The paper reports behaviour of magnesium alloy AZ31 (nominal composition 3 % Al - 1 % Zn – balance Mg) with an addition of 0.5 wt. % Ca at high strain rates. Samples were prepared by the squeeze cast technology. Dynamic compression Hopkinson tests were performed at room temperature with impact velocities ranging from 11.2 to 21.9 m.s-1. A rapid increase of the flow stress and the strain rate sensitivity was observed at high strain rates. Transmission electron microscopy showed extremely high dislocation density and mechanical twins of two types. Adiabatic shear banding is discussed as the reason for the observed behaviour at high strain rates. </span

Josef Pešička

Pavel Lukáč

Tomáš Podrábský

Zuzanka Trojanová

The paper reports behaviour of magnesium alloy AZ31 (nominal composition 3 % Al - 1 % Zn – balance Mg) with an addition of 0.5 wt. % Ca at high strain rates. Samples were prepared by the squeeze cast technology. Dynamic compression Hopkinson tests were performed at room temperature with impact velocities ranging from 11.2 to 21.9 m.s-1. A rapid increase of the flow stress and the strain rate sensitivity was observed at high strain rates. Transmission electron microscopy showed extremely high dislocation density and mechanical twins of two types. Adiabatic shear banding is discussed as the reason for the observed behaviour at high strain rates

Trojanová, Zuzanka

Lukáč, Pavel

Podrábský, Tomáš

Pešička, Josef

Materials Engineering - Materiálové inžinierstvo (MEMI)

Z. Trojanová et al.: High strain rate behaviour of an AZ31+ 0.5 Ca magnesium alloy  
Materials Engineering - Materiálové inžinierstvo 19 (2012) 12-17 
12  
HIGH STRAIN RATE BEHAVIOUR  
OF AN AZ31 + 0.5 Ca MAGNESIUM ALLOY  
 
Zuzanka Trojanová1,∗, Pavel Lukáč1, Tomáš Podrábský2, Josef Pešička1 
 
1Department of Physics of Materials, Faculty of Mathematics and Physics, Charles University in Prague, Ke 
 Karlovu 5, 121 16 Praha 2, Czech Republic 
2Istitute of Materials Science and Engineering, Faculty of Mechanical Engineering, Brno University 
 of Technology, Technická 2896/2, CZ-616 69 Brno, Czech Republic 
∗Corresponding author, e-mail address: ztrojan@met.mff.cuni.cz 
 
 
Resume 
The paper reports behaviour of magnesium alloy AZ31 (nominal 
composition 3 % Al - 1 % Zn – balance Mg) with an addition of 0.5 wt. % 
Ca at high strain rates. Samples were prepared by the squeeze cast 
technology. Dynamic compression Hopkinson tests were performed at 
room temperature with impact velocities ranging from 11.2 to 21.9 m.s-1. 
A rapid increase of the flow stress and the strain rate sensitivity was 
observed at high strain rates. Transmission electron microscopy showed 
extremely high dislocation density and mechanical twins of two types. 
Adiabatic shear banding is discussed as the reason for the observed 
behaviour at high strain rates. 
 
 
 
 
Available online: http://fstroj.uniza.sk/journal-mi/PDF/2012/02-2012.pdf 
Article info 
Article history: 
Received 6 August 2011  
Accepted 10 October 2011 
Online 27 November 2011 
 
Keywords: 
Mechanical Properties;  
Magnesium Alloy; 
High Strain Rates; 
Dislocations; 
Mechanical Twins 
 
ISSN 1335-0803 (print version) 
ISSN 1338-6174 (online version) 
 
1. Introduction 
The strength of many metallic materials 
increases with increasing strain rate and 
decreases with increasing temperature. This 
behaviour is explained by thermally activated 
dislocation motion and interaction between 
dislocations and solute atoms. When temperature 
increases, there is more thermal energy available 
for dislocation motion, whereas when the strain 
rate increases the time necessary for overcoming 
of local obstacles in the slip plane is shorter. At 
low temperature and low and intermediate strain 
rates the deformation process is approximately 
isothermal. At higher strain rates, thermal 
conditions gradually change to adiabatic and the 
internal temperature of the sample increases. 
Then the deformation temperature is higher than 
ambient temperature. The strain hardening in 
magnesium alloys, i.e. increase of dislocation 
density during deformation, can be modified by 
mechanical twinning. Twins may contribute to 
straining but on the other hand, small twins are 
obstacles for dislocation motion; they contribute 
to the hardening. The high strain rate behaviour 
of metallic materials has been reported in 
various papers [1-4]. Recently, the critical 
review of high strain rate properties was done by 
Armstrong and Walley [5]. At high strain rates 
some critical strain rate exists at which the 
thermally activated rate controlling mechanism 
changes to viscous phonon drag [6]. Zerilli and 
Armstrong modified this idea including the 
dislocation drag into the model of thermal 
activation [7]. 
Mg-Al-Zn alloys offer good 
combination of the room temperature strength 
and ductility, good salt spray corrosion 
resistance and excellent die castability. They 
have been widely used in the automotive and 
electronic industries [8]. However, all applications 
of these alloys are limited to components T
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This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. 
To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/3.0/ or send a letter to Creative 
Commons, 444 Castro Street, Suite 900, Mountain View, California, 94041, USA. 
Z. Trojanová et al.: High strain rate behaviour of an AZ31+ 0.5 Ca magnesium alloy 
Materials Engineering - Materiálové inžinierstvo 19 (2012) 12-17 
13 
operating at temperatures lower than 400 K 
because of their rapid strength reduction at 
higher temperatures. In order to overcome this 
disadvantage, Ca - containing Mg alloys were 
developed with the aim to improve mechanical 
properties at elevated temperature. Ca is cheap 
and light alloying element [9]. Additionally, the 
Ca addition to magnesium alloys improves the 
creep resistance at elevated temperatures [10, 11]. 
The addition of Ca can refine the grain size, 
disperse the particle and break down the dendritic 
morphology of particle into round and well 
distributed small particles [8]. 
The objective of this work is to investigate 
the deformation behaviour of an AZ31 alloy 
with Ca addition in dynamic experiments at 
various strain rates.  
 
