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An additively manufactured and direct-aged AlSi3.5Mg2.5 alloy with superior strength
and ductility: micromechanical mechanisms
X.X. Zhang1,*, A. Lutz2, H. Andrä
1, M. Lahres2, D. Sittig3, E. Maawad4, W.M. Gan4, D.
Knoop5
1 Fraunhofer Institute for Industrial Mathematics ITWM, Fraunhofer-Platz 1, 67663
Kaiserslautern, Germany
2 Mercedes Benz AG, Research and Development Department, Leibnizstraße 2, 71032
Böblingen, Germany
3 External Research Projects & Standardization, Concept Laser GmbH, An der Zeil 8, 96215
Lichtenfels, Germany
4 Institute of Materials Physics, Helmholtz-Zentrum Hereon, Max-Planck-Str. 1, 21502
Geesthacht, Germany
5 Leibniz-Institut für Werkstofforientierte Technologien (IWT), Badgasteiner Straße 3, 28359
Bremen, Germany
Abstract
An AlSi3.5Mg2.5 (wt%) alloy with excellent mechanical properties was produced via
laser powder bed fusion in this study. The yield strength, tensile strength, and elongation of
this as-built AlSi3.5Mg2.5 alloy reach about 406 MPa, 501 MPa, and 8.6%, respectively.
These properties are dramatically superior to the current additively manufactured Al-Si-Mg
alloys. A direct-aging treatment at 170 °C for one hour increases the yield strength and
ductility further to about 417 MPa and 11.0%, respectively, with the tensile strength
remaining the same level. The microstructures and strengthening mechanisms of the as-built
and direct-aged samples were investigated systematically. The underlying micromechanical
mechanisms of the as-built and direct-aged samples were examined based on a combination
of in-situ synchrotron X-ray diffraction and three-dimensional crystal plasticity modeling. The
as-built AlSi3.5Mg2.5 alloy possesses a fine microstructure, including fine grains and
nano-sized Mg2Si and Si precipitates. After direct-aging treatment, additional Mg2Si and Si
precipitate out. Besides, element diffusion upon aging treatment causes migration of cell
boundaries and relaxation of residual stress. The direct-aging treatment leads to an increased
Orowan strengthening, dislocation strengthening, and load-bearing strengthening effects.
Moreover, the variations of microstructure and residual stress after the aging treatment change
the dislocation behavior and increase the dislocation storage capacity, causing an increased
ductility. Nevertheless, the aging treatment does not alert the type of damage and fracture.
*Corresponding author. Present address: Heinz Maier-Leibnitz Zentrum (MLZ), Technical University of
Munich, Lichtenbergstrasse 1, 85748 Garching, Germany; E-mail: xingxing.zhang@frm2.tum.de
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This study provides valuable insights to tailor the microstructure and mechanical properties of
additively manufactured Al-Si-Mg alloys.
Keywords: Additive manufacturing; laser powder bed fusion (LPBF); aluminum alloy;
synchrotron X-ray diffraction (SXRD); strengthening mechanism; heat treatment
1. Introduction
Aluminum (Al) alloys produced via additive manufacturing (AM) have attracted
increasing interest in various industries due to the Al alloys’ high strength-to-weight ratio and
the complex geometries enabled by AM (Aboulkhair et al., 2019; Bonatti and Mohr, 2017;
Ghoncheh et al., 2020; Liu et al., 2021; Zhang et al., 2017). However, one critical issue that
hinders AM of Al alloys from maturation to the full potential is that only a few Al alloys are
available for the AM industry. Most of these alloys are commercial cast Al-Si-(Mg) alloys
such as AlSi10Mg (Biffi et al., 2018; Chen et al., 2017; Trevisan et al., 2017), AlSi7Mg
(Kimura and Nakamoto, 2016; Pereira et al., 2020; Wang et al., 2019a), and AlSi12 (Li et al.,
2016; Prashanth et al., 2017; Suryawanshi et al., 2016). To fulfill diverse applications in
industries, broaden the range of Al alloys specifically for AM is vital. Some novel AM Al
alloys have been developed by adding a significant amount of precious elements such as Sc
(Li et al., 2020a; Spierings et al., 2017a; Wang et al., 2019b) and Ce (Plotkowski et al., 2017;
Plotkowski et al., 2020). Although these AM Sc- or Ce-containing Al alloys show excellent
mechanical properties, they are resource-dependent, expensive, and difficult to recycle
(Spierings et al., 2016).
Without adding rare-earth elements, the Al-Si-Mg alloy system is a good start point to
develop new AM Al alloys because this alloy system offers good cast-ability and corrosion
resistance (DebRoy et al., 2018; Herzog et al., 2016; Oliveira et al., 2020). For example,
(Geng et al., 2021) developed a novel AlSi8.2Mg1.4 (wt%) alloy produced via laser powder
bed fusion (LPBF) with a yield strength of ~341 MPa, an ultimate tensile strength of ~518
MPa, and a total elongation of ~7.1%. Our previous investigations revealed that the novel
AlSi3.5Mg2.5 alloy produced via LPBF shows a promising combination of strength and
ductility (Knoop et al., 2020; Lutz et al., 2020; Zhang et al., 2021b). The yield strength,
tensile strength, elongation of 381 MPa, 483 MPa, and 6.1% were reported for the as-built
AlSi3.5Mg2.5 alloy (Knoop et al., 2020). However, these mechanical properties still cannot
satisfy the demand for many applications where high load carrying capacity is critical.
According to the characteristics of AM Al-Si-Mg alloys, the question is whether it is
possible to enhance the strength and elongation of low-cost AM Al-Si-Mg alloys without
adding a significant amount of precious elements or external particles, e.g., TiB2? We know
that the Al matrix in the AM Al-Si-Mg alloys is a supersaturated solid solution due to the
extremely high cooling rate (105-106 K/s) (Aboulkhair et al., 2019). Meanwhile, the
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track-by-track and layer-by-layer manufacturing process causes repeated thermal cycles with
varying peak temperatures, leading to in-situ precipitation of strengthening particles in the
heat-treatable alloys. This intrinsic heat treatment effect has been reported in (Kurnsteiner et
al., 2017; Kurnsteiner et al., 2020; Zhang et al., 2021b). Therefore, by tailoring the solid
solution strengthening mechanism and strengthening mechanisms caused by precipitate
particles, a higher strength could be achieved in the AM Al-Si-Mg alloys.
Additionally, previous investigations have shown that the dislocation behavior is unique
in the AM Al-Si-Mg alloys. (Li et al., 2020c) showed that the LPBF AlSi10Mg alloy is
characterized by a remarkably improved exhaustion rate of mobile dislocations compared
with the annealed AlSi10Mg alloy. Our previous investigations revealed that the LPBF
AlSi10Mg alloy exhibits a multistage strain hardening behavior due to the interactions
between dislocations and eutectic cell boundaries (Zhang et al., 2021a; Zhang et al., 2021c).
Hence, improved ductility could be obtained by modifying the dislocation behavior.
How can we realize the above objectives? Post-heat treatments are often employed to
enhance the mechanical properties of AM Al alloys. For instance, an aging treatment
significantly increases the strengths of the AM Zr/7075Al (Martin et al., 2017), Al-Mg-Sc-Zr
(Scalmalloy) (Spierings et al., 2017b), Al-Mn-Mg-Sc-Zr (Jia et al., 2019), and
Al-Mg-Si-Mn-Sc-Zr (Li et al., 2020a) alloys. However, an aging treatment usually decreases
ductility (Jia et al., 2019; Spierings et al., 2017b). In contrast, an annealing treatment
significantly increases the ductility of the AM Al alloys at the expense of strength (Wang et al.,
2019a; Zhuo et al., 2019).
Can we increase the strength and ductility of AM Al-Si-Mg alloys simultaneously
through a post-heat treatment? Several investigations have shown promising results. (Kimura
and Nakamoto, 2016) showed that the yield strength of the LPBF AlSi7Mg0.3 alloy increases
from 200 MPa (as-built) to 225-250 MPa after aging at 150 oC for five hours without losing
ductility. (Pereira et al., 2020) indicated that the elongation of the LPBF AlSi7Mg0.6 alloy
increases from 6.1±0.3% (as-built) to 6.8±1.4% after aging at 160 oC for six hours without
decreasing the strength. Moreover, (Li et al., 2020a) found that the elongation of the AM
AlMg8.0Si1.3Mn0.5Sc0.5Zr0.3 (wt.%) alloy increases significantly from 11% (as-built) to
17% after aging at 360 oC for eight hours, with the tensile strength rising from 497 to 506
MPa. They explained that the improved ductility and strength are associated with soft coarse
grains and hard fine grains after aging treatment (Li et al., 2020a). Nevertheless, the
micromechanical mechanisms that simultaneously provide superior strength and ductility for
the AM Al-Si-Mg alloys after aging treatment remain poorly understood.
