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Article
Separation of the Formation Mechanisms of Residual
Stresses in LPBF 316L
Alexander Ulbricht 1,*, Simon J. Altenburg 1, Maximilian Sprengel 1, Konstantin Sommer 1,
Gunther Mohr 1,2, Tobias Fritsch 1, Tatiana Mishurova 1, Itziar Serrano-Munoz 1,
Alexander Evans 1, Michael Hofmann 3and Giovanni Bruno 1,4
1Bundesanstalt für Materialforschung und -prüfung (BAM), Unter den Eichen 87, 12205 Berlin, Germany;
[email protected] (S.J.A.); Maximilian.Spr[email protected] (M.S.); [email protected] (K.S.);
Gunther[email protected] (G.M.); [email protected] (T.F.); tatiana.mishur[email protected] (T.M.);
Itziar[email protected] (I.S.-M.); alexander[email protected] (A.E.); [email protected] (G.B.)
2Institute of Machine Tools and Factory Management, Chair of Processes and Technologies for Highly
Loaded Welds, Technische Universität Berlin, Straße des 17. Juni 135, 10623 Berlin, Germany
3Heinz Maier-Leibnitz Zentrum (MLZ), Technische Universität München, Lichtenbergstraße 1,
85747 Garching, Germany; [email protected]
4Institute of Physics and Astronomy, University of Potsdam, Karl-Liebknecht-Straße 24/25,
14476 Potsdam, Germany
*Correspondence: alexander[email protected]; Tel.: +49-308-104-4140
Received: 29 July 2020; Accepted: 3 September 2020; Published: 14 September 2020


Abstract:
Rapid cooling rates and steep temperature gradients are characteristic of additively
manufactured parts and important factors for the residual stress formation. This study examined the
influence of heat accumulation on the distribution of residual stress in two prisms produced by Laser
Powder Bed Fusion (LPBF) of austenitic stainless steel 316L. The layers of the prisms were exposed
using two different border fill scan strategies: one scanned from the centre to the perimeter and the
other from the perimeter to the centre. The goal was to reveal the effect of different heat inputs on
samples featuring the same solidification shrinkage. Residual stress was characterised in one plane
perpendicular to the building direction at the mid height using Neutron and Lab X-ray diffraction.
Thermography data obtained during the build process were analysed in order to correlate the cooling
rates and apparent surface temperatures with the residual stress results. Optical microscopy and
micro computed tomography were used to correlate defect populations with the residual stress
distribution. The two scanning strategies led to residual stress distributions that were typical for
additively manufactured components: compressive stresses in the bulk and tensile stresses at the
surface. However, due to the different heat accumulation, the maximum residual stress levels differed.
We concluded that solidification shrinkage plays a major role in determining the shape of the residual
stress distribution, while the temperature gradient mechanism appears to determine the magnitude
of peak residual stresses.
Keywords:
additive manufacturing; Laser Powder Bed Fusion; LPBF; AISI 316L; online process
monitoring; thermography; residual stress; neutron diffraction; X-ray diffraction; computed
tomography
1. Introduction
In recent years, Additive Manufacturing (AM) has evolved from a method for rapid prototyping
to a mature production process for certain parts in industries, such as the aerospace industry [
1
].
Among the different AM manufacturing techniques, Laser Powder Bed Fusion (LPBF) is an important
technique for the production of net shaped metallic parts [
2
]. Early research conducted by Mercelis and
Metals 2020,10, 1234; doi:10.3390/met10091234 www.mdpi.com/journal/metals
Metals 2020,10, 1234 2 of 15
Kruth [
3
] showed that metallic parts made by LPBF inherently contain residual stresses (RS). They had
described two driving mechanisms for the formation of RS: the Temperature Gradient Mechanism
(TGM) and the Solidification Shrinkage Mechanism (SSM). The two mechanisms are interlinked and
their combined effect on RS in AM 316L is a topic of current research [
4
–
7
]. Wang et al. [
6
] showed
within long bars of LPBF 316L that scan strategies using shorter scan tracks reduced RS and attributed
this to lower solidification shrinkage. Roehling et al. [
7
] observed a decrease of RS in samples with a
bridge geometry manufactured by LPBF of 316L due to post-solidification heating of each layer during
the build job using selective large-area diode surface heating. This method aimed to decrease the
cooling rate. Each of the two publications had mainly utilized one of the two mechanisms to reduce RS:
Wang et al. [
6
] mainly utilized the SSM, whereas Roehling et al. [
7
] mainly utilized the TGM. In both
cases, a reduction of RS was observed. However, there is still a level of uncertainty on the magnitude
of the influence of each mechanism onto the shape of the resulting RS field.