2. Experimental procedure 
0.5 wt. % of calcium was added to the 
commercial Mg alloy AZ31 (nominal 
composition: 3%Al, 1%Zn, balance Mg). The 
material was prepared using the squeeze casting 
technology. Cylindrical specimens of 9 mm 
diameter and 9 mm length were machined from 
the cast discs. The dynamic compression 
experiments were performed using split 
Hopkinson pressure bar (SHPB) technique. The 
SHPB test is the most commonly used method 
for determining material properties at high strain 
rates. The split Hopkinson bar apparatus consists 
of two long slender bars that sandwich a short 
cylindrical specimen between them. By striking 
the end of a bar, a compressive stress wave is 
generated that immediately begins to traverse 
towards the specimen. Upon arrival at the 
specimen, the wave partially reflects back 
towards the impact end. The remainder of the 
wave transmits through the specimen and into 
the second bar causing irreversible plastic 
deformation in the specimen. It is shown that the 
reflected and transmitted waves are proportional 
to the specimen’s strain rate and stress, 
respectively. Specimen strain can be determined 
by integrating the strain rate. By monitoring the 
strains in the two bars, specimen stress-strain 
properties can be calculated. The stress is done by  
( ) ( ) ( )[ ]ttt
S2
ES)t( tri
sam
bar ε+ε+ε=σ              (1) 
and 
( ) ( ) ( )[ ]∫ ε−ε−ε=ε
t
0
tri
sam
0 ttt
L
C)t( ,          (2) 
where εi(t), εr(t), εt(t) are incident, reflected and 
transmitted axial strains. Correspondent strain 
and strain rate can be calculated as 
( ) ( ) ( ) ( )[ ]ttt
L
C
t rri
sam
0 ε−ε−ε=ε& .             (3) 
In equation (3) E is the elastic modulus 
of bars, Sbar, Ssam are cross−sections of bar or 
sample, Lsam length of sample and C0 sound 
velocity. HSBP tests were performed at 
temperature of 28.5 °C. For comparison quasi-
static compression experiments at a strain rate of 
8.3x10-3  s-1 were performed. The activation 
volume was estimated in the stress relaxation 
test. Transmission electron microscopy (TEM) 
investigations were performed with a Jeol 2000 
FX electron microscope operated at 200 kV.  
 
3. Experimental results and discussion  
Transmission electron micrograph of the 
as prepared alloy is introduced in Fig. 1.  
 
Fig. 1. TEM micrograph of the as prepared alloy 
Z. Trojanová et al.: High strain rate behaviour of an AZ31+ 0.5 Ca magnesium alloy  
Materials Engineering - Materiálové inžinierstvo 19 (2012) 12-17 
14  
Relatively high dislocation density is 
a characteristic feature of this state. Segments of 
the dislocation network are visible in Fig. 1. It is 
a consequence of the squeeze cast technique 
used for the preparation of the material. 
Engineering stress-strain curves obtained for 
various impact velocities are introduced in Fig. 2 
for various impact velocities.  
 
strain ε
0.00 0.04 0.08 0.12 0.16
σ
 
(M
Pa
)
0
50
100
150
200
250
300
11.5
15.8
21.9
20.4
18.7
 
Fig. 2. Engineering stress-strain curves obtained 
for various impact velocities (in ms-) 
 
strain ε
0.00 0.04 0.08 0.12
st
ra
in
 
ra
te
 
dε
/d
t (s
-
1 )
0
500
1000
1500
2000
2500
3000
11.5 15.8
21.9
20.418.7
Fig. 3. Strain rate as a function of strain for various 
impact velocities (in ms-1) 
 
The strains dependences of the strain rate given 
in Fig. 3 were estimated for various impact 
velocities. The strain rate increases with 
increasing strain approaching its maximum value 
at a strain of approximately 0.02. 
The strain rate dependence of the yield stress is 
introduced in Fig. 4. Rapid increase of the strain 
rate sensitivity at high strain rates can be seen 
from Fig. 4. It should be note that each 
experiment at higher strain rates was performed 
several times. Values of the yield stress 
introduced in Fig. 4 are the mean values. The 
maximum strain rate dependence of the 
elongation to fracture εf is introduced in Fig. 5. 
Similarly as in the case of the yield stress the 
values of the fracture strain are the mean values 
estimated form the several experiments. 
Comparing with ductility estimated in the 
quasi−static experiment at room temperature, the 
fracture strain decreases, but in the high strain 
rate region it increases again with an increase in 
the strain rate.  
 
