MKS application to fatigue of Al 7075-T6

1. Al 7075-T6 Multiaxial Fatigue
Paul Kern and Chris Shartrand

2. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Overview
• Introduction
• Motivation
• Objectives
• Data
• Workflow
• Results
• Conclusions

3. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Introduction
• Al 7075-T6 is an older aluminum alloy
which is often used in aerospace
applications in a rolled sheet form.
• During processing it is common for
µm-sized particles to become
ingrained in the matrix
• The rolling leads to an interesting,
anisotropic distribution of constituent
particles.
[1]

4. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Motivation
• Fatigue due to cyclic loading
leads to component failure
• Early replacement of components
can waste millions of dollars
• Accurate life predictions reduce
this cost by extending usable part
life
• Current microstructurally small
fatigue predictions are too
conservative for shear loading

5. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Objectives
• Utilize reduced cost model to study particle distribution effect
on strain intensification
• Provide Fatigue Indicator Parameter (FIP) distribution to multi-
stage pipeline which will incorporate for microstructurally small
crack growth simulations

6. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Data
• Crystal Plasticity Calibration
 6 21x21x21 delta microstructure simulations to train MKS influence coefficients
• Microstructure Reconstructions
 10 200x200x200 reconstructions
 Generated using David Turner’s neighborhood reconstruction software
• Microstructure Scans
 6 scans of varying resolution from James Harris’ thesis
 Between 100x100 μm and 1000x1000 μm
• Verification Microstructures
 5 21x21x21 microstructures with particles to verify MKS predictions

7. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Reconstruction
[1]

8. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
MKS Introduction
• We will use a method typically referred to as MKS
 Response localization for material informatics
 Influence coefficients which act on the microstructure function
• Assume influence coefficients are independent of the
microstructure topology
 Depends on thorough selection of microstructure function
 First order calibration and summation
' '
' '
' '
...h h hh h h
s t s t tt s t s t t
h t h h t t
p m m m p    
 
   
 
 
*h h
k k k
h
P M p
 
  
 

[2]

9. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
MKS Explanation
[2]

10. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
MKS Explanation
[2]

11. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Material System Definition
• Microstructure function 𝑚 𝑠
ℎ|𝑠 = 0,1, … , 𝑆 − 1; ℎ = 1,2
 h=1, matrix
 h=2, particle
 s=spatial bins varying over the S volume
• Particle
 Young’s Modulus: 169 GPa
 Poisson Ratio: 0.34
• Matrix
 Young’s Modulus: 69 Gpa
 Poisson Ratio: 0.34

12. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Workflow
Simulated
Data
Train
Models
• Place into
wrapper
• Pickle
Test
Models
Quantify
Error
Predict
Strain
Field For
Large SVE
Predict
FIPs

13. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Fatigue Extrapolation
11 11
22 22
33 33
23 23
13 13
12 12
1 0 0 0
1 0 0 0
1 0 0 0
0 0 0 (1 2 ) / 2 0 0(1 )(1 2 )
0 0 0 0 (1 2 ) / 2 0
0 0 0 0 0 (1 2 ) / 2
E
   
   
   
  
 
 
    
        
    
    
     
    
    
       
1
2
p
FS
y
FIP k
 

  
     
  
3 2
2 3
p p p
ij ij ij ijS S     
( )
3
tr
S I

 
[3]

14. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Reconstruction
[1]

15. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
2-Point Statistics

16. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Scaling Problem
Particle AutocorrelationMatrix Autocorrelation

17. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Trimmed 2 Point Statistics

18. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Error Quantification
Random “Particle” DistributionReconstruction

19. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Reconstruction Confidence Intervals

20. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
MKS Validation

21. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Predictions of FIPs
Shear 0.2% Uniaxial 0.2%

22. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Volumetric Averaging
• Analyzed varying sized
Gaussian kernels
• Apply kernel and normalize
by a blurred mask to negate
influence of 0 FIP particle
elements
• Reflect damage process
zone and reduce extreme
value problem caused by
discrete elements

23. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Predictions of FIPs
Shear 0.2% Uniaxial 0.2%

24. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Computational Efficiency
• Most costly part is generating reconstruction
 6 hr per reconstruction on 4 cores
• Storage is cheap because binary microstructure function
 87 kb per reconstruction
 Develop and keep a library of reconstructions
• Predictions
 1 hr average time for computation and analysis of FIPs for reconstruction on single core
 Require large amount of memory in Python implementation (~100 GB)
 Not feasible to explore this space using a crystal plasticity model and our current cluster
capability (~1600 elements per core for efficiency leads to 5000 cores)

25. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Conclusions
• Successfully implemented MKS for prediction of full strain
tensor for arbitrary loading conditions
• Incorporated plasticity extrapolation
• Verified reconstructions
• Sampled FIP distributions
• Anisotropic particle distributions contribute to observed fatigue
life disparity, but are not the only determining factor at this
scale

26. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Future Work
• Incorporate fully into multi-stage crack prediction model
• Pseudo-particles and local intensification effects added to
homogenized model
• Study crack nucleation under different loading conditions
 Requires explicit crack modeling
 Contrast issue for MKS

27. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Acknowledgements
• Dr. McDowell
• Dr. Kalidindi
• Postdoc
 Dr. Hafeez
• Graduate Students
 David Brough
 Yuksel Yabansu

28. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Sources
1. Rollett, Anthony D., Robert Campman, and David Saylor.
"Three dimensional microstructures: statistical analysis of
second phase particles in AA7075-T651." Materials science
forum. Vol. 519. 2006.
2. http://materialsinnovation.github.io/pymks/rst/elasticity_2D.ht
ml
3. Fatemi, Ali, and Darrell F. Socie. "A Critical Plane Approach
to Multiaxial Fatigue Damage Including out‐of‐Phase
Loading." Fatigue & Fracture of Engineering Materials &
Structures 11.3 (1988): 149-165.

29. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Backup

30. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Cracked Particle
• Deformation can cause particles to become cracked
 Cracks from particles often extend into the matrix and eventually cause part failure

31. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Uniaxial Fatigue Lives

32. The George W. Woodruff School of Mechanical Engineering School of Materials Science and Engineering
Fatigue Extrapolation