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Cyclic Stress-Strain Behavior of SAC305 Lead Free Solder: Effects of Aging,
Temperature, Strain Rate, and Plastic Strain Range
Nianjun Fu, Jeffrey C. Suhling, Pradeep Lall
Center for Advanced Vehicle and Extreme Environment Electronics (CAVE3), and
Department of Mechanical Engineering
Auburn University
Auburn, AL 36849, USA
E-Mail: jsuhling@auburn.edu
Abstract—Solder joints in electronic assemblies are often
subjected to cyclic (positive/negative) mechanical strains and
stresses. Such exposures can occur in variable temperature
application environments or during accelerated life thermal
cycling tests used for qualification. Cyclic loading leads to
damage accumulation, crack initiation, crack propagation, and
eventually to fatigue failure. In this investigation, we have
examined the effects of prior aging conditions, strain range,
strain rate, and testing temperature on the cyclic stress-strain
behavior of SAC305 lead free solder. Newly designed micro-
cylinder shaped uniaxial lead free solder test specimens have
been prepared in glass tubes using a vacuum suction process.
Prior to testing, the samples were aged for various durations (0
to 360 days) at 125 ºC. After aging, the fabricated samples
were then subjected to cyclic stress-strain loading under several
different conditions. From the recorded cyclic stress-strain
curves, we have been able to characterize and empirically
model the evolution of the solder hysteresis loops with aging
duration. It has been observed that aging leads to the
microstructural coarsening and degrades the mechanical
fatigue properties, and those degradations are much more
significant at the first few days of aging. The effects of aging on
the cyclic stress-strain behavior have also been quantified for
the first time for different testing temperatures, strain rates,
and plastic strain ranges. At elevated test temperatures or
lower test strain rates, an increase in the plastic strain range
and a drop of the peak stress and loop area were found.
Additionally, the plastic strain range, loop area, and peak load
increased as expected with greater applied total strain range.
Keywords-lead free solder; SAC alloy; cyclic stress-strain
curve; hysteresis loop; aging; strain rate; plastic strain range
I. INTRODUCTION
Fatigue of solder joints exposed to thermal cycling is a
common electronic packaging failure mode. Stresses and
strains often result in electronic assemblies exposed to a
temperature changing environment due to mismatches in the
coefficients of thermal expansion (CTE) of the soldered
components and the printed circuit board (PCB). Therefore,
cyclic temperature changes can lead to alternating stresses
and strains within the solder joints. Such exposures can
occur in products that experience power cycling or during
accelerated life thermal cycling tests used for qualification.
Cyclic loading typically leads to micro cracks forming
within the solder material, followed by macro cracks and
eventually to fatigue failure. Energy dissipation occurs
during cyclic loading due to yielding and occurrence of
viscoplastic deformations, and can be quantified using the
area of the cyclic stress-strain curve hysteresis loops, which
is equal to the strain energy density dissipated per cycle.
The cyclic stress-strain behavior of Sn-Pb solder
materials has been studied extensively in the past [1-14].
For example, Hall [1-2] measured deformations and stress-
strain hysteresis experimentally during the thermal cycling
of a leadless ceramic chip carrier (LCC) mounted to an
organic PCB. In addition, Pao [3-5] measured the thermo-
mechanical hysteresis of a variety of Sn-based alloys used a
2-beam geometry, and Haacke, et al. [6] characterized both
hysteresis and thermomechanical fatigue for Sn-Pb solder.
Finally, several investigators have developed models to
predict fatigue life of Sn-Pb solders under thermal cycling or
thermomechanical fatigue loading [7-17].
For lead free solders, Raeder and co-workers [18] have
explored thermomechanical deformation behavior of Sn-Bi
eutectic solder under fatigue loading, and the findings were
quantified using the plastic strain energy density. In
addition, Dusek, et al. [19] have investigated the cyclic
stress-strain behavior and hysteresis loop evolution for Sn-
Ag-Cu (SAC) lead free solders during isothermal fatigue at
several different temperatures (T = 24, 30, 60, and 125 oC).
They reported that the number of cycles to failure increases
with higher temperatures for the same stress level, and
attributed this to the use of slow cycling, where creep and
stress relaxation play dominant roles. Kanchanomai, et al.
[20] have performed uniaxial fatigue tests on Sn-Ag solder,
while Pang and coworkers [21] have performed uniaxial
fatigue tests on SAC387 lead free solder. Andersson, et al.
