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High temperature deformation behavior of Mg-5wt.%Y binary alloy:

Constitutive analysis and processing maps

Article  in  Materials Science and Engineering A · February 2020

DOI: 10.1016/j.msea.2020.139051

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 High temperature deformation behavior of Mg-5wt.%Y
binary alloy: Constitutive analysis and processing maps

Nooruddin Ansari1, Brian Tran2, Warren J. Poole2, Sudhanshu. S. Singh3,

Krishnaswamy Hariharan4, Jayant Jain1*
1
Department of Materials Science and Engineering, Indian Institute of Technology Delhi,
New Delhi 110016, India
2
Department of Materials Engineering, The University of British Columbia, Vancouver,
Canada, V6T 1Z4
3
Department of Material Science and Engineering, Indian Institute of Technology Kanpur,
Uttar Pradesh 208016, India
4
Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai,
600036, India

*Corresponding Author:
Email: jayantj@iitd.ac.in (J. Jain)

Abstract

The high temperature deformation behavior of a Mg-5wt.%Y (Mg-5Y) binary alloy has been
investigated using uniaxial compression tests in the temperature range of 523 K-723 K and
strain rate of 0.001 s-1 – 10 s-1. The true stress-strain curves depict that flow stress significantly
decreases with the increase in temperature and decrease in the strain rate and vice-versa. An
Arrhenius based hyperbolic sine equation was used to model the flow stress of the alloy at high
temperature. Processing maps were developed for true strains of 0.25 and 0.45, which
represents the strain near the peak stress and steady-state region, respectively. The safe region
is found to be in the strain rate range of 0.001 s-1 – 0.1 s-1 and temperature range of 623 K –
723 K, while the unstable region is found to be in strain rate range of 1 s-1 – 10 s-1 at a
temperature range of 523 K–723 K. In the safe region, characterization of deformed
microstructures using electron backscatter diffraction (EBSD) shows that prominent
deformation mechanism is continuous dynamic recrystallization (CDRX) and discontinuous
dynamic recrystallization (DDRX) with manifestation of twin induced DRX and particle
stimulated nucleation (PSN). The unstable region, however, consists of cracks, voids and
deformation twins with little evidence of DRX.

Keywords: Mg alloy; EBSD; processing map; recrystallization; constitutive analysis

1
1. Introduction

Magnesium and its alloys are potential materials for automobile, aerospace and electronic
sectors due to their favorable physical and mechanical properties including density, specific
strength, particularly in bending applications and thermal conductivity [1]. However, a major
challenge in developing these alloys is poor formability at room temperature due to activity of
insufficient slip systems [2]. The mechanical properties of Mg alloys can be improved by
changing the alloying chemistry and/or by optimizing the processing route. Many elements
such as Al, Zn, Sn and Ca are added to enhance the properties of Mg alloys [3,4]. However,
the shortcomings of these alloys are low creep resistance and poor strength at elevated
temperature [5]. In contrast, the addition of rare earth (RE) elements (e.g. Y, Dy, La) in Mg
have been found to be promising in terms of mechanical response at elevated temperatures [6].
Among the several RE elements, Yttrium (Y) is considered to be one of the most effective
elements as it improves the ductility over a wide range of temperatures [7]. Yttrium has a
solubility of 12.5 wt.% at 839 K decreasing to 6.5 wt.% at 673K [8]. Moreover, it has been
reported that the addition of Y weakens the texture after wrought processing of Mg alloys and
thereby improves the formability [9,10]. Nevertheless, there has been debate about exact role
of RE solutes in enhancing the ductility. The work of Yin et al. [11] suggested differing effects
of solute on the stacking faults and the dislocations of two pyramidal planes could be
responsible for enhanced ductility in Y containing Mg alloys. Most recently, Wu et al. [12]
suggested the favourable effect of Y is derived from increased <c+a> cross slip and its
multiplication rates.

During high temperature deformation, DRX has been observed to be one of the main
deformation mechanisms in materials like copper and stainless steel which exhibits low
stacking fault energy [13,14]. DRX is mainly of two forms, namely discontinuous DRX
(DDRX) and continuous DRX (CDRX). DDRX is the conventional DRX process in which the
nucleation occurs at prior grain boundaries and twin boundaries. In this mechanism nucleation
and growth stages can be identified distinctly. Whereas, CDRX process involves the subgrains
rotation near prior grain boundaries when the material is strained. This creates a misorientation
gradient from the centre to the edge of the parent grains. The local misorientation on the grain
boundary increases further at larger strains and develops high angle grain boundaries (HAGBs)
[15].

