Creep behaviour of eutectic SnBi alloy and its constituent phases
using nanoindentation technique
Lu Shen a,b , Pin Lu a , Shijie Wang a , Zhong Chen b,⇑
a Institute of Materials Research and Engineering, A STAR (Agency for Science, Technology and Research), 3 Research Link, Singapore 117602, Singapore
b School of Materials Science and Engineering, Nanyang Technological University, Nanyang Avenue, Singapore 639798, Singapore
Received 29 December 2012
Received in revised form 3 April 2013
Accepted 9 April 2013
Available online 15 April 2013
Constant strain rate
Eutectic SnBi, with a melting point of 139 °C, is one of the
favourite lead-free solders which draw a lot of interests due to
comparable mechanical strength with traditional SnPb solders
[1–3]. However, due to its relatively high homologous temperature,
eutectic SnBi may suffer from serious creep-related issues
at service conditions. It is thus crucial to understand the creep
behaviour of this alloy before it can be widely adopted in the
microelectronic industry. Conventional creep studies show that
creep behaviour of eutectic SnBi is stress sensitive [1,4–7]. At high
stress region, creep rate of the alloy is controlled by dislocation
climb; while at low stress region, it is controlled by diffusional
creep at grain boundaries.
With the increasing trend of microelectronic miniaturization,
technique such as nanoindentation has been widely adopted to
evaluate elastic–plastic properties for millimetre to micron-sized
features such as solder joints [3,8–10]. In evaluating the timedependent
plastic properties using this technique, two testing
schemes, i.e., constant load hold (CLH) and constant strain rate
(CSR), are generally used. These methods are analogous to the conventional
constant stress and constant strain rate tests.
⇑ Corresponding author. Tel.: +65 6790 4256; fax: +65 6790 9081.
E-mail address: ASZChen@ntu.edu.sg (Z. Chen).
0925-8388/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved.
Journal of Alloys and Compounds 574 (2013) 98–103
Contents lists available at SciVerse ScienceDirect
Journal of Alloys and Compounds
journal homepage: www.elsevier.com/locate/jalcom
Creep behaviour of eutectic tin–bismuth (SnBi) and its constituent phase materials was studied using
constant strain rate (CSR) nanoindentation. Eight strain rates from 5 10 4 to 0.1 s 1 were used to assess
their strain rate–stress relationship. The stress exponents of 12.25 and 10.09 were found for Sn–3%Bi and
pure Bi, respectively, suggesting power-law breakdown (PLB) as the rate controlling mechanism for the
two constituent single-phase materials. Strain bursts that appear at the initial stage of loading of the
single-phase materials were found to be a prerequisite to cause dislocation creep at the later stage of
deformation. Grain boundary sliding (GBS) was found as the complementary mechanism to accommodate
grain shape change in Sn–3%Bi and pure Bi as proven by post-indent microstructural examination.
Eutectic SnBi showed bi-linear strain rate dependent creep behaviour with the transition at around
2 10 3 s 1 . Stress exponent of 2.35 was found at low strain rate region suggesting that GBS dominates
the creep deformation. At the high strain rate region, stress exponent of 5.20 suggests that dislocation
climb in the crystal lattice is the creep mechanism.
Ó 2013 Elsevier B.V. All rights reserved.
Conventionally, CLH is widely adopted by researchers due to its
easiness in test control using an indentation system [8–13]. The
stress and strain rate responses are collected along the constant
load holding process. However, during the holding process of a
CLH test, the indenter continuously penetrates into the material,
making the contact stress a variable during the holding period.
As discussed in our previous paper , genuine steady-state
may not be achieved in load holding test. As a result, creep mechanism
deduced from such testing scheme is ambiguous as the analytical
models for the calculation of stress exponent and activation
energy are developed based on single steady-state creep model
 or transient creep model . Lately, constant strain rate
(CSR) test was developed owing to the advancement in nanoindentation
instrumentation. The measured creep properties from such
test method are matched well with those obtained by conventional
tensile creep studies [16,17]. One distinct advantage of CSR over
CLH test is that steady-state creep stage can be readily achieved
in the deformation process [14,16]. Stress–strain rate curves are
obtained from multiple tests which resemble the conventional tensile
creep test. In this paper, the stress exponents of eutectic SnBi
alloy and its two constituent phase materials, Sn–3 wt%Bi and pure
Bi, were evaluated by nanoindentation CSR method. The creep
mechanisms are suggested by correlation with the stress exponents
as well as observation of the microstructure of the deformed
surface around indentation area.