Diffraction is a well-known non-destructive method to evaluate RS [
8
–
10
]. Determining elastic
strains by measuring the variation of lattice spacing provides a powerful method to identify RS. This is
achieved at the surface by Lab X-ray Diffraction (XRD), up to a depth of about
5µm
in metals, as well
as in the bulk by Neutron Diffraction (ND) up to a depth of about a few mm to a few cm [
11
–
13
].
In this work, the bulk triaxial RS state was determined using ND and was combined with the Lab
XRD biaxial RS state at the surface. This methodology allows for the mapping of the RS distribution
across the complete cross-sectional plane. Such residual stress tends to be compressive in the bulk and
tensile near the surface [
14
]. ND enables the non-destructive determination of the triaxial RS state over
a complete two-dimensional (2D) plane or three-dimensional (3D) volume. Destructive methods, such
as incremental or deep hole drilling, slitting, or contour method, would also yield stress depth profiles,
but it would be extremely difficult to determine triaxial stress states over a complete cross-section.
To exploit the benefits of lightweight, load driven structural designs for LPBF metallic parts,
it is necessary to understand RS in those parts, since their effect on fatigue life can be significant [
15
].
In order to understand RS, it is necessary to decouple the contributing mechanisms, especially if we
aim at modelling the manufacturing process.
Therefore, this study aims at unravelling the contributions of the two mechanisms, to provide a
basis for discussion on the length scale of RS introduced into parts by the TGM and the SSM. Therefore,
the specimen design was chosen to provide similar solidification shrinkage, but at the same time
different cooling rates without changing the volumetric energy density (VED) of specimens. Based on
this design, similar RS results should be assigned to equal solidification shrinkage, whereas differences
should be caused by the different cooling rates. Online monitoring by thermography during the build
process was used in order to assess these cooling rates and their effect on RS formation.
The TGM is mainly related to process parameters (e.g., VED) and the SSM is mainly related to
the length of shrinking scan tracks. Therefore, the results of this study might help to decide which
approach is more suitable to reduce RS for a specific part design and its expected load profile.
Additionally, the results from Micro Computed Tomography (
µ
CT) and Optical Microscopy (OM)
were evaluated to link RS fields and defect distributions, with the aim to produce a holistic approach
towards the analysis of the interconnection of TGM and SSM.
2. Materials and Methods
2.1. Material and LPBF Processing Conditions
Austenitic stainless steel 316L powder was processed by the commercial LPBF system SLM280 HL
(SLM Solutions Group AG, Lübeck, Germany). The powder was characterised by its supplier: it has
an apparent density of
4.58gcm−3
and a mean diameter of
34.69µm
. The cumulative mass values of
the particle size distribution are:
D10 =18.22µm
,
D50 =30.50µm
,
D90 =55.87µm
. The LPBF system
uses a single
400W
continuous wave ytterbium fibre laser with a spot size of approx.
80µm
in a focal
position. The processes were conducted in an argon gas atmosphere with an oxygen content of less
Metals 2020,10, 1234 3 of 15
than 0.1%. The parts were manufactured on a stainless steel substrate plate, which was heated up to
100
◦
C as a preheating temperature before the start of the build process. Two prismatic specimens of
the dimension
24mm×36mm ×24.5mm
were manufactured in two separate built processes. In order
to remove specimens from the base plate a band saw was used. This reduced the height to a final value
of
21mm
. A specimen design of low aspect ratio was chosen for this experiment in order to prevent
significant RS relaxation due to distortion after the removal from the substrate plate. Such a distortion
had been reported in literature for LPBF 316L [
16
,
17
]. Although the removal from the substrate plate
may have caused a degree of RS relaxation, the overall relative trend between the specimens was
considered to be mainly unaffected. The specimens were placed close to the border of the base plate
to fit within the field of view of the thermography camera setup. The specimens were manufactured
using the following process parameters: layer thickness
t=50µm
, scanning velocity
v=700mms−1
,
laser power
P=275W
, and hatch distance
h=0.12mm
. Two different so-called border fill scanning
strategies were applied, which scan along the edges of the rectangular cross sections of the parts:
for one the scanning sequence starts in the centre of the part with growing rectangles towards the
perimeter and the other has a converse scanning sequence (see Figure 1). The interlayer time (according
to Mohr et al. [
18
]) was approximately 27.6
±
1.0 s due to time variations between re-coating forwards
and backwards. Therefore, the total time for each build process of 490 layers added up to 3.76 h.