2
Most of the bulk forming processes such as forging, rolling and extrusion employ compressive
forces at high temperature and strain rate. The constitutive behavior of the material in the
allowable range of temperature and strain rate should be appropriately modeled to design and
analyze these forming processes. An Arrhenius-type constitutive equation for the relationship
between the flow stress, temperature and strain rate is often used to model the stress-strain
curve of materials over a wide range of conditions [16]. The variables of the phenomenological
models such as stress exponent (n) and activation energy (Q) are often deduced to understand
the deformation behaviour of the materials [17–19]. Several contributions have been made to
understand the effect of temperature and strain rate on the deformation behavior of Mg alloys
[17,18,20].

The manufacturing process design involves the estimation of a suitable range of deformation
parameters for which the material can be deformed safely without failure. This is accomplished
by constructing the processing map of a particular alloy [21]. A processing map is an
imposition of two maps, namely power dissipation and instability maps, which correlate the
deformation mechanism and material failure, respectively. Processing maps mainly consist of
stable and unstable region. A stable region is the desired region where softening mechanism
like DRX activates, and unstable region is the undesired region where failure is possible in the
form of cracks and voids. Wang et al. [22] investigated the hot deformation behavior of WE43
magnesium alloy using a processing map and estimated optimum parameters to be 748 K and
strain rate of 0.1 s-1. Kwak et al. [23] generated the processing map of ZW92 magnesium alloy
and found out the optimum condition (peak efficiency) at a temperature of 673 K and a strain
rate of 0.03 s-1. They also reported the unstable region to be prevailed for strain rate more than
0.1 s-1. Xia et al. [24] generated the processing map of Mg-Gd-Y-Nd-Zr alloy and found the
optimum condition with the occurrence of dynamic recrystallization (DRX) in the temperature
range of 723 K – 813 K and strain rate range of 0.005 s-1 – 0.5 s-1.

Constitutive modeling coupled with a processing map has been successfully employed to
analyze the hot deformation behavior for a number of Mg alloys [17,18,24,25]. Shalbafi et al.
[18] studied the high temperature deformation behavior of a Mg-10Li-1Zn alloy using
constitutive modeling and processing map and reported that dislocation climb is the prominent
deformation mechanism. However, to the author’s best knowledge no prior literature on the
high deformation behavior of Mg-Y binary alloy through processing maps have been reported
so far.

3
The present study aims to investigate the high deformation behavior of Mg-5Y binary alloy.
Hot compression tests were performed in the temperature range of 523 K – 723 K and strain
rate of 0.001 s-1 – 10 s-1 and a processing map is constructed to estimate the optimum hot
working conditions. The microstructure during deformation is correlated with the different
regions of the processing map. The outcome of the work can be leveraged when designing the
processing route for Mg-5Y alloy.

2. Experimental Methods

2.1. Materials and Processing

A Mg-5wt.% Y alloy was used as the starting material. The alloy was prepared by mixing
99.9% commercially pure magnesium and master alloy of Mg-30 wt.% Yttrium in a
Swamequip bottom pouring vacuum die casting setup. The molten alloy was poured in a steel
mold of dimensions 15 mm x 100 mm x 250 mm and cooled in a vacuum environment to
minimize the casting defects. As-cast alloy was homogenized at 500°C for 24 h followed by
water quenching. These samples were further pre-heated at 420° C for 4 h before rolling and
then 40% reduction in thickness was imparted. The as-rolled samples were then annealed at
400°C for 20 min to obtain an equiaxed grain structure. Finally, the annealed samples were
solution treated at 500°C for 24 h to ensure the complete dissolution of second phase particles
before compression.

