This Is AuburnElectronic Theses and Dissertations

Measurement and Modeling of Damage in Mechanically Cycled Lead Free Solders




Haq, Mohammad Ashraful

Type of Degree

PhD Dissertation


Mechanical Engineering

Restriction Status


Restriction Type


Date Available



Solder joints in electronic packages often experience fatigue failures due to cyclic mechanical stresses and strains in fluctuating temperature environments. This cyclic loading of the solder is induced by mismatches in coefficients of thermal expansion and leads to damage accumulation that contributes to crack initiation, crack propagation, and eventually failure. During thermos-mechanical modeling researchers often consider the properties of the solder to remain constant during cycling. In practice, solders exhibit evolving properties that change significantly with cycling as well as isothermal aging. This dissertation focuses on the evolution of mechanical properties of SAC and SAC+X alloys when subjected to isothermal mechanical cycling. A new approach of cycling material at a constant initial damage level is proposed along with a damage parameter that can account for the changes in properties with mechanical cycling and temperature. In this work, the effects of isothermal room and elevated temperature mechanical cycling on damage accumulation in lead free SAC305 bulk solder alloys have been investigated. Material behaviors of the pre-cycled solder were characterized at the various damage levels per cycle and durations of cycling. One goal of this investigation was to identify a damage parameter that can be used to predict the observed material property degradations occurring during cyclic loading of solder irrespective of the way that the damage is accumulated. The total energy dissipation occurring in the solder during cycling was found to correlate well with the evolution of mechanical properties, independent of the damage level applied during each cycle. This study was also extended to investigate how the addition of Bi as an alloying element affects the evolution of mechanical properties with cycling. The effect of Bi on the fatigue property of SAC+ X Bi (X=1, 2, and 3%) was investigated using constant initial plastic energy accumulation cycling. This approach removed the limitations from previous fatigue life studies where a constant strain range was used across all the alloys, which resulted in various hysteresis loop sizes. Rectangular cross-sectioned and polished samples of all the alloys were also cycled at the same corresponding strain ranges to study the change in the microstructure of the alloys with mechanical cycling. This has helped us gain a better understanding of how the bismuth percentage in an alloy affects the microstructure evolution during mechanical cycling. Finally, it was deduced that the total energy dissipation that had occurred in the sample (sum of DW for all cycles) could be used as a governing failure variable independent of the damage level applied during each cycle. This has motivated using a scalar damage parameter in the constitutive model for the investigated SAC305 alloy following the basic concepts of continuum damage mechanics. In this study, a damage parameter was proposed by correlating the material degradation with the energy dissipation at cyclic load conditions. A scalar damage parameter was introduced as a state variable in the constitutive relations for elastic visco-plastic deformation of solder alloys. Since, total energy dissipation is mainly responsible for the damage, damage parameter, D is assumed to be a function of total inelastic energy dissipation per volume, W. A non-linear two-parameter exponential relationship between D and W yielded a good fit between the experimental data and damage mechanics prediction model.