(
a
)
p N q
Centre to Perimeter (CtP)
(
b
)
p H q
Perimeter to Centre (PtC)
Figure 1.
Schematics of both border fill scan strategies. (
a
) Describes the Centre to Parameter (CtP)
strategy indicated by the green arrow, while (
b
) shows the Parameter to Centre (PtC) scan strategy
indicated by the blue arrow. The black arrows show the direction of scan of the laser around each
border fill scan.
2.2. Thermography
An ImageIR 8300 hp camera (Infratec GmbH, Dresden, Germany) working in the spectral range
of 2–
5.7µm
was used for thermographic measurements. It was mounted on top of the SLM280 HL
machine’s build chamber, observing the build plate through a sapphire window. The chosen subframe
image had a size of
160px ×114px
featuring a geometric resolution on the build plate of
360µmpx−1
.
The acquisition frame rate was set to
1000Hz
. The camera was calibrated for black body radiation.
Due to the fact that the emissivity of the used material is well below unity [
19
] and the process was
observed through optical elements, the calibration is not valid for quantitative evaluation of the
obtained thermography data. Nonetheless, assuming that the emissivity remains (approximately)
constant during the build process, the obtained apparent temperatures enable comparisons within a
single build process and between the two different build processes. The thermography data for the two
specimens were obtained during the build process while using two different calibration ranges:
673K
to
1073K
for the CtP specimen (
p N q
) and
623K
to
973K
for PtC specimen (
p H q
). Several overlapping
ranges were being tested during this experiment to find the optimum for these specimens. Values
within the overlapping apparent temperature range of
673K
to
973K
can be compared between the two
build processes. For quantitative evaluation of the process, it would also be necessary to address the
Metals 2020,10, 1234 4 of 15
additional error in temperature estimation introduced by the limited spatial resolution of
360µmpx−1
.
This error diminishes once the spatial temperature gradients have decreased due to lateral heat
flow. These limitations are discussed in more detail by Mohr et al. [
20
]. Despite these limitations,
qualitative analysis of the thermography data revealed results that contribute to the understanding of
the presented RS results.
2.3. Lab X-ray Diffraction
A StressTech Xstress G3 X-ray diffraction instrument (Stresstech GmbH, Rennerod, Germany)
was used in order to determine the RS distribution at the surface of the specimens according to the
sin2ψ
-method. Based on the assumption that that principal stresses are aligned with the geometrical
axes of the specimens and the normal stress component can be neglected at the surface, the RS could
be calculated from the slope of the linear fit of the lattice spacings over
sin2ψ
-plot [
9
,
21
]. The
ψ
-tilt
was carried out in the angular range of
ψ=−45◦
to
ψ=45◦
in 19 steps. The specimens were
tilted around two perpendicular axes, to yield two perpendicular stress components. On the
36mm
surface, this corresponds to seven measurement positions of the prisms’ normal and longitudinal
stress component (see blue circles in Figure 2b). On the
24mm
surface, five measurement positions
correspond to the normal and transversal component of the RS distribution of the prisms. The exposure
time for each acquisition was
5s
. The 311 diffraction line at a corresponding 2
ϑ
angle of
152.26◦
was
acquired using a MnK
α
radiation source and a
2mm
diameter collimator. Further details of the setup
were described by Thiede et al. [
13
]. The software Xtronic (Stresstech GmbH, Rennerod, Germany)
was used for data processing. The peak fitting process was performed using the Pearson VII function
and the background was fitted with a parabolic function. The diffraction elastic constants (DEC)
were calculated for austenitic steel 316L based on the Eshelby–Kroener model [
22
]. The calculated
Young’s modulus of
E311 =184GPa
and Poisson’s ratio
ν311 =0.294
agree with values reported by
Rangaswamy et al. [
23
], as well as with results from measurements and simulations of the DEC values
of LPBF 316L reported by Chen et al. [24].
2.4. Neutron Diffraction
Stress determination by neutron diffraction (ND) was carried out at the STRESS-SPEC diffraction
instrument [25] at the neutron facility FRMII in Munich, Germany (Figure 2a).
gauge
volume
collimator
sample on
xyzω-table
beam
stop
monochromator
neutron beam
detector
2θ
beam
defining
slits
(
a
) principle sketch of the
STRESS-SPEC beamline at
FRMII, Munich
(
b
) map of measurement positions: blue
circles (surface), grey cubes (bulk)
Figure 2. Beamline setup and measurement positions.
A bent Si
400
single crystal monochromator was used to select the wavelength of
1.550Å
.