V~300b3
maximum strain rate (s-1)
10-3 10-2 10-1 100 101 102 103 104
yie
ld
 
st
re
ss
 
(M
Pa
)
60
70
80
90
100
110
120
V~1b3
V~500 b3
Fig. 4. Strain rate dependence of the yield stress 
 
maximum strain rate (s-1)
0 500 1000 1500 2000 2500
fra
ct
u
re
 
st
ra
in
 
ε f
0.00
0.05
0.10
0.15
0.20
0.25
0.30
 
Fig. 5. Strain rate dependence of the fracture strain 
 
3.1 Thermal activation 
The strain rate, ε& , and temperature, T, 
dependence of the flow stress, σ, depends on the 
Z. Trojanová et al.: High strain rate behaviour of an AZ31+ 0.5 Ca magnesium alloy 
Materials Engineering - Materiálové inžinierstvo 19 (2012) 12-17 
15 
dislocation rate controlling deformation 
mechanism. Usually this dependence is 
described by the Arrhenius equation: 





 ∆
−ε=ε
Tk
G
exp
B
0&&   ,                       (4) 
where 0ε& is the pre-exponential term, ∆G the 
Gibbs free enthalpy depending on the thermal 
(effective) stress σ* = σ−σi (σi is the internal 
stress). Kocks et al. [6] found the following 
empirical relationship for this dependence 
qp
0
0 1GG


















σ
σ
−∆=∆
∗
∗
 .                     (5) 
Model parameters p and q describe the statistical 
shape of the local obstacle profile. ∆G0 is the 
Gibbs free enthalpy necessary for overcoming a 
short range obstacle without the stress and *0σ  is 
the thermal stress at 0 K.  
The activation volume is defined as 
*
0
B*
/lnTkGV
σ∂
εε∂
=
σ∂
∆∂
=
&&
                   (6) 
and substituting from (5), we obtain 
1p
*
0
*
1qp
*
0
*
*
0
0 1pqGV
−
−








σ
σ


















σ
σ
−
σ
∆
= .        (7) 
Two sets of values are typically used [7]. The set 
p = q = 1 corresponds to a “rectangular” obstacle 
profile and a regular lattice arrangement of 
obstacles and leads to a constant activation 
volume V = m.kT/σ*. The set p = l/2 and q = 3/2 
corresponds to a more realistic obstacle shape 
and distribution. Geometrically, the activation 
volume V = b.d.L, where d is the obstacle width 
and L is the mean length of dislocation segments 
between obstacles. The strain rate sensitivity 
parameter  
ε








ε∂
σ∂
=
,T
*
*
ln
ln
m
&
 is often defined by its inverse,  
the stress sensitivity parameter m 
p
*
0
*
1qp
*
0
*
B
pq0
,T
*
1*
1
Tk
G
ln
ln
mm








σ
σ


















σ
σ
−
∆
=





σ∂
ε∂
==
−
ε
−
&
                 (8) 
Rapid increase of the strain rate sensitivity at 
higher strain rates is obvious from Fig. 3. 
Similar dependence was observed also in fcc 
metals (see for example [8]). The activation 
volume estimated at higher strain rates exhibits 
very small values, approximately V~b3, where b 
is the Burgers vector of dislocations. The value 
of the activation volume estimated at room 
temperature in the quasi−static experiment in the 
vicinity of the yield stress was V~500b3. The 
limiting small value of the activation volume 
estimated at high strain rates and rapid increase 
of the flow stress indicate a change in 
deformation mechanism. One possibility how to 
explain this behaviour is to consider the 
transition from thermal activation to drag-
controlled deformation that occurs when a 
constant structure is subjected to increasing 
stresses or strain rates. Zerilli and Armstrong [9] 
proposed a new model introducing the 
dislocation drag into the model of the thermal 
activation. They estimated that the dislocation 
drag may significantly change the strain rate 
dependence of the flow stress. From the results 
by Zerilli and Armstrong, it may be concluded 
that the dislocation drag at the strain rates in the 
order 103 s-1 has only marginal influence. The 
strong upturn observed for the flow stress is not 
caused by the dislocation drag. 
 