Here, we demonstrate that the LPBF AlSi3.5Mg2.5 alloy with refined microstructure can
achieve excellent mechanical properties. A direct-aging treatment further increases both
strength and ductility of the LPBF AlSi3.5Mg2.5 alloy. The as-built and direct-aged
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AlSi3.5Mg2.5 samples were machined and subjected to microstructure characterizations
using the optical microscope (OM), electron backscatter diffraction (EBSD), transmission
electron microscope (TEM) analyses, as well as mechanical tests. In-situ synchrotron X-ray
diffraction (SXRD) was carried out to explore the microscopic strains, phase stresses, and
dislocation densities in the samples under loading. Crystal plasticity modeling based on
three-dimensional representative volume element (RVE) was employed to analyze the
microscopic deformation behavior. The micromechanical mechanisms of strengthening, strain
hardening, damage, and fracture were discussed. Based on this investigation, the relation
between the microstructures, direct-aging treatment, strengthening mechanisms, dislocation
behavior, damage and fracture mechanisms is established. This study provides in-depth
knowledge for the further development of high-performance and low-cost AM Al alloys.
2. Experimental and modeling procedures
2.1 Materials and LPBF process
The novel AM Al alloy in this investigation has a nominal composition of AlSi3.5Mg2.5
(wt%). The alloy contains trace elements Mn and Zr for grain refinement. A Concept Laser
M2 UP1 cusing laser system (400 W) was utilized with a laser power of 370 W and a laser
spot diameter of 0.1 mm. The scanning speed was 1300 mm/s, the layer thickness was 0.05
mm, and the hatch distance was 0.11 mm. The platform was pre-heated to 80 ℃ upon the
LPBF process. The laser scanning strategy was bidirectional and alternating exposure. Both
as-built and heat-treated samples were investigated, namely AsB (as-built) and HTS
(heat-treated), respectively. The HTS samples were subjected to a direct-aging treatment at
170 oC for one hour after LPBF.
Fig. 1 Manufactured vertical cylinders together with the base plate.
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The cylindrical samples were manufactured vertically (i.e., the Z building direction is the
direction of the cylinder’s height) via the LPBF method. Fig. 1 shows the arrangement of the
as-built samples. The as-built cylindrical samples have a length of 105 mm and a diameter of
14 mm. The as-built and heat-treated samples were machined into dog-bone-shaped samples.
The machined samples for in-situ testes have a total length of 50 mm, and their parallel part
has a length of 20 mm and a diameter of 4 mm. The total length, parallel part length and
diameter of the machined samples for ex-situ tests are 76, 30 and 6 mm, respectively. The
detailed geometry and size of the in-situ and ex-situ samples can be found in our previous
publication (Zhang et al., 2021c).
2.2 Microstructure characterization
The OM characterization of the samples’ threaded part was conducted on a Zeiss Axio
Scope.A1 microscope. The samples were polished and not etched. The normal vector of the
2D OM images was horizontal, i.e., perpendicular to the building direction.
The EBSD samples were prepared through ion milling using a Hitachi ArBlade IM5000
system with Ar-ion. The electron microscope Zeiss Auriga with EBSD detector Symmetry
(Oxford Instruments) was employed to investigate the EBSD microstructure. The increment
was 0.5 µm. The grain size was calculated using the equivalent circle diameter. The grains at
the borders of the images were excluded.
TEM analysis was performed on a Jeol ARM200 with a Cs corrector. The scanning mode
(STEM) with the annular dark field detector and the Jeol Dual energy-dispersive X-ray
spectroscopy (EDX) system was utilized for element analysis. The TEM samples were
prepared from non-deformed parts using a focused ion beam. The transmission direction was
parallel to the building direction.
2.3 Ex-situ tensile tests
Two AsB specimens and three HTS specimens were subjected to ex-situ uniaxial tensile
tests at room temperature with a nominal tensile strain rate of 1.0
10-3 s-1. The strain during
tensile deformation was measured by a high-accuracy extensometer.
2.4 In-situ SXRD experiments
The in-situ SXRD experiments were carried out at the side station of the High Energy
Materials Science (HEMS) beamline P07B managed by the Helmholtz-Zentrum Hereon at
PETRA III, DESY. Both AsB and HTS specimens were subjected to in-situ uniaxial tensile
tests to measure the lattice strains, phase stresses, and dislocation densities. The crosshead
displacement speed was set to 3.0×10-3 mm/s leading to a nominal strain rate of 1.5
10-4 s-1.
Besides, the initial bulk textures of the AsB and HTS samples were measured using the SXRD,
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with the sample table rotating around the longitudinal axis of the specimens from -70° to 70°.
The diffraction images were collected at every 5° for texture measurements.
The wavelength of the synchrotron X-ray was 0.14235 Å. The incident beam size was
0.7×0.7 mm2. A Perkin Elmer XRD 1622 flat panel detector with a pixel size of 200×200 μm2
and 2048×2048 pixels was employed. The specimen-to-detector distance was fixed to 1028.3
mm as calibrated using a LaB6 powder standard, which was the same for both in-situ tensile
tests and texture measurements.
2.5 Calculations of lattice strains and average phase stresses
The 10º cake segments from the measured 2D diffraction images at positions of 0º±5º
and 90º±5º were used to calculate the intensity-
2
diffraction spectrums for the TD and LD,
respectively, using software Fit2D (Zhang et al., 2021c). Equivalent 10º cake segments at
positions of 180º±5º and 270º±5º were also used for the TD and LD, respectively. More
details about the data processing can be found in our previous report (Zhang et al., 2021c).
The hkl lattice strain
,si
hkl
in phase i (i = Al, Mg2Si, or Si) along with direction s (s = LD
or TD) is calculated by
,,0
,,
sin 1
sin
si
hkl
si
hkl si
hkl
, (1)
where
is the peak position, subscript 0 denotes the reference condition prior to loading.
There is no Einstein summation on s, i, or hkl.
The clear Al {311} and Si {311} peaks were selected to calculate the stresses and strains
of Al and Si. Besides, the clear Mg2Si (400) peak was chosen because it has the highest peak
intensity and almost has no overlap with other peaks. In contrast, other Mg2Si peaks either
overlap seriously with the Al and Si peaks or have very weak intensities. According to
previous investigations (Ungar et al., 2014; Van Petegem et al., 2016; Yamashita et al., 2020;
Zhang et al., 2021c), the longitudinal stress
LD
i
in phase i can be approximately calculated
by
LD DEM LD
i i i
E
, (2)
where
Al LD,Al
LD 311
,
22
Mg Si L,Mg Si
LD 400
,
Si LD,Si
LD 311
, and
DEM
i
E
is the corresponding diffraction
elastic modulus.
2.6 Evaluation of dislocation density
The dislocation density was determined using the modified Williamson-Hall method and
the modified Warren-Averbach method (Sahu et al., 2012; Zhang et al., 2021c). The LaB6
standard powder was used to measure the instrumental effects. Details about evaluating
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dislocation density can be found in our previous investigation (Zhang et al., 2021c).
2.7 Crystal plasticity simulation
A crystal plasticity model was employed to simulate the heterogeneous stress and strain
properties at the microscale. Accordingly, the multiplicative decomposition of the deformation
gradient F is given by
ep
F FF
, (3)
where
e
F
and
p
F
are the elastic and plastic deformation gradient, respectively. From the
elastic deformation gradient
e
F
, the elastic Green-Lagrange strain Ee can be calculated by
T
e e e
1
=2E F F I
, (4)
where
I
is the second rank identity tensor.
In the simplest hyperelastic material law (Saint Venant-Kirchhoff model), the second
Piola-Kirchhoff stress S is related to the elastic Green-Lagrange strain Ee by
e
:SEC
, (5)
where C is the fourth-order elastic stiffness tensor. This constitutive model is an extension of
the geometrically linear elastic case.
The evolution of
p
F
is determined by the plastic velocity gradient Lp:
p p p
F L F
. (6)
For elastic materials, we have Lp = 0. For elasto-viscoplastic materials, based on the
kinematics of slip motion, the plastic velocity gradient Lp is defined by
pu u u
u
L s n
, (7)
where
u
is the shear rate on slip system u,
u
s
and
u
n
are the unit vectors of slip direction
and slip plane normal, and
denotes the tensor product.
The kinetic law on slip system u reads (Roters et al., 2010)
0c
sgn
m
u
uu
u
, (8)
where
0
is the reference shear rate,
u
the resolved shear stress,
c
u
the slip resistance,
and m the rate sensitivity of slip.
The hardening law that describes the effect of any slip system v on the hardening
behavior of the slip system u is (Roters et al., 2010)
c
uv
uv
vh
with
c0
0
u
t
, (9)
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where
uv
h
is the hardening matrix,
0 the initial flow resistance. The hardening matrix
uv
h
is
further determined by (Roters et al., 2010)
0 c sa
1a
v
uv uv
h q h
, (10)
where h0, a, and
sa are slip hardening parameters.