The Fe
311
-peak was selected in order to characterise the RS distribution due to the low accumulation
Metals 2020,10, 1234 5 of 15
of inter-granular stresses reported for this reflection in conventional face-cubic-centred (fcc) iron
materials [10].
To map the RS in the cross sectional plane at the mid build height of the specimen, a gauge volume
of
2mm ×2mm ×2mm
was used in a grid of 7
×
5 measurement points. (see grey cubes in Figure 2b).
The coordinate system is depicted in Figure 2b.
σL
represents the RS along the
y
-direction,
σT
along
the x-direction and σNalong the z-direction, which was also the build direction.
A stress-free reference was needed to calculate strains from the measured
d311
lattice-spacing.
A small cube with the size of
3mm×3mm ×3mm
was sectioned from the bottom corner of a separate
test build job of the PtC specimen (
p H q
). This cube was regarded as free of TypeI macro-stresses [
9
],
due to the mechanical relaxation during sectioning. The strain can subsequently be derived from the
measured ϑangles using Bragg’s law [9].
ε=d311 −d0
d0=sinϑ311
sinϑ0
−1 (1)
Assuming that the principal geometric directions correspond with the principal stress directions
Hooke’s law reads as the following, as described by Holden et al. [26]:
σL,T,N=E311
(1+ν311) (1−2ν311)h1−ν311εL,T,N+ν311 (εT,N,L+εN,L,T)i(2)
The
d0
value was derived from the average of the
ϑ311
measurements of the cube in
longitudinal (
L
), transversal (
T
) and normal (
N
) direction, where the normal direction corresponds
to the build direction (as depicted in Figure 2b). The same DECs that were derived from the
Eshelby–Kroener model were applied to both Lab XRD and ND results (see Section 2.3).
2.5. Micro Computed Tomography
The small reference cube for ND was studied using Micro Computed Tomography (
µ
CT) to obtain
a detailed dataset of the internal defect structure. The
μ
CT measurements were performed at a GE
v|tome|
×
180/300 CT scanner (GE Sensing & Inspection Technologies GmbH, Wunstorf, Germany)
using the
180kV
source at a voltage of
150kV
and a current of
40µA
without any metal pre-filter.
A voxel size of
(3µm)3
was achieved. The analysis of the data was performed using the commercial
software VG Studio MAX version 3.2.1 (Volume Graphics GmbH, Heidelberg, Germany). A lower
threshold limit of 8 voxels was used for pore detection.
2.6. Optical Microscopy
For Optical Microscopy (OM) investigations of the microstructure, the bottom faces of the samples
were ground, polished, and etched. Emery papers with 180, 320, 600 and 1200 grits followed by clothes
with
3µm
and
1µm
were used. For etching the Bloech & Wedl II method [
27
] (a solution of
50mL
H
2
O,
50mL
HCl,
0.6g
K
2
S
2
O
5
) was applied. The microstructure was captured using a Olympus BX53M
microscope with a DP74 camera module (Olympus Corporation, Tokyo, Japan). The analysis was
performed using the software Olympus Stream Essentials (Olympus Corporation, Tokyo, Japan).
3. Results
3.1. In-Situ Thermography
The build jobs of both samples were supervised in-situ by thermography in order to receive more
detailed information on the local variation of the temperature gradient and cooling rates. Figure 3a,b
display the maximum apparent temperatures at the mid-height layer.
The thermography data were averaged over 40 layers at the mid build-height to reduce noise
and the influence of smoulder and spatter. In relation to the height of the specimens of
21mm
,
Metals 2020,10, 1234 6 of 15
these 40 layers represent an average of the height range from
9.35mm
to
11.35mm
. The number of
40 layers (=2 mm) was chosen, since this corresponds to the size of the used gauge volume for ND
(2mm ×2mm ×2mm).
The scan strategy of the PtC specimen (
p H q
) resulted in an increased heat accumulation in the
center, compared to the CtP specimen (p N q). This could be observed as an increase in the maximum
temperature at the centre, when comparing Figure 3d,c.
Figure 3d shows the different apparent temperature values for the four sections of the plane.
These differences were caused by a combination of the different surface roughness of each section and
of the shadowing effects from the smoulder.
(a)p N q CtP specimen’s mid-height layer (b)p H q PtC specimen’s mid-height layer
(
c
)
p N q
CtP specimen: 40 layers at
mid-height averaged
(
d
)
p H q
PtC specimen: 40 layers at
mid-height averaged
Figure 3.
Apparent (uncalibrated) maximum temperature of the two specimens obtained from
thermography data acquired during the build process at the sample’s mid build height. Each border
fill scan started and ended at the bottom right hand laser turn position of the images. (
a
,
b
) display the
mid-height layer, (c,d) display an average of 40 layers at the mid-height.
