1. MEMS 5510 - Finite Element Analysis
Washington University
Department of Mechanical Engineering & Materials Science
MEMS Finite Element Analysis
Chapter 8

2. Validation pyramid
Source: EADS
MEMS 5510

3. Focus: Prediction of local failure
Shear clip
Structural analysis: Scale of meters. Details are not accounted for.
Size of fasteners 5 mm
Size of cracks to be predicted: 0.25 mm (0.01”)
Size of defects that may cause cracks: about 0.1 mm
MEMS 5510

4. The process zone
MEMS 5510
MEMS 5510

5. Data analysis 7050-T7451 (MIL-HDBK-5H)
MEMS 5510
MEMS 5510

6. Miner’s rule
MEMS 5510
MEMS 5510

7. Cycle ratio
MEMS 5510
MEMS 5510

8. Data analysis T7451
MEMS 5510
MEMS 5510

9. MIL-HDBK - 5H (10/1/01) Product: 7050 – 7451 plate, 1 inch thick
Specimen: Unnotched, 0.30 inch diameter. Surface condition: Not specified.
Empirical formula obtained by nonlinear regression (ksi units):
Std. Error of Estimate, Log(Life) = 0.490
Std. Deviation, Log(Life) = 0.942
R2 = 73 %
“Caution: The equivalent stress model may provide unrealistic life predictions for stress ratios beyond those represented above.”
This means R > Typical flight spectra for rotorcraft: 0.6 < R < 0.8.
MEMS 5510
MEMS 5510

10. Remarks
Mathematical models must provide reliable information outside of the range of calibration.
The goal of validation is to test the predictive capabilities of models outside of the range of validation.
Metrics and tolerances.
Poor performance of models outside of the range of validation is evidence that the aleatory and epistemic uncertaities are mixed. If the prescribed tolerance is exceeded then
The model is rejected – return to conceptualization
The tolerances are increased – poor model definitions are compensated by large factors of safety. This imposes weight penalties and shortens inspection intervals.
MEMS 5510
MEMS 5510

11. Model problem Assumptions: i σmax Ri ni 1 200 -1 3000 2 400 2000 3 500
The interpretation of calibration data in MIL-HDBK-5H is OK
The curves represent mean values
The standard deviation is independent of R and its value is 0.490
The log10(Nf) data have normal distribution. That is, Nf is (almost) log-normal
A validation experiment is to be performed. The goal is to predict the number of times the sequence of loading shown in the table below can be repeated prior to the occurrence of fatigue failure using Miner’s rule. Stresses are in MPa units. i
σmax Ri ni 1
200 -1
3000 2
400
2000 3
500
0.5
1000
MEMS 5510
MEMS 5510

12. Histogram
Histogram obtained by 1000 Monte Carlo iterations for one block of loading
MEMS 5510
MEMS 5510

13. CDF for one block of loading
MEMS 5510
MEMS 5510

14. Prediction
MEMS 5510
MEMS 5510

15. Rejection criteria
Suppose that only one validation experiment will be performed and we have selected tL = tH = t = This means that we will reject the model if the outcome of the experiment has a probability of occurrence, as predicted by our model, smaller than 10%.
Selection of t is subjective. The model will not be rejected for smaller t.
Suppose that 5 experiments were performed and the CDF of the experiments is G (x) shown on the previous slide. In this case the model will not be rejected because the prediction was that 20% of the outcomes will be outside of the ramge (ML, MH).
MEMS 5510
MEMS 5510

16. Paris’ law
MEMS 5510
MEMS 5510

17. The problem with LEFM
LEFM is based on the assumption that the stress field is 2D. However calibration of (ΔKI)th can be performed in 3D only
MEMS 5510

18. Austempered ductile iron in air
The problem with LEFM
Austempered ductile iron in air
These results indicate that the coefficient C in Paris’ law is a function of the cycle ratio R.
The singularity at points at A and B are not the same as the singularity assumed by Paris’law.
MEMS 5510

19. The problem with Kt A B
For this problem the stress concentration factor Kt is not associated with a clearly defined notch radius.
Therefore the methods developed by Neuber, Peterson and others are not applicable.
MEMS 5510

20. Dilbert on data
MEMS 5510
MEMS 5510

21. Family of models for damage accumulation
MEMS 5510