3.2. Adiabatic shear banding 
The mean velocity of dislocations v is 
connected with the plastic strain rate by the 
Orowan equation 
vb)/1( mρψ=ε&                      (9) 
where ρm is the density of mobile dislocations 
and ψ is Taylor orientation factor. In Eq. (9) 
the mobile dislocation density is considered to be  
Z. Trojanová et al.: High strain rate behaviour of an AZ31+ 0.5 Ca magnesium alloy  
Materials Engineering - Materiálové inžinierstvo 19 (2012) 12-17 
16  
constant in a certain strain interval. At high 
strain rates the mobile dislocation density ρm 
changes and the different equation must be used: 
xb
dt
d)/1( ρψ=ε& ,                             (10) 
where dρ/dt is the dislocation generation rate 
and x is the average distance moved by 
dislocations. Equation (9) is usually used at low 
or intermediate 
strain rates while the equation (10) is more 
suitable for high strain rates. The sample 
temperature may be influenced by the 
experimental conditions. A direct conversion of 
mechanical work produced during deformation 
to heat produces an average rise in temperature, 
∆T, within a material volume without loss of 
heat from it. ∆T in the absence of any change in 
internal energy of the material (∆E = 0) is 
obtained as [10] 
∫
ε
εσ=∆
p
0
p
v
d
c
1T ,                      (11) 
where cv is the specific heat per unit volume, σ is 
the applied stress, and εp is plastic strain. The 
strain dependence of the heating is directly 
proportional to the value of σ. 
vp cd
dT σ
=
ε
                             (12) 
For the maximum strain rate of 2.427x103 s-1 the 
corresponding stress is 150 MPa. With 
cv = 1.85x106 Jm-3K-1 for AZ31 alloy a value of 
dT/dεp = 81 K per unit strain may be calculated. 
A rise of temperature of a few degrees is 
obtained for each percent of strain which the 
material undergoes. This relatively small 
increase of temperature is due to the averaging 
and presuming of continuity of the plastic flow 
process. On the other hand, Armstrong et al. [10] 
considered only localized rise of temperature 
which may be followed by the adiabatic shear 
banding. Such adiabatic forming of shear bands 
was also used to explain the discontinuous 
plastic deformation at very low temperatures 
[11].  
TEM showed very high dislocation density 
in the deformed samples as it is 
demonstrated in Fig. 6.  
The density of dislocations was 
estimated to be 7−8x 1014 m-2. At higher strain 
rates the waiting time of dislocations at the local 
obstacles is very small. This may contribute to 
the formation of dislocation pile−ups. The 
locally concentrated stress (and therefore plastic 
work) at the tip of the pile−ups allows reaching a 
higher local temperature. Strong internal obstacles 
 
 
Fig. 6. TEM micrograph of the sample deformed 
at highest strain rate 
 
 
 
Fig. 7. Massive twins observed in deformed samples 
 
Z. Trojanová et al.: High strain rate behaviour of an AZ31+ 0.5 Ca magnesium alloy 
Materials Engineering - Materiálové inžinierstvo 19 (2012) 12-17 
17 
existing in the material can be overcome by the 
sudden release of pile−ups (or analogous 
deformation twins or cleavage cracks). 
Extensive twinning was found almost in all areas 
of the specimen. Observed twins were of two 
types. Between massive twins presented in Fig. 
7, micro-twins were observed (Fig. 8). The 
density of these micro-twins increased with 
increasing strain rate. The adiabatic heating 
causes also the observed increase of the fracture 
strain with increasing strain rate in the dynamic 
tests.  
 
Fig. 8. Micro-twins observed in regions 
between massive twins 
 
4. Conclusions 
The experiments performed using the split 
Hopkinson pressure bar showed: 
• rapid rise of the flow stress at high strain 
rates; 
• rapid increase of the strain rate 
sensitivity at high strain rates; 
• limiting low value of the activation 
volume (~b3); 
• extremely high dislocation density in 
deformed samples. 
Experiments at high strain rates and the TEM 
analysis allow us to conclude that the main 
deformation mechanism at high strain rates is the 
adiabatic shear banding with the high rates of 
dislocation and twins formation. 
 
 
Acknowledgements 
This work is a part of the Research 
Project 1M 2560471601 "Eco-centre for Applied 
Research of Non-ferrous Metals" that is financed 
by the Ministry of Education, Youth and Sports 
of the Czech Republic. The support of the Grant 
Agency of the Academy of Sciences of the Czech 
Republic by the Grant Nr. IAA201120902 is also 
greatly acknowledged.  
 
References 
[1] R. Kapoor, J.B. Singh, J.K. Chakravartty: Mater. 
Sci. Eng. A 496 (2008) 308-315. 
[2] M.A. Meyers, Y.B. Xu, Q. Xue, M.T. Perez-
Prado, T.R. McNelley: Acta Mater. 51 (2003) 
1307-1325.  
[3] G. Dirrasa, A. Ouarem, H. Couque, J. Gubicza, 
P. Szommer, O. Brinza: Mater. Charact. 62 
(2011) 480-487. 
[4] M.G. da Silva, K.T. Ramesh: Mater. Sci. Eng. 
232 (1997) 11-22. 
[5] R.W. Armstrong, S.M. Waley: Inter. Mater. Rev. 
53 (2008) 105-128. 
[6] U.F. Kocks, A.S. Argon, M.F. Ashby: Progress 
in Mater. Sci. 19 (1975) 1-207. 
[7] 1.G. Regazzoni, U.F. Kocks, P.S. Follansbee: 
Acta Metall. 35 (1987) 2865-2875. 
[8] P.S. Follansbee, G. Regazzoni, U.F. Kocks: Ins. 
Phys. Conf. Ser. 70 (1984) 71-80.  
[9] F.J. Zerilli, R.W. Armstrong: Acta Metall. Mater. 
40 (1992) 1803-1808. 
[10] R.W. Armstrong, S.C. Coffey, W.I. Elban: Acta 
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[11] V.I. Startsev: Dislocations in Solids Vol. 6 (Ed. 
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pp. 145-233. 
 