2.2. Uniaxial Compression tests

Cylindrical compression samples (diameter 4.7 mm and height 7 mm) were machined by wire
electric discharge machine (EDM). Uniaxial compression test was conducted on a Gleeble
3500 thermomechanical simulator (Dynamic System Inc. Poestenkill, NY). Nickel anti-seize
paste (Loctite 77124) was used as a lubricant between anvil and sample surface to ensure the
uniform deformation. The strain was measured using a dilatometer (Gleeble model 39018)
attached at mid-specimen length. The tests were conducted within the range of 523 K – 723 K
and 0.001 s-1 – 10 s-1. All the samples were heated to the desired temperature at a rate of 5 K/s
and stabilized for three minutes prior to deformation. The temperature was continuously
measured through a thermocouple (k-type) spot welded to the sample. After deformation, the
samples were air-cooled by natural convection to room temperature.

4
2.3. Microstructural characterization

Samples for microscopy were sectioned parallel to the compression axis from the middle region
of the deformed specimen. Standard metallographic preparation using SiC papers of different
grades (300-4000 grit) and subsequent cloth polishing using alumina (1 µm) and colloidal silica
(0.05 µm) were employed. The samples were characterized using scanning electron microscope
(SEM) (JEOL 7800F) equipped with electron backscatter diffraction (EBSD) (Oxford, Nordlys
detector). The EBSD scan was performed at an accelerating voltage of 20 kV and a probe
current of ~ 14 nA with a step size of 1 µm. HKL Channel 5 was used for post-processing and
data analysis. The phases were characterized using EDS (Oxford) equipped in SEM and X-ray
diffraction (XRD) (Rigaku). Cu target was used in XRD to scan from 10° to 90°.

3. Constitutive Analysis and Processing Maps

3.1. Basics of Constitutive Analysis

Plastic deformation is a thermally activated process [26]. The dependence on the strain, strain
rate, and temperature are modeled by many empirical relations, such as that proposed by Sellars
and McTegart [16] is given by :

𝑄
𝜀̇ = 𝐴 [𝑠𝑖𝑛ℎ(𝛼𝜎)𝑛 exp (− )] (1)
𝑅𝑇

where, σ, 𝜀̇, T, n, Q, R refers to the flow stress (MPa), strain rate (s-1), absolute temperature
(K), stress exponent, activation energy (kJmol-1) and universal gas constant (8.314 Jmol-1K-1),
respectively. A is the material constant, and α is the stress multiplier used to scale the value of
flow stress in a given range.

Equation (1) can be simplified as a power law for relatively low flow stress range (ασ < 0.8)
[27]:

′ 𝑄
𝜀̇ = 𝐴′ 𝜎 𝑛 exp(− 𝑅𝑇) (2)

where, 𝑛′ and 𝐴′ are stress exponent and material constant, respectively. 𝑛′ can be estimated
from the slope of ln𝜀̇ and ln𝜎 at constant temperature.

At relatively high flow stress (ασ > 0.8), Eq.(1) can be best expressed using an exponential law
[28]:

𝑄
𝜀̇ = 𝐴′′ exp(𝛽𝜎) 𝑒𝑥𝑝 (− 𝑅𝑇) (3)

5
where, 𝐴′′ and β both are material constants and β can be estimated from the slope of ln𝜀̇ vs σ
at constant temperature.

Further, stress multiplier, α (in Eq.1) can be estimated from the following equation [28]:

𝛽
𝛼= (4)
𝑛′

The activation energy of the material can be calculated from equation (1), which when
rewritten,

𝑄
𝑙𝑛𝜀̇ = 𝑙𝑛𝐴 + 𝑛 ln[𝑠𝑖𝑛ℎ(𝛼𝜎)] − (5)
𝑅𝑇

Equation (5) is further differentiated with respect to 1/T and rearranged to get Q as:

𝜕𝑙𝑛𝜀̇ 𝜕 ln(sinh(𝛼𝜎))
𝑄 = 𝑅 {𝜕 ln(sinh(𝛼𝜎))} 𝑇 { 1 } = 𝑅∗𝑛∗𝑏 (6)
𝜕( )
𝑇 𝜀̇

The first differential term of the above equation, denoted by ‘n’, refers to the slope between
ln𝜀̇ vs ln[sinh(ασ)] at constant temperature. The value of stress exponent (n) indicates the hot
deformation mechanism of the material [29]. The second differential term known as ‘b’ can be
estimated by averaging the slope of plot ln[sinh(ασ)] vs 1/T.

