Metals 2021, 11, 377. https://doi.org/10.3390/met11030377 www.mdpi.com/journal/metals
Article
Adjustment of the Mechanical Properties of Mg2Nd and
Mg2Yb by Optimizing Their Microstructures
Jonas Schmidt
1,
*, Irene J. Beyerlein
2
, Marko Knezevic
3
, Walter Reimers
1
1
Institute of Material Science and Technology, Technische Universität Berlin, Ernst-Reuter-Platz 1, 10587
Berlin, Germany; [email protected]
2
Department of Mechanical Engineering, Materials Department, University of California, Santa Barbara, CA
93106, USA; beyerlein@ucsb.edu
3
Department of Mechanical Engineering, University of New Hampshire, Durham, NH 03824, USA;
* Correspondence: jonas.schmidt@tu-berlin.de; Tel.: +49-030-314-26715
Abstract: The deformation behavior of the extruded magnesium alloys Mg2Nd and Mg2Yb was
investigated at room temperature. By using in situ energy-dispersive synchrotron X-ray diffraction
compression and tensile tests, accompanied by Elasto-Plastic Self-Consistent (EPSC) modeling, the
differences in the active deformation systems were analyzed. Both alloying elements change and
weaken the extrusion texture and form precipitates during extrusion and subsequent heat treat-
ments relative to common Mg alloys. By varying the extrusion parameters and subsequent heat
treatment, the strengths and ductility can be adjusted over a wide range while still maintaining a
strength differential effect (SDE) of close to zero. Remarkably, the compressive and tensile yield
strengths are similar and there is no mechanical anisotropy when comparing tensile and compres-
sive deformation, which is desirable for industrial applications. Uncommon for Mg alloys, Mg2Nd
shows a low tensile twinning activity during compression tests. We show that heat treatments pro-
mote the nucleation and growth of precipitates and increase the yield strengths isotopically up to
200 MPa. The anisotropy of the yield strength is reduced to a minimum and elongations to failure
of about 0.2 are still achieved. At lower strengths, elongations to failure of up to 0.41 are reached. In
the Mg2Yb alloy, adjusting the extrusion parameters enhances the rare-earth texture and reduces
the grain size. Excessive deformation twinning is, however, observed, but despite this the SDE is
still minimized.
Keywords: Mg-RE alloys; extrusion; mechanical properties; microstructure; in situ diffraction; crys-
tal plasticity; deformation twinning; texture
1. Introduction
Magnesium is one of the lowest density (
ρ
= 1.7 g/cm
3
) metallic structural materials.
Due to its high specific strengths, it is suitable for lightweight construction applications
in the electronic industry, the biomedical industry, and the sports equipment sector [1–4].
However, the poor formability at room temperature limits the processing possibilities of
magnesium alloys [5,6].
The low ductility and formability is caused by the hexagonal crystal system of mag-
nesium, which only offers primary deformation systems in the basal plane. The <a> basal
slip contributes to plastic deformation at low applied stresses due to its small critical re-
solved shear stresses (CRSS). Together with the <a> prismatic slip system, which requires
higher activation energies, deformation can only can be realized in the <a> direction. De-
formation in the <c> direction is only possible with <c + a> pyramidal slip systems, which
are hard to activate [7–10]. Recently published studies show that <c + a> pyramidal slip is
important for high elongations of magnesium alloys [11].
Citation: Schmidt, J.; Beyerlein, I.J.;
Knezevic, M.; Reimers, W. Adjust-
ment of the Mechanical Properties of
Mg2Nd and Mg2Yb by Optimizing
Their Microstructures. Metals 2021,
11, 377.
https://doi.org/10.3390/met11030377
Academic Editor: Dmytro Orlov
Received: 15 January 2021
Accepted: 19 February 2021
Published: 25 February 2021
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Attribution (CC BY) license
(http://creativecommons.org/licenses
/by/4.0/).
Metals 2021, 11, 377 2 of 20
Plastic deformation can also be realized by twinning. In twinning, the crystal struc-
ture is reoriented by a defined angle along a plane of symmetry [12,13]. This induces a
microscopic change in length and contributes to macroscopic deformation [14,15]. The
twin systems are divided into {10.1} tension twinning (TTW-ing) and {10.2} compression
twinning (CTW-ing), depending on the stress applied along the c-axis of the unit cell.