Figure 4shows the cooling rate of both specimens. The cooling rate—
dT
/
dt
was obtained by
comparing two images at
t=1ms
and
t=2ms
after an apparent temperature of
700K
was reached
for the last time at the surface. Typical times for cooling from the maximum temperature to
700K
were between
2ms
and up to
15ms
. The cooling time of
15ms
was observed at the centre of the PtC
specimen (p H q).
As displayed in Figure 4d, the PtC specimen (
p H q
) also featured a lower cooling rate in the centre
of the plane in addition to the higher maximum temperature depicted in Figure 3d. The CtP specimen
(
p N q
) shows a low cooling rate at the edges of the specimen indicating that the surrounding metal
powder served as an heat insulator for conduction, as assumed in modelling [28].
Metals 2020,10, 1234 7 of 15
(a)p N q CtP specimen’s mid-height layer (b)p H q PtC specimen’s mid-height layer
(
c
)
p N q
CtP specimen: 40 layers at
mid-height averaged
(
d
)
p H q
PtC specimen: 40 layers at
mid-height averaged
Figure 4.
Cooling rates measured by the different between images taken at
t=1ms
and
t=2ms
after an apparent temperature of
700K
was observed for the last time. Thermography data for both
samples was obtained during the build process at the middle of the total build height. (
a
,
b
) display the
mid-height layer, (c,d) display an average of 40 layers around the middle of the total build height.
3.2. Combined Neutron and Lab X-ray Diffraction
The ND results (bulk RS) were combined with Lab XRD results (surface RS) to show the complete
stress distribution across the full cross section of the specimens’ middle plane. The contour plot
function of the commercial software Origin 2018 (OriginLab Corporation, Northampton, USA),
which is based on the Delaunay triangulation, was used to visualise the combined results. Figure 5
shows the combination of ND and XRD results. The RS distribution is visualised in longitudinal,
transversal, and normal direction, where the normal direction corresponds to the build direction
(Figure 2b). The XRD technique used only allows for the determination of stress components which
are parallel to the surface (i.e., in-plane). Therefore, to visualise the third orthogonal stress component
(perpendicular to the surface) in Figure 5the following boundary condition was used: at the surfaces
of the specimens corresponding to positions at
y=0mm
and
y=36mm
, the value of the longitudinal
stress component was assumed to
σL=0MPa
. For the value of the transversal stress component
at
x=0mm
and
x=24mm
it was assumed
σT=0MPa
, since these are free surfaces in these
corresponding stress directions. In general, for the two scan strategies, a similar RS distribution was
observed in the longitudinal, transversal and normal direction. This distribution is characterised by
compressive RS within the bulk, balanced by tensile RS at the surface. Instead, the RS distribution in
the longitudinal and transversal direction of each specimen is similar in terms of shape and magnitude,
the RS distribution in the normal (i.e., building) direction differed from the other directions in terms of
shape and magnitude.
Metals 2020,10, 1234 8 of 15
0
- 2 0 0
0
- 1 0 0
0
0
6
1 2
1 8
2 4
0 6 1 2 1 8 2 4 3 0 3 6
Y / m m
X / m m
- 3 0 0
- 2 0 0
- 1 0 0
0
100
200
300
σL / M P a
(
a
)
p N q
Longitudinal residual stresses
(RS) component for CtP border fill
strategy
- 3 0 0
0
- 2 0 0
- 1 0 0
0
0
6
1 2
1 8
2 4
0 6 1 2 1 8 2 4 3 0 3 6
Y / m m
X / m m
- 3 0 0
- 2 0 0
- 1 0 0
0
100
200
300
σL / M P a
(
b
)
p H q
Longitudinal RS component for
PtC border fill strategy
100
100
- 1 0 0
100
0
0
6
1 2
1 8
2 4
0 6 1 2 1 8 2 4 3 0 3 6
Y / m m
X / m m
- 3 0 0
- 2 0 0
- 1 0 0
0
100
200
300
σT / M P a
(
c
)
p N q
Transversal RS component for
CtP border fill strategy
- 1 0 0
0
0
6
1 2
1 8
2 4
0 6 1 2 1 8 2 4 3 0 3 6
Y / m m
X / m m
- 3 0 0
- 2 0 0
- 1 0 0
0
100
200
300
σT / M P a
(
d
)
p H q
Transversal RS component for
PtC border fill strategy
- 2 0 0
- 1 0 0
0
100
200
0
6
1 2
1 8
2 4
0 6 1 2 1 8 2 4 3 0 3 6
Y / m m
X / m m
- 3 0 0
- 2 0 0
- 1 0 0
0
100
200
300
σN / M P a
(
e
)
p N q
Normal RS component for CtP
border fill strategy
- 2 0 0
- 2 0 0
- 1 0 0
0
100
200
0
6
1 2
1 8
2 4
0 6 1 2 1 8 2 4 3 0 3 6
Y / m m
X / m m
- 3 0 0
- 2 0 0
- 1 0 0
0
100
200
300
σN / M P a
(
f
)
p H q
Normal RS component for PtC
border fill strategy
Figure 5.
