*2.3. Test Profile*

Two profiles are employed to explore the effects of creep and fatigue in addition to quantifying them. First, a stress-controlled cyclic fatigue test is implemented to examine fatigue effect only, as shown in Figure 5. Cyclic-defined stress is applied at a constant ramp rate of 0.1 mm/s on the solder joint and switched between stress extremes (positive and negative) until complete joint failure (no dwelling conditions). The second profile is of two parts: a stress-controlled followed by a strain-controlled condition, as shown in Figure 6. As soon as the predefined value of stress is reached (stress-controlled) at a positive extreme, the strain is held constant (strain-controlled) for a certain dwelling period. During this part, the material suffers from stress relaxation and/or creep; therefore, it is described as creep–relaxation. Once the dwelling is over, the joint is cycled (switched) to the negative stress extreme with the same conditions of stress and dwelling. The second test is utilized to explore the combined effects of creep and fatigue. The maximum dwelling was 180 s because negligible stress drop (damage) was observed after this duration.

**Figure 5.** Mechanical fatigue testing profile.

**Figure 6.** Combined creep–fatigue testing profile.

All experiments were performed at room temperature under several stress magnitudes (16, 20, and 24 MPa) and various dwelling periods (0, 10, 60, and 180 s). A constant ramp rate was employed of 0.1 mm/s for all replicates where seven joints were the sample size for each combination. Picking shear rate is critical in these tests due to viscoplastic behavior on SAC alloys. Faster ramp rate will cause the joints to resist more and does not give it enough time to creep. However, lower rates would cause the creep to be the dominant without allowing any effect for the fatigue. So, the defined shear rate was picked carefully based on previous studies [9–11,20,21] at such types of joints. The test matrix is shown in Table 1.



#### **3. Results and Discussions**

*3.1. Weibull Plots Analysis and Prediction Modeling*

3.1.1. Mechanical Fatigue Condition

Weibull Plots

Two parameter Weibull plots are generated for each testing combination to describe the fatigue behavior of solder joints. To demonstrate the degradation in fatigue life or joint reliability, a two-parameter Weibull equation [48] is applied as shown in Equation (1).

$$\mathcal{R}(t) = \mathbf{e}^{-\left(\frac{t}{\hbar}\right)^{\beta}} \tag{1}$$

where *R*(*t*) is the reliability at time *t* (the probability of not fail), *t* is the time or number of cycles, *θ* is the scale parameter or characteristic life, and *β* is the shape parameter. Figure 7 shows the Weibull plot for joints cycled according to the mechanical fatigue profile (no dwelling) with various stress amplitudes. A significant reduction in joints reliability is observed at higher stress levels. Weibull distribution plots were constructed using Minitab Software for each stress level, considering the maximum likelihood estimation method as the parametric estimation method. The variability of data is low according to the shape (*β*) parameter values.
