Prediction Modeling

The characteristic life and stress amplitude are related according to power equation [48] shown in Equation (2).

$$N\_{63} = \mathbb{C} \times P^{-n} \tag{2}$$

where *N*63 is the characteristic life, *P* is the stress magnitude, *C*, *n* are material constants. *n* is called the ductility factor where lower value implies higher ductility. Figure 8 illustrates the fatigue life as a function of stress amplitude. Seven solder joints are cycled until complete failure with each stress level. The fatigue life is reduced drastically at higher stress levels.

**Figure 8.** The fatigue life of SAC305 solder joints as a function of stress amplitude.

Characteristic life is a vital parameter to define reliability as a function of stress level according to Equation (1). Therefore, the characteristic life of SAC305 joints as a function of stress amplitude at the "no dwelling" condition is plotted, as shown in Figure 9. Data were fitted to a power equation which was found satisfactory to describe the characteristic life of joints as a function of stress amplitude according to Equation (2). It is concluded that the power value for the generated power equation is −4.34, which reflects the fatigue ductility exponent coefficient of the material. Moreover, increasing the stress value by a factor of 2 will lead to life reduction by a factor of 19. The ductility index (*n*) represents the material ductility, where the higher value of n means lower ductility. Similar results were found by others [21,66]. C constant in the stress life equation works as a scale parameter of the relationship between the fatigue life and the stress level, and n coefficient provides the shape of this relationship.

**Figure 9.** Characteristic life as a function of stress amplitude for SAC305 solder joints at no dwelling.

3.1.2. Dwelling (Creep–Fatigue) Condition Weibull Plots

In order to examine the effects of dwelling on the fatigue life of the solder joints at different stress conditions, individual solder joints were tested at amplitudes of 16, 20, and 24 MPa with different dwell times of 0, 10, 60, and 180 s at 25 ◦C. The shape and scale parameters of the Weibull distribution were obtained for all combinations. In Figure 10, the Weibull plots for 10 s of dwelling level are generated. At certain dwelling times, increasing the stress amplitude leads to substantial fatigue life reduction. The same trend is found for other dwelling periods of 60 and 180 s. Moreover, at a certain stress level, the fatigue

life is decreased extremely with dwellings of 10 s. Life continues to decrease with longer dwellings but in a smaller amount, as shown in Figure 11. Based on the preliminary life data analysis, only one data point was found as an outlier for the solder joints that were cycled at the 16 MPa stress level with a 180 s dwell time. This data point was eliminated from the reliability analysis. In Figure 12, characteristic life as a function of dwell time for various stress amplitudes is plotted. Creep effect (due to dwelling) was found to be substantial. There are some results for less life of lower stress and higher dwelling conditions than ones cycled with higher stress and shorter dwellings.

**Figure 10.** Weibull distributions for SAC305 joints cycled at different stress amplitudes at 10 s dwelling.

**Figure 11.** Weibull distributions for SAC305 joints cycled at different dwellings with 16 MPa stress level.

**Figure 12.** Characteristic life as a function of dwell time for SAC305 solder joints cycled with various stress levels.