[22] compared the fatigue properties of bulk lead-free solder
specimens to those found for solder joints.
The initial microstructure of a solder test specimen will
dramatically influence the results of any mechanical test
performed on that material. Isothermal aging changes the
microstructure of lead free solders, causing grain and phase
coarsening, as well as potential recrystallization at Sn grain
boundaries. Thus, the prior aging (preconditioning) of a
solder sample will greatly affect the measured mechanical
response. The literature on lead free solder materials has
shown that aging is universally detrimental to their
constitutive and failure behaviors [23]. In particular, large
degradations have been observed in ball shear strength [24],
elastic modulus [25], drop reliability [26], fracture behavior
[27], microstructure [28], creep behavior [29-33], thermal
2016 IEEE 66th Electronic Components and Technology Conference
978-1-5090-1204-6/16 $31.00 © 2016 IEEE
DOI 10.1109/ECTC.2016.345
1119
cycling reliability [34-38], Anand model parameters [37-38],
nanoindentation joint modulus and hardness [39-41], high
strain rate mechanical properties [42], uniaxial cyclic stress-
strain curves and fatigue life [43-44], and shear cyclic stress-
strain curves and fatigue life [45-46].
Apart from aging, various testing parameters such as
testing temperature and strain rate (frequency) also have a
significant influence on the cyclic stress-strain and fatigue
behaviors of solders [8, 15-16, 20, 22], and several models
have been developed to describe the effects of these testing
parameters. In these studies, the influence of aging (initial
microstructure) of the test samples was not examined. We
believe that a better understanding of the effects of aging
and test conditions on the cyclic mechanical behavior of
solder materials is critical to resolving the large
discrepancies in solder fatigue data found in the literature.
In this investigation, we have examined the effects of
prior aging conditions and several testing parameters on the
cyclic stress-strain behavior of SAC305 lead free solder.
Newly designed micro-cylinder shaped uniaxial lead free
solder test specimens have been prepared in glass tubes
using a vacuum suction process. Prior to testing, the
samples were aged for various durations (0 to 360 days) at
125 ºC. After aging, the fabricated samples were then
subjected to cyclic stress-strain loading under several
different conditions. The examined range of cyclic loading
test parameters included testing temperature (25 to 100 ºC),
testing strain rate (0.0001 to 0.001 sec
-1
), and total strain
range (0.004 to 0.013). For each set of cyclic stress-strain
data, a four-parameter hyperbolic tangent empirical model
has been used to fit the entire cyclic stress-strain curve and
the hysteresis loop size (area) was calculated using definite
integration for a given strain limit. This area represents the
energy dissipated per cycle, which is correlated to the
damage accumulation in the specimen. At the same time, the
plastic strain range and peak stress were also determined
from the fitting curves.
From the recorded cyclic stress-strain curves, we have
been able to characterize and empirically model the
evolution of the solder hysteresis loops with aging duration.
Finally, the effects of aging have been quantified for the first
time for different testing temperatures, strain rates, and
plastic strain ranges. In our current ongoing work, we are
also subjecting the solder samples to cyclic loading until
failure, to determine the effects of aging and other
parameters on the material fatigue life. The ultimate goal is
to fully understand the effects of aging on the
thermomechanical fatigue life of lead free solders.
II. E
XPERIMENTAL
P
ROCEDURE
A. Uniaxial Test Sample Preparation
Solder uniaxial samples are often fabricated by
machining of bulk solder material, or by melting of solder
paste in a mold. These methods have several disadvantages
as discussed in [29-33]. In the current study, we have
avoided the issues present with machining or molding
samples by using a novel procedure where solder uniaxial
test specimens are formed in high precision glass tubes using
a vacuum suction process. Unlike prior studies that used
rectangular cross-section glass tubes [29-33, 43-46], we
adopted glass tubes with circular cross-sections in this work
to produce cylindrical specimens that are more resistant to
buckling during the compression portions of a cyclic stress-
strain curve.
