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Fatigue Life Assessment
Fatigue Life
Fatigue occurs when a material is subjected to repeated loading and unloading.
If the fatigue is accumulated beyond a certain limit, the object will fracture.
The fatigue life of solder is an important factor in the electronics industry.
It can be assessed for the creep or elasto-plastic materials in the static multi-step analysis or multi-step thermal load analysis.
The Manson-Coffin law is used for the assessment.
How to Calculate the Fatigue Life
Where the stress is high and the inelastic strain is exhibited, the object might fracture just in low number of repetitions of such stress.
It is called the low-cycle fatigue and characterized by the Manson-Coffin law.
(The repetition is allowed up to 105 cycles)
- Equation 1
Nf is the number of stress cycles sustained before failure, Δεne is the equivalent inelastic strain amplitude (Unit: %)
C is the number of stress cycles sustained before failure when Δεne is 1%.
n is the influence parameter of Δεne.
C and n are specific to the material.
Δεne can be calculated from the accumulated equivalent inelastic strain obtained by the multi-step analysis or multi-step thermal load analysis of creep or elasto-plastic material.
The formula is shown below: Complete two cycles of loading/unloading. Acquire the accumulated equivalent inelastic strain after the first cycle and that of the second cycle.
Divide the difference of those strains by 2
Enter the step number of the first step into Reference step.
Enter the step number of the second step into Final step.
- Equation 2
Setting Items
Set steps for 2 cycles on the Step/Thermal Load tab. Set the reached temperature at the end time of each step in the case of temperature cycles.
2 steps are required because the change of equivalent inelastic strain is not stable in the first step.
Set the time dependency on the Mechanical tab for the mechanical loading/unloading cycles.
In the example below, the first cycle finishes at Step 4. The second cycle finishes at Step 8.
Select "Fatigue life assessment" on the Step/Thermal Load tab.
Enter the step numbers required for the calculation. In this example, Reference step is 4 and Final step is 8.
The accumulated equivalent inelastic strain will be calculated from Equation 2.
Enter the values for C and n. The fatigue life will be calculated from Equation 1.
Left figure: Step setting, Right figure: Load setting
Accumulated equivalent inelastic strain against time
Output Items
The minimum value of Nf calculated by Equation 1 is shown on the output window.
Δεne of Equation 2 and Nf of Equation 1 can be displayed by contour diagram.
See also [Fatigue Life Assessment in the Stress Analysis].
Cautions:
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Each element's life is calculated from the average.
Where the strain is concentrated, therefore, the life might vary depending on the mesh size.
To compare the life with different models or under different analysis conditions, keep the mesh size same for the body which is expected to fracture due to the fatigue.
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The low-cycle fatigue (less than 105 cycles) is assumed.
For the body where no fatigue is expected, the life is significantly long and indicates 109 cycles. The life beyond that cannot be calculated.