Zener-Holloman parameter (Z) is used to show the flow stress correlation with the temperature
and strain rate of the hot deformation by following equation [30]:

𝑄
𝑍 = 𝜀̇ exp(𝑅𝑇) (7)

By using equation (1) and equation (7), we can get

𝑄
𝑍 = 𝜀̇ exp (𝑅𝑇) = 𝐴[sinh(𝛼𝜎)]𝑛 (8)

The intercept value of the plot between the lnZ vs. ln[sinh(ασ)] gives the value of lnA.

The linearity of the plots assumed in determining the parameters such as activation energy is
valid only for a particular deformation mechanism. Therefore, it is pertinent to identify
characteristic flow stress states that confirm to specific deformation mechanisms. The
characteristic stress can either be the initial yield stress, the peak stress or a strain dependent
flow stress that can critically ensure common deformation mechanism under all the
experimental conditions. Generally, peak stress is used as a characteristic value in magnesium

6
[17,18,25,31], aluminum [32] and copper alloys [33]. At peak stress work hardening is
balanced by the softening mechanism such as DRX.

In the present study, peak stress during monotonic loading is used as a characteristic stress for
the constitutive analysis of Mg-Y binary alloy. Substituting the values of α, A, n and Q in
equation (1), the constitutive behavior under hot deformation of Mg-5Y binary alloy can be
modeled.

3.2. Processing Maps

While the constitutive model can describe the stress-strain relation, it is insufficient to optimize
the process. Similarly, the constitutive model does not explicitly define the instability limits
during processing. Processing maps can overcome these limitations and are used in industries
for process parameter optimization and defect avoidance during process design [34]. The
processing map, which is constructed by superposing power dissipation and instability maps,
essentially shows the influence of temperature and strain rate on the microstructure for a given
strain. The power dissipation map gives the efficiency with which the power is dissipated due
to microstructural changes and the dominant deformation mechanism involved. Instability
map, as the name suggests, identifies the state of deformation where cracks, flow localization
and voids formation can possibly occur and must be avoided in process design [21]. According
to dynamic material model (DMM), based on which processing maps are plotted, the power
dissipated at a given strain rate during deformation can be decomposed into two parts [21,35]
as follows:

𝜀̇ 𝜎
𝑃 = 𝐺 + 𝐽 = 𝜎𝜀̇ = ∫0 𝜎𝑑𝜀̇ + ∫0 𝜀̇𝑑𝜎 (9)

where, σ is the flow stress and 𝜀̇ is the strain rate. P is the total power dissipated and G and J
are components of the dissipated power. The G content represents the temperature rise due to
visco-plastic deformation and the J co-content complements the energy associated with
microstructural changes.

Assuming power law relation between 𝜎 and 𝜀̇ given by 𝜎 = 𝑘 𝜀̇ 𝑚 (where m is the strain rate
sensitivity and k is a material constant), the co-content in the above equation is given by:
𝑚
𝐽= 𝜎𝜀̇ (10)
𝑚+1

An ideal case of linear dissipation with m =1 corresponds to the theoretical maximum power
dissipated for microstructural changes, i.e.,

7
 𝜎𝜀̇
𝐽𝑚𝑎𝑥 = (11)
2

When the dissipation is non-linear (when m <1) the efficiency of power dissipation (η) can be
represented using a dimensionless parameter

𝐽 2𝑚
𝜂= = (12)
𝐽𝑚𝑎𝑥 𝑚+1

The flow instability caused due to damage mechanisms (adiabatic shear bands, twins, dynamic
strain aging etc.) was modeled by Prasad et al. [21] based on the Ziegler’s [36] criteria for
irreversible large plastic strain as:
𝑚
𝜕ln( )
𝑚+1
𝜁(𝜀̇) = +𝑚 <0 (13)
𝜕𝑙𝑛𝜀̇

Where the dimensionless parameter ζ (𝜀̇) describes the locus of flow instability.

The procedure for plotting a processing map is well established [21]. For a given strain and
temperature, m can be estimated from the logarithmic plot of 𝜎 𝑣𝑠. 𝜀̇. The plot is usually linear
only for a small range and often a polynomial curve fit is used to represent 𝑚(𝜀̇). A similar
procedure can be repeated for isothermal tests at different temperatures. Using 𝑚(𝜀̇, 𝑇),
contours of power dissipation and instability can be interpolated from estimates of 𝜂 and 𝜁.