The solder is first melted in a quartz crucible using a pair
of circular heating elements (see Fig. 1). A thermocouple
attached on the crucible and a temperature control module is
used to direct the melting process. One end of the glass tube
is inserted into the molten solder, and suction is applied to
the other end via a rubber tube connected to the house
vacuum system. The suction forces are controlled through a
regulator on the vacuum line so that only a desired amount
of solder is drawn into the tube. The specimens are then
cooled to room temperature using a user-selected cooling
profile (can be the same as actual solder joints). Typical
cylindrical glass tube assemblies filled with solder and a
final extracted specimen are shown in Fig. 2. The solder
samples can be easily pulled out from the tubes due to the
differential expansions that occur when cooling the low CTE
glass tube and higher CTE solder alloy.
The nominal diameter of the uniaxial specimens in this
work was 1.2 mm. The described sample preparation
procedure yielded repeatable samples with controlled
cooling profile (i.e. microstructure), oxide free surface, and
uniform dimensions. Sample cross-sectioning has shown
that the microstructure of any given sample was consistent
throughout the volume of the sample, and that repeatable
sample microstructures were obtained from sample to
sample for a given solidification temperature profile. With
proper experimental techniques, samples with no flaws and
voids were generated.
Figure 1. Specimen preparation hardware.
(a) Within glass tube.
(b) After extraction.
Figure 2. Cylindrical uniaxial test specimen.
1120
B. Mechanical Testing System
The MT-200 tension/torsion thermo-mechanical test
system from Wisdom Technology, Inc., shown in Fig. 3 was
used to perform the cyclic stress-strain testing in this work.
The system provides an axial displacement resolution of 0.1
micron, and universal 6-axis load cell was utilized to
simultaneously monitor three forces and three moments
during sample mounting and testing. Use of the pictured
heating chamber allowed samples to be tested up to +200
°C. In order to grip the cylindrical specimens properly,
gripping fixtures with V-shaped grooves were designed and
introduced as shown in Fig. 4.
Figure 3. MT-200 testing system with solder sample.
(a) Front & rear views of the fixture.
(b) Testing system with the fixture.
Figure 4. Specimen gripping fixtures.
The axial stress and axial strain during testing were
calculated from the measured applied force and cross-head
displacement using
LL
L
A
FG
'
H V (1)
where V is the uniaxial stress, H is the uniaxial strain, F is
the measured uniaxial force, A is the original cross-sectional
area, G is the measured crosshead displacement, and L is the
specimen gage length (initial length between the grips).
The cross-section microstructural studies in this work
were done using the scanning electron microscope (SEM)
shown in Figure 5.
Figure 5. JEOL JSM-7000F Field Emission SEM.
C. Test Conditions
Using specimens fabricated with the casting procedure
described above, cyclic stress-strain behavior for SAC305
lead free solder has been explored under various test and
thermal aging conditions. A water quenched cooling profile
was utilized in this investigation. After solidification and
cooling, the test specimens were subjected to various
durations (0 to 360 days) of aging at 125 oC. The 0-day
aging specimens represented non-aged samples, which were
tested within a few minutes after solidification. The samples
were cooled to room temperature (25 oC) after aging, and
then they were subjected to cycling mechanical loading
(strain controlled) under several different conditions of
applied strain range, strain rate, and temperature. As stated
before, the examined range of cyclic loading test parameters
included testing temperature (25 to 100 ºC), testing strain
rate (0.0001 to 0.001 sec-1), and total strain range (0.004 to
0.013). The gage length was chosen as 10 mm, and at least
8 tests were conducted for the solder under each set of
testing conditions.
D. Cyclic Stress-Strain Curve Processing
A typical set of cyclic stress-strain curves for SAC solder
are shown in Fig. 6. In this case, a rather stable set of
hysteresis loops were found to occur for several cycles.
Although several different empirical models can be used to
represent the observed stress-strain data for solder, we have
found that a four parameter hyperbolic tangent model is best
able to represent experimental SAC solder stress-strain
curves [43]. To process the cyclic stress-strain data and
calculate the areas of the associated hysteresis loops, a pair
of hyperbolic tangent empirical models has been used to
represent the tension portion and the compression portion of
the stress-strain behavior in each cycle. Fig. 7 illustrates the
definitions of the two portions of the stress-strain cycle and
the empirical fits )(f1H for the compression loading region
1121
(bottom of the hysteresis loop) and )(f2H for the tensile
region (top of the hysteresis loop).
Figure 6. Typical solder cyclic stress-strain curves [43].
Figure 7. Solder stress-strain curves and empirical model.