English

HIGH STRAIN RATE BEHAVIOUR OF AN AZ31 + 0.5 Ca MAGNESIUM ALLOY

The paper reports behaviour of magnesium alloy AZ31 (nominal composition 3 % Al - 1 % Zn – balance Mg) with an addition of 0.5 wt. % Ca at high strain rates. Samples were prepared by the squeeze cast technology. Dynamic compression Hopkinson tests were performed at room temperature with impact velocities ranging from 11.2 to 21.9 m.s-1. A rapid increase of the flow stress and the strain rate sensitivity was observed at high strain rates. Transmission electron microscopy showed extremely high dislocation density and mechanical twins of two types. Adiabatic shear banding is discussed as the reason for the observed behaviour at high strain rates. </span

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Z. Trojanová et al.: High strain rate behaviour of an AZ31+ 0.5 Ca magnesium alloy  Materials Engineering - Materiálové inžinierstvo 19 (2012) 12-17 12  HIGH STRAIN RATE BEHAVIOUR  OF AN AZ31 + 0.5 Ca MAGNESIUM ALLOY   Zuzanka Trojanová1,∗, Pavel Lukáč1, Tomáš Podrábský2, Josef Pešička1  1Department of Physics of Materials, Faculty of Mathematics and Physics, Charles University in Prague, Ke  Karlovu 5, 121 16 Praha 2, Czech Republic 2Istitute of Materials Science and Engineering, Faculty of Mechanical Engineering, Brno University  of Technology, Technická 2896/2, CZ-616 69 Brno, Czech Republic ∗Corresponding author, e-mail address: ztrojan@met.mff.cuni.cz   Resume The  paper  reports  behaviour  of  magnesium  alloy  AZ31  (nominal composition 3 % Al - 1 % Zn – balance Mg) with an addition of 0.5 wt. % Ca  at  high  strain  rates.  Samples  were  prepared  by  the  squeeze  cast technology.  Dynamic  compression  Hopkinson  tests  were  performed  at room temperature with impact velocities ranging from 11.2 to 21.9 m.s-1. A rapid  increase  of  the  flow  stress  and  the  strain  rate  sensitivity  was observed at high strain rates. Transmission electron microscopy showed extremely high dislocation density and mechanical twins of two types. Adiabatic  shear  banding  is  discussed  as  the  reason  for  the  observed behaviour at high strain rates.     Available online: http://fstroj.uniza.sk/journal-mi/PDF/2012/02-2012.pdf Article info Article history: Received 6 August 2011  Accepted 10 October 2011 Online 27 November 2011  Keywords: Mechanical Properties;  Magnesium Alloy; High Strain Rates; Dislocations; Mechanical Twins  ISSN 1335-0803 (print version) ISSN 1338-6174 (online version)  1. Introduction The strength of many metallic materials increases  with  increasing  strain  rate  and decreases  with  increasing  temperature.  This behaviour  is  explained  by  thermally  activated dislocation  motion  and  interaction  between dislocations and solute atoms. When temperature increases, there is more thermal energy available for dislocation motion, whereas when the strain rate increases the time necessary for overcoming of local obstacles in the slip plane is shorter. At low temperature and low and intermediate strain rates the  deformation  process is approximately isothermal.  At  higher  strain  rates,  thermal conditions gradually change to adiabatic and the internal  temperature  of  the  sample  increases. Then the deformation temperature is higher than ambient  temperature.  The  strain  hardening  in magnesium  alloys,  i.e.  increase  of  dislocation density during deformation, can be modified by mechanical  twinning.  Twins  may  contribute  to straining but on the other hand, small twins are obstacles for dislocation motion; they contribute to the hardening. The high strain rate behaviour of  metallic  materials  has  been  reported  in various  papers  [1-4].  Recently,  the  critical review of high strain rate properties was done by Armstrong and Walley [5]. At high strain rates some  critical  strain  rate  exists  at  which  the thermally  activated  rate  controlling  mechanism changes to viscous phonon drag [6]. Zerilli and Armstrong  modified  this  idea  including  the dislocation  drag  into  the  model  of  thermal activation [7]. Mg-Al-Zn  alloys  offer  good combination  of  the  room  temperature  strength and  ductility,  good  salt  spray  corrosion resistance  and  excellent  die  castability.  