4. Results and Discussion

4.1. Initial microstructure

Figures 1(a) and (b) show the SEM micrographs of as-cast Mg-5Y binary alloy. The magnified
SEM image (Figure 1(b)) confirms the dendritic morphology of the second phase. Figures 1(c)
and (d) show the EDS elemental area maps of the second phase magnified in Figure 1(b), which
indicate that these consists of less magnesium and higher yttrium than the matrix. The XRD
pattern of the as-cast material, as shown in Figure 2, confirms the presence of Mg24Y5 phase
apart from α-Mg, which is in agreement with earlier reports [37]. Figure 3 shows the
compression axis inverse pole figure (IPF) map of Mg-5Y prior to compression. The initial
microstructure consists of coarse grains with random texture with an average grain size of ~80
µm. Some of the undissolved Y particles can also be observed by black color which are not
indexed.

8
Figure 1: (a) SEM micrograph of as-cast Mg-5Y alloy showing dendritic morphology of
precipitates, (b) SEM micrograph of a precipitate at higher magnification, (c, d) EDS elemental
area maps of the precipitate (shown in Figure 1(b)) showing distribution of Mg and Y.

Figure 2: XRD pattern of the as-cast Mg-5Y alloy.

9
 Figure 3: An EBSD compression axis IPF map of Mg-5Y alloy before compression.

4.2. Flow stress behaviour

Figure 4 shows the true stress-strain curves of Mg-5Y binary alloy at different temperatures
(523 K-723 K) and strain rates (0.001 s-1 – 10 s-1). The flow curves are mainly consisting of
three regions, which can be described on the basis of dominance of work hardening, balance
of hardening and softening and dominance of softening mechanisms. In the work hardening
stage, flow stress increases rapidly with an increase in strain. This can be attributed to the
increase in the dislocation density and subsequent accumulation [38,39].The flow stress
increases up to the peak value beyond which softening mechanisms dominates. After peak
stress, the flow stress decreases to a steady state value as work hardening is complemented
with softening mechanisms such as dynamic recovery (DRV) and DRX [40]. In the softening
stage, when the accumulation of dislocation reaches critical strain, DRX starts. The nucleation
and growth of DRX causes dislocation annihilation which decreases flow stress from the peak
value. Finally, in the steady stage the work hardening is balanced by the softening mechanisms
(DRV and DRX) [39,41]. The amount of work hardening is observed to be greater at higher
strain rates and lower temperatures as because of increase in the dislocation density and the
decrease in DRX, whereas the softening mechanisms are observed to be more prominent at
higher temperature and lower strain rates. Figure 5 shows the dependence of the peak stress on
the temperatures at different strain rates. The peak stress increases with strain rate and
decreases with an increase in temperature, following the usual trend of dependence of stress on

10
temperature and strain rate. Nevertheless, the presence of Y in solution is expected to slow
dynamic recovery and dynamic recrystallization owing to enhanced dislocation-solute
interactions.

Figure 4: True stress-strain curves at fixed strain rates of (a) 0.001 s-1, (b) 0.1 s-1, (c) 1 s-1 and
(d) 10 s-1.

11
 Figure 5: Dependence of peak stress on temperature at different strain rates.

4.3. Constitutive Analysis

Figure 6 shows the plots used to calculate the value of the material constants using the
procedure outlined in Section 3.1. The average value of the constants 𝑛′ (from Figure 6a) and
𝛽 (from Figure 6b) are found to be 10.63 and 0.1239, respectively. Further, α is calculated
using the equation (4) and found to be 0.0117. Figure 6(c) shows the value of n, obtained from
the slope of ln𝜀̇ vs. ln[sinh(ασ)], to be 7.66. Figure 6(d) gives the average value of b as 3155.
Therefore, the value of activation energy as per equation (6) is found to be:

𝑄 = 𝑅 ∗ 𝑛 ∗ 𝑏 = 8.314 ∗ 7.66 ∗ 3155 = 200.93 𝑘𝐽/𝑚𝑜𝑙 (14)

