Creep behaviour of eutectic SnBi alloy and its constituent phases ...

Creep behaviour of eutectic SnBi alloy and its constituent phases ...

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

article info

Article history:

Received 29 December 2012

Received in revised form 3 April 2013

Accepted 9 April 2013

Available online 15 April 2013





Constant strain rate

Strain burst

1. Introduction


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: (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:

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 [14], 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

[13] or transient creep model [15]. 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. Theory

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

(h) [16,18]:


_e ¼


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

material [19].

_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:




1 v2



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



p 1

pffiffiffiffiffi S ð5Þ

2 Ac

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 [20].

3. Experimental

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 [21], 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

Table 1

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

Section 4.3.

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.

Table 2

Steady-state stresses (MPa) of Sn–3%Bi, pure Bi and eutectic SnBi measured at eight

strain rates.

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 [26] 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 [27] 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. [24] 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 [29] defined power-law creep when n is observed between

4 and 5. A higher stress exponent indicates a power-law breakdown

(PLB) behaviour. Nabarro [30] 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 .

5. Conclusions

(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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