Comparison of RS maps of the tw scan strategies including results from lab X-ray diffraction
at the surface (The big semi-translucent squares in the bulk represent the almost cubic ND gauge
volume (orientated differently for different stress components), whereas the small semi-translucent
squares at the edges represent the lab X-ray measurement positions).
The highest magnitude of RS of each specimen (maximum tensile or maximum compressive)
were observed in the normal direction. However, the PtC specimen (
p H q
) displayed higher bulk
compressive stresses in all three orthogonal directions. The different stress values in the normal
direction, as compared to the longitudinal and transversal direction, are also reflected in the lattice
spacing of the the
d0
cube. Whereas, the
d
-spacing in the longitudinal and transversal direction are
relatively similar to each other, in the normal direction a larger lattice spacing was measured (see
Metals 2020,10, 1234 9 of 15
Table 1). The
d0
value was obtained from averaging the three measured directions. This averaged
value was used as a stress-free lattice parameter to calculate the RS.
Table 1. Distribution of orthogonal d-spacing values of the reference cube.
Orientation d-Spacing Error
Longitudinal 1.07449Å 2.36 ×10−5Å
Transversal 1.07448Å 2.71 ×10−5Å
Normal 1.07493Å 2.41 ×10−5Å
3.3. Micro Computed Tomography
The reference cube was analysed by
μ
CT to provide an example of local defect distribution in the
specimen. Because it was cut from the corner where the laser path started and ended, it represented
the area where the highest amount of defects was expected. The
μ
CT results presented in Figure 6
reveal a network of defects at the location where the laser started and ended, as well as between the
hatches. Because the same scan vector was used on each hatch and layer, the projection of defects
onto one plane (Figure 6c) reveals the lack of fusion between neighbouring hatches. As reported in
literature [
29
,
30
] alternating the orientation of scan vectors between layers prevents the formation of
lack of fusion defects. Because the effect of shrinkage on RS was the subject of this study, scan vectors
were not altered between layers to magnify such effect.
The largest defects were situated close to the edge of the sample (Figure 6b,c). A total porosity of
0.28% was observed.
(
a
) slice of the cube
perpendicular to the
build direction
(
b
) 2D projection of the 3D
rendered of the segmented
defects within the cube
perpendicular the build
direction
(
c
) 3D rendering of the
segmented defects
Figure 6. µCT reconstructions of the ND reference cube sectioned from a twin PtC specimen (p H q).
3.4. Optical Microscopy
Optical microscopy images of the polished and etched specimen’s bottom surface are shown in
Figure 7. Defects at the turn location of the laser are visible (Figure 7d,e). The bottom surface of both
specimens are expected to be less effected by heat accumulation due to the smaller build height at the
time the microstructure froze, and a better heat conduction into the build plate as compared to the top
layers of the specimens. Nonetheless, defects (pores and voids) were observed in both specimens at
the positions, where the laser turns by 90◦.
Metals 2020,10, 1234 10 of 15
(
a
)
p N q
full sized image of CtP specimen (
b
)
p H q
full sized image of PtC specimen
(
c
)
p N q
magnified upper right section of
CtP specimen
(
d
)
p H q
magnified upper right section
section of PtC specimen
(
e
)
p N q
magnified section of the centre
of CtP specimen
(
f
)
p H q
magnified section of the centre
of PtC specimen
Figure 7. Optical microscopy images of the samples’ bottom surface after polishing and etching.
4. Discussion
As mentioned in the introduction, Mercelis and Kruth [
3
] described two major driving
mechanisms for the formation of RS in AM metallic parts made by LPBF: the temperature gradient
mechanism (TGM) and the solidification shrinkage mechanism (SSM). Both of the mechanisms induced
compressive stresses into the bulk material. The combined data of ND and Lab XRD showed the
Metals 2020,10, 1234 11 of 15
typical stress distribution pattern for metallic AM parts: compressive stresses in the bulk and tensile
stresses close to the surface.
