This is the third, final part of a series. Click here to read Part 1, and here for Part 2.

Vibration Fatigue life Assessment  

 The vibration fatigue assessment models provide an estimate of the fatigue life for component interconnects (e.g., solder-joints and component leads) based on input from the vibration analysis and transportation/usage profiles. Failures occur due to stresses developed in the leads and solder joints from the difference in relative curvature of the components and PCB and from in-plane accelerations acting on the components. Relative curvature and in-plane accelerations continually change based on the input vibration load.

One of the most well known simplified models in the area of PCB vibration fatigue is Steinberg’s model. Steinberg has proposed an empirical equation (1) for designing PCBs in vibration environments where the maximum deflection of the PCB is less than a critical displacement value, d [3] :                                                  

where
B = length of PCB edge parallel to component (in.),
L = length of electronic component (in.),
t = thickness of PCB (in.),
c = constant for different types of electronic components.

It is necessary to understand the probability distribution function to predict the probable acceleration levels the electronic equipment will see in a random vibration environment. Steinberg’s 3-Band technique divides the random vibration input acceleration levels into three segments based on an assumed stationary Gaussian distribution of the input load. The Gaussian distribution curve shown in Figure 14 represents the probability for the value of the instantaneous acceleration levels at any time.

Figure 14. Gaussian distribution curve.

Using S-N curves and the relationship (2),

where
N = number of cycles,
σ = RMS stress,
b = fatigue exponent,

the number of cycles to fail at each stress level can be determined. Then, using the Miner’s rule (3), the accumulative damage can be approximated as follows:

where n₁ is the actual number of cycles at 1σ levels,
N₁ is the total number of cycles to fail at 1σ levels,
n₂ is the actual number of cycles at 2σ levels,
N₂ is the total number of cycles to fail at 2σ levels,
N₃ is the actual number of cycles at 3σ levels,
N₃ is the total number of cycles to fail at 3σ levels.