2.1. Indentation stress and strain rate
Representative stress (r) from an indentation test is defined as
the instantaneous load (P) divided by projected contact area (Ac),
which is also the definition of indentation hardness (H):
r ¼ H ¼ P
The representative strain rate is defined as the indentation displacement
rate ð _ h ¼ dh=dtÞ divided by the instantaneous displacement
2.2. Calculation of stress exponent
Stress exponent (n) describes the stress-dependence of the
materials’ deformation rate during steady state creep process. A
power-law creep behaviour can be described by Eq. (3), in which
r is stress, n is stress exponent and E is elastic modulus of the
_e ¼ A r n
2.3. Elastic modulus evaluated from nanoindentation test
The elastic modulus, E, of the test specimen is related to the indenter
modulus (Ei) and reduced modulus (Er) with the relationship
following contact mechanics:
2 1 v
L. Shen et al. / Journal of Alloys and Compounds 574 (2013) 98–103 99
Fig. 1. (a) SEM image of eutectic SnBi alloy showing two distinct constituent phases. (b) Optical microscope (OM) image of etched surface of Sn–3%Bi. (c) OM image of etched
pure Bi surface.
where the subscript i denotes the property of the indenter. t is Poisson’s
ratio and a value of 0.35 is used for Sn-based alloys. Ei = 1140 -
GPa and ti = 0.07 for the diamond indenter.
Er is calculated from stiffness (S) according to:
Er ¼ 1
pffiffiffiffiffi S ð5Þ
where S is obtained along indentation loading in which an oscillated
force is superimposed on the nominal force. b is a geometrical constant
taken as 0.75 for Berkovich indenter .
3.1. Materials and sample preparation
Eutectic SnBi alloy was prepared by heating eutectic SnBi paste (ESL EUROPE Ò )
at 300 °C for 1 h followed by air-cooling. The obtained alloy beads with a diameter
of about 4 mm were embedded in an epoxy mould. The samples were then grinded
and polished for subsequent microstructure and nanoindentation studies. According
to SnBi phase diagram , at room temperature negligible amount of Sn is dissolved
in the Bi phase, thus subsequently the phase is denoted as pure Bi phase.
Around 3 wt% of Bi is soluble in the Sn phase. Fig. 1a shows the polished cross-sectional
area of the SnBi alloy, in which two distinct phases are present. The bright
region is the pure Bi phase; while the dark region is the Sn-rich (3 wt.% Bi) phase.
Single-phase Sn–3%Bi and pure Bi samples were separately prepared in order to
compare their mechanical properties with those of the two-phase SnBi alloy. Pure
Bi (99.99%, Sigma–Aldrich Ó ) with a diameter of approximately 4 mm were used
in the as-received form. The Sn–3%Bi sample was prepared by mixing small chunks
of pure Sn with Bi powders (99.99%, Sigma–Aldrich Ó ) at a weight ratio of 97:3. The
mixture was heated up to 300 °C for 1 h before air-cooled. Fig. 1b and c shows the
microstructure of etched cross-sections of Sn–3%Bi and Bi, which show polycrystalline
structure with average grain size of 9 lm and 111.1 lm, respectively.
3.2. Nanoindentation CSR experiment
The nanoindentation tests were performed using an MTS Nano Indenter XP Ò
system with a Berkovich indenter. Eight constant strain rates ranging from
5 10 4 s 1 to 0.1 s 1 were applied until the indenter reaches 4 lm deep into
the samples. The load was then held constant for 10 s followed by unloading. Five
measurements were performed for each strain rate condition. The indenter area
function, which was used to describe the actual shape of the indenter tip, was
100 L. Shen et al. / Journal of Alloys and Compounds 574 (2013) 98–103
Fig. 2. Load–displacement curves of (a) SiO 2, (b) eutectic SnBi alloy, (c) Sn–3%Bi,
and (d) Bi obtained at three strain rates.
calibrated using standard fused silica (SiO 2) sample. Constant strain rate tests were
also performed on the silica sample as a reference. It is expected that strain rate
should have no effect on the stresses in the silica sample at the test temperature.