Using the approach presented by Mustafa, et al. [43], the
upper and lower curves were represented as:
12432211 ))(Atanh(A))(Atanh(Af VHHHH H
21431212 ))(Btanh(B))(Btanh(Bf VHHHH H (2)
21 HdHdH
From the stress-strain data for each cycle, the constants in
the empirical models in (2) can be determined through a
nonlinear regression analysis. The hysteresis loop area can
then be evaluated using
>@
HHH ' ³
H
H
d ffW
2
1
12 (3)
This area represents the energy density dissipated per cycle
during the cyclic loading.
III. CYCLIC TESTING RESULTS
A. Effects of Aging
The effects of prior aging (up to 150 days) have been
studied on the cyclic stress-strain behavior of SAC305 lead
free solder. After solidification, the samples were subjected
to aging at 125 oC for various durations. The samples were
cooled to room temperature after aging, and then they were
subjected to cyclic mechanical loading (strain controlled)
with applied strain limits of ±0.005, strain rate of H
= 0.001
sec-1, and temperature of T = 25 oC. The hysteresis loops
were studied at the 10th cycle, when the loops tend to be
more stable from one loop to the next.
Fig. 8 shows the evolution of the hysteresis loops with
increased aging. It is observed that the cyclic stress-strain
curves compressed vertically while expanded horizontally
with increasing aging time. The most noticeable changes of
occurred during the first 5 days of aging, with slower
changes occurring for longer aging times. From the
recorded cyclic stress-strain curves, the areas of the
hysteresis loops were calculated using the procedure
outlined above. In addition, the plastic strain ranges and
peak stresses were determined as illustrated in Fig. 9. The
plastic strain range is equal to the total strain range minus
the elastic strain range, which is the distance between the
two strain axis intercepts on the graph. The peak stress is
simply the maximum stress recorded during the cycle. The
loop area and plastic strain range are usually considered as
fatigue damage driving forces, and are widely used in
models to predict fatigue life of solders [47].
Figure 8. Aging induced evolution of the hysteresis loops.
To better understand aging induced evolution of the
solder cyclic stress-strain behavior, the evolution has been
examined in three parts, i. e., evolutions of loop area, peak
stress, and plastic strain range. It is observed that loop area
and peak stress dropped with increased aging times, while
plastic strain range increased with aging. Dramatic changes
of all three parameters occurred within the first few days of
aging. Morrow [48] suggested that on the microscopic level,
Strain, H
-0.003 -0.002 -0.001 0.000 0.001 0.002 0.003
Stress, V (MPa)
-40
-30
-20
-10
0
10
20
30
40
Strain, H
-0.003 -0.002 -0.001 0.000 0.001 0.002 0.003
Stress, V (MPa)
-40
-30
-20
-10
0
10
20
30
40
A
B
C
Strain,
H
(x 10
-3
)
-10 -5 0 5 10
Stress,
V
(MPa)
-80
-60
-40
-20
0
20
40
60
80
Experimental Data (10
th
Cycle)
Fitting Curve
Hysteresis Loop Area
)(f)( 11 H HV
)(f)( 22 H HV
1
V
2
V
2
H
1
H
AreaW '
Strain,
H
(10
-3
)
-10-8-6-4-2 02 4 6 8 10
Stress,
V
(MPa)
-80
-60
-40
-20
0
20
40
60
80
No Aging, (0.6278 MJ/m
3
)
5 Days Aging, (0.4023 MJ/m
3
)
10 Days Aging, (0.3862 MJ/m
3
)
20 Days Aging, (0.3760 MJ/m
3
)
30 Days Aging, (0.3666 MJ/m
3
)
45 Days Aging, (0.3504 MJ/m
3
)
60 Days Aging, (0.3394 MJ/m
3
)
80 Days Aging, (0.3614 MJ/m
3
)
110 Days Aging, (0.3571 MJ/m
3
)
150 Days Aging, (0.3349 MJ/m
3
)
1122
cyclic plastic strain is related to the dislocation movements
while the cyclic stress is related to the ability to resist the
movements. With increased aging times, the increase of
plastic strain range means more dislocation movements
occurred during the test. Aging also caused decrease of the
peak stress, which indicates the specimen was losing ability
to resist the movements of dislocations. The decrease of the
hysteresis loop area with increased aging suggests that
energy dissipation was mitigated with aging. However, the
reduction in loop area occurred primarily because a strain
controlled method was used in the testing, and thus all tests
were performed using the same total strain range (0.01), or
width of the hysteresis loop. Aging led to large drop of peak
stress (vertically height of hysteresis loop), and a relatively
smaller increase of plastic strain range. As a result, the loop
area dropped as the aging duration increased.
