The anand parameters of aging resistant doped solder alloys

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Sudan Ahmed, Jeffrey C. Suhling, Pradeep Lall
Department of Mechanical Engineering, and
Center for Advanced Vehicle and Extreme Environment Electronics (CAVE3)
Auburn University
Auburn, AL 36849
Phone: +1-334-844-3332
FAX: +1-334-844-3124
E-Mail: jsuhling@auburn.edu
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Due to growing environmental concerns, lead-free solder
materials are being widely used in electronic assemblies. The
Anand viscoplastic constitutive model is frequently used to
represent mechanical behavior of lead-free solder materials in
finite element simulations. However, prior experimental
results have demonstrated that properties of lead-free solder
materials degrade over time when exposed to isothermal
aging. These aging-induced degradations are more severe in
harsh environments (e.g. high temperature). Our previous
studies have revealed that dopants in SAC (Sn-Ag-Cu) alloys
can be successfully used to reduce, and in some cases prevent,
aging-induced degradations.
In the present study, we have explored the mechanical
properties of a new lead-free doped SAC solder alloy referred
to as SAC_Q (commercially known as CYCLOMAX).
SAC_Q has been recommended for high-reliability
applications by its vendor. Uniaxial samples were prepared
for the alloy, and some samples were aged in an oven at T =
100 oC for 3 months. Uniaxial tensile tests were performed
with the doped alloy of both non-aged and aged
microstructures. Testing conditions included three different
strain rates (0.001, 0.0001 and 0.00001 sec-1) and five
different test temperatures (25, 50, 75, 100 and 125 oC).
Tensile test results for the doped alloy, before and after aging,
were compared with those of standard SAC305.
Anand parameters of the doped alloy for the various
aging conditions were determined from the stress-strain test
results. A good correlation was found between Anand model
predictions and the experimentally obtained results. A
microstructure study has revealed that the Bismuth (Bi)
present as a dopant in the SAC_Q alloy plays an important
role to make the alloy relatively insensitive to aging-induced
degradations.
.(< :25'6  Lead Free Solder, Aging, Doped Alloy,
SAC-Bi Solder, SAC_Q, Anand Model, Microstructure
,1752'8&7,21
Solder joint fatigue that occurs during thermal or
mechanical cycling is often the predominant failure mode
exhibited by lead free electronic assemblies. Thus, engineers
must have accurate constitutive equations and failure criteria
for lead free solder materials for use in mechanical design and
reliability assessment. Ma, et al. [1] have reviewed the
literature on the mechanical behavior of lead free solders.
The mechanical properties of a solder are strongly influenced
by its microstructure, which is controlled by its thermal
history including its solidification rate and thermal exposures
after solidification.
Exposure of lead free solder joints to isothermal
conditions leads to microstructure evolution including
coarsening of intermetallic phases and subgrains, breakdown
of dendrite structures, as well as potential recrystallization at
Sn grain boundaries. Such aging effects are greatly
exacerbated at higher temperatures (e.g. T > 100 oC), but
significant changes occur even during room temperature
exposures. Aging of lead free solders leads to degradations in
their constitutive and failure behaviors [1-31]. For example,
research in the literature has shown that aging leads to large
reductions in solder material properties including shear
strength [2], elastic modulus [3-5], nanoindentation joint
modulus and hardness [6-9], high strain rate mechanical
behavior [10], creep response [3-5, 11-13], and Anand model
parameters [14-17]. Other studies have shown that aging
causes severe degradations in uniaxial cyclic stress-strain
curves and fatigue life [18-21], shear cyclic stress-strain
curves and fatigue life [22-23], fracture behavior [24], drop
reliability [25], and thermal cycling reliability [26-31].
Dopants have also been found to strongly influence the
properties and behaviors of lead free solders. For example,
addition of Bismuth (Bi) as a dopant has been demonstrated to
have several beneficial effects. Bi helps to reduce melting
temperature and increases strength by solid solution
strengthening [32]. The Effect of Bi on the mechanical
properties of a SAC (Sn3.5Ag0.9Cu) alloy was investigated
by Matahir and coworkers [33]. They reported that the shear
strength increased with increasing Bi addition up to 2% (wt).