They have  been  widely  used  in  the  automotive  and electronic industries [8]. However, all applications of  these  alloys  are  limited  to  components This copy of the article was downloaded from http://www.mateng.uniza.sk , online version of Materials Engineering / Materiálové inžinierstvo journal, ISSN 1335-0803 (print version), ISSN 1338-6174(online version)  This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/3.0/ or send a letter to Creative Commons, 444 Castro Street, Suite 900, Mountain View, California, 94041, USA. Z. Trojanová et al.: High strain rate behaviour of an AZ31+ 0.5 Ca magnesium alloy Materials Engineering - Materiálové inžinierstvo 19 (2012) 12-17 13 operating  at  temperatures  lower  than  400  K because  of  their  rapid  strength  reduction  at higher temperatures. In order to overcome this disadvantage,  Ca  -  containing  Mg  alloys  were developed with the aim to improve mechanical properties at elevated temperature. Ca is cheap and light alloying element [9]. Additionally, the Ca  addition  to  magnesium  alloys  improves  the creep resistance at elevated temperatures [10, 11]. The  addition  of  Ca  can  refine  the  grain  size, disperse the particle and break down the dendritic morphology  of  particle  into  round  and  well distributed small particles [8]. The objective of this work is to investigate the  deformation  behaviour  of  an  AZ31  alloy with  Ca  addition  in  dynamic  experiments  at various strain rates.   2. Experimental procedure 0.5  wt. %  of  calcium  was  added  to  the commercial  Mg  alloy  AZ31  (nominal composition:  3%Al,  1%Zn,  balance  Mg).  The material was prepared using the squeeze casting technology.  Cylindrical  specimens  of  9  mm diameter and 9 mm length were machined from the  cast  discs.  The  dynamic  compression experiments  were  performed  using  split Hopkinson pressure bar (SHPB) technique. The SHPB test is the most commonly used method for determining material properties at high strain rates. The split Hopkinson bar apparatus consists of two long slender bars that sandwich a short cylindrical specimen between them. By striking the end of a bar, a compressive stress wave is generated  that  immediately  begins  to  traverse towards  the  specimen.  Upon  arrival  at  the specimen,  the  wave  partially  reflects  back towards  the  impact  end.  The  remainder  of  the wave  transmits  through  the  specimen  and  into the  second  bar  causing  irreversible  plastic deformation in the specimen. It is shown that the reflected and transmitted waves are proportional to  the  specimen’s  strain  rate  and  stress, respectively. Specimen strain can be determined by integrating the strain rate. By monitoring the strains in the two bars, specimen stress-strain properties can be calculated. The stress is done by  ( ) ( ) ( ) [ ] t t tS 2ES) t ( t r isambar ε + ε + ε = σ              (1) and ( ) ( ) ( ) [ ] ∫ ε − ε − ε = εt0t r isam0 t t tLC) t ( ,          (2) where εi(t), εr(t), εt(t) are incident, reflected and transmitted  axial  strains.  Correspondent  strain and strain rate can be calculated as ( ) ( ) ( ) ( ) [ ] t t tLCt r r isam0 ε − ε − ε = ε & .             (3) In equation (3) E is the elastic modulus of  bars,  Sbar,  Ssam  are  cross−sections  of  bar  or sample,  Lsam  length  of  sample  and  C0  sound velocity.  HSBP  tests  were  performed  at temperature of 28.5 °C. For comparison quasi-static compression experiments at a strain rate of 8.3x10-3  s-1  were  performed.  The  activation volume  was  estimated  in  the  stress  relaxation test.  Transmission  electron  microscopy  (TEM) investigations were performed with a Jeol 2000 FX electron microscope operated at 200 kV.   3. Experimental results and discussion  Transmission  electron  micrograph  of  the as prepared alloy is introduced in Fig. 1.   Fig. 1. TEM micrograph of the as prepared alloy Z. Trojanová et al.: High strain rate behaviour of an AZ31+ 0.5 Ca magnesium alloy  Materials Engineering - Materiálové inžinierstvo 19 (2012) 12-17 14  Relatively  high  dislocation  density  is a characteristic feature of this state. Segments of the dislocation network are visible in Fig. 1. It is a  consequence  of  the  squeeze  cast  technique used  for  the  preparation  of  the  material. Engineering  stress-strain  curves  obtained  for various impact velocities are introduced in Fig. 2 for various impact velocities.   strain ε0.00 0.04 0.08 0.12 0.16σ (MPa)05010015020025030011.515.821.920.418.7 Fig. 2. Engineering stress-strain curves obtained for various impact velocities (in ms-)  strain ε0.00 0.04 0.08 0.12strain rate dε/dt (s-1)05001000150020002500300011.5 15.821.920.4 18.7Fig. 3. Strain rate as a function of strain for various impact velocities (in ms-1)  The strains dependences of the strain rate given in  Fig.  3  were  estimated  for  various  impact velocities.  The  strain  rate  increases  with increasing strain approaching its maximum value at a strain of approximately 0.02. The strain rate dependence of the yield stress is introduced in Fig. 4. Rapid increase of the strain rate sensitivity at high strain rates can be seen from  Fig. 4.  It  should  be  note  that  each experiment at higher strain rates was performed several  times.  