured in a set of test samples having different kinds
of process parameters. Thus, the effect of the process
parameters on the residual stress can be concluded. Finally,
some guidelines are presented to reduce the residual stress in
SLS and SLM.
The difference between SLS and SLM concerns the
binding mechanism that occurs between the powder particles
(Kruth et al., 2004). In SLS, either a combination of a low
melting binder and high melting structural material is used -
called liquid phase sintering (LPS) or the powder particles are
just partially molten. In case of LPS, a post treatment is
generally necessary to enhance the mechanical properties and
to increase the part’s density. In SLM, the powder particles
are fully molten. Since the border between SLS and SLM is
rather vague, the stress inducing mechanisms are explained
generally for the case of SLM. In the case of partial melting
without infiltration, the same stress inducing mechanisms will
occur. On the other hand, in the case of the LPS mechanism,
the furnace cycle that is used to infiltrate the parts, will result
in stress relaxation, so the resulting parts can be expected to
be stress free.
The origin of residual stresses
Residual stresses are stresses that remain inside a material, when
it has reached equilibrium with its environment. Residual stresses
are generally classified according to the scale at which they occur
(Withers and Bhadeshia, 2001). This investigation includes only
The current issue and full text archive of this journal is available at
www.emeraldinsight.com/1355-2546.htm
Rapid Prototyping Journal
12/5 (2006) 254 – 265
q Emerald Group Publishing Limited [ISSN 1355-2546]
[DOI 10.1108/13552540610707013]
This research was funded by the IAP project P5-08 of the Belgian Federal
Science Policy and the GOA/2002/06 project from KU Leuven.
Received: 1 Januar y 2006
Revised: 1 March 2006
Accepted: 23 June 2006
254
type I residual stresses, which vary over large distances, namely
the dimensions of the part. These macro stresses can result in
large deformations of the part. Type II and type III residual
stresses, which occur due to different phases in the material and
due to dislocations at atomic scale, are not considered in this
study, since they are of less importance for the material’s
strength. Moreover, the measurement resolution of most test
methods is not small enough to measure type II and type III
residual stresses.
Residual stresses are not always disadvantageous, e.g. glass
plates are many times rapidly cooled to introduce compressive
stress in the surface area of the plate, thus increasing the
overall loading resistance and preventing crack growth at
the surface. However, in most cases, residual stresses are
unwanted, since they result in deformat ions from
the intended shape. Moreover, tensile pre-stress adds to the
stresses caused by external loading, thus reducing the strength
of the parts and favoring propagation of cracks from the
surface.
Each production process introduces some amount of
residual stress (Withers and Bhadeshia, 2001). However, the
amount of residual stress that is introduced varies a lot among
different production processes. Laser based processes (laser
welding, SLM, etc.) are known to introduce large amounts of
residual stress, due to the large thermal gradients which are
inherently present in the processes. In case of laser bending,
these stresses are, e.g. used to deform sheet metal plates to a
desired shape. Two mechanisms can be distinguished which
cause residual stresses.
The first mechanism introducing residual stress is called the
temperature gradient mechanism (TGM, Figure 1). It results
from the large thermal gradients that occur around the laser
spot. The TGM mechanism is commonly used for laser
bending of sheets along straight lines. Owing to the rapid
heating of the upper surface by the laser beam and the rather
slow heat conduction, a steep temperature gradient develops.
The material strength simultaneously reduces due to the
temperature rise. Since the expansion of the heated top layer
is restricted by the underlying material, elastic compressive
strains are induced. When the material’s yield strength is
reached, the top layer will be plastically compressed. In
absence of mechanical constraints, a counter bending away
from the laser beam would be perceived. During cooling the
plastically compressed upper layers start shrinking and a
bending angle towards the laser beam develops. This
mechanism is also present in SLS and SLM, where the
underlying layers inhibit the expansion of the heated top
layers. It is important to notice that this mechanism does not
require the material to be molten.
A second mechanism that induces residual stresses is the
cool-down phase of the molten top layers (in SLM). The
latter tend to shrink due to the thermal contraction. This
deformation is again inhibited by the underlying material,
thus introducing tensile stress in the added top layer and
compressive stress below.