Beyond that point, the shear strength decreased with
increasing Bi%. The improved shear strength was attributed
to the role of Bi on the morphology of the microstructure and
distribution of dominant intermetallic compound (IMC)
Ag3Sn. Reduction of strength at higher Bi content was due to
the evolution of Bi rich phase and fragmentation of the IMC.
Pandher, et al. [34] also reported that addition of up to 2% Bi
in SAC alloys improved wetting and alloy spreading. Witkin
[35] and Delhaise et al. [36] studied the effect of aging of Bi
doped SAC alloys. In both study, the authors reported an
elimination or at least reduction of aging induced degradation
in SAC-Bi alloys.
Dopants are also added to alloys in very small amounts
(microalloy additions). Zhao, et al. [37] found that addition of
0.02% Ni to SAC105 increased the formation of NiCuSn IMC
and reduced the localized grain size at solder/NiAu pad
interfaces. In addition, the effects of using various low level
978-1-5090-2994-5/$31.00 ©2017 IEEE 1416 16th IEEE ITHERM Conference

doping elements (i.e. Co, Fe, In, Ni, Zn, and Cu) in SAC305
BGA solder joints on Cu pads were studied by De Sousa, et
al. [38]. They concluded that addition of low levels of Zn had
a significant beneficial effect on the interfacial IMC. Lee and
coworkers [39] found that micro-alloying SAC alloys with Ni
and Bi improved thermal fatigue life and drop impact
resistance. Yeung, et al. [40] studied a novel lead-free solder
SACQ. Based on drop test, thermal cycling, and finite
element simulation, they conclude that the doped alloy has
improved board level reliability when compared to SAC105.
Additional literature publications on the effects of dopants
have been reviewed in reference [13].
In our previous study [41, 42], the mechanical properties
and microstructures of three new doped SAC alloys referred
to as Ecolloy (SAC_R), CYCLOMAX (SAC_Q), and Innolot
were explored. Being motivated by the promising results, we
are extending this research to investigate aging effects on
these doped alloys. In the present study, we explored the
mechanical properties of a new lead-free doped SAC solder
alloy named as SAC_Q (commercially known as
CYCLOMAX). It has been recommended for high-reliability
applications by the vendor. Uniaxial samples were prepared
for the alloy, and some samples were aged in an oven at T =
100
o
C for 3 months. Uniaxial tensile tests were performed
with the doped alloy of both non-aged and aged
microstructures. Testing conditions included three different
strain rates (0.001, 0.0001 and 0.00001 sec
-1
) and five
different test temperatures (25, 50, 75, 100 and 125
o
C).
Tensile test results for the doped alloy, before and after aging,
were compared with those of standard SAC305.
Anand parameters of the doped alloy for the various
aging conditions were determined from the stress-strain test
results. A good correlation was found between Anand model
predictions and the experimentally obtained results. A
microstructure study has revealed that the Bismuth (Bi)
present as a dopant in the SAC_Q alloy plays an important
role to make the alloy relatively insensitive to aging-induced
degradations.
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The Anand viscoplastic model [43] has been commonly
adopted to represent the material behavior of lead free solders
in finite element simulations to predict solder joint reliability.
Details of the Anand model formation can be found in the
literature [15-16, 43-45]. The model includes three equations:
(1) stress equation, (2) flow equation, and (3) evolution
equation. The 9 material parameters (constants) in the model
are denoted A, ȟ, Q/R, m, ho, a, s
o
,dž, and n. They can be
determined by measuring stress-strain curves at several
different temperatures and strain rates, and then using a least-
squares regression fitting procedure to extract the optimal set
of 9 Anand parameters [15-16, 43-45].