TTWs are formed when applying either tension along the c-axis or compression perpen-
dicular to it and feature an 86° rotation about a <11.0> axis [12,13,16]. TTWs usually have
a low CRSS and are, therefore, more easily activated. In contrast, CTWs with a higher
CRSS feature a 56° rotation about a <11.0> axis when compression stress is applied parallel
to the c-axis.
Twin formation is a unidirectional deformation mechanism that depends on the ori-
entation of the crystals and the applied stress. In both monocrystalline and polycrystalline
magnesium products, the properties depend on the orientation of the crystals and are af-
fected by the production parameters. Typically extruded AZ31-alloys show fiber textures
after extrusion [17] in which the basal planes are oriented parallel to the direction of ex-
trusion. When compressive stress is applied along the extrusion direction, the perpendic-
ular aligned c-axes of the grains are subjected to tensile stress, preferably forming tensile
twins [18]. Due to the low CRSS of tensile twins, the compressive yield strength (CYS) is
much lower than the tensile yield strength (TYS) in the extrusion direction. This asym-
metric mechanical behavior is described by the Strength Differential Effect (SDE) [19,20].
For practical applications of structural materials, it is desirable to have a symmetrical ma-
terial behavior, equivalent to an SDE close to 0.
The texture can be modified by changing the production/extrusion parameters and
alloying elements. Studies have shown that rare earth [RE] elements can have a strong
influence on the recrystallization texture [17,21,22]. They alter the grain orientations and
weaken the texture during hot deformation/extrusion. Depending on the resulting orien-
tations, various deformation mechanisms are active during subsequent cold deformation.
The CRSS and the contribution to the total deformation of the individual systems have an
influence on the resulting macroscopic mechanical properties.
RE solutes are used in the Mg alloys of the WE-series, containing 7 to 9% RE, mainly
yttrium (Y) and neodymium (Nd) [23,24]. Although the alloys are characterized by high
strength, high costs make it desirable to reduce the RE content while maintaining the ad-
vantageous properties. Neodymium in particular is suitable, as it achieves good proper-
ties and strongly influences the texture [25]. Seitz et al. [26] extruded an Mg2wt.%Nd alloy
and found a small asymmetry in the tension and compression.
For this study, two magnesium alloys with 2 wt.% rare earth content, Mg2Nd and
Mg2Yb, were investigated with regard to their microstructure, deformation behavior, and
mechanical properties. By varying the process parameters, the microstructure can be
changed so that the strength and ductility can be adjusted over a wide range. In particular,
a significant reduction in the SDE can be achieved.
In a first step, two casted billets of each alloy were extruded, varying the cooling
conditions. The extruded bars were investigated by electron microscopy (SEM, TEM), la-
boratory X-ray texture measurements, and mechanical testing (compression, tension) to
determine the mechanical properties, the microstructure, and their changes during defor-
mation. To gain further insight into the different deformation behavior, a combination of
in situ energy-dispersive X-ray synchrotron diffraction and simulations with the elasto-
plastic self-consistent (EPSC) model was used [27]. The particular version of the model
used in the present work is from [28]. These methods allow an analysis of the active de-
formation mechanisms as a function of load. Furthermore, the parameters of a dislocation
density-based strain hardening model of the different deformation mechanisms are ob-
tained. By adding Nd, an advantageous texture can be achieved. The texture activates
similar deformation systems at the beginning of plastic preforming and, in particular, ef-
fectively suppresses the formation of tensile twins under compressive stress. The addition
Metals 2021, 11, 377 3 of 20
of Yb has a lower impact on the texture and a more pronounced dynamic recrystallization
can be observed. This results in low strengths and high SDEs.
In the next step, heat treatments and variations in extrusion parameters were used to
modify the microstructure and thus the mechanical properties. The grain size was reduced
while maintaining or even improving the advantageous texture. Due to the low solubility
of Nd and ytterbium (Yb) in Mg, subsequent heat treatments were used to further increase
the strength. In the Mg2Nd alloy, subsequent heat treatments lead to the formation of fine
precipitates, generating a significant hardening effect. In the case of the Mg2Yb alloy, heat
treatments for precipitation hardening are less effective. However, by adjusting the pro-
cess parameters the grain size can be reduced and the texture improved as well, so that,
despite differences in plastic deformation, the yield strengths in compression are almost
equal to the yield strengths in tension. This resulted in high strengths and low SDEs.