It should be noted that this value of activation energy is more than the self-diffusion activation
energy of pure Mg (135 kJ/mol) [42]. One may relate this to the presence of Y in the matrix.
The matrix containing solute atoms might produce solute drag effect which in turn could result
in a higher value of activation energy. Chen et al. [43] also reported that the dislocation
movement is restricted by the presence of solute atoms, which led to higher activation energy
required for the dislocation climb. Note that the activation energy value of this alloy is similar
to some other Mg alloys previously reported in the literature [17,18,25]. The plot of ln Z vs.
ln[sinh(ασ)] is linear (Figure 7) and lnA is calculated to be 36.49. Therefore, the constitutive
equation of Mg-5Y binary alloy can be expressed by substituting the values of Q, A and n in
Equation (1) as follows:

12
 200930
𝜀̇ = 7.04𝑥1015 𝑠𝑖𝑛ℎ[0.0117𝜎]7.66 𝑒𝑥𝑝 (− ) (15)
𝑅𝑇

Figure 6: Plots between (a) ln 𝜀̇ vs. ln σ at different temperatures, (b) ln 𝜀̇ vs. σ at different
temperatures, (c) ln 𝜀̇ vs. ln[sinh(ασ)] at different temperatures, and (d) ln[sinh(ασ)] vs. 1/T at
different strain rates.

Figure 7: Plot between ln[sinh(ασ)] vs. ln Z.

13
4.4. Processing Maps

Figure 8 shows the processing map generated by the superimposition of power dissipation map
over instability map at 0.25 strain (strain near peak stress) and 0.45 strain (steady-state region).
The efficiencies of power dissipation are represented in percentage by contour numbers in the
processing map. The efficiencies here denote the level of energy dissipation possible at a
particular deformation condition. A high value of efficiency also indicates that high driving
force is available for the nucleation and growth of dynamically recrystallized grains. The
unstable region here is represented by the dashed region where 𝜁 < 0 , following equation 13.
The negative value of the instability parameter means the flow will not be stable and can cause
voids and cracks. Figure 8(a) depicts the processing map at 0.25 strain having four domains.
Domains I and II represent the stable region of the high temperature working, while the other
two domains III and IV represent the region of instability. Domain I is the high-efficiency
region, with 33% maximum efficiency, within the strain rate range of 0.001 s-1 – 0.1 s-1 and
temperature range of 660 K – 723 K. Domain II is the medium efficiency region, with
maximum efficiency of approximately 20% obtained at 0.1 s-1 strain rate and within the
temperature range of 575 K-625 K. Domain III and IV are the regions of instability; domain
III occurs at a strain rate range of 1 s-1-10 s-1 and temperature range of 523 K-623 K, while
domain IV also occurs in the strain rate range of 1 s-1-10 s-1 and temperature of 660 K-723 K.
Similarly, at 0.45 strain, the processing map consists of three main domains (Figure 7 (b)).
Domain I is the high-efficiency region, with 35% maximum efficiency, in the strain rate range
of 0.001 s-1 – 0.1 s-1 and a temperature range of 660 K – 723 K. Domain II is the medium
efficiency region, with approximately 19% maximum efficiency at the strain of 0.1 s-1 and a
temperature range of 575K – 625K. Domain III is the unstable region occurs within the strain
rate range of 1 s-1 – 10 s-1 and temperature range of 523 K– 723 K. Increasing the strain from
0.25 to 0.45 has the least difference in the peak power dissipation efficiency from 33% to 35%
with a few changes in the efficiency contour patterns. However, there is a difference in the
region of instability, where the unstable region was observed to exists for complete temperature
range at higher strain rates, hence the safe region is shrunk. Therefore, the domain of safe
region is found to be in strain rate range of 0.001 s-1 – 0.1 s-1 and temperature range of 623 K

14
– 723 K, while instability domain is found to be in strain rate range of 1 s-1 – 10 s-1 at a
temperature range of 523 K – 723 K.

Figure 8: Processing maps of Mg-5Y alloy at (a) 0.25 strain, and (b) 0.45 strain. Note that
domains I and II are the safe regions and domains III and IV are the instable regions. The color
scale indicates the scale of efficiency of power dissipation (%).