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Test Matrix
Mechanical stress-strain tests have been performed on
SAC_Q solder samples. Test specimens were prepared using
a nine-zone reflow (RF) oven and a typical BGA solder joint
temperature profile. Some of the reflowed samples were
exposed to isothermal aging at T = 100
o
C (RF + 3 Months
Aging) for 3 months. The stress-strain tests were performed
before and after aging, at 15 different test conditions achieved
by a combination of three strain rates ( H
 = 0.001, 0.0001,
and 0.00001 sec
-1
) and five test temperatures (T = 25, 50, 75,
100, and 125
o
C). From the experimental stress-strain data,
the nine Anand constitutive model parameters were
determined for the alloy SAC_Q in two different aging
conditions (i.e. RF + No Aging and RF + 3 Months Aging).
Uniaxial Test Sample Preparation
Bulk solder samples were cut into small pieces and were
melted into a quartz crucible by induction heating. Molten
solder was then drawn into glass tubes with rectangular cross-
sections by a vacuum suction method [3-4, 13]. The glass
tube solder samples were next cooled to solidify the solder in
the tubes and form the uniaxial tensile specimens. All
samples were initially water quenched and then passed
through a solder reflow oven to re-melt the solder in the tube
and then re-solidify the solder using a controlled reflow
profile similar to that used for SMT (Surface Mount
Technology) assembly. These samples were then
mechanically tested to yield the RF microstructure results.
Additional samples were formed using the RF cooling profile
and then subsequently aged for 3 months at T = 100
o
C to
further coarsen the reflowed microstructure before mechanical
testing.
Solidified solder test samples were extracted by breaking
the glass tubes. The typical dimensions of the final test
samples were 80 x 3 x 0.5 mm, and the gage length during the
uniaxial testing was 60 mm. After solidification, the test
samples were kept in low temperature freezer to eliminate or
minimize any unintentional aging effects.
Mechanical Testing System and Data Processing
The MT-200 tension/torsion thermo-mechanical test
system from Wisdom Technology, Inc., shown in Figure 1
was used to perform the 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.

Figure 1- Mechanical Test System with Solder Sample

At least 5 stress-strain tests were performed for a given
solder alloy microstructure at each temperature and strain rate.
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 empirical
model is best able to represent experimental SAC solder
stress-strain curves:
)Ctanh(C)Ctanh(C4321 HH V (1)
This model was used to fit each set of 5 experimental
stress-strain curves and yield an “average” experimental
stress-strain representation. The plots shown in the remainder
of this paper are the fits of eq. (1) to the experimental data.
Sample Preparation for Microstructure Analysis
For microstructure analysis, solder samples were potted
in epoxy. Details of the preparation process included
mechanical grinding with several SiC papers (#320 to #400,
#600, #800 and #1200), and then final polishing with 0.02 μm
colloidal silica suspensions. This procedure resulted in mirror
finish samples suitable for Scanning Electron Microscopy
(SEM).
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Chemical Composition
Energy Dispersive X-Ray Spectroscopy (EDX) was used
to explore the chemical composition of the doped alloy. The
results are presented in Table 1 along with the composition of
the traditional SAC305 alloy. The doped alloy was found to
employ Bismuth (Bi) as the primary X-additive. The silver
contents of SAC_Q is similar to SAC305, at 3.41%. Besides,
it has additional 3.30% Bi.
Table 1 - Chemical Compositions of the Solder Alloys
Alloy Sn Ag Cu Bi Ni
SAC_Q 92.77 3.41 0.52 3.30 0.00
SAC 305 95.50 3.00 0.50 0.00 0.00
Stress-Strain Data for Various Temperatures and Strain Rates
The recorded stress-strain curves for SAC_Q (RF) at strain
rates of 0.001, 0.0001, and 0.00001 sec-1 are shown in Figures
2a, 2b, and 2c, respectively. Each curve in these plots is an
“average” stress-strain curve representing the fit of the
empirical model in eq. (1) to the 10 recorded stress-strain
curves for the particular strain rate and temperature. The five
different colored curves in each graph are the results for the 5
testing temperatures (T = 25, 50, 75, 100, and 125 oC). As
expected, the initial elastic modulus, yield stress, and UTS
decrease with increasing temperature. In addition, they also
decrease with decreasing strain rate. Analogous results were
found for the SAC_Q samples with RF + Aging condition as
shown in Figure 3.