Values  of  the  yield  stress introduced in Fig. 4 are the mean  values. The maximum  strain  rate  dependence  of  the elongation to fracture εf is introduced in Fig. 5. Similarly as in the case of the yield stress the values of the fracture strain are the mean values estimated  form  the  several  experiments. Comparing  with  ductility  estimated  in  the quasi−static experiment at room temperature, the fracture strain decreases, but in the high strain rate region it increases again with an increase in the strain rate.   V~300b3maximum strain rate (s-1)10-3 10-2 10-1 100 101 102 103 104yield stress (MPa)60708090100110120V~1b3V~500 b3Fig. 4. Strain rate dependence of the yield stress  maximum strain rate (s-1)0 500 1000 1500 2000 2500fracture strain εf0.000.050.100.150.200.250.30 Fig. 5. Strain rate dependence of the fracture strain  3.1 Thermal activation The strain rate,  ε & , and temperature, T, dependence of the flow stress, σ, depends on the Z. Trojanová et al.: High strain rate behaviour of an AZ31+ 0.5 Ca magnesium alloy Materials Engineering - Materiálové inžinierstvo 19 (2012) 12-17 15 dislocation  rate  controlling  deformation mechanism.  Usually  this  dependence  is described by the Arrhenius equation:    ∆− ε = εT kGexpB0 & &   ,                       (4) where  0 ε & is  the  pre-exponential  term,  ∆G  the Gibbs  free  enthalpy  depending  on  the  thermal (effective) stress  σ*  =  σ−σi  (σi  is  the  internal stress).  Kocks  et  al.  [6]  found  the  following empirical relationship for this dependence q p00 1 G Gσσ− ∆ = ∆∗∗ .                     (5) Model parameters p and q describe the statistical shape  of the  local  obstacle  profile.  ∆G0  is  the Gibbs free enthalpy necessary for overcoming a short range obstacle without the stress and  *0 σ  is the thermal stress at 0 K.  The activation volume is defined as *0B */ lnT kGVσ ∂ε ε ∂=σ ∂∆ ∂=& &                   (6) and substituting from (5), we obtain 1 p*0*1 q p*0**00 1pq GV− −σσσσ−σ∆= .        (7) Two sets of values are typically used [7]. The set p = q = 1 corresponds to a “rectangular” obstacle profile  and  a  regular  lattice  arrangement  of obstacles  and  leads  to  a  constant  activation volume V = m.kT/σ*. The set p = l/2 and q = 3/2 corresponds  to  a  more  realistic  obstacle  shape and  distribution.  Geometrically,  the  activation volume V = b.d.L, where d is the obstacle width and L is the mean length of dislocation segments between  obstacles.  The  strain  rate  sensitivity parameter  εε ∂σ ∂=, T**lnlnm& is often defined by its inverse,  the stress sensitivity parameter m p*0*1 q p*0*Bpq 0, T*1 *1T kGlnlnm mσσσσ−∆=   σ ∂ε ∂= =−ε− &                 (8) Rapid  increase  of  the  strain  rate  sensitivity  at higher  strain  rates  is  obvious  from  Fig.  3. Similar  dependence  was  observed  also  in  fcc metals  (see  for  example  [8]).  The  activation volume estimated at higher strain rates exhibits very small values, approximately V~b3, where b is the Burgers vector of dislocations. The value of  the  activation  volume  estimated  at  room temperature in the quasi−static experiment in the vicinity  of  the  yield  stress  was  V~500b3.  The limiting  small  value  of  the  activation  volume estimated at high strain rates and rapid increase of  the  flow  stress  indicate  a  change  in deformation mechanism. One possibility how to explain  this  behaviour  is  to  consider  the transition  from  thermal  activation  to  drag-controlled  deformation  that  occurs  when  a constant  structure  is  subjected  to  increasing stresses or strain rates. Zerilli and Armstrong [9] proposed  a  new  model  introducing  the dislocation drag into the model of the thermal activation.  They  estimated  that  the  dislocation drag  may  significantly  change  the  strain  rate dependence of the flow stress. From the results by Zerilli and Armstrong, it may be concluded that the dislocation drag at the strain rates in the order  103  s-1  has  only  marginal  influence. The strong upturn observed for the flow stress is not caused by the dislocation drag.  3.2. Adiabatic shear banding The  mean  velocity  of  dislocations  v  is connected  with  the  plastic  strain  rate  by  the Orowan equation v b ) / 1 ( m ρ ψ = ε &                      (9) where ρm is the density of mobile dislocations and  ψ  is  Taylor  orientation  factor.  In  Eq.  (9) the mobile dislocation density is considered to be  Z. Trojanová et al.: High strain rate behaviour of an AZ31+ 0.5 Ca magnesium alloy  Materials Engineering - Materiálové inžinierstvo 19 (2012) 12-17 16  constant  in  a  certain  strain  interval.  At  high strain  rates  the  mobile  dislocation  density  ρm changes and the different equation must be used: x bdtd) / 1 (ρψ = ε & ,                             (10) where  dρ/dt  is  the  dislocation  generation  rate and  x  is  the  average  distance  moved  by dislocations. Equation (9) is usually used at low or intermediate strain  rates  while  the  equation  (10)  is  more suitable  for  high  strain  rates.  