15
4.5. Interpretation of processing maps

4.5.1. Stable region

Figure 9 shows the EBSD IPF maps of deformed samples corresponding to the high and
medium efficiency stable region (Domain I and II) of the processing map. In all the maps, high
angle grain boundaries (HAGBs) (misorientations > 15º) are shown by black boundaries, while
the low angle grain boundaries (LAGBs) (misorientations 2º-15°) are shown by white
boundaries. Figure 9(a) shows the EBSD IPF maps of the material deformed at 723 K and
0.001 s-1, where fine and equiaxed grains can be observed along with a very few coarse grains.
The fine grains may arise by the formation of new grains at prior grain boundaries and as well
as at twin boundaries consistent with DDRX mechanism.

The arrow “A” in Figure 9(a) shows the evidence of formation of a new grain at prior grain
boundary which might presumably be due to grain boundary bulging. Further, the formation of
LAGBs adjacent to the grain boundaries of the parent grains is shown by an arrow B in Figure
9(a). These LAGBs inside coarse grains, on further strain, might change into HAGBs, which
could result in formation of fine recrystallized grains inside parent grains, consistent with
previous reports [15]. Figure 9(a) also shows the evidence of particle stimulated nucleation
(PSN) (arrow C). The dark regions in the map are undissolved Y particles, which have not been
indexed. This mechanism of particle stimulated nucleation (PSN) has also been reported earlier
in magnesium alloys [44,45]. The size of the undissolved Y particles is on the order of few
microns, which is greater than the reported critical size of particles (0.1µm) to trigger PSN
reported by Mackenzie et al. [46]

16
Figure 9: EBSD compression axis IPF maps of high efficiency stable region deformed at (a)
723K and 0.001 s-1, (b) 723K and 0.1 s-1, (c) cumulative misorientation profile along the line
A in b, (d) medium efficiency stable region deformed at 623K and 0.1 s-1 (white boundaries
denotes 2º-15° misorientation and black boundaries denotes > 15º misorientation).

Figure 9(b) shows the EBSD IPF map of the high efficiency stable region (Domain I of the
processing map deformed at 723K and 0.1 s-1. The presence of new small recrystallized grains
found near the grain boundaries forming a necklace type structure would be consistent with
observation of CDRX. In this, DRX is mainly due to the sub-grain rotation, which results in
the formation of local misorientation [15]. Further increase in strain causes the accumulation
of these misorientations resulting in the formation of LAGBs that develop into HAGBs. One
of the methods to identify CDRX is to check for an increase in the misorientation from the

17
centre of the parent grain to the edge, where new recrystallized grains are formed [15]. Figure
9(c) shows the cumulative misorientation profile of one of the parent grains from the centre to
the grain boundary (denoted by D in Figure 9(b)). A significant increase in the misorientation
along the line was observed. Also, near the grain boundaries, LAGBs are observed (denoted
by E), which on further strain change into HAGBs, i.e., new dynamically recrystallized grains.

The observed two distinct types of DRX behavior in the high efficiency stable regions might
be attributed to the difference in the strain rates. The high strain rate (0.1 s-1) causes progressive
rotation of subgrains near the original grain boundaries which in turn develops misorientation
gradient from the center to the edge of the parent grains. Therefore, in the center of the parent
grains, no subgrains are formed due to very low misorientations but at the grain boundaries due
to high misorientation, HAGBs are formed at higher strain. This process is progressive without
a clear distinction between the nucleation and grain growth stages.

Figure 9(d) shows the EBSD IPF map of the medium efficiency stable region (Domain II) of
the processing map deformed at the temperature of 623 K and strain rate of 0.1 s-1. The map
shows the evidence of fewer recrystallized grains. This is because of lower temperature and
higher strain rate than region I which reduces the time for dislocation annihilation and hence
the formation of new recrystallized grains is also reduced. In Figure 9(d), F shows the evidence
of dynamically recrystallized grains inside the twins and G denotes the nucleation of the grains
along the grain boundary. This twin induced DRX was also observed in several other
magnesium alloys [47,48].

It is noteworthy to point here that the IPF maps shown in Figure 9 show considerable difference
in DRX grains with the change in temperature and strain rate. At high temperature, enough
driving force is available for the grain boundary migration which accelerates the DRX, whereas
at high strain rate, the lack of deformation time limits the formation of DRX grains [41]. The
similar observations were also made in the present study wherein at low strain rate and high
temperature, shown in Figure 9 (a), the DRX was more pronounced, whereas for high strain
rate and low temperature, shown in Figure 9 (d), the DRX was inconspicuous.