It is interesting to note that there are no easily apparent
visual differences between the results in Figures 2 and 3,
suggesting that the SAC_Q alloy is resistant to aging effects.
Values of ultimate tensile strength (UTS) before and after
aging for all the 15 test condition are presented in Table 2. It
is evident from the results that isothermal aging at 100 oC
does not have any significant influence on UTS of the
material.
(a)
(b)
(c)
Figure 2 - Stress-Strain Curves Obtained for SAC_Q
(RF, No Aging)
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Figure 3 - Stress-Strain Curves Obtained for SAC_Q
(RF, 3 Months Aging)
Table 2 - Ultimate Tensile Strength (UTS) of SAC_Q with
No Aging and 3 Months of Prior Aging
T
(oC)
1
sec001.0 
H
1
sec0001.0 
H
1
sec00001.0 
H

UTS
(MPa)
No
Aging
UTS
(MPa)
3M
Aging
UTS
(MPa)
No
Aging
UTS
(MPa)
3M
Aging
UTS
(MPa)
No
Aging
UTS
(MPa)
3M
Aging
25 69 ± 5 70 ± 3 61 ± 4 60 ± 4 53 ± 2 53 ± 2
50 60 ± 3 60 ± 2 53 ± 1 52 ± 1 45 ± 1 47 ± 2
75 53 ± 2 52 ± 2 45 ± 1 45 ± 3 39 ± 1 40 ± 3
100 46 ± 4 45 ± 2 39 ± 3 40 ± 2 33 ± 2 34 ± 1
125 39 ± 3 40 ± 2 34 ± 2 35 ± 3 28 ± 1 28 ± 1
The data in Figures 2-3 were used to extract the nine
Anand parameters for the SAC_Q material for each aging
conditions (RF and RF+Aging). As discussed previously, a
least-squares regression fitting procedure was utilized to
extract the optimal set of Anand parameters using the stress-
strain curves for each microstructure at 5 different
temperatures and 3 different strain rates. The calculated
Anand parameters are tabulated in Table 3.
Table 3 - Anand Parameters for SAC_Q
Par.
No.
Anand
Par. Units RF RF+Aging
1 so MPa 27.93 27.90
2 Q/R 1/K 10750 10750
3 A sec-1 8500 6500
4ȟ - 6 6
5 m - 0.32 0.32
6 ho MPa 65200 65200
7dž MPa 54 54
8 n - 0.0039 0.0032
9 a - 1.56 1.56
The calculated values of the Anand parameters were used
to predict stress-strain behavior for the SAC_Q solder alloy
with the various microstructures. For example, the results for
SAC_Q (RF) are presented in Figures 4(a), 4(b) and 4(c) for 3
different strain rates (i.e. 0.001, 0.0001 and 0.00001 sec-1).
Reasonable correlations were found for all of the
temperatures. Analogous results were found for the other
aging condition as well.
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(b)
(c)
Figure 4 – Comparison between Anand Model Predictions and
Experimental Data for SACQ (RF, No Aging)
Stress-Strain Data Comparisons (SAC_Q and SAC305)
Selected stress-strain curves for SAC_Q in Figures 2-3
have been replotted in Figure 5 for a strain rate of H
= 0.001
sec-1, temperatures of T = 25 oC, and the two aging conditions
(no aging and 3 months aging). The analogous curves for
SAC305 [45] are plotted in Figure 6. It is observed that large
aging induced degradations occur for the SAC305 alloy (the
dashed curves for the RF+Aging microstructure are
significantly below the solid curves for the RF
microstructure). For the SAC_Q alloy, there appear to be no
aging induced degradations. These observations are further
demonstrated in Figure 7, where analogous results for SAC_Q
and SAC305 are directly compared. In addition, similar
results were found for all 5 testing temperatures and 3 strain
rates. In our previous study on doped alloys [13, 42], it was
demonstrated that addition of only Bi significantly reduced or
eliminate aging effects in SAC solders.
