A NON-LINEAR DAMAGE MODEL WITH LOAD DEPENDENT EXPONENTS FOR SOLDERS UNDER SEQUENTIAL CYCLIC SHEAR LOADS
Pecht, Michael G
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The damage state of a material subject to cyclic loads is often characterized by the cycle ratio of applied cycles to the number of survivable cycles. The damage in a material under sequential cyclic loading is widely estimated using Miner’s rule. Miner’s rule assumes that damage in a material accumulates linearly under cyclic loading and the damage path is independent of the applied load level. Due to these inherent assumptions, Miner’s rule inaccurately estimates life under sequential loading conditions for solders. To improve the accuracy of damage estimation, a non-linear damage accumulation model based on damage curve approach that takes into account the effect of loading sequence under sequential loading conditions is proposed for solders in this dissertation. In the proposed non-linear damage model, damage is related to the cycle ratio using a power law relationship where the power law (damage) exponent is defined as a function of the applied load level (cycles to failure). An experimental approach is proposed to determine the load dependent exponents of the non-linear model under three load levels. The test matrix consisted of a series of single level cyclic and sequential cyclic shear tests in a thermo-mechanical micro analyzer. Load dependent exponents were developed for SAC305 (96.5%Sn+3.0%Ag+0.5Cu) solder material and the applicability of these exponents were validated by tests under a new loading condition and reverse loading sequence. Experimental results revealed that the value of damage exponent decreased with the severity of the applied load level. Additionally, taking damage analogous to crack growth, an analytical relationship between the damage exponent and the applied load level was developed from the Paris’ law for crack propagation. This enables determination of non-linear damage curves at different load levels without conducting extensive experimentation. The damage due to crack initiation was assumed to be 10% of the total damage and sensitivity analysis was carried out to determine the effect of this assumption. The load dependence of the Paris’ law exponent (m) was also derived for SAC305 solder material. Analysis of the failed specimens revealed fatigue crack in the solder joints along the tin grain boundaries.