IEEE TRANSACTIONS ON ELECTRONICS PACKAGING MANUFACTURING, VOL. 32, NO. 4, OCTOBER 2009 221
Constitutive and Aging Behavior of
Sn3.0Ag0.5Cu Solder Alloy
Kaushik Mysore, Ganesh Subbarayan, Senior Member, IEEE, Vikas Gupta, and Ron Zhang
Abstract—We describe double-lap shear experiments on
Sn3.0Ag0.5Cu solder alloy, from which fits to Anand’s viscoplastic
constitutive model, power-law creep model, and to time-hardening
primary-secondary creep model are derived. Results of monotonic
tests for strain rates ranging from 4.02E-6 to 2.40E-3 , and
creep response at stress levels ranging from 19.5 to 45.6 MPa are
reported. Both types of tests were conducted at temperatures of
25 C, 75 C, and 125 C. Following an earlier study where Anand
model and time hardening creep parameters for Sn3.8Ag0.7Cu
and Sn1.0Ag0.5Cu solder alloys were reported, here we report
power law model parameters so as to enable a comparison between
all three alloys. Primary creep in Sn3.0Ag0.5Cu solder alloy is
shown to be significant and are considered in addition to secondary
creep and monotonic behavior. Aging influence on behavior is
also shown to be significant. On the basis of experimental data,
the following four aspects are discussed: 1) difference between
testing on bulk versus joint specimen; 2) consistency between the
creep and monotonic behaviors; 3) comparison against behaviors
of Sn1.0Ag0.5Cu and Sn3.8Ag0.7Cu alloys as well as aganist
Sn40Pb, 62Sn36Pb2Ag and 96.5Sn3.5Ag alloys; and 4) compar-
ison of Sn3.0Ag0.5Cu and Sn3.8Ag0.7Cu relative to their aging
response.
Index Terms—Aging, Anand model, lead-free solders, power-law
model, primary creep, time-hardening creep model.
I. INTRODUCTION
S
OLDER alloys operate at high homologous temperatures,
and therefore exhibit a wide range of rate-dependent be-
haviors. Several viscoplasticity models, motivated by consider-
ations of physical processes have been proposed to describe this
behavior. These models often involve either external state vari-
ables such as stress, strain, strain rate, or internal state variables
such as backstress. They may also involve a yield function, a
flow rule, and a set of equations describing the evolutions of
the state variables [1], [2]. Hardening, when observed, is com-
monly modeled as isotropic hardening or as kinematic/direc-
tional hardening. If yield functions are used, hardening can also
be understood through expansion and motion of the yield sur-
face in stress space. Hardening processes that strengthen the ma-
terial as well as the recovery processes that soften the material
Manuscript received October 13, 2008; revised February 25, 2009. First pub-
lished September 09, 2009; current version published October 07, 2009. This
work was recommended for publication by Associate Editor R. Gedney upon
evaluation of the reviewers comments.
K. Mysore and G. Subbarayan are with the Department of Mechanical En-
gineering, Purdue University, West Lafayette, IN 47907-2088 USA (e-mail:
ganeshs@purdue.edu).
V. Gupta is with Texas Instruments, Dallas, TX 75243 USA.
R. Zhang is with the Sun Microsystems, Santa Clara, CA 95054 USA.
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TEPM.2009.2024119
have both been addressed in solder alloys along with creep-plas-
ticity interactions [3].
The macroscopic rate-dependent response is the result of var-
ious physical mechanisms at the microstructural level. The mi-
crostructure of materials in general, and SnAgCu solder alloys
in particular, is not uniform; it is often characterized by the pres-
ence of dislocations, grain boundaries, solute atoms, and pre-
cipitates. The fundamental creep mechanisms are known to be
diffusion controlled and are understood through grain boundary
diffusion, lattice diffusion, and through the motion of disloca-
tions and their interactions with the precipitates [2], [4]. Inter-
actions of physical processes (such as diffusion and dislocation
motion) with heterogeneities that characterize microstructure
form the physical basis of many existing constitutive models.
Both isotropic and kinematic strengthening mechanisms are at-
tributed to the existence of such heterogeneities [2]. State vari-
able theories attempt to account for the above mechanisms by
identifying both the state variables related to the specific phys-
ical mechanisms, and the forms of their evolution equations.
Viscoplasticity models can be broadly classified as either uni-
fied or nonunified models. Unified refers to the lack of distinc-
tion between creep and plastic behaviors as they are both pri-
marily known to be caused by dislocation motion. Both unified
and nonunified models can be further classified as models with
or without yield surfaces. Such viscoplasticity models include
those by Hart [5] which was expanded by Korhonen et al. [6]
to include transient response, and later applied to solder defor-
mation by Wilcox et al. [7], Anand’s model [1], [8] which was
developed for rate-dependent deformation of metals at high tem-
peratures and thereafter applied to describe solder behavior by
many authors [9]–[14], models by Busso [15], [16] motivated
specifically by solder behavior, model based on overstress by
Krempl [17]–[20], subsequently applied to study solder defor-
mation by Maciuescu et al. [21], unified creep-viscoplasticity
model to study solder material behavior by McDowell [3], sub-
sequently expanded by Stolkarts et al. [22] to describe solder
deformation. The models by McDowell and Stolkarts include a
yield function of the Von Mises type, while the other models do
not include a yield function definition.
For solder alloys, along with the physical processes, other im-
portant considerations apply while selecting a particular model
for characterizing behavior: 1) predictive ability over a range
of experimentally observed behaviors including tensile tests at
different strain rates and temperatures as well as creep tests at
different stress levels and temperatures; 2) minimum number of
material parameters that fully describe the observed behavior; 3)
number and complexity of experiments required to characterize
behavior; and 4) successful prior application to describe solder
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