Because of the same geometric dimensions, it can be assumed that the solidification shrinkage
effects in the two samples were equal. This implies that any differences in the RS distributions of the
two samples should be attributed to the TGM.
According to the SSM, the induced RS distribution by solidification shrinkage depends on the
length of the scanned laser tracks. The shrinkage of longer laser tracks introduces higher RS than
shorter laser tracks [
31
]. Therefore, the longer laser tracks parallel to the
y
-axes of the specimens
presented in Figure 5a–d) appear to be the main reason for the higher compressive stresses in the
longitudinal stress distributions of the two specimens, as compared to the shorter laser tracks parallel
to the
x
-axes, which seemed to result in lower compressive stresses for the transversal RS distributions
of the two specimens.
The distribution of the normal component of the RS was assumed to be mostly independent of
the SSM, since there were almost no restrictions to solidification shrinkage due to the free top surface
during the layer-wise production. Therefore, the TGM was assumed to be the main mechanism to
shape the RS distribution of the normal component. The RS distribution has the shape of a butterfly
(see Figure 5e,f). The spikes of this butterfly pattern match the location where the laser turned by
90◦
(see Figure 8).
(
a
)
p N q
Normal stress component
(Figure 5e) over thermography results
(Figure 3c)
(
b
)
p H q
Normal stress component
(Figure 5f) over thermography results
(Figure 3d)
Figure 8.
Normal (i.e., build direction) stress component (contour lines) in
MPa
(Figure 5e,f)
overlayed with thermography results (Figure 3c,d) to highlight the compressive stresses at the laser’s
turn locations.
It is also observed that the normal component exhibits the highest tensile stresses (see Figure 5
and Table 2). The determined RS values are below the tensile yield strength ranges for LPBF 316L
(450MPa to 590MPa) as reported by Wang et al. [32].
Table 2. Max. and min. values of the orthogonal stress components in the plane.
Stress Component Centre to Perimeter p N q Perimeter to Centre p H q
Max. [MPa] Min. [MPa] Max. [MPa] Min. [MPa]
σL100.8 ±16.9 −253.4 ±15.8 086.4 ±10.2 −304.2 ±15.6
σT140.6 ±10.4 −103.6 ±15.4 122.6 ±11.0 −134.0 ±15.8
σN295.6 ±10.5 −202.1 ±14.2 290.5 ±10.6 −245.8 ±19.5
Figure 8b shows that higher compressive stresses in the PtC specimen (
p H q
) are localised close to
the zone of the highest heat accumulation. This is in contrast to the CtP specimen (
p N q
), which shows
lower and more evenly distributed compressive stresses in the plane (see Figure 5). The higher
Metals 2020,10, 1234 12 of 15
maximum temperatures at the centre of the PtC specimen (
p H q
) in combination with the slower
cooling rate seem to result in larger RS in the centre of the plane as compared to the CtP specimen
(
p N q
). Lower contributions from the TGM to the compressive stress profile of the CtP specimen (
p N q
)
might be a result of the lack of heat accumulation in the centre of its plane (see Figures 3c and 8a) and
a faster cooling rate (see Figure 4c).
Line stress profiles (Figure 9) that were derived from the in-plane data presented in Figure 5at a
middle line of the plane at
x=12mm
emphasise the conclusion of SSM being the major mechanism to
define the shape of the RS distribution. However, the TGM appears to influence the magnitude of the
peak compressive stresses (see Figure 9).
It should be noted that, in Figure 9, only measured values are displayed. Therefore, the boundary
condition values of
0MPa
were excluded from the longitudinal stress profile at
y=
0 and
y=
36 (see
Figure 9a). The measured bulk values close to these surfaces support the assumption of zero stress at
these surfaces.
0 6 1 2 1 8 2 4 3 0 3 6
- 3 0 0
- 2 0 0
- 1 0 0
0
100
200
300
σL / M P a
Y / m m
c e n t r e > p e r im e t e r
p e r im e t e r > c e n t r e
(
a
) Longitudinal RS component at
x=12mm
(
b
) Transversal RS component at
x=12mm
(
c
) Normal RS component (=build direction) at
x=12mm
Figure 9.
Line scans in both samples for all three orthogonal directions using the combined data from
ND and lab XRD.
Since the TGM does not require melting [
33
], it can be assumed that the compressive stress
components induced by the TGM were formed in subjacent layers within the heat affected zone of the
melt pool but below the layers that were remolten. It should be noted that a linear interpolation was
applied to combine the surface measurement positions and the neutron data in Figure 9. Therefore,
any possible sub-surface tensile peaks that had been reported by Mishurova et al. [
11
,
34
] in LPBF
Ti-6Al-4V were not be taken into account in this study.
