1. Capturing Size Effect in Unidirectional Fiber Composites Employing Stochastic Finite Element Simulations By Thomas Bilodeau Advisor: Dr. Fertig May 2, 2015

2. Background on Problem Catastrophic failure Composites focus on average behavior Safety issue Length scale dependence or “size effect” Composite application in aerospace technology (admc.edsrtechnology.com) 2

3. What is a Composite? Two or more materials Chosen for – Chemical behavior – Mechanical behavior Used in – Buildings – Aerospace – Roads – etc. Fig. 1-General Composite Structure (Wikimedia Commons) 3

4. Unidirectional Fiber Composites Unidirectional Fiber Composite (efunda.com) Fibers made of carbon Fibers impregnated in epoxy 4

5. Ideal Composite Structure Hexagonal Packing – “Hexpack” Real structures – Closest to hex Ideal configuration Actual configuration 5

6. Fiber Volume Fraction Optical picture of an alignment fibers within a composite (Fertig, AIAA) Not constant Results in property variability 6

7. Size Effect Statistical distribution of material defects 7

8. Random Seeding of Fiber Volume Fraction 21 Materials Autodesk Composite Simulation Analysis – Failure of cells 8

9. Fiber Distribution Min 0.45 Average at 0.59 Max 0.73 Distribution of bins over fiber volume fraction 9

10. Hex-Pack Properties Hex-pack model 5 fiber volume fraction points define strength – Quadratic curve fit to the strengths Elasticity defined by individual bins 10 Hexpack model result

11. Hex-Pack Strengths Hexpack created in Abaqus 5 points (including min/max) Curve fit to the strengths Hexpack model stress picture here 11

12. Randomized Sample Tests Sample sizes – 9mm – 125mm Only elasticity varied Only strength varied 12

13. Results Elasticity variation – Little to no change – Deviation change Strength variation ―Higher end projects more? ―Deviation change Property Varying 9mm Average 9mm Deviation 125mm Average 125mm Deviation Elasticity53.3MPa1.9MPa52.8MPa0.46MPa Strength52.4MPa5.4MPa55.5MPa0.44MPa 13

14. Conclusion Size effect not captured (yet) – Variability in strength – Variability in elasticity Bug in the code – Not enough loading More work to be done – Fix current bug – Seeding individual fibers How failure should look My results 14

15. Acknowledgements Dr. Ray Fertig Hamid Sanei NASA Space Grant Consortium ―"This work funded by Wyoming NASA Space Grant Consortium, NASA Grant #NNX10A095H." (Nasa.gov) 15

16. References Fertig, Jensen, Malusare. Effect of Fiber Volume Fraction Variation Across Multiple Length Scales on Composite Stress Variation: The Possibility of Stochastic Multiscale Analysis. AIAA 2014 http://upload.wikimedia.org/wikipedia/commons/1/13/Composite_3d.png http://www.efunda.com/formulae/solid_mechanics/composites/images/Lamin a_PrincipalDir.gif http://www.efunda.com/formulae/solid_mechanics/composites/images/Lamin a_PrincipalDir.gif 16

17. Questions? 17