4. Results and discussion
4.1. Load–displacement (P–h) curves
Fig. 2a through d plot the P–h curves of the materials tested under
different strain rates. Three strain rates, i.e., 0.1, 0.01, and
Characteristics of the first strain burst event in Sn–3%Bi and pure Bi at different strain
Materials Strain rate (s 1 ) p0 (mN) h0 (nm) s0 (N/m) Modulus
Sn–3%Bi 0.001 0.148 53.95 2745.3 49.34 ± 1.67
Sn–3%Bi 0.005 0.066 30.15 2189.1 49.34 ± 2.67
Sn–3%Bi 0.05 0.106 34.62 3061.8 49.04 ± 0.82
Sn–3%Bi 0.1 0.100 36.41 2816.6 47.34 ± 0.69
Bi 0.001 0.079 64.67 1263.4 25.33 ± 0.89
Bi 0.005 0.015 15.24 984.3 26.51 ± 2.41
Bi 0.05 0.010 8.92 1070.6 25.88 ± 2.04
Bi 0.1 0.025 20.89 1228.5 25.84 ± 2.34
Load on sample (mN)
Load on sample (mN)
Strain rate = 0.005 s -1
0 1000 2000 3000 4000 5000
Indentation depth (nm)
Strain rate = 0.1 s -1
0 1000 2000 3000 4000 5000
Indentation depth (nm)
Fig. 3. Load–displacement curves of Sn–3%Bi, Bi and eutectic SnBi obtained at strain
rate of (a) 0.005 s 1 and (b) 0.1 s 1 .
0.001 s 1 , were chosen for comparison. The reference silica, as a
verification of the measurement, displays insensitivity to strain
rate as the three curves obtained at different strain rates overlap
(Fig. 2a). For the other three materials, distinct strain rate sensitivity
is displayed on the plots where the P–h curves obtained at lower
strain rates are incubated by those tested at faster strain rates. In
general, the stress increases for all three materials when deformed
at a higher strain rate.
The response of polycrystalline material to indentation load is
subject to the change in the indentation location if the indentation
size is comparable with the grain size. However, for fine grained
homogeneous materials, the measured creep data should remain
unchanged because of the microstructural uniformity around the
indentation area. In the present study, the average inter-phase
spacing of the eutectic SnBi alloy is about 2.62 lm. The length of
the triangle edge from the indentation is 20–30 lm. Therefore it
is reasonable that the indentation location should have no influence
on the measurement as it averages the contributions from different
phases/grains under one indent. On the other hand, the
average grain sizes for pure Bi and Sn–3%Bi are 9 lm and
111.1 lm, respectively. Multiple indents have been made at each
testing condition on these two materials. The repeatability of
Load on sample (mN)
Load on sample (mN)
Strain rate = 0.001 s
0 50 100 150 200
Indentation depth (nm)
Strain rate = 0.1 s -1
0 50 100
Indentation depth (nm)
Fig. 4. (a) The initial 200 nm P–h curves of Sn–3%Bi, Bi and eutectic SnBi obtained at
0.001 s 1 . (b) The initial 150 nm P–h curves obtained at 0.1 s 1 strain rate.
Fig. 5. Stress variation with indentation depth measured at strain rate of 0.05 s 1
for eutectic SnBi and its two constituent phases.
measurement is good as the maximum modulus variation from different
locations of the same sample is no more than ±9.1% as tabulated
in Table 1.
Fig. 3a compares the P–h curves of the SnBi alloy and the singlephase
materials at the same strain rate, 0.005 s 1 . The curve of SnBi
alloy is found to be sandwiched by the curves of the single-phase
materials. However, the situation changes when a higher strain
rate is applied. Fig. 3b shows the P–h curves of the same set of
materials deformed at 0.1 s 1 . The curve of SnBi alloy is found
above the two single-phase materials. This is believed to be attributed
to the different deformation mechanisms between SnBi alloy
and the single-phase materials. Detailed discussion will be made in
4.2. Discrete deformation at initial loading stage
Fig. 4a and b shows the P–h curves of the Sn–3%Bi, Bi and SnBi
alloy at the initial 200 nm range. Discontinuities, which are documented
as ‘strain bursts’, are clearly present on the initial loading
L. Shen et al. / Journal of Alloys and Compounds 574 (2013) 98–103 101
Fig. 6. Stress of SnBi, Sn–3%Bi and pure Bi measured at different strain rates.
Steady-state stresses (MPa) of Sn–3%Bi, pure Bi and eutectic SnBi measured at eight
Strain rate (s 1 ) Sn–3%Bi Bi Eutectic SnBi
0.1 271.9 ± 24.5 161.3 ± 6.9 320.9 ± 5.6
0.05 254.7 ± 20.1 157.1 ± 4.8 287.3 ± 25.1
0.02 252.2 ± 19.1 142.1 ± 7.7 243.1 ± 18.9
0.01 224.3 ± 11.2 134.3 ± 1.2 203.2 ± 16.8
0.005 208.0 ± 16.4 125.7 ± 5.7 170.5 ± 11.3
0.002 195.8 ± 12.2 112.8 ± 8.6 163.5 ± 7.7
0.001 188.9 ± 16.8 104.3 ± 4.9 131.4 ± 5.4
0.0005 183.1 ± 12.8 97.7 ± 4.5 91.7 ± 2.7
Fig. 7. The strain rate versus the modulus compensated stress curves for Sn–3%Bi,
pure Bi and SnBi alloy.