Figure 9. Determination of plastic strain range.
The effects of aging on the solder specimen cross-
sectional microstructure were also studied using SEM. Fig.
10 shows typical microstructures of SAC305 before and
after aging. The microstructure of non-aged SAC305
consists of -Sn dendrites (primary phase), and Ag3Sn and
Cu6Sn5 intermetallic compounds (IMCs). The -Sn
dendrites are surrounded by the fine intermetallic particles,
and most of the IMCs are Ag3Sn. This kind of structure can
effectively pin and block the dislocation movements. With
aging, there is a disappearance of the dendritic structures and
the coalescence and coarsening of IMCs, which leads to an
increased ability for dislocation movements.
B. Effects of Test Temperature
The effects of the test temperature on cyclic stress-strain
behavior have been studied by performing a series of
experiments with the same total strain range of 0.01 (strain
limits of ±0.005) and same strain rate (frequency) of 0.001
sec-1. The test temperatures considered were T = 25 ºC, 50
ºC, 75 ºC, and 100 ºC. Initially, the effects of temperature
were investigated for non-aged samples. Fig. 11 illustrates
how the cyclic stress-strain curves change with an increase
of test temperature. It is observed that the loop compressed
in the vertical direction while expanded horizontally. To be
more specific, peak stress and loop area dropped while
plastic strain range increased during the cyclic loading at
elevated testing temperatures.
(a) No aging. (b) 20 days of aging at 125 oC.
Figure 10. Microstructure of SAC305.
Fig. 12 shows a quantitative comparison of the loop
areas for different test temperatures. Due to the increase of
creep and dislocation movements at higher temperatures, the
peak stress and loop area dropped while plastic strain range
increased. In general, significant creep is expected with a
homologous temperature (the ratio of ambient temperature to
melting temperature) larger than 0.5. For Sn-Ag-Cu lead
free solders, creep is not negligible even at room
temperature (T = 25 oC), at which the homologous
temperature is 0.61. At elevated temperatures, creep is more
severe because thermally activated dislocations are able to
move along preferred slip plans or cut through dislocation
barriers [49, 50]. In addition, the interstitial atoms and
lattice vacancies tend to migrate along the gradient of a grain
boundary in the presence of tensile or compressive pressure
in reversed directions [51].
Figure 11. Effects of test temperature (no aging).
Similar trends for elevated test temperatures have been
observed for samples subjected to aging before testing. In
addition to the non-aged specimens, tests were also
performed on samples aged for 5, 10, and 20 days at T = 125
oC prior to testing. In these experiments, the same total
strain range of 0.01 (strain limits of ±0.005) and same strain
rate (frequency) of 0.001 sec-1 were also used. Plots of the
loop area, peak stress, and plastic strain range as a function
of aging time for the various test temperatures are shown in
Strain,
H
(10
-3
)
-10 -5 0 5 10
Stress,
V
(MPa)
-80
-60
-40
-20
0
20
40
60
80
p
H'
t
H'
V'
2
e
H' 2
e
H'
E
E
Strain,
H
(10-3)
-10-8-6-4-2 0 2 4 6 810
Stress,
V
(MPa)
-80
-60
-40
-20
0
20
40
60
80
T = 25
o
C
T = 50
o
C
T = 75
o
C
T = 100
o
C
1123
Figs. 13-15, respectively. The experimental data points in
each curve can be fit well with a universal empirical model
that includes exponential and linear terms:
tk
ek1
k
Q4
tk
2
1
3
(4)
where Q denotes the quantity being plotted (i.e. hysteresis
loop area, peak stress, or plastic strain range), t is the aging
duration, and k1, k2, k3 and k4 are temperature dependent
material constants. From Figs. 13-15, the variations with
aging are similar from one test temperature to another. It is
also observed that the plastic strain range is less sensitive to
aging in the first few days of aging, relative to the loop area
and peak stress. The total strain range applied in these
experiments was 0.01. Thus, it is evident that plastic
deformation was dominant during these tests as the plastic
strain range accounts for around 80% of the total strain
range for each condition (see Fig. 15).
Figure 12. Drop of loop area with increased test temperature (no aging).