The average Cauchy stress
i
of phase i is computed via the following volume
averaging method
1
i
ii
d
V
, (11)
where Vi is the volume of phase i,
i
the computational domain of phase i.
Fig. 2 The microstructures used in the CPFFT simulations. RVEs for (a) AsB, 3776 Al grains,
1512 Si particles, and 2927 Mg2Si particles; (b) HTS, 3783 Al grains, 1764 Si particles, and
3589 Mg2Si particles. Si particles are marked with black color and Mg2Si particles with white
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color. (c) and (d) show the macroscopic pole figures measured from the SXRD and used to
define the grain orientations.
Figs. 2(a) and (b) show the used three-dimensional RVEs. Periodic microstructures were
generated. Each RVE was discretized into 128×128×128 (=2,097,152) voxels to balance the
computational cost and accuracy. The volume fractions of Mg2Si and Si were defined by the
experimental values obtained from the Rietveld analysis. The measured phase contents will be
analyzed in section 3.2, showing that the contents of Mg2Si and Si are higher in HTS than in
AsB. The Al grains in the RVEs were approximated by equiaxed grains. The Al grain
orientations were generated using the measured bulk textures via the SXRD (Figs. 2(c) and
(d)). The maximum intensity values of the <001>//Z fiber texture determined from bulk
measurements are only about 2.2 and 2.1 multiples of a random density (MRD) in AsB and
HTS, respectively. These results indicate a weak bulk texture in both AsB and HTS. The color
bars in Figs. 2(c) and (d) are set from 0 to 1.6 to visualize the pole figures better. The
crystallographic orientations of the Mg2Si and Si particles were assumed to be random.
In this study, the crystal plasticity model was solved using the fast-Fourier-transform
based spectral solver implemented in the software DAMASK (Eisenlohr et al., 2013; Roters
et al., 2019; Shanthraj et al., 2015). Periodic boundary conditions were applied, with the
tensile loading direction along the Z direction of the RVEs. The 12 {111}<110> slip systems
for the face-centered cubic Al phase were considered. The Mg2Si and Si phases were modeled
with elastic constitutive laws. The used material parameters for the crystal plasticity
simulations are summarized in Table 1. The slip hardening parameters (h0, a, and
sa) and the
initial flow resistance
0 were fitted for AsB and HTS, so that the predicted macroscopic
stress-strain responses agree with the measured data. The fitted
0 and
sa values of HTS are
higher than those of AsB.
Table 1 Material parameters used in the crystal plasticity model.
Phase
Parameter
Value
Reference
Al
C11
108.2 GPa
(Zhang et al., 2021c)
C12
61.3 GPa
C44
28.5 GPa
0
0.001
(Li et al., 2020b; Rossiter et al., 2010; Saai
et al., 2016)
m
50
(Li et al., 2020b; Rossiter et al., 2010)
a
1.25
Fitted
h0
1000 MPa
Fitted
0
163 MPa for AsB
168 MPa for HTS
Fitted
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sa
244 MPa for AsB
252 MPa for HTS
Fitted
Mg2Si
C11
126.0 GPa
(Huang et al., 2012)
C12
26.0 GPa
C44
48.5 GPa
Si
C11
165.6 GPa
(Barhoumi et al., 2021; Gong et al., 2020)
C12
63.9 GPa
C44
79.5 GPa
3. Results
3.1 Macroscopic mechanical properties
Table 2 summarizes the macroscopic mechanical properties of the ex-situ and in-situ
specimens. According to the ex-situ tests, the average yield strength, tensile strength, and
elongation increase simultaneously from 406.2±3.5 MPa, 501.3±1.4 MPa, and 8.6±0.1%
(AsB) to 417.1±2.9 MPa, 505.3±4.0 MPa, and 11.0±0.4% (HTS), respectively. The relative
increase in total elongation is about 28%. The results indicate that the direct-aging treatment
is useful to improve both yield strength and ductility of the LPBF AlSi3.5Mg2.5 alloy.
Table 2. Mechanical properties of the AsB and HTS specimens.
Specimen
, s-1
y
, MPa
t
, MPa
EL, %
AsB, ex-situ
1.0
10-3
406.2±3.5
501.3±1.4
8.6±0.1
AsB, in-situ
1.5
10-4
407.0
505.6
8.6
HTS, ex-situ
1.0
10-3
417.1±2.8
505.3±3.5
11.0±0.4
HTS, in-situ
1.5
10-4
416.4
507.5
10.3
Here,
is the tensile strain rate,
y
the 0.2% offset yield strength,
t
the tensile strength,
and EL the maximum plastic strain measured from the strain-stress curve.
Fig. 3(a) shows the engineering strain-stress curves of AsB and HTS measured from the
in-situ tests. Fig. 3(b) summarizes the yield strength versus elongation results of different
LPBF Al alloys free of rare earth elements and wrought 2024Al alloys from the literature
(Aboulkhair et al., 2019; Croteau et al., 2018; Knoop et al., 2020; Lutz et al., 2020; Martin et
al., 2017; Nie et al., 2019; Ponnusamy et al., 2020; Zhang et al., 2016; Zhang et al., 2021b)
and our work. It can be seen that the yield strength of the other LPBF Al-Si-Mg alloys (such
as AlSi10Mg, AlSi12, and AlSi7Mg) is commonly lower than 280 MPa. Surprisingly, the
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yield strength of the present as-built AlSi3.5Mg2.5 alloy is dramatically higher than the other
AM Al-Si-Mg alloys and even higher than the LPBF Zr/7075Al-T6 alloy (Martin et al., 2017).
Meanwhile, the elongation of the present as-built AlSi3.5Mg2.5 alloy is higher than most of
the other AM Al-Si-Mg alloys. The mechanical properties of the present as-built
AlSi3.5Mg2.5 alloy are comparable to the wrought 2024Al alloy (including the T361, T4, and
T81 states) (Committee, 1990; Zhang et al., 2016). The direct-aging treatment further exploits
the potential of this novel AlSi3.5Mg2.5 alloy.
Fig. 3 Mechanical properties: (a) engineering stress-strain curves of AsB and HTS from the
in-situ tests, where the inserted figure shows a zoomed plastic region; (b) yield strength
versus elongation data of different LPBF Al alloys without rare earth elements from the
literature and this work. Typical mechanical properties of the wrought 2024Al alloys are also
shown in (b).
It is known that the Al-Si-Mg alloys are well suited for AM and dominate the market of
AM Al alloys due to their desirable castability, low shrinkage, and superior corrosion
resistance (Zhang et al., 2021c). However, the strength and ductility of current AM Al-Si-Mg
alloys are relatively low, limiting their applications. This novel AlSi3.5Mg2.5 alloy shows
excellent promise in structural applications in terms of superior mechanical properties.
Moreover, it contains no rare-earth elements. Hence, the novel AlSi3.5Mg2.5 alloy is less
resource-dependent, economical, and easy to recycle (Zhang et al., 2021b). It opens a new
window to develop high-performance and low-cost AM Al alloys.
3.2 Microstructures
Fig. 4(a) shows a typical OM image of the un-etched AsB specimen, where the pores
with different sizes are observed. Based on nine OM images of AsB, a porosity of 0.55±
0.17% is measured. Note that one pixel of the OM image represents 1.49 μm. Hence, the fine
pores with diameters smaller than this image resolution cannot be detected. Pore statistics are
shown in Fig. 4(b). About 82% of pores have diameters less than or equal to 9.0 μm, while the
maximum diameter of the observed pores is about 82 μm. The arithmetic and lognormal mean
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pore sizes are 7.0±8.0 and 5.5±0.5 μm, respectively. Almost all pores have a spherical shape.
Fig. 4 Porosity: (a) a typical OM image of AsB; (b) statistics of pores using nine OM images.
It is known that two types of porosity exist: metallurgical pores and keyhole pores
(Aboulkhair et al., 2014). Metallurgical pores are generated from trapped gases, so they are
also called hydrogen porosity. They typically have a spherical shape and small sizes (usually
below 100 μm) (Aboulkhair et al., 2014). In contrast, keyhole pores are created due to
keyhole instability (Gan et al., 2021). They usually have irregular shapes and large sizes
(commonly above 100 μm). Based on the spherical shape and small sizes, the observed pores
in the as-built AlSi3.5Mg2.5 alloy belong to metallurgical pores (Fig. 4(a)). Since porosity
promotes early fracture and reduces fatigue strength and life (du Plessis et al., 2020;
Muhammad et al., 2021; Sanaei and Fatemi, 2021; Tang and Pistorius, 2017; Voisin et al.,
2018), further optimization of LPBF process is necessary to enhance the density and
mechanical properties of the produced components in the future.
