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 1521-334X/$26.00 © 2009 IEEE