It is clear that aging degrades the mechanical properties
of SAC305 solder, and testing at elevated test temperatures
exacerbates the degradations. The degradations caused by
aging and test temperature can be quantified by comparing
results for SAC305 (no aging) tested at 25 ºC with results for
SAC305 (20 days aging) tested at 100 ºC. The degradations
in loop area, peak stress, and plastic strain range are 58.3%,
66.0%, and 19.7%, respectively (Table 1).
TABLE 1. DEGRADATIONS CAUSED BY AGING AND TEMPERATURE
SAC305 Loop Area,
(MJ/m3)
Peak Stress,
(MPa)
Plastic Strain
Range, (x 10-3)
No Aging,
T = 25 ºC 0.6278 52.36 7.240
20 Days Aging,
T = 100 ºC 0.2620 17.80 8.667
Degradation % 58.3% 66.0% 19.7%
C. Effects of Strain Rate and Plastic Strain Range
The effects of the strain rate (frequency) on the cyclic
stress-strain behavior have been studied by performing a
series of experiments on non-aged and aged samples with
the same total strain range of 0.01 (strain limits of ±0.005)
and temperature T = 25 oC. The strain rates considered were
0.0001, 0.0002, 0.0005 and 0.0010 sec-1. As shown in Figs.
16-18, the effects of strain rate on the loop area, peak stress,
and plastic strain range are opposite to the effects of test
temperature. Specifically, the loop area and peak stress
increased at higher strain rates for all aging times. Similarly,
the plastic strain range dropped at higher strain rates for all
aging times. In other words, the hysteresis loops stretched
vertically and shrunk horizontally with increasing strain rate
(frequency). This is because creep and dislocation
movement are curtailed when testing samples at a higher
strain rates.
Figure 13. Effects of aging and temperature on loop area.
Figure 14. Effects of aging and temperature on peak stress.
Figure 15. Effects of aging and temperature on plastic strain range.
Test Te mperature , T (
o
C
)
0 20406080100120
Loop Area, 'W (MJ/m
3
)
0.0
0.2
0.4
0.6
0.8
Aging Time, t (Days)
0 5 10 15 20 25
Loop Area, 'W (MJ/m
3
)
0.0
0.2
0.4
0.6
0.8
T = 25 oC
T = 50 oC
T = 75 oC
T = 100 oC
Aging Time, t (Days)
0 5 10 15 20 25
Peak Stress, V (MPa)
0
10
20
30
40
50
60
T = 25
o
C
T = 50
o
C
T = 75
o
C
T = 100
o
C
Agi ng Time, t (D ays)
0 5 10 15 20 25
Plastic Strain Range, 'H
p
0.000
0.002
0.004
0.006
0.008
0.010
T = 25
o
C
T = 50
o
C
T = 75
o
C
T = 100
o
C
1124
Experiments have also been done to investigate the
effects of plastic strain range including aging on the cyclic
stress-strain behavior of SAC305. A series of tests were
performed on non-aged and aged samples with the same
strain rate of 0.001 sec-1 and temperature T = 25 oC. Four
different total strain ranges were applied including 0.004,
0.007, 0.010 and 0.013 (the total strain range was specified
instead of the plastic strain range during the cyclic loadings
because of the difficulty of maintaining a fixed plastic strain
range for different tests). The results for the loop area, peak
stress, and plastic strain range as a function of aging time
and total strain range are shown in Figs. 19-21. In general,
an increase in the total strain range led to a larger plastic
strain range, which represents more plastic deformation
occurring per cycle (Fig. 21). Additionally, a greater applied
total (or plastic) strain range tended to increase the loop area
and peak stress (Figs. 19, 20), as expected.
Figure 16. Effects of aging and strain rate on loop area.
Figure 17. Effects of aging and strain rate on peak stress.
IV. SUMMARY AND CONCLUSIONS
In this investigation, we have examined the effects of
prior aging conditions and several testing parameters on the
cyclic stress-strain behavior of SAC305 lead free solder.