Fig. 5 shows the EBSD microstructures of AsB and HTS. In the vertical section of AsB,
the grain structure within melt pools is clear (Fig. 5(a)). The columnar grains in each melting
pool generally grow towards the center of the melt pool. Meanwhile, some grains at the
bottom of melt pool boundaries and the overlap regions between adjusting melt pools tend to
be equiaxial. These observations agree with previous results (Knoop et al., 2020; Rakesh et al.,
2019; Takata et al., 2018; Zhang et al., 2019). In the horizontal section of AsB, parallel melt
pools are visible (Fig. 5(b)). In the vicinities of the melt pool boundaries, many small
equiaxed grains (less than 3 μm) appear. These small grains have a mixture of blue-green-red
colors, indicating a random texture. In contrast, most of the grains in the center of melt pools
have sizes of 10-20 μm.
Figs. 5(c) and (d) show that the grain structures and textures of HTS are similar to those
of AsB. The lognormal mean grain sizes of AsB in the vertical and horizontal sections are
2.6±0.6 and 3.3±0.6 μm, respectively. The corresponding values of HTS are 3.0±0.5 and
2.9±0.4 μm, respectively. It can be seen that the aging treatment almost does not influence the
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grain size and structure. In our previous investigation (Knoop et al., 2020), the lognormal and
arithmetic mean grain sizes in the horizontal section of the as-built AlSi3.5Mg2.5 produced
with a different LPBF condition were 5.0±1.0 and 6.2±5.7 μm, respectively. Hence, the
present AsB and HTS specimens have finer microstructure than the previous investigation
(Knoop et al., 2020).
Fig. 5 EBSD microstructures of AlSi3.5Mg2.5: (a) vertical and (b) horizontal sections of AsB,
(c) vertical and (d) horizontal sections of HTS. The melt pool boundaries are marked with
white dotted curves.
Fig. 5 shows that in both AsB and HTS most of the grains have their <001> direction
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parallel to the building direction (i.e., the red grains), indicating a <001>//Z fiber texture that
remains after the direct-aging treatment (Thijs et al., 2013). The 100 pole figures confirm this
<001>//Z fiber texture. Such a texture forms because the primary growth direction <001> is
along the temperature gradient vector during the LPBF cooling process (Liu and To, 2017;
Tan et al., 2020). The 100 pole figure in Fig. 5 indicates that the maximum texture intensity
ranges from 4.24 to 9.37 MRD. However, the EBSD results are obtained from local
observations. So, we further measured the bulk textures of AsB and HTS before deformation
using the SXRD with a gauge volume of 0.7×0.7×4.0 mm3. The determined bulk textures
confirm a <001>//Z fiber texture in both AsB and HTS, as shown in Figs. 2(c) and (d).
In Fig. 5, the grain boundaries with misorientation angles larger than 10° are defined as
high angle grain boundaries (HAGBs, black line). In comparison, those less than or equal to
10° are defined as low angle grain boundaries (LAGBs, gray line). It can be seen that LAGBs
exist in both AsB and HTS. Hence, the direct-aging treatment cannot remove the LAGBs,
indicating the thermally stable grain structure at 170 ℃.
Based on the SXRD spectrums of AsB and HTS before deformation (Fig. 6), three
phases are identified clearly: Al, Si, and Mg2Si, which agree with our previous investigation
(Zhang et al., 2021b). The presence of Mg2Si has also been confirmed in the LPBF AlSi7Mg
alloy (as-built state) via a combination of X-ray diffraction and high-resolution TEM
techniques (Wang et al., 2019a). Here, the contents of the Mg2Si, Si, and Al phases in both
AsB and HTS were obtained via Rietveld analysis using the software MAUD (MAUD, 2019).
The results are summarized in Table 3. The determined volume fractions of Si and Mg2Si are
1.56% and 3.06%, respectively. The Si content in AsB is slightly lower than the previous
result (1.91%), while the Mg2Si content here is somewhat higher than the last result (2.87%)
(Zhang et al., 2021b). After direct-aging, the volume fractions of Si and Mg2Si in HTS
increase to 1.80% and 3.72%, respectively.
Fig. 7(a) shows that the microstructure of AsB is characterized by a cell boundary
network and some isolated precipitates inside cells, in agreement with our previous
investigations (Knoop et al., 2020; Lutz et al., 2020). The cells have diameters ranging from
about 0.5 to 1.5 μm. Such a heterogeneous microstructure is an intrinsic feature of the LPBF
Al-Si-Mg and Al-Si alloys, as reported in the literature (Chen et al., 2017; Kempen et al.,
2012; Thijs et al., 2013). Besides, Fig. 7(a) shows that the LAGBs run along the cell
boundaries, in agreement with previous investigations (Li et al., 2020c; Voisin et al., 2021). In
contrast, Fig. 7(b) shows that the cell boundary network is hardly visible, resulting from cell
boundary migration associated with element diffusion upon the direct-aging treatment. The
isolated precipitates embedded in the Al matrix dominate the microstructure of HTS. Fig. 7(b)
also confirms the presence of LAGBs after the direct-aging treatment. The STEM-ADF and
EDX maps of AsB in Fig. 7(c) show the morphology of the Si, Mg2Si, and Mn-rich phases
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(Lutz et al., 2020), which are distributed along the cell boundaries. Fig. 7(d) confirms that the
isolated particles characterize the microstructure of HTS.
Fig. 6 SXRD spectrums of (a) AsB and (b) HTS before deformation, where the Mg2Si, Si, and
Al peaks are marked. The fitting residual is shown at the bottom of each plot. The empty
black rhombuses denote the measured data, and the red line shows the Rietveld fitted pattern
using the software MAUD.
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Fig. 7 STEM microstructures of (a) AsB and (b) HTS, with the transmission direction
perpendicular to the LPBF platform plane. The blue dashed lines in (a) and (b) indicate the
LAGBs. STEM-ADF microstructures parallel to the Z plane and EDX maps of Al, Si, Mg,
Mn, and Zr elements for (c) AsB and (d) HTS. Note that the STEM-ADF image, Si and Mg
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element maps in (c) were cited from (Lutz et al., 2020).
Table 3. Phase contents obtained from Rietveld analysis.
Specimen
Determined weight fraction, wt.%
Converted volume fraction, vol.%
Mg2Si
Si
Al
Mg2Si
Si
Al
AsB
2.26±0.09
1.33±0.08
96.42±0.00
3.06
1.56
95.37
HTS
2.74±0.10
1.53±0.10
95.73±0.00
3.72
1.80
94.48
3.3 Evolutions of lattice strains
Fig. 8 shows the lattice strains in the Al, Mg2Si, and Si phases. The maximum
measurement uncertainties
(definition can be found in the literature (Zhang et al., 2021c))
of the lattice strains during the entire loading are shown. The evolutions of the lattice strains
include four regions. The microscale elastic stage and the elastoplastic transition (EPT) stage
can be defined as regions 1 and 2. Figs. 8(a) and (b) show that the yielding sequence of the
selected Al grain families is {420} {311} {200} {111}. At the end of region 2, the
differences between the Al {111} and {420} lattice strains in the LD are large, revealing
obvious load-redistribution among different Al grain families. Meanwhile, the Mg2Si and Si
lattice strains start to increase rapidly in region 2 due to an increased inter-phase load transfer
effect (Figs. 8(c)-(f)). In region 3, the Al matrix experiences sufficient plastic slips. The
increments of Mg2Si and Si lattice strains in the LD are still quite fast (Figs. 8(c)-(f)).
A prominent damage stage is detected and defined as region 4 in Fig. 8. This damage
stage was not observed in previous investigations (Zhang et al., 2021a; Zhang et al., 2021b;
Zhang et al., 2021c). It happens when the average stress in the hard and brittle particles
reaches a critical value; particle damage occurs by either particle fracture or particle/matrix
interface decohesion. This reduces the load-bearing capacity of the particles, so the
magnitudes of lattice strains decrease. As shown in Figs. 8(c)-(d), region 4 starts from the
applied true stress of 522 MPa in AsB and 531 MPa in HTS according to the drops of Mg2Si
lattice strains in the LD. In contrast, the Si {311} LD lattice strain increases slowly in region 4,
while a slight reduction in the magnitude of Si {311} TD lattice strain is visible (Figs.
8(e)-(f)). The magnitude of Si TD lattice strain decreases from the applied true stress of 538
MPa in AsB and 546 MPa in HTS. These results suggest that the onset of Si damage should
be later than that of Mg2Si damage.
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Fig. 8 Evolutions of lattice strains with applied true stress for: Al in (a) AsB and (b) HTS,
Mg2Si in (c) AsB and (d) HTS, Si in (e) AsB and (f) HTS. The maximum uncertainties
of
lattice strains are shown.