Figure 5 - Stress-Strain Curves for SAC_Q with
and without Prior Aging
Figure 6 - Stress-Strain Curves for SAC305 with
and without Prior Aging
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Figure 7 - Comparison of Stress-Strain Curves for
SAC305 and SAC_Q
Microstructural Analysis
The microstructure of SAC305 is mainly composed of a ȕ-
Sn matrix and two different intermetallic compounds (IMC)
namely, Ag
3
Sn and Cu
6
Sn
5
. The reduction of strength of
SAC305 after aging can be attributed to 2 major facts [46].
First, aging causes coarsening of the Ag
3
Sn and Cu
6
Sn
5
intermetallic compounds and hence reduces their ability to
block dislocation movements. Second, the ȕ-Sn phase also
coarsens/grows with aging, and hence reduces the strength of
the alloy. For the SAC_Q alloy, Bi doesn’t form any IMC
with Sn. Therefore, the IMC’s that should present in
microstructure of SAC_Q are same as SAC305 (i.e. Ag
3
Sn
and Cu
6
Sn
5
). From the Sn-Bi phase diagram (see Figure 8), it
is observed that Bi has a good (~1.8%) solid solubility in Sn
at room temperature. Hence Bi contributes to some
enhancement in strength of the doped alloy before aging by
the solid solution strengthening mechanism.
Figure 8: Sn-Bi Phase Diagram
[http://www.metallurgy.nist.gov/]
(a) (b)
Figure 10: SEM Image for SAC305 Microstructure (a) Low
Magnification (500X) and (b) High Magnification (2000X)
(a) (b)
Figure 11: SEM Image for SAC_Q Microstructure (a) Low
Magnification (500X) and (b) High Magnification (2000X)
(a) (b)
Figure 12: SEM image for Aged SAC_Q Microstructure
(a) Low Magnification (500X) and (b) High Magnification
(2000X).
Non-aged microstructures of SAC305 and SAC_Q are
presented in figures 10 and 11, respectively. As expected, we
found a similarity between the microstructure of SAC305 and
SAC_Q at low magnification (10(a) and 11(a)). But at higher
magnification, we can clearly see the precipitation of
remaining Bismuth (Bi), which could not go to the solid
solution with Sn. In our previous study [42] on SAC_R, it has
been demonstrated that Bi phase present in the as reflowed
microstructure goes into ȕ- Sn matrix during aging at 100
o
C
and enhance strength by solid solution strengthening. The
increases in strength from solid solution strengthening might
nullify any reductions in strength caused by IMC and ȕ-Sn
phase coarsening. As a result, we did not get any significant
difference in stress-strain behavior before and after aging.
6800$5<$1'&21&/86,216
In this work, we explored the mechanical properties of a
new lead-free doped SAC solder alloy named as SAC_Q
(commercially known as CYCLOMAX). It has been
recommended for high-reliability applications by their vendor.
Samples were prepared with the alloy and kept inside a
heating oven for aging to take place for 3 months. Uniaxial
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tensile tests were performed with the doped alloy at different
aging times. Test condition includes three different strain rate
(0.001, 0.0001 and 0.00001 sec-1) and five different test
temperatures (25 oC, 50 oC, 75 oC, 100 oC and 125 oC).
Tensile test results of the doped alloy, before and after aging,
were compared with those of standard SAC305.
Anand parameters of the doped alloy for all the aging
conditions were determined from stress-strain test results. A
good correlation was found between Anand model predicted
and experimentally obtained results. Microstructure study has
revealed that Bismuth (Bi), presents as a dopant in the alloy,
plays an important role to make these doped alloys insensitive
to aging-induced degradation.
$&.12:/('*0(176
This work was supported by the NSF Center for Advanced
Vehicle and Extreme Environment Electronics (CAVE3).
5()(5(1&(6
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