Newly designed micro-cylinder shaped uniaxial lead free
solder test specimens have been prepared in glass tubes
using a vacuum suction process. Prior to testing, the
samples were aged for various durations (0 to 360 days) at
125 ºC. After aging, the fabricated samples were then
subjected to cyclic stress-strain loading under several
different conditions. The examined range of cyclic loading
test parameters included testing temperature (25 to 100 ºC),
testing strain rate (0.0001 to 0.001 sec-1), and total strain
range (0.004 to 0.013). For each set of cyclic stress-strain
data, a four-parameter hyperbolic tangent empirical model
has been used to fit the entire cyclic stress-strain curve and
the hysteresis loop size (area) was calculated using definite
integration for a given strain limit. This area represents the
energy dissipated per cycle, which is correlated to the
damage accumulation in the specimen. At the same time, the
plastic strain range and peak stress were also determined
from the fitting curves.
Figure 18. Effects of aging and strain rate on plastic strain range.
Figure 19. Effects of aging and strain range on loop area.
Figure 20. Effects of aging and strain range on peak stress.
Aging Time, t (Days)
0 5 10 15 20 25
Loop Area, 'W (MJ/m
3
)
0.0
0.2
0.4
0.6
0.8
Strain Rate = 1 x 10
-4
sec
-1
Strain Rate = 2 x 10
-4
sec
-1
Strain Rate = 5 x 10
-4
sec
-1
Strain Rate = 10 x 10
-4
sec
-1
Aging Time , t (Days)
0 5 10 15 20 25
Peak Stress, V (MPa)
0
10
20
30
40
50
60
Strain Rate = 1 x 10
-4
sec
-1
Strain Rate = 2 x 10
-4
sec
-1
Strain Rate = 5 x 10
-4
sec
-1
Strain Rate = 10 x 10
-4
sec
-1
Aging Time, t (Days)
0 5 10 15 20 25
Plastic Strain Range, 'H
p
0.000
0.002
0.004
0.006
0.008
0.010
Strain Rate = 1 x 10
-4
sec
-1
Strain Rate = 2 x 10
-4
sec
-1
Strain Rate = 5 x 10
-4
sec
-1
Strain Rate = 10 x 10
-4
sec
-1
Aging Ti me, t (Days)
0 5 10 15 20 25
Loop Area, 'W (MJ/m
3
)
0.0
0.2
0.4
0.6
0.8
1.0
Total Strain Range = 0.004
Total Strain Range = 0.007
Total Strain Range = 0.010
Total Strain Range = 0.013
Aging Time, t (Days)
0 5 10 15 20 25
Peak Stress, V (MPa)
0
10
20
30
40
50
60
Total Strain Range = 0. 004
Total Strain Range = 0. 007
Total Strain Range = 0. 010
Total Strain Range = 0. 013
1125
Figure 21. Effects of aging and strain range on plastic strain range.
From the recorded cyclic stress-strain curves, we have
been able to characterize and empirically model the
evolution of the solder hysteresis loops with aging duration.
Finally, the effects of aging have been quantified for the first
time for different testing temperatures, strain rates, and
plastic strain ranges. It was observed that with increased
aging, the hysteresis loop area and peak stress dropped while
the plastic strain range increased. All changes were most
dramatic within the first 5 days of aging. The plastic strain
range increased with aging, meaning that more dislocation
movements occurred. Aging also caused a decrease in the
peak stress, which indicates the specimen was losing ability
to resist the movements of dislocation. The decrease of the
hysteresis loop area with increased aging suggests that
energy dissipation was mitigated with aging. However, this
decrease as mainly due to the decrease in peak stress during
aging, while doing strain controlled tests. In addition, it has
been found that the increase of dislocation movements with
aging was caused by the disappearance of dendrite structure
and the coalescence and coarsening of IMCs.
The Effects of test temperature, strain rate, and plastic
strain range were investigated by subjecting non-aged and
aged samples to cyclic loadings under different conditions.
At elevated test temperatures or lower test strain rates, an
increase in the plastic strain range and a drop of the peak
stress and loop area were found for all aging times, which
indicates more creep and dislocation movements occurred
during the cycling. Moreover, the plastic strain range, loop
area, and peak load increased as expected with greater
applied total strain range. In our current ongoing work, we
are subjecting solder samples to cyclic loading until failure,
to determine the effects of aging and other parameters on the
material fatigue life. The ultimate goal is to fully understand
the effects of aging on the thermomechanical fatigue life of
lead free solders.
ACKNOWLEDGMENTS
This work was supported by the US Army and the NSF
Center for Advanced Vehicle and Extreme Environment
Electronics (CAVE3). We also acknowledge the fellowship
support for Nianjun Fu provided by the China Scholarship
Council (CSC).
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