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3.4 Phase stresses and particle damage
Figs. 9(a)-(b) show the evolutions of average phase stresses in the LD of Al, Mg2Si, and
Si. Both measured and predicted results are plotted. In the macroscale elastic stage, all phase
stresses increase linearly with applied true stress. In the macroscale plastic stage, the Mg2Si
and Si phase stresses increase quickly. Generally, the predictions agree with measurements for
the Al and Si phases. In contrast, the measured average phase stresses of Mg2Si in both AsB
and HTS reach the same maximum value of 1990 MPa. Afterward, the measured Mg2Si phase
stresses decrease in both AsB and HTS. However, the predicted Mg2Si phase stresses increase
continuously. The prediction reveals that if no damage occurs in the Mg2Si phase, the average
phase stress of Mg2Si will grow continuously. This discrepancy in the average phase stress of
Mg2Si between the prediction and measurement confirms that the stress drop of Mg2Si is a
clear indicator of the damaging effect. The measured maximum Si stresses in AsB and HTS
are 2388 and 2318 MPa, respectively.
Fig. 9 Evolutions of measured and predicted phase stresses in (a) AsB and (b) HTS.
3.5 Dislocation density during plastic deformation
Fig. 10 shows the evolutions of dislocation densities in AsB and HTS. Only the
dislocation densities during the uniform deformation are investigated because the SXRD
gauge volume may not be the activated plastic deformation region after necking due to local
plastic deformation. The dislocation density increases fast in AsB during the early plastic
deformation; afterward, it grows slowly. The dislocation density in HTS is close to that in
AsB when the applied strains are smaller than ~2.5%. Then, the dislocation density in HTS
becomes higher, and the gap between HTS and AsB increases as the deformation proceeds.
These results reveal that the dislocation storage capacity is much higher in HTS than in AsB,
which is offered by the direct-aging treatment.
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Fig. 10 Evolution of dislocation density with macro plastic strain.
4. Discussions
4.1 Microstructure and residual stress
Figs. 2(c)-(d), and 4-7 reveal the microstructures responsible for the excellent
mechanical properties of the as-built and direct-aged AlSi3.5Mg2.5 samples. The porosity in
AsB was low. Only metallurgical pores were detected, while no keyhole pores were observed,
suggesting that the employed LPBF process parameters are reasonable (Aboulkhair et al.,
2019; Khairallah et al., 2016). The direct-aging treatment should only have a weak effect on
the porosity considering the low aging temperature of 170 ℃ and the short soaking time of
one hour. For reducing the porosity in the AM materials via post-heat treatment, a hot isostatic
pressing (HIP) treatment may be applied (Lewandowski and Seifi, 2016; Tradowsky et al.,
2016). However, a HIP treatment can reduce the strength significantly compared with the
as-built state (Tradowsky et al., 2016). Besides, a HIP process could cause grain coarsening
when the grain size distribution is inhomogeneous at the as-built state (Spierings et al., 2018).
Therefore, more attention should be paid to the LPBF process optimization to reduce the
porosity and enhance the mechanical properties (Aboulkhair et al., 2019).
Fig. 5 reveals that the LAGBs are thermally stable at the aging temperature of 170 ℃.
Besides, Figs. 2(c)-(d) and Fig. 5 demonstrate that the texture also stays stable in HTS.
Therefore, the grain size, grain structure, and grain orientation are almost not influenced by
the direct-aging treatment. The good thermal stability of LAGBs in the LPBF alloys has been
reported in the literature. (Voisin et al., 2021) investigated the microstructure and mechanical
properties of the LPBF 316L austenitic stainless steel samples with and without annealing
treatments. They found that the LAGBs remain stable up to 1000 ℃ (Voisin et al., 2021). The
LAGBs are beneficial to strengthening due to the dislocation-LAGB interactions. These
LAGBs are also related to ductility. In the as-built AlSi3.5Mg2.5 alloy, the LAGBs coincide
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with the cell boundaries, where the Si and Mg2Si phases appear and act as barriers to the
dislocation motions. Therefore, most moving dislocations are trapped within cells. The
dislocations are only allowed to pass through those cell boundaries or LAGBs where large
inter-particle distances exist (Chen et al., 2017). In contrast, after the direct-aging treatment,
the cell boundary network migrates and forms isolated particles. Therefore, dislocation slip
across the LAGBs becomes evident (Bieler et al., 2019), which is beneficial to ductility.
Figs. 7(a) and (c) show that the cellular-dendritic alpha-Al, inter-dendritic Si, Mg2Si and
Mn-rich particles characterize the microstructure of the as-built AlSi3.5Mg2.5 alloy. The
formation of Mg2Si particles should be associated with the intrinsic heat treatment during the
LPBF process (Bayoumy et al., 2021; Kurnsteiner et al., 2020; Luo and Zhao, 2019). During
this intrinsic heat treatment, the cell boundaries and grain boundaries may act as the
diffusional pathway through which the Mg2Si particles form and grow. Similarly, the Mn-rich
particles prefer to develop along the cell and grain boundaries (Bayoumy et al., 2021). Note
that the intrinsic heat treatment includes many thermal cycles with different peak
temperatures, and the peak temperatures of some thermal cycles can reach high values near
the melting point (Bayoumy et al., 2021; Kurnsteiner et al., 2020; Luo and Zhao, 2019).
Therefore, the intrinsic heat treatment dynamics during the LPBF process differ from that of
traditional aging treatment at a constant and elevated temperature significantly.
Although the direct-aging treatment virtually does not affect the porosity, grain size,
grain structure, and texture, it has three effects on the microstructure and residual stress
evolutions. Firstly, although the Si and Mg2Si particles form upon the LPBF process, some Si
and Mg atoms remain in the alpha-Al matrix forming a supersaturated solid solution in the
as-built AlSi3.5Mg2.5 alloy because of the rapid cooling rate. During direct-aging treatment,
additional Si and Mg2Si precipitate out, as shown in Table 3. (Pereira et al., 2020) also
revealed that new Mg2Si particles precipitate out in the LPBF AlSi7Mg0.6 alloy after a
direct-aging treatment at 160 oC for six hours.
Secondly, the original thin cell boundaries (commonly less than 100 nm, Fig. 7(a))
migrate due to element diffusion upon the direct-aging treatment (Fig. 7(b)). Such a cell
boundary migration has also been reported in the literature (Kimura and Nakamoto, 2016; Li
et al., 2020c; Pereira et al., 2020). For instance, (Kimura and Nakamoto, 2016) investigated
the effect of heat treatment on the microstructure and mechanical properties of the LPBF
A356 (AlSi7Mg0.3) alloy. They found that after annealing at 150 to 250 ℃ for five hours, the
cell boundaries migrate through Si diffusion and become thinner. Accordingly, the constraint
effect of cell boundaries on dislocation motions is weaker after annealing, leading to
increased ductility (Kimura and Nakamoto, 2016).
Thirdly, the direct-aging treatment also relieves residual stress. Residual stress generates
upon the LPBF process due to two main reasons (Chen et al., 2019; Liang et al., 2021). On
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the one hand, a steep temperature gradient exists around the melt pool during the LPBF
process. On the other hand, the deformation of the LPBF Al-Si-Mg alloys is inhomogeneous
at the microscale due to its microstructure heterogeneity. The residual stress created during
the LPBF process can be relieved through post-heat treatments. The residual stress-relaxation
effect can be inferred by comparing the lattice parameters of each phase between the as-built
and direct-aged AlSi3.5Mg2.5 samples. Based on the Rietveld analysis, the determined lattice
parameters of Al, Si, and Mg2Si in AsB are 4.0491, 5.4255, and 6.3280 Å, respectively. In
contrast, these values in HTS are 4.0486, 5.4334, and 6.3324, respectively, and the standard
lattice parameters of pure Al, Si, and Mg2Si are 4.0478, 5.4309, and 6.3380 Å, respectively. It
can be seen that after direct-aging treatment, the lattice parameters of all phases are closer to
the standard values, revealing a residual stress-relief effect.
The effect of heat treatment on residual stress in AM alloys has also been reported in the
references (Li et al., 2015; Rao et al., 2017; Wang et al., 2019a). (Wang et al., 2019a) showed
that the Raman peak position of Si in the LPBF AlSi7Mg alloy moves closer to its standard
position after annealing treatment due to residual stress relief. It should be mentioned that
residual stress relief is beneficial to ductility. Otherwise, superposition of loading stress and
local residual stress could cause stress concentration and promote early fracture.
The dislocation annihilation phenomenon should occur if the heat treatment temperature
is very high and the soaking time is very long. Here, such a dislocation annihilation
phenomenon was not detected. Fig. 11 shows that the dislocation densities in AsB and HTS at
the beginning of plastic deformation are almost identical. Besides, we can compare the raw
full width at half maximum (FWHM) values of the SXRD spectrums between AsB and HTS
before deformation. The measured FWHM values of Al {311} and {220} in AsB are 0.0390°
and 0.0363°, respectively. In contrast, these two values in HTS are 0.0396° and 0.0364°,
respectively. The Al {311} and {220} FWHM variations between AsB and HTS are only
1.5% and 0.2%, respectively, confirming almost the same dislocation density in AsB and HTS
before deformation. This phenomenon should be associated with the relatively low aging
temperature and the short soaking time.