curves of the two single-phased samples. Such discontinuities
were reported as a result of dislocations nucleation in bulk crystal
lattice [22–25]. Feng and Ngan  studied the relationship between
creep behaviour and strain burst using metals with high
and low melting temperatures. Strain burst is shown as a prerequisite
to engage dislocation creep in the later stage of deformation
for both high and low melting temperature metals. Before the first
strain burst, low melting point metal, e.g. Indium, displayed diffusional
creep behaviour where the stress exponent is found to be
1.5. On the other hand, no creep could be identified in the high
melting point metal, e.g., Aluminium, before strain burst occurs.
Chen and Bull  reported the correlation of strain burst events,
which occur during constant load hold process in CLH test, with
grain boundary sliding (GBS) using in situ imaging approach during
indentation test. The dimension change in such GBS-related strain
burst is in the range of 200–800 nm. However, in this study, the
dimension change due to the bursts is much smaller (Fig. 4). They
are few tens nm and likely related to emission of bunch of dislocations.
GBS is thus excluded from the possible mechanisms to have
caused the strain burst observed in the current study.
102 L. Shen et al. / Journal of Alloys and Compounds 574 (2013) 98–103
Fig. 8. Post-indent surfaces of (a) Sn–3%Bi, (b) pure Bi (the black arrows indicating the grain boundaries). (c) SnBi alloy deformed at low strain rate and (d) high strain rate.
Table 1 summarises the characteristics of the first strain burst
event in the two single-phase materials, including load (p 0), depth
(h0), and the initial positive slope (s0) at various strain rates from
0.001 s 1 to 0.1 s 1 . In spite of the differences in p 0 and h 0, the
slope (s0) does not vary much with different strain rate for the
same material. Rabkin et al.  reported the strain bursts on
indentation curve of ultra-thin Ni films. They claimed that the initial
loading curve before the first burst is well described by Hertz’s
elastic contact model. Indeed based on elastic contact theory, the
initial slope (s 0) is related to the elastic modulus of the material.
By comparing the slopes at the initial loading, the elasticity of
the materials can be ranked by values of s0. In this study higher
s0 is found in Sn–3%Bi than that of pure Bi, hence higher elasticity
constant is expected for Sn–3%Bi. Table 1 lists the elastic modulus
of the two materials measured at deeper indentation depth according
to Eqs. (4) and (5). The modulus of Sn–3%Bi and pure Bi are
approximately 49 GPa and 25 GPa, respectively. This elastic constant
was found to be insensitive to strain rate change. The results
of elastic modulus obtained by indentation validate the approach
of ranking the elastic modulus of the two single-phase materials
by comparison of s 0 on the loading curve.
At high strain rate condition (Fig. 4b), fewer pop-in events were
observed in the initial loading curve of eutectic SnBi alloy. They
occurred with smaller magnitude than those appeared in the single-phase
materials. As the strain burst is indicative of dislocation
generation, it is believed that certain amount of dislocation motion
has occurred at the beginning of a fast loading test. At lower strain
rate, the initial P–h curve is rather smooth (Fig. 4a). Based on the
above discussion, dislocation-related creep is thus excluded from
being the dominate creep mechanism in the deformation process
at later stage.
4.3. Creep stress exponents
Fig. 5 shows the indentation stress of eutectic SnBi and two single-phase
materials measured at 0.05 s 1. The stress becomes stable
after approximate 2 lm, indicating that steady-state creep has
been achieved after this depth. The average stress in the range of
2–4 lm is used to represent the steady-state stress during creep.
Fig. 6 shows the strain rate and stress relations for the three materials.
Each strain rate–stress data point in the plot is the average of
five measurements. The steady-state stresses of the three materials
obtained at eight strain rates are listed in Table 2. Comparing with
the other two samples, SnBi alloy shows much faster rate of increment
in stress with increasing strain rate.
Fig. 7 re-plots the relationship of strain rate and moduluscompensated-stress
in logarithmic scale. The average modulus
measured from eight strain rates were used for the plot. The
repeatability of the results is good as the largest variation of
stress is no more than ±9% at each strain rate. In the stress range
of 3:7 10 3 < r E < 5:5 10 3 , the slopes of the two curves of Bi
and Sn–3%Bi are 10.09 and 12.25, respectively. The values are
close to the stress exponents of pure metals in which the creep
rate is controlled by a dislocation-related mechanism [28,29].