The
µ
CT results (Figure 6) reveal a network of defects at the laser’s start and stop position.
OM results (Figure 7d,e) show defects at the turn locations of the scan track. These regions have
been measured to be under higher tensile RS (in particular,
σT
), which is assumed to arise from the
Metals 2020,10, 1234 13 of 15
longitudinal and transversal solidification shrinkage, as depicted in Figure 5. Therefore, any defects
in these regions might have served as micro-crack initiators. The combination of pores and tensile
stress at corners could also explain why the defects observed by
µ
CT (Figure 6b) seem to be larger
towards the outer edge: the tensile stress due to solidification shrinkage increases towards the edges
of the specimens due to an increase length of the laser tracks. The analysis of the optical microscopy
and
µ
CT data indicates that an unknown amount of RS might had been relaxed by micro-cracks at the
laser’s start and stop location.
5. Conclusions
Two prismatic AISI316L specimens using a border fill scan strategy were produced in order
to differentiate the effect of the temperature gradient mechanism from the solidification shrinkage
mechanism in AM metallic parts produced by LPBF. The following conclusions could be made:
1.
A combination of surface and bulk residual stress results was needed to fully cover the (surface)
tensile and (bulk) compressive regions of the in-plane stress distribution.
2.
By comparing the two samples, a similar stress distribution was revealed for each of the
three orthogonal directions (see Figures 5and 9), indicating that the solidification shrinkage
mechanism is the main mechanism controlling the shape of the RS distribution in these samples.
The temperature gradient mechanism seems to influence the magnitude of the compressive
stresses without changing the overall pattern of the stress distribution.
3.
In-situ thermography results of the sample exposed from the perimeter to the centre revealed
a heat accumulation, which corresponds to highly localised compressive stresses due to the
temperature gradient mechanism.
6. Outlook
In-situ Thermography recorded a detailed data set of apparent surface temperatures and enables
an analysis of cooling rates. These data can be used in future simulations in order to model the RS
field at the specimens’ mid height. In future studies, the RS distribution in the subsurface region might
be resolved using additional techniques, such as hole drilling, slitting, X-ray with layer removal, deep
hole drilling, or contour method.
Additionally, twin specimens of the two prisms will allow further experiments to study the
effect on maximum values of the RS distribution, if the reference cube is cut from different positions
within these twin specimens. In addition, these twins will allow a systematic
µ
CT analysis of different
positions within the two specimens, in particular to relate RS and defect distributions.
Author Contributions:
Conceptualization, A.U., T.F., G.M. and S.J.A.; methodology, A.U., G.M., M.S., K.S., S.J.A.,
T.M., I.S.-M., T.F., M.H.; formal analysis, A.U., S.J.A., M.S., K.S.; investigation, A.U., M.S., K.S., S.J.A., T.M., I.S.-M.,
T.F., M.H.; writing—original draft preparation, A.U., G.M., M.S., K.S., S.J.A.; writing—review and editing, A.U.,
G.M., M.S., S.J.A., T.M., I.S.-M., M.H., A.E., G.B., T.F.; visualization, A.U., S.J.A.; supervision, A.E., G.B.; project
administration, A.E., G.B.; funding acquisition, G.B. All authors have read and agreed to the published version of
the manuscript.
Funding: This research received no external funding.
Acknowledgments:
This work has been funded by the BAM Focus Area Materials project AGIL “Microstructure
Development in Additively Manufactured Metallic Components: from Powder to Mechanical Failure” and
ProMoAM “Process monitoring of Additive Manufacturing”. We are thankful for the financial support and the
fruitful cooperation with all partners. This work is based upon experiments performed at the STRESS-SPEC
instrument operated by FRMII at the Heinz Maier-Leibnitz Zentrum (MLZ), Garching, Germany.
Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design of the
study; in the collection, analyses, or interpretation of data; and in the decision to publish the results.
Metals 2020,10, 1234 14 of 15
Abbreviations
The following abbreviations are used in this manuscript:
AM Additive Manufacturing
FRMII Forschungs-Neutronenquelle Heinz Maier-Leibnitz (Research Reactor Munich II)
µCT Micro Computed Tomography
ND Neutron Diffraction
LPBF Laser Powder Bed Fusion
OM Optical Microscopy
RS Residual Stress
SSM Solidification Shrinkage Mechanism
TGM Temperature Gradient Mechanism
VED Volumetric Energy Density
XRD (Lab) X-Ray Diffraction
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