Simplified theoretical model
To get an idea of the residual stress profiles that would be
found in SLM samples, a simplified theoretical model was
developed. Assume that a part is being built on top of a base
plate with height h
b
. The part that was built so far has height
h
p
and the layer thickness is t (Figure 2). This simple
theoretical model assumes that:
.
the base plate and the part being built are at room
temperature;
.
the upper layer induces stress due to its shrinkage (
a
DT);
the tensile stress is equal to the material’s yield strength
s
(since a strain of
a
DT would result in a stress much larger
than the material’s yield strength);
.
the stress
s
xx
is independent of the y coordinate, i.e. the
variation of the normal stress across the part’s width is
neglected;
.
the general beam theory is valid; and
.
no external forces are applied to the combination part-
base plate.
At each moment, the equilibria of force equation (1) and
moment equation (2) need to be obeyed, since there are no
external forces acting on the system:
Z
s
xx
ðzÞdz ¼ 0 ð1Þ
Z
s
xx
ðzÞzdz ¼ 0 ð2Þ
Owing to the continuity of the deformation at the border
between the base plate, following strain profile is assumed
over the combination base plate-part:
e
xx
ðzÞ¼az þ b ð3Þ
Owing to the different stiffness of the base plate and the part
material, this deformation results in different stress levels; the
stress profile reveals a jump at the border between the base
plate and the part. Suppose that m represents the ratio of base
plate stiffness to the part’s stiffness:
m ¼
E
base
E
part
ð4Þ
Using this assumption, the equilibrium conditions can be
rewritten as:
Figure 1 TGM inducing residual stress
Figure 2 Simplified theoretical model of the SLM process
Residual stresses in selective laser sintering and selective laser melting
Peter Mercelis and Jean-Pierre Kruth
Rapid Prototyping Journal
Volume 12 · Number 5 · 2006 · 254 –265
255
Z
h
b
0
mðazþbÞdzþ
Z
h
b
þh
p
h
b
ðazþbÞdzþ
Z
h
b
þh
p
þt
h
b
þh
p
s
dz¼ 0 ð5Þ
Z
h
b
0
mðazþbÞzdz þ
Z
h
b
þh
p
h
b
ðazþbÞzdzþ
Z
h
b
þh
p
þt
h
b
þh
p
s
zdz ¼ 0 ð6Þ
From equations (5) and (6), the coefficients a and b can be
derived:
a ¼ 26
s
t
ð2mh
b
h
p
þ mh
b
h
p
t þ h
2
p
þ h
p
t þ mh
2
b
Þ
ð4mh
3
b
h
p
þ h
4
p
þ m
2
h
4
b
þ 6mh
2
b
h
2
s
þ 4mh
b
h
3
p
Þ
ð7Þ
b ¼
s
t
ð2mh
3
b
þ 6h
p
mh
2
b
þ 3mh
2
b
t þ 6h
b
h
2
p
þ 6h
b
h
p
t þ 2h
3
p
þ 3h
2
p
tÞ
ð4mh
3
b
h
p
þ h
4
p
þ m
2
h
4
b
þ 6mh
2
b
h
2
s
þ 4mh
b
h
3
p
Þ
ð8Þ
Equations (5) and (6) assume that the part and the base plate
are equally wide. Usually the base plate is wider than the part.
Including the widths of the part and the base plate in the
equations would result in a different m factor: m ¼ E
base
w
base
/
E
part
w
part
. The influence of a wider base plate can thus be
simulated by increasing the E modulus of the base plate.
After the production, the parts produced are generally
removed from the base plate. To simulate this, a relaxation
stress must be added to the stress profile calculated in the
part. This relaxation stress has a linear profile (z
0
¼ z-h
b
,
Figure 2):
s
relaxation
ðz
0
Þ¼cz
0
þ d ð9Þ
The constant par t of the relaxation stress corresponds to a
uniform shrinkage of the part that is being removed from the
base plate. The linear part results in a curvature of the part.
The coefficients c and d can be determined by recalculating
the equilibrium conditions for the produced part (with h
c
the
height of the part in the new coordinate system X, Y, Z
0
):
c ¼ 26
22
R
h
c
0
z
0
s
ðz
0
Þdz
0
þ h
c
R
h
c
0
s
ðz
0
Þdz
0
h
3
c
ð10Þ
d ¼ 2h
c
R
h
c
0
s
ðz
0
Þdz
0
2 3h
c
R
h
c
0
z
0
s
ðz
0
Þdz
0
h
2
c
ð11Þ
Theoretical residual stress profiles
When a layer is added to the base plate, it induces a
compressive stress in the upper part of the base plate and a
tensile stress in the lower part. When successive layers are
added on top, each layer induces a certain stress profile in the
base plate, but also in the underlying solidified layers, thus
reducing the initial tensile stress present in these layers.