Recalling the drastic strain burst events observed in the two single-phase
materials, it is believed that sufficient number of dislocations
have formed during the initial stage of deformation which
would warrant the dislocation creep in the later stage. Frost and
Ashby  defined power-law creep when n is observed between
4 and 5. A higher stress exponent indicates a power-law breakdown
(PLB) behaviour. Nabarro  compared the physical
processes of the two types of creep behaviour, i.e., power-law
creep and PLB. The experiment shows a distinction between the
two: power-law creep is a homogenous deformation occurred
within the grains; PLB is mainly occurred by a process of GBS.
To assist the understanding of the deformation mechanism
involved in indentation process in single-phased materials, the indented
surfaces were examined by scanning electron microscopy
(SEM). As shown in Fig. 8a and b, discernible GBS appears around
the indented area for both samples. Considering the high stress
exponents found in these two materials, it is believed that PLB
is the dominant mechanism controlling the creep. GBS serves as
a complementary mechanism to accommodate grain shape
change in the materials.
As shown in Fig. 7, the strain rate–stress curve of eutectic SnBi
shows bi-linear behaviour with a transition occurring around at
_e 2 10 3 s 1 . Below this transition strain rate, the strain rate–
stress curve of SnBi alloy is above those of the two single-phased
materials, indicating less stress is required to induce the same
creep rate for the two-phase eutectic SnBi. The stress exponent
in this range is found to be 2.35, which falls in the typical range
of GBS dominated creep behaviour [31–33]. In the initial P–h curve
of this alloy (Fig. 4a), lack of strain burst at lower strain rate range
suggests that the dislocation-related mechanism is unlikely to be
the controlling creep mechanism at the later stage. Post-indent
microstructure study shows delamination/sliding of grain boundaries
has occurred at the SnBi sample after the material was deformed
at 5 10 4 s 1 (Fig. 8c). Some of the small grains
surrounding the indentation mark have been shifted out of the surface
plane. The abundant phase/grain boundaries in SnBi alloy are
believed to facilitate GBS and even dominate the creep deformation
at the lower strain rate test condition.
Beyond the transition strain rate, the stress exponent is found to
be 5.20, which is a typical value of power-law creep in which dislocation
climb controls the creep. Dislocations formed at the initial
loading stage provide resources to accommodate plastic deformation
in the later stage. Compared to the single-phased materials,
fewer strain bursts and smaller magnitude were observed at the
initial deformation curve of eutectic SnBi (Fig. 4b). Close microstructure
examination of the indented area at high strain rate
(Fig. 8d) reveals that small amount of phase-boundary sliding
(PBS) has participated in the creep process. It is believed that there
are more than one mechanism in operation for eutectic SnBi deformed
at the high strain rate, during which dislocation climb
dominates the creep process and PBS complements the shape
change in grains and phase particles.
When tested at the higher strain rate region, different bulk
creep mechanisms are found to operate inside individual grains
of the SnBi alloy and the two single-phase materials. However, better
creep resistance is found in SnBi alloy, as shown in Fig. 7, which
creeps more slowly than single phase Sn–3%Bi and Bi at the same
creep stress. It is believed that smaller grain size in SnBi attributes
to the superior creep resistance as the grain boundaries act as an
effective barrier to the dislocation propagation. Thus, further
refinement of grain size could offer opportunities to enhance the
creep resistance of the two-phase eutectic SnBi when it is deformed
at strain rate higher than 2 10 3 s 1 .
(1) The strain burst observed in the initial P–h curves corresponds
to dislocation emission inside the grains. It serves
as prerequisite for the dislocation creep to control the creep
rate in the later stage of deformation in the two single-phase
(2) The creep stress exponents of the single-phase Sn–3%Bi and
pure Bi are found to be 12.25 and 10.09, respectively, suggesting
that the power-law breakdown (PLB) is the dominant
mechanism. Grain boundary sliding (GBS) serves as a
complementary mechanism to accommodate grain shape
change in the materials.
L. Shen et al. / Journal of Alloys and Compounds 574 (2013) 98–103 103
(3) Stress exponent of 2.35 is found in the two-phase eutectic
SnBi alloy tested at the low strain rate range (lower than
2 10 3 s 1 ) in which GBS is the dominant creep
(4) At the high strain rate region, dislocations participate in the
creep deformation for eutectic SnBi. Stress exponent of 5.20
suggests that the creep rate is limited by dislocation climb in
grain lattice. Phase boundary sliding serves as a complementary
mechanism to accommodate shape change due to large
deformation inside each individual grains.
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