From the above, it can be concluded that in the stable region, different deformation mechanisms
are involved. DDRX and CDRX being the prominent deformation mechanisms, with some
manifestation of twin induced DRX and PSN.

18
4.5.2. Unstable region

Figure 10 shows the EBSD IPF map (compression axis) of the unstable region (Domain III) of
the processing maps deformed at the temperature of 523 K and strain rate of 10 s-1. The map
clearly shows the presence of cracks, voids, and deformation twins, which are the sign of
unstable flow and was accurately predicted by the processing map (Figure 8). At room
temperature, the favorable deformation mechanism for Mg alloy is basal slip due to low CRSS
as compared to other slip systems, such as prismatic or pyramidal. Twins get activated at room
temperature due to lack of sufficient slip systems. While at high temperatures, CRSS decreases
for all the slip systems, activating other slip systems and suppressing the twin formation.
However, in the present case at the temperature of 523 K, twins are observed because of high
strain rate (10 s-1) deformation and the relatively low temperature. At higher strain rates, there
is not enough time available for the dislocation accumulation and hence the CRSS of slips
systems is not decreased, even at high temperature. The twins are thus observed at this
temperature which also accommodate the deformation. Two types of deformation twins are
mainly activated in this region, one is {101̅2} extension twin and other is {101̅1}-{101̅2}
double twin. Their boundaries are denoted by white (86° misorientation about <112̅0>) and
blue (38° misorientation about <112̅0>) color, respectively, as shown in Figure 10. As can be
noticed double twins are more in numbers than extension twins with the potential cracks
formed along former as indicated by A in Figure 10. The observation of cracks and voids along
these double twins are consistent with previous reports [49,50]. Further, B in Figure 10
indicates the formation of cracks along the grain boundaries at high strain rates. The formation
of the intergranular crack at high strain rate was earlier reported for other magnesium alloys
[22,25]. This can be attributed to the grain boundary sliding phenomenon, which is one of the
mechanisms of stress relieving and it plays a pivotal role in the nucleation of cracks. If the
stress concentration resulting from grain boundary sliding is not dissipated effectively, wedge
cracks can initiate at grain boundary triple points. The nucleation, growth and coalescence of
cracks and cavities results into intergranular crack [51]. It can be seen that the unstable region
of the processing map of the alloy consists of twins, voids, and cracks which are undesirable
and the processing parameter of this region must be avoided.

19
Figure 10: EBSD compression axis IPF maps of an unstable region deformed at 523K and 10
s-1 (black boundaries denotes grain boundaries > 15º misorientation, white boundaries
denotes {101̅2} TTW boundaries and blue boundaries denotes {101̅1}-{101̅2} DTW
boundaries).

5. Conclusions

The high temperature workability of Mg-5Y binary alloy was investigated in the temperature
range of 523 K – 723 K and strain rate range of 0.001 s-1 – 10 s-1. The processing routes are
optimized using the processing map, and different domains are characterized using EBSD.
Also, the flow stress behavior was modeled using the Arrhenius hyperbolic sine equation. The
following are the main conclusions:

1. The value of stress exponent and the activation energy was found to be 7.66 and 200
kJ/mol, and the constitutive equation of Mg-5Y binary alloy developed for high
temperature deformation is:
200930
𝜀̇ = 7.04𝑥1015 𝑠𝑖𝑛ℎ[0.0117𝜎]7.59 𝑒𝑥𝑝 (− )
𝑅𝑇
2. The two processing maps developed at 0.25 and 0.45 strains. The domain of safe region
is found to be in strain rate range of 0.001 s-1 – 0.1 s-1 and temperature range of 623 K
– 723 K, while instability domain is reported to be in strain rate range of 1 s-1 – 10 s-1
at temperature of 523 K – 723 K.
3. In the stable region, DRX grains are observed with prominent deformation
mechanisms being DDRX and CDRX, with some manifestation of twin induced DRX

20
 and PSN. The unstable region, however, consists of cracks, voids and deformation
twins with no evidence of DRX.

Acknowledgements

JJ would like to thank Aeronautics Research and Development Board (AR&DB) for providing
the financial support to this work under project number 1823. JJ also acknowledges the support
received from the University of British Columbia during his stay.

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