4.2 Origin of the yield strength: strengthening mechanisms
So far, the detailed strengthening mechanisms of the novel LPBF AlSi3.5Mg2.5 alloy
remain poorly understood. Here, we systematically assessed the detailed strengthening
mechanisms and connected the mechanical properties to the microstructure features via
classic analytical models. The grain sizes of the LPBF alloys are fine, leading to the
Hall-Petch strengthening
HP
. It can be calculated by
HP Al
kD
, (12)
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where k is a constant with a value of about 50
MPa μm
(Li et al., 2017).
Al
D
is the grain
size, which was determined from the EBSD images in section 3.2.
The dislocations in the alloys lead to dislocation strengthening
dislocation
, which can be
estimated by the Taylor equation (Kocks and Mecking, 2003; Zhao et al., 2021)
dislocation M Gb
, (13)
where M is the average Taylor factor (= 3.06 for the face-centered cubic metals),
the
strengthening coefficient, G the shear modulus (= 26.38 GPa for the Al phase), and b Burgers
vector (= 0.286 nm for the Al phase). The dislocation densities are shown in Fig. 11. At the
yield stresses of the alloys, the dislocation densities are about 6.08
1014 and 5.68
1014 m-2 in
AsB and HTS, respectively. The
value will be discussed in section 4.3.
The fast cooling rate upon the LPBF process causes supersaturated solid solution,
leading to solid solution strengthening. The increment in yield strength due to the solid
solution strengthening
solution
j
(j = Mg or Si) can be estimated by (Huskins et al., 2010)
solution j
n
jjj
HC
, (14)
where Hj and nj are constants for element j, Cj is the solute concentration (at.%) of element j.
For the Mg element, HMg = 12.1
Mg
MPa at.% n
, and nMg = 1.14 (Huskins et al., 2010). For
the Si element, HSi = 12.8
Si
MPa at.% n
, and nSi = 0.50 (Uesugi and Higashi, 2010). The
solute concentration Ci can be calculated by subtracting the element content of the Mg2Si or
Si phase from the nominal content of element j in the alloy, provided that all left Mg and Si
atoms dissolve in the Al matrix. The Mg2Si and Si phase contents are summarized in Table 3.
Due to the precipitate-dislocation interactions, the Mg2Si and Si precipitates introduce
Orowan strengthening
Orowan
w
(w = Mg2Si or Si), which can be estimated by (Chen et al.,
2015; Li et al., 2017)
Orow
13
an 6
2
ww
w
f
Gb
d
, (15)
where dw and fw are the average size and volume fraction of the precipitate w, respectively.
The average sizes of the Mg2Si and Si particles were obtained from the Rietveld analysis. The
determined
2
Mg Si
d
and
Si
d
of AsB are 55.1 and 94.7 nm, respectively.
2
Mg Si
d
and
Si
d
of
HTS are 55.4 and 96.2 nm, respectively. These values have the same magnitude as the
previous results. (Li et al., 2017) showed that the average Si size in the LPBF AlSi10Mg is
about 70 nm. (Li et al., 2020a) reported that the average Mg2Si size is about 15.7 nm in the
LPBF Al-Mg-Si-Sc-Zr alloy. (Hadadzadeh et al., 2018a) showed that the average Si sizes in
the vertical and horizontal samples of the LPBF AlSi10Mg are about 25 and 62 nm,
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respectively.
The calculated contributions to the yield strength for AsB and HTS are listed in Table 4.
Compared with AsB, the increased yield strength of HTS is mainly caused by its higher
contents of Mg2Si and Si, introducing a more substantial Orowan effect. This is accompanied
by a reduction in the solid solution strengthening effect due to a lower solution concentration
in the Al matrixes after the aging treatment. The dislocation strengthening also plays an
important role. The dislocation strengthening effect is more substantial in HTS than in AsB
because of a higher
value in HTS. It will be discussed in detail in the following section.
Besides, according to section 3.4, the Mg2Si and Si phases also introduce load-bearing
strengthening (Chen et al., 2015; Li et al., 2017). In order to estimate the load-bearing
strengthening effect, the shear-lag model could be used, indicating that the increased strength
depends on the volume fraction and the aspect ratio of the particles, and the yield strength of
the matrix. However, the experimental values of the average aspect ratio are not known for
Mg2Si and Si. Here, the load-bearing strengthening effect is assessed qualitatively. According
to Fig. 9, the average phase stresses of Mg2Si and Si at the yield strength of AsB are 653.2
and 760.8 MPa, respectively. In HTS, these two values increase to 764.0 and 920.0 MPa,
respectively. Considering the higher volume fractions of Mg2Si and Si in HTS than in AsB,
the Mg2Si and Si phases should introduce a slightly stronger load-bearing strengthening effect
in HTS than in AsB, contributing to a higher yield strength of HTS.
Furthermore, other strengthening mechanisms may exist in the AM Al-Si-Mg alloys.
(Geng et al., 2021) observed the Mg-Si atomic clusters in the Al matrix of the LPBF
AlSi8.2Mg1.4 alloy. These Mg-Si atomic clusters are precursors of the Mg2Si phase. In the
present case, the Mg-Si atomic clusters or even other metastable phases may appear. However,
extracting their morphology (sizes and shapes), volume fractions, and properties is not easy.
Therefore, it is challenging to calculate the strength contributions of the metastable phases,
which probably demands a separate investigation in the future.
Table 4. Strengthening contributions to the yield strength of AsB and HTS.
Contribution
AsB, MPa
HTS, MPa
Variation, MPa
HP
28.9
28.9
0.0
dislocation
18.7
26.0
+7.3
solut
Mg ion
14.7
10.0
-4.7
solut
Si ion
14.5
12.3
-2.2
2
Orowa
in
Mg S
106.2
112.8
+6.6
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Orow
Si an
49.4
51.0
+1.6
4.3 Scaling law of strain hardening mechanism
During plastic deformation, the Taylor model correlates the mechanical stress
ms
with
the total dislocation density
by (Kocks and Mecking, 2003)
ms 0 M Gb
, (16)
where
0
is the internal friction stress. Then, the strengthening coefficient
can be
determined from the
ms
versus
curve by
ms
1
MGb
. (17)
Because the Al matrix is responsible for the plastic deformation through dislocation motions,
the mechanical stress
ms
equals the Al phase stress, i.e.,
Al
ms L
.
Fig. 11 Dislocation mechanisms: evolution of Al phase stress with
in (a) AsB and (b)
HTS; relationship between measured
and separated Al plastic strain using crystal
plasticity simulations for (c) AsB and (d) HTS.
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Figs. 11(a) and (b) show the Al stress versus
relations for AsB and HTS. Fig. 11(a)
shows that the Al stress versus
curve is a piecewise linear function, including stages A
and C. This phenomenon reveals a multistage strain hardening behavior, and each stage has its
value. This phenomenon has been detected and analyzed in our previous investigations
(Zhang et al., 2021a; Zhang et al., 2021c). In contrast, Fig. 11(b) shows that the Al stress in
HTS increases linearly and monotonously with
. Based on the linear regressions in Fig.
11(a), the measured
values of AsB in the microscale EPT stage and stage II are 0.033 and
0.18, respectively. The determined
value of HTS is 0.047.
4.4 Origin of the improved ductility: dislocation behavior
Since the direct-aging treatment changes the microstructure, residual stress, and
mechanical properties of the AlSi3.5Mg2.5 alloy, one question arises: how does the
dislocation behavior change after the direct-aging treatment? This knowledge is crucial for
understanding the ductility of the alloys and developing refined crystal-plasticity models in
the future (Ghorbanpour et al., 2020; Ghorbanpour et al., 2017; Pokharel et al., 2019). Here,
the Kocks-Mecking (K-M) model describing the evolution of total dislocation density
is
used to assess the dislocation behavior. The K-M model reads (Estrin and Mecking, 1984)
12
p
dkk
d
. (18)
It reveals that both dislocation generation and annihilation are active during the entire
deformation process. The term
1
k
accounts for the dislocation generation during plastic
deformation, which dominates at low strains and is linked with the athermal hardening. The
term
2
k
is associated with dislocation annihilation due to dynamic recovery, which is
thermally activated. The term
2
k
increases gradually as the plastic deformation proceeds,
leading to a reduction in the strain hardening effect. The K-M model is a single-variable
model, where the total dislocation density
is the only governing parameter.