Figure 3 shows the resulting stress profile in the part and
baseplate, after 50 layer s (proper ties: base plate
thickness ¼ 20 mm, E
base
¼ 210 GPa, E
part
¼ 110 GPa,
t ¼ 50
m
m,
s
¼ 300 MPa). It can be seen that the stress at
the last added layer equals the yield stress of the material.
When the part is removed from the base plate, the stress state
in the part is drastically changed; due to the relaxation, the
resulting stress in the part will be much lower. The constant part
of the relaxation stress corresponds to the shrinkage of the part,
whereas the linear part of the relaxation stress corresponds to
the bending deformation. Figure 4 shows the relaxation
principle and the resulting stress in the part.
Influence of number of layers, base plate geometry and
material properties
Number of layers
Figure 5 shows the influence of the number of layers on the
residual stress profile. Before part removal, the stress in the part
equals the yield strength at the top. However, when the number
of layers keeps increasing , compressive stresses occur at the
bottom of the part. It can also be seen that the stresses in
the base plate become very large, so plastic deformation of the
base plate could occur. However, this behaviour is not included
in the model. After part removal, a more or less symmetrical
stress profile remains in the part. At the top and bottom of the
part, tensile residual stress remains, with a zone of compressive
stress in between. The tensile residual stress is somewhat larger
at the bottom than at the top surface.
Figure 6 shows the influence of the number of layers on the
relaxation stresses. It can be seen that the constant par t,
which relates to the shrinkage in X direction, is reduced by
adding more layers, while the linear part is increased.
However, one should not conclude that this would increase
the part’s bending deformation, since the surface moment of
inertia increases with the number of layers (according to h
3
).
Base plate geometry
Since the model assumes that the general beam bending theory
is valid, the width of the base plate can be combined with its E
modulus to represent the stiffness. The base plate height,
however, must be treated separately. Figure 7 shows the
influence of the base plate height on the stress profiles.
According to this simple theoretical model, the height of the
base plate has a clear influence on the residual stress
distribution. Before part removal, a higher height results in a
lower stress level in the base plate itself and a more uniform
stress level in the part. This means that a thick base plate results
in a smaller deformation due to part removal, compared to a
thin base plate. Since almost all stress is released by a uniform
shrinkage, only little residual stress remains in the part after
removal. Figure 8 shows the influence of the base plate height on
the relaxation stress components.
Material properties
Figure 9 shows the influence of the mater ial’s yield strength
on the residual stress being developed. The higher the yield
Figure 3 Residual stress in the part and the base plate
Residual stresses in selective laser sintering and selective laser melting
Peter Mercelis and Jean-Pierre Kruth
Rapid Prototyping Journal
Volume 12 · Number 5 · 2006 · 254 –265
256
strength, the higher the stresses being developed. The stresses
after part removal are also larger.
Conclusions
.
Stress profiles before removal consist of a large zone
of tensile stress at the upper zone of the part being built. The
maximum stress is reached at the surface of the part (equal to
the yield stress). The stress reduces with decreasing Z
values. The lower part of the base plate is under tensile
stress, the upper part is under compressive stress.
.
Part removal drastically reduces the residual stresses
which are present in the part; the residual stress relaxes by
a uniform shrinkage and a bending deformation. The
residual stress after removal consists of a zone of tensile
stress at the upper and lower zone of the part and a
compressive stress zone in between. The stresses after part
removal are much smaller than before part removal.
Figure 4 Relaxation of the residual stress and resulting stress in the part
Figure 5 Influence of the number of layers on the residual stress profile
Figure 6 Influence of the number of layers on the relaxation stress
Residual stresses in selective laser sintering and selective laser melting
Peter Mercelis and Jean-Pierre Kruth
Rapid Prototyping Journal
Volume 12 · Number 5 · 2006 · 254 –265
257
Figure 7 Influence of the base plate height on the residual stress profile
Figure 8 Influence of the base plate height on the relaxation stress components
Figure 9 Influence of the materials yield strength on the residual stress profile
Residual stresses in selective laser sintering and selective laser melting
Peter Mercelis and Jean-Pierre Kruth
Rapid Prototyping Journal
Volume 12 · Number 5 · 2006 · 254 –265
258