The  sample temperature  may  be  influenced  by  the experimental conditions. A direct conversion of mechanical  work  produced  during  deformation to heat produces an average rise in temperature, ∆T,  within  a  material  volume  without  loss  of heat from it. ∆T in the absence of any change in internal  energy  of  the  material  (∆E = 0)  is obtained as [10] ∫εε σ = ∆p0pvdc1T ,                      (11) where cv is the specific heat per unit volume, σ is the applied stress, and εp is plastic strain. The strain  dependence  of  the  heating  is  directly proportional to the value of σ. v p c ddT σ=ε                             (12) For the maximum strain rate of 2.427x103 s-1 the corresponding  stress  is  150  MPa.  With cv = 1.85x106 Jm-3K-1 for AZ31 alloy a value of dT/dεp = 81 K per unit strain may be calculated. A  rise  of  temperature  of  a  few  degrees  is obtained  for  each  percent  of  strain  which  the material  undergoes.  This  relatively  small increase of temperature is due to the averaging and presuming of continuity of the plastic flow process. On the other hand, Armstrong et al. [10] considered  only  localized  rise  of  temperature which may be followed by the adiabatic shear banding. Such adiabatic forming of shear bands was  also  used  to  explain  the  discontinuous plastic  deformation  at  very  low  temperatures [11].  TEM showed very high dislocation density in  the  deformed  samples  as  it  is demonstrated in Fig. 6.  The  density  of  dislocations  was estimated to be 7−8x 1014 m-2. At higher strain rates the waiting time of dislocations at the local obstacles is very small. This may contribute to the  formation  of  dislocation  pile−ups.  The locally concentrated stress (and therefore plastic work) at the tip of the pile−ups allows reaching a higher local temperature. Strong internal obstacles   Fig. 6. TEM micrograph of the sample deformed at highest strain rate    Fig. 7. Massive twins observed in deformed samples  Z. Trojanová et al.: High strain rate behaviour of an AZ31+ 0.5 Ca magnesium alloy Materials Engineering - Materiálové inžinierstvo 19 (2012) 12-17 17 existing in the material can be overcome by the sudden  release  of  pile−ups  (or  analogous deformation  twins  or  cleavage  cracks). Extensive twinning was found almost in all areas of  the  specimen.  Observed  twins  were  of  two types. Between massive twins presented in Fig. 7,  micro-twins  were  observed  (Fig.  8).  The density  of  these  micro-twins  increased  with increasing  strain  rate.  The  adiabatic  heating causes also the observed increase of the fracture strain with increasing strain rate in the dynamic tests.   Fig. 8. Micro-twins observed in regions between massive twins  4. Conclusions The  experiments  performed  using  the  split Hopkinson pressure bar showed: •  rapid rise of the flow stress at high strain rates; •  rapid  increase  of  the  strain  rate sensitivity at high strain rates; •  limiting  low  value  of  the  activation volume (~b3); •  extremely  high  dislocation  density  in deformed samples. Experiments  at  high  strain  rates  and  the  TEM analysis  allow  us  to  conclude  that  the  main deformation mechanism at high strain rates is the adiabatic  shear  banding  with  the  high  rates  of dislocation and twins formation.   Acknowledgements This  work  is  a  part  of  the  Research Project 1M 2560471601 "Eco-centre for Applied Research of Non-ferrous Metals" that is financed by the Ministry of Education, Youth and Sports of the Czech Republic. The support of the Grant Agency of the Academy of Sciences of the Czech Republic by the Grant Nr. IAA201120902 is also greatly acknowledged.   References [1]  R. Kapoor, J.B. Singh, J.K. Chakravartty: Mater. Sci. Eng. A 496 (2008) 308-315. [2]  M.A.  Meyers,  Y.B.  Xu,  Q.  Xue,  M.T.  Perez-Prado,  T.R.  McNelley:  Acta  Mater.  51  (2003) 1307-1325.  [3]  G. Dirrasa, A. Ouarem, H. Couque, J. Gubicza, P.  Szommer,  O.  Brinza:  Mater.  Charact.  62 (2011) 480-487. [4]  M.G.  da  Silva,  K.T.  Ramesh:  Mater.  Sci.  Eng. 232 (1997) 11-22. [5]  R.W. Armstrong, S.M. Waley: Inter. Mater. Rev. 53 (2008) 105-128. [6]  U.F. Kocks, A.S. Argon, M.F. Ashby: Progress in Mater. Sci. 19 (1975) 1-207. [7]  1.G.  Regazzoni,  U.F.  Kocks,  P.S.  Follansbee: Acta Metall. 35 (1987) 2865-2875. [8]  P.S. Follansbee, G. Regazzoni, U.F. Kocks: Ins. Phys. Conf. Ser. 70 (1984) 71-80.  [9]  F.J. Zerilli, R.W. Armstrong: Acta Metall. Mater. 40 (1992) 1803-1808. [10] R.W. Armstrong, S.C. Coffey, W.I. Elban: Acta Metall. 30 (1982) 2111-2116. [11] V.I. Startsev: Dislocations in Solids Vol. 6 (Ed. F.R.N.  Nabarro)  North  Holland  Publishing Company, Amsterdam- NewYork-Oxford, 1983, pp. 145-233.  

HIGH STRAIN RATE BEHAVIOUR OF AN AZ31 + 0.5 Ca MAGNESIUM ALLOY

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