Unfortunately, it is not convenient to apply Eq. (18) in practice directly because of the
derivative
p
dd
. In reality, local oscillations in the measured
values always exhibit
due to experimental errors, as shown in Fig. 10. Then one often gets negative
p
dd
values, although the general tendency of
increases with plastic strain
p
. To overcome
this practical issue, one needs to smoothen the
versus
p
curve to avoid the negative
p
dd
problem. Such a smoothening process introduces artificial error. This problem can
be solved without an artificial smoothening process by introducing the integral K-M model.
In Eq. (18), k1 and k2 can be assumed as a constant for a certain microstructure, e.g., if
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the dislocation arrangement does not change a lot (He et al., 2018; Liang et al., 2015). If both
k1 and k2 are constants, then Eq. (18) can be integrated into
p 0 1 2
2
2lnk k k
k
, (19)
where
0
k
is a material parameter depending on k1, k2, and the dislocation density
0
prior
to plastic deformation, which reads
0 1 2 0
2
2lnk k k
k
. (20)
Eq. (19) reveals an explicit relation between the plastic strain
p
and
.
Note that the differential form of the K-M model (Eq. (18)) is suitable for general cases
where k1 and k2 may not be constants (Kocks and Mecking, 2003). However, the integral form
of the K-M model (Eq. (19)) is only appropriate for limited cases where k1 and k2 are
constants. For instance, Eq. (18) is adequate for creep tests at constant stress (where the strain
rate varies) and uniaxial tension/compression tests at constant strain rate and temperature
(Estrin and Mecking, 1984; He et al., 2018; Liang et al., 2015). In contrast, Eq. (19) only
works for the latter case. The significant advantage of Eq. (19) over Eq. (18) is that no
derivative is required; therefore, the negative
p
dd
problem is solved.
It is worth noting that the plastic strain
p
of the Al phase for Eq. (19) is determined
from the crystal plasticity modeling results. Figs. 9(a)-(b) show that the Al phase stress is well
captured by the crystal plasticity model for both AsB and HTS. Hence, using the predicted
stress-strain response of the Al phase from the crystal plasticity simulations, the plastic strain
p
of the Al phase can be determined. This is a major difference between the present K-M
modeling and our previous K-M modeling, where the plastic strain of Al was assumed to
equal the macro plastic strain approximately, i.e., an iso-strain assumption (Zhang et al.,
2021b). This iso-strain assumption works well for the metal matrix if the following two
conditions are satisfied. Firstly, the contents of the second-phase particles are small, e.g.,
smaller than 20%. This is also true in the present case. Secondly, the macroscopic strain is
accurately measured. In our previous experiment, the macroscopic strains of each specimen
during in-situ loading were determined using the average values of two strain gauge
measurements (Zhang et al., 2021b). The measured Young’s modulus of the LPBF Al-Si-Mg
specimens ranges from 67.0 to 74.1 GPa, indicating reasonable macroscopic strain
measurements (Zhang et al., 2021b). However, in this investigation, the measured Young’s
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modulus of AsB and HTS was 47.4 and 47.1 GPa, respectively. These results imply that the
measured macroscopic strains of AsB and HTS upon in-situ loading include measurement
errors on the level of 0.003 (i.e., 0.3%, absolute strain error value). In this case, the
macroscopic plastic strains cannot be determined accurately, especially in the early plastic
stage. Therefore, the crystal plasticity simulations have to be used here to determine the
plastic strain
p
of the Al phase.
Figs. 11(c)-(d) show the relationship between
and the Al plastic strain, which can
be well captured by the integral K-M model. In particular, AsB is described by a piecewise
K-M model with two sets of (k0, k1, k2). In stage A of AsB, k1=7.93
109 m-1 and k2=111.83. In
stage C of AsB, k1=1.06
109 m-1 and k2=10.00. Both the dislocation generation and
annihilation rates decrease dramatically in stage C of AsB. As a result, the increasing rate of
dislocation density decreases notably in stage C of AsB, as shown in Fig. 11(c). In contrast,
the dislocation behavior in HTS can be well predicted by a monotonous K-M model with
k1=6.80
109 m-1 and k2=77.37.
The above results indicate that HTS exhibits simultaneously higher dislocation
generation and annihilation rates than those in stage C of AsB, which should be associated
with their different microstructures. In AsB, dislocation pile-ups near the cell boundaries
generate back-stress fields, impeding dislocation motions and generations. After aging
treatment, the cell boundaries migrate in HTS (Fig. 7), weakening the dislocation pile-ups
near the cell boundaries (Kimura and Nakamoto, 2016). Dislocations could move more
straightforward within the Al matrix of HTS. Consequently, dislocation-dislocation and
dislocation-precipitate interactions promote further generations of dislocations. Meanwhile, as
the plastic deformation proceeds, cross-slip may also be more accessible in HTS since the cell
boundaries migrate, promoting the dislocation annihilation in HTS.
Identifying the K-M model is beneficial to understand the underlying dislocation
mechanisms governing the alloys’ plastic deformation and is fundamental for developing
advanced full-field crystal plasticity models (Ghorbanpour et al., 2020; Ghorbanpour et al.,
2017; Pokharel et al., 2019). For instance, by employing the K-M model, (Ghorbanpour et al.,
2020) developed a dislocation density-based crystal plasticity model to interpret the
temperature-dependent deformation behavior of the AM Inconel 718 alloy.
Overall, the direct-aging treatment leads to the migration of cell boundaries, further
precipitation of strengthening particles, relaxation of residual stress in HTS, and in turn
variation of the dislocation behavior. HTS is characterized by higher dislocation generation
and annihilation rates than AsB. Meanwhile, HTS allows a much higher net accumulation of
dislocation density than AsB in the later plastic deformation, indicating a superior dislocation
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storage capacity in HTS. These aspects are essential mechanisms leading to higher ductility in
HTS than in AsB (He et al., 2017; Huang and He, 2018).
4.5 Damage and fracture mechanisms
In multiphase materials, the rigid particles carry high stresses when the materials are
subjected to loading. Their higher elastic constants partially cause the high stresses in the stiff
particles. Besides, the strain mismatch during the plastic stage further increases the stresses in
the rigid particles. In this case, dislocations accumulation in the vicinities of particle/matrix
interfaces during plastic deformation is often observed (Hadadzadeh et al., 2018b). The high
stresses in the rigid particles play a vital role in the damage mechanism. If the stresses in the
particles exceed their strength, particle fracture occurs.
So far, several investigations on the fracture strengths of Mg2Si and Si have been
conducted. A first-principles calculation indicated that the theoretical tensile strength of
Mg2Si is 5.63 GPa (Fan et al., 2013). The fracture strength of nano-sized Si polycrystals
ranges from about 5 to 8 GPa, whereas micro-sized Si polycrystals range from about 0.5 to 5
GPa (DelRio et al., 2015). (Mueller et al., 2016) reported that the Si particles containing
defects fracture at surface stresses range from 1.1 to 4.7 GPa in a eutectic Al-12.6%Si alloy.
Later, (Mueller et al., 2018) indicated that the Si particles containing defects fracture at
surface stresses ranging from 2 to 6 GPa in an A356 alloy. If the rigid particles have high
strengths, interface decohesion appears instead of particle fracture. No matter it is particle
fracture or interface decohesion, the carried load in the particles decreases.
Fig. 12 shows the von Mises stress fields of Si and Mg2Si at the applied strain of 6.4%,
revealing highly inhomogeneous stress distributions at the microscale. The predicted
maximum von Mises stress of Si is 9.27 and 10.81 GPa, respectively, in AsB and HTS at the
applied strain of 6.4%. The corresponding values of Mg2Si are 9.20 and 9.58 GPa. In reality,
such high local stresses in Si and Mg2Si are probably not allowed due to the damaging effect.
Fig. 13 shows the von Mises equivalent strain fields of the Al matrix in both AsB and
HTS. The strain distribution at the grain scale is highly heterogeneous. The Si and Mg2Si
particles cause strain concentrations in the Al matrix, leading to the local deformation bands
near the particle tips. In reality, when the Si or Mg2Si particles are fractured or the interfaces
are damaged, the micro-cracks serve as additional stress concentrators, resulting in further
local deformation. As the plastic deformation proceeds, damage initiates in the local deformed
zones and propagate along with the local deformation bands until the final fracture.
It is known that the AM Al alloys prefer to fracture along the melt pool boundary.
Therefore, the scan tracks can be observed on the fracture surfaces (Aboulkhair et al., 2016;
Delahaye et al., 2019; Zhang et al., 2019). More precisely, (Delahaye et al., 2019) have
revealed that the heat-affected zone in the melt pool boundary is the preferential region where
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the fracture is likely to occur for the AM AlSi10Mg alloy. Figs. 14(a)-(b) show that scan
tracks are visible on the fracture surfaces, confirming that both AsB and HTS fracture along
the melt pool boundaries. At high magnification, dimples with particles dominate the fracture
surfaces of both AsB and HTS (Figs. 14(c)-(d)). Therefore, the fracture of both AsB and HTS
is a ductile fracture, including void nucleation near the particle/matrix interface, growth, and
coalescence (Aboulkhair et al., 2016; Delahaye et al., 2019; Zhang et al., 2019).