2. Materials and Methods
2.1. Material, Microstructure
The extrusion billets had a nominal composition of Mg2wt.%Nd (Mg2Nd) and
Mg2wt.%Yb (Mg2Yb) with a diameter of 123 mm and a length of 115 mm. They were
casted at the Helmholtz-Zentrum Geesthacht (HZG). The billets were homogenized and
solution annealed in the single-phase region of the phase diagram [29]. Depending on the
composition and phase diagram, the temperature was 500 °C (6 h) for the Mg2Nd alloy
and 450 °C (10 h) for Mg2Yb with an 8 h heating period. After the heat treatment, the
billets were quenched in water. Prior to extrusion, the billets were inductively heated rap-
idly to extrusion temperature and then immediately extruded. The indirect extrusion pro-
cess was carried out at the Technische Universität Berlin, Extrusion Research and Devel-
opment Center, varying some of the extrusion parameters including billet temperature
(TB), cooling method, extrusion ratio (R), and product speed (vP), as shown in Table 1.
To improve the mechanical properties with regard to technological application, the
extruded bars were subsequently heat-treated at different temperatures (150, 204, and 300
°C). To determine the heat treatment duration, hardness tests were performed on samples
of different ageing times. Samples with the highest hardness were further selected for me-
chanical testing with tensile and compression tests.
Table 1. Extrusion parameters.
Alloys Series TB (°C) Cooling R vP (m/min)
Mg2Nd
A 400 Air 61:1 0.5
B 400 Water 61:1 0.5
C 400 Water 61:1 0.25
Mg2Yb
A 400 Air 61:1 1.3
B 400 Water 61:1 1.6
C 300 Water 61:1 1.8
For optical microscopy and grain size analyses, the as-extruded specimens were pre-
pared by grinding and polishing and subsequent chemical polishing with a solution of 12
mL hydrochloric acid (37%), 8 mL nitric acid (65%), and 100 mL ethanol. Etching with a
picric etching solution (4.2 g picric acid, 10 mL acetic acid, 10 mL H2O, and 70 mL ethanol)
revealed the grain structure. To examine precipitates in the SEM, polished samples in the
as-extruded and heat-treated states were used.
Thin TEM foils were cut, mechanically polished, and electrolytically thinned by a
twin-jet TenuPol 3 with a solution of 5.3 g lithiumchloride, 11.16 g magnesiumperchlorate,
500 mL methanol, and 100 mL 2-butoxy-ethanol.
HR-TEM images were recorded on a FEI Tecnai G2 20 S-TWIN TEM and a FEI Titan
80–300 Berlin Holography Special TEM (Technische Universität Berlin,
Zentraleinrichtung Elektronenmikroskopie).
Metals 2021, 11, 377 4 of 20
For energy-dispersive synchrotron in situ tests, compression specimens with a diam-
eter of 7 mm and a length of 15 mm and tensile specimens with a diameter of 6 mm and a
length of 36 mm were used.
The texture of the polished specimens in the as-extruded conditions and deformed
state were measured with the laboratory X-ray diffraction method using CoKα radiation
and a 3 mm collimator. The experimental pole figures for the (10.0), (0002), (10.1), (10.2)
and (11.0)-reflections were measured and the inverse pole figures were calculated from
the experimental data using the MTEX software package [30].
Compression samples (D = 10 mm, l0 = 20 mm) and tensile samples (D = 6 mm, l0 = 36
mm) were machined from the extruded bar. Compression samples were compressed up
to engineering strains of −0.01, −0.04, −0.08, −0.15, and to fracture, while tensile samples
were deformed to fracture. The quasi-static tension and compression tests were carried
out with a universal testing machine (MTS810) with strain rates of 2.5 × 10−4 s−1.
For extruded magnesium alloys, the yield strength in tension (TYS) has been reported
to be higher than the yield strength in compression (CYS). This difference in strength is
called the strength differential effect (SDE) and can be expressed as:
SDE = |CYS||TYS|
|CYS||TYS|. (1)
2.2. In Situ Energy Dispersive Synchrotron X-Ray Diffraction
In situ energy-dispersive synchrotron X-ray diffraction experiments were carried out
at the 7T-MPW-EDDI-beamline at the BESSY-II synchrotron [31]. The beamline is
equipped with a superconducting 7T multipole wiggler, which provides a white beam
with a usable range of about 8 to 150 keV. For the experiments, an energy range of 20 to
60 keV and the Bragg angle 2θ of 10.34° were used. The beam was limited by slit systems
to 1 × 2 mm2 on the incoming and 0.1 × 7 mm2 on the detector side. The in situ compression
and tensile tests were carried out with a tensile-compressive loading device designed by
Fa. Walter+Bai AG, which is mounted on a 4-axes positioner to allow x-y-z translation and
Ψ rotation around the axis of the beam.
