Critical Accumulated Strain Energy (Case) Failure Criterion for Thermal Cycling Fatigue of Solder Joints

In the automotive and computer industries, a perennial challenge has been to design an adequate and efficient accelerated thermal cycling test which would correspond to field service conditions. Failures, induced in both thermal cycle testing and field service, are characterized by thermal fatigue behavior. Several fatigue models have been proposed, none of these models take into account all of the many parameters of the test or service environment. In thermal cycling, for example, the temperature range, ramp rate, hold time, and stepped heating and cooling are known to influence the number of cycles to failure. In this study, a critical accumulated strain energy (CASE) failure criterion is proposed to correlate the fatigue life to both the plastic and creep strain energies, which accumulate in solder joints during the thermal cycling. This criterion suggests that solder joints fail as the strain energy accumulates and reaches a critical value. By using finite element analysis with a “ladder” procedure, both time-independent plastic strain energy and time-dependent creep strain energy are quantified. These are related to fatigue life by the equation: C = N*_f (E_p + 0.13E_c), where C is the critical strain energy density, N_f is the fatigue life, E_p and E_c are plastic and creep strain energy density accumulation per cycle, respectively, for the eutectic Sn-Pb solders. By analyzing Hall and Sherry’s thermal cycling data (Hall and Sherry, 1986), it is found that creep is the predominant factor in deciding fatigue life. Creep accounts for 51 to 97 percent of the total accumulated strain energy, depending on the cycling profiles. This criterion is used to simulate crack propagation in a solder joint by analyzing the strain energy in small “domains” within the joint.