Here, which mechanism (particle fracture or interface decohesion) dominates the damage
initiation remains an open question. For materials reinforced with micron-sized particles, the
damage mechanism can be directly examined via SEM or computed tomography techniques,
as shown in the literature (Schöbel et al., 2019). However, it is challenging to characterize the
dominant damage mechanism of the Si and Mg2Si particles in this investigation. On the one
hand, the Si and Mg2Si particles are nano-sized. It is not easy to observe whether the
nano-sized particles are fractured or not using SEM. On the other hand, the volume fractions
of Si and Mg2Si are relatively low. Only a few particles can be seen in one SEM or TEM
viewing field under a high magnification mode.
Fig. 12 The von Mises stress fields in (a) Si of AsB, (b) Si of HTS, (c) Mg2Si of AsB, and (d)
Mg2Si of HTS at the applied strain of 6.4%. The tensile loading direction is along the Z axis.
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Fig. 13 The von Mises equivalent strain fields of the Al matrix in (a) AsB and (b) HTS at the
applied strain of 6.4%. All particles are black colored. The tensile loading direction is along
the Z axis.
Fig. 14 Fracture morphology of AlSi3.5Mg2.5: (a) AsB and (b) HTS at low magnification, (c)
AsB and (d) HTS at high magnification. White arrows mark some particles within dimples.
In the literature (Delahaye et al., 2019), the Si volume fraction is much higher, and the Si
particle size is larger than in the present case. The authors speculated that the Al-Si interface
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decohesion might cause microscale damage. Nevertheless, direct and clear observation of the
damage initiation location was lacking. (Wang et al., 2019a) investigated the cross-section of
the fractured LPBF AlSi7Mg specimen. They found that the fine Si network coalesced much
more quickly, leading to reduced elongation for the as-built AlSi7Mg alloy. However, the
fracture surface was etched. It is difficult to ascertain the damage initiation location at the
microscale. In the future, a further experimental investigation is deserved to extract the
dominant mechanism of damage initiation in AM Al-Si-Mg alloys.
4.6 Remarks on the present combined experiment and simulation investigation
Our previous investigations have employed the in-situ SXRD and neutron diffraction to
explore the dislocation annihilation phenomenon (Zhang et al., 2021a), the anisotropic lattice
strains, the evolutionary phase stresses, and the unusual dislocation behavior in the as-built
AM Al-Si-Mg alloys (Zhang et al., 2021b; Zhang et al., 2021c). However, the
micro-mechanisms that govern and improve the strength and ductility of the AM Al-Si-Mg
alloys simultaneously after the direct-aging treatment remain poorly understood and deserve
in-depth exploration.
Here, we demonstrate that the strengthening mechanisms can be revealed systematically
through in-situ SXRD. The type, content, and average particle size of each second phase can
be determined through Rietveld analysis. These data (phase content and size, phase stresses,
and dislocation density) are statistical from the large diffraction gauge volume (0.7×0.7×4.0
mm3 in this study), representing the bulk properties of the target alloy. Based on the measured
results using the in-situ SXRD, various strengthening mechanisms were ascertained, including
dislocation strengthening, solid solution strengthening, and Orowan strengthening. Together
with the EBSD observations, the Hall-Petch strengthening was also investigated. Based on
these results, we found that the strengthening particles with higher volume fractions cause
improved strength after the direct-aging treatment.
Although some other investigations also discussed the strengthening mechanisms in AM
Al alloys, previous results had some common limitations. Firstly, previous studies usually
assumed that the Taylor strengthening coefficient is about 0.2-0.3 for calculating the
dislocation strengthening. However, our in-situ measurements revealed that the Taylor
strengthening coefficient
of the Al phase varies from case to case, and its value can be far
away from 0.2-0.3, e.g., 0.033 and 0.047 in the present case. Secondly, researchers commonly
use TEM techniques to measure the contents and particle sizes of the second phase. Then, the
precipitate strengthening was analyzed based on the TEM observations. However, the TEM
observations only reflect local results. Some deviations exist when these results are used to
represent the bulk properties, depending on how many TEM images are considered.
Furthermore, as discussed in our previous investigation, if the iso-strain assumption is
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not suited, it is better to use a full-field computational model for separating the phase-specific
stress-strain responses (Zhang et al., 2021b). The latter case is what we conducted in this
study, where a combination of in-situ SXRD and crystal plasticity simulation was performed.
As shown in Fig. 10, the dislocation density and its evolution in both AsB and HTS are very
close in the early plastic stage. Hence, we expect that the k1 and k2 coefficients of the K-M
model should be close for stage A of AsB and HTS. This is true, as shown in Figs. 11(c)-(d).
Then, based on the K-M model analysis, we found that the increased ductility after the
direct-aging treatment is associated with the change in dislocation behavior.
However, suppose we use the iso-strain assumption to identify the K-M model
coefficients. Then, we have k1=5.49
109 m-1 and k2=45.28 for stage A of AsB. k1=1.18
109
m-1 and k2=10.50 for stage C of AsB. k1=7.20
109 m-1 and k2=88.04 for HTS. These
determined k1 and k2 coefficients of the K-M model for stage A of AsB are far away from
those of HTS. This is because that the plastic strain of Al was not accurately measured upon
the early plastic stage in the present case. We also found that the identified k1 and k2
coefficients of the K-M model are less affected for stage C of AsB and HTS if the iso-strain
assumption is used. This is as expected since the inaccurate measurements of total strain at the
macroscale mainly affect the plastic strain values in the early plastic stage, where the plastic
strain magnitude is very close to the elastic strain magnitude. The above issues are solved
using a combination of experiment and crystal plasticity simulation.
5. Conclusions
(1) The Mg2Si and Si phases precipitate out in the as-built AlSi3.5Mg2.5 alloy due to the
intrinsic heat treatment upon the LPBF process. However, some Mg and Si atoms still
dissolve into the Al matrix forming a supersaturated solid solution. After the direct-aging
treatment, more Mg2Si and Si precipitate out. Accordingly, the strength of the alloy increases
after the aging treatment due to the increased Orowan strengthening, dislocation strengthening,
and load-bearing strengthening mechanisms.
(2) The Mg2Si and Si phases bear high stresses during the plastic deformation. Damages
of the Mg2Si and Si particles are detected later in plastic deformation, where the lattice strains
and stresses in these phases reduce. Meanwhile, micro-voids nucleate near the particle/matrix
interface due to stress concentration. The void growth and coalescence lead to the final
fracture along with the melt pool boundaries. Both the as-built and the direct-aged alloys obey
this type of damage and fracture.
(3) A new integral form of the Kocks-Mecking model was proposed, which is much
more robust than the original differential form for regression analysis of experimental data.
The Kocks-Mecking model analysis reveals that the as-built AlSi3.5Mg2.5 alloy exhibits a
multistage strain hardening behavior, which can be well captured by a piecewise Taylor model
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and a piecewise Kocks-Mecking model. After direct-aging treatment, the cell boundaries
migrate, so the original cell boundary network is hardly visible. Furthermore, the dislocation
behavior changes after direct-aging treatment, which can be reproduced by a monotonous
Taylor model and a monotonous Kocks-Mecking model.
(4) Compared with the as-built alloy, the direct-aged alloy exhibits much higher
dislocation generation and annihilation rates. This is mainly because the microstructure with
isolated precipitates in the direct-aged alloy has weaker constraints on the dislocations than
the cell boundary network in the as-built alloy. Meanwhile, the direct-aged alloy shows a
superior dislocation storage capacity than the as-built alloy.
Overall, the present AM AlSi3.5Mg2.5 alloy shows a much better combination of
strength and ductility than other AM Al-Si-Mg alloys. The mechanical properties of the
as-built AlSi3.5Mg2.5 alloy are on the same level as the wrought 2024Al alloy. A direct-aging
treatment further enhances both yield strength and elongation of the AlSi3.5Mg2.5 alloy. The
direct-aging treatment leads to the migration of cell boundaries, additional precipitation of
strengthening particles, relaxation of residual stress, and variation of dislocation behavior.
These aspects are the main mechanisms causing higher yield strength and ductility in the
direct-aged alloy than the as-built alloy. This study provides valuable insights to tailor the
microstructure and mechanical properties of low-cost AM Al-Si-Mg alloys.
Acknowledgments
The authors gratefully acknowledge support from the project CustoMat_3D, which was
sponsored by the German Federal Ministry of Education and Research (BMBF) with No.
03XP0101I. This work was also supported by the Fraunhofer Cluster of Excellence
“Programmable Materials” (CPM). The authors are very grateful to Prof. H-G. Brokmeier’s
group and the GEMS-P staff at DESY, Hamburg, Germany, for their kind support of the
experiments.
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