In the unloaded sample state, the lattice spacings d0hkil were measured in 11 Ψ angles
between 0 and 89.9° with an exposure time of 60 s. These data were used for the determina-
tion of d0hkil. During mechanical testing, the dhkil were measured at several uniaxial tensile
and compression steps at 0° and 89.9° to determine the elastic lattice strains εhkil in the
axial and transversal direction by Equation (2) [32]:
εhkil = dhkil
d0hkil -1 = E0hkil
Ehkil – 1. (2)
Here, dhkil, d0hkil, and Ehkil, E0hkil are the lattice spacings and their corresponding dif-
fraction lines at a load step and prior loading. The in situ measurements were stress con-
trolled in the linear elastic region. After reaching the yield strength, displacement control
was used.
2.3. EPSC Modeling
The elasto-plastic self-consistent (EPSC) model [27] is a polycrystal plasticity model
which simulates the constitutive response of a material based on single crystal data, a
hardening model, given texture, and initial grain shape and size. A recent description of
the formulation used here can be found in [28,33,34].
To describe hardening, separate models are employed for slip and twinning. For slip,
a dislocation density-based hardening model for the CRSS values in different crystallo-
graphic slip systems is employed [35,36]. For twinning, a model for the domain reorien-
tation and twin expansion as well as the twin boundary effect on slip is used, as described
Metals 2021, 11, 377 5 of 20
by the composite grain model [37]. To activate twinning, we employ the finite initial frac-
tion (FIF) assumption [7], which states that twin nucleation is accompanied by twin
growth to a finite initial fraction. For the simulations here, an FIF of 0.01 is used.
The material parameters used in the model pertain to elasticity, the initial stress to
activate slip, the rates of dislocation storage, and the critical stress for twin growth. These
are listed in Table 3. For the first of these, we used single-crystal elastic constants for Mg,
which are C11 = 59.5 GPa, C12 = 26.1 GPa, C13 = 21.8 GPa, C33 = 65.6 GPa, and C44 = 16.3 GPa
for both alloys. The remaining parameters were identified iteratively and specifically for
each alloy until the simulation results matched all the experimental results. The simula-
tion results enable da direct comparison with the synchrotron X-ray diffraction measure-
ments from the compression and tensile tests. The average stress–strain response, the tex-
ture evolution, and the elastic lattice strains allow to check the EPSC predictions by the
experimental diffraction data. The EPSC simulation further gives information on the ac-
tive deformation modes and their CRSS as a function of the strain. For the final simulation,
a grain set of 10,000 grains, which represent the as-extruded texture, was used.
3. Results
3.1. Microstructure
The microstructure of the as-extruded material is presented in Figure 1 via optical
micrographs to show the grain structure and inverse pole figures to show the texture. The
microstructures of all three series are dominated by globular recrystallized grains. The
average grain size of the Mg2Nd alloy decreases from 13 ± 1 µm for the air-cooled A-series
to 7 ± 1 µm for the water-quenched B-series. This is due to hindered grain growth after
the dynamic recrystallization caused by the rapid drop in temperature. An additional de-
crease to an average grain size of 3 ± 1 µm for the C-series was achieved by reducing the
extrusion speed. The Mg2Yb alloy shows an average grain size of 49 ± 4 µm for the air-
cooled A-series and 26 ± 2 µm for the water-quenched B-series. Extrusion at a reduced
temperature decreases the grain size of the C-series to 8 ± 2 µm. In the slower extruded C-
series of the Mg2Nd alloy and both water-quenched series of the Mg2Yb alloy, elongated
grains that are not fully recrystallized are occasionally found in the longitudinal sections
(Figure 1h,n,q).
The X-ray diffraction texture measurements reveal pronounced RE-fiber-textures
with overall low maximum intensities (Figure 1). The texture of the A-series of the Mg2Nd
alloys has a maximum at the <11.2>pole and the B-series shows additional intensity be-
tween the <10.2> and <10.1>pole. The C-series has its maximum at the <10.0> pole with
additional intensities at the <10.1> and<11.2> pole. The A- and C-series of the Mg2Yb al-
loys show a very weak extrusion texture with of maximum of just 1.3 multiples of random
distribution (mrd) and 1.5 mrd, respectively, and intensities at the <10.2> and <11.2> pole.
The B-series, in contrast, shows the highest observed intensity of 2.3 mrd at the <10.0>
pole. The texture of the C-series is similar to the A-series, with an additional intensity at
the <10.0> pole.
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