1. “STRENGTH PREDICTION IN OPEN HOLE LAMINATED COMPOSITES BY USING REGULARIZED X-FEM” Michael Swindeman 2,Endel Iarve 1,2, David Mollenhauer 1, Stephen Hallett 3, Robert Brockman 2 1 Air Force Research Laboratory, Materials and Manufacturing Directorate, AFRL/RX, Wright-Patterson Air Force Base, Ohio 45433 2 University of Dayton Research Institute, Dayton OH AF Contract FA8650-10-D-5011 3 University of Bristol, UK 5 th International Conference on Composites Testing and Model Identification Lausanne, Switzerland February, 2011

2. Contents Motivation Method Description –X-FEM and Regularized X-FEM Results –Quasi-Isotropic open hole laminate

3. Motivation Composite failure is dominated by interactions between matrix cracks & delaminations Strength of notched and unnotched composite laminates can be predicted accurately by modeling critical events involving matrix crack patterns and delamination interactions Carlos DáVila, “The Long Road To Virtual Testing of Composite Structures, Are We There Yet?,” Keynote Address at 2 nd ECCOMAS, London, April 2009.

4. Goal: Discrete modeling of matrix cracking and delamination networks General approach based on X-FEM ideas (Moes, et. al., 1999, IJNME). 1) preserves the kinematics of true displacement continuity 2) allows direct application of fracture mechanics criteria for propagation Modifications needed to accommodate cracking and delamination interaction Emerging Modeling Techniques

5. Modeling Goal [1]Van der Meer F P and Sluys L J, (2 nd ECCOMAS, 2009) [2]Qingda Yang and Brian Cox, (CompTest, 2008) [3] Iarve et al. (Composites A, 2005; IJMS, 2007) [4]…..

6. Moes, Dolbow, and Belytschko (1999) Hansbo and Hansbo (2004) 6 Nodes Integration Points Duplicated Nodes u=H(f  ) u 1 +(1-H(f  ) )u 2  =H(f  )  1 +(1-H(f  ) )  2  =H(f  )  1 +(1-H(f  ) )  2 H(f  )=0 H(f  )=1 -Strain Energy - Cohesive Energy

7. xx Element Length The Heaviside function is replaced by a continuous function Crack location

8. Instead of a sharp transition, the crack is resolved within a band of width equal to the element diameter.

9. Connection Between Plies The original Gauss integration schema is preserved for any crack orientation Adjacent plies tied through node/and or surface element integration contact Propagation is through cohesive zone method MIC & Delamination Interaction and Propagation

10. General Modeling Flow 1.Step i=0 is thermal pre-stress 2.Add axial displacement increment 3.Perform Newton-Raphson iterations to converge damage variables in delam and MIC cohesive laws 4.Check matrix failure criteria 5.Add damage and repeat 2-5 Matrix Failure Criteria - Dávila, Camanho, and Rose, “Failure criteria for FRP laminates,” J. of Composite Materials, Vol.39 2005. Cohesive Zone Propagation - Turon, Camanho, Costa, and Dávila, “A damage model for the simulation of delamination in advanced composites under variable-mode loading,” Mechanics of Materials, Vol.38, 2006. Mesh Independent Cracks - Iarve, “Mesh independent modeling of cracks by using higher order shape functions,” Int. J. Num. Meth. Eng., Vol.56, 2003. Numerical Model Details

11. Stress Based Failure Criterion Used for MIC Initiation -Yc Yt S Matrix failure Tension Compression Fiber failure Tension Compression LaRC03- Dávila, Camanho, and Rose, “Failure criteria for FRP laminates,” J. of Composite Materials, Vol.39 2005.

12. n  u n – normal displacement discontinuity vector  u – total displacement discontinuity vector  u| T=(1-d)K  u + nonpenetration  T | B=1 B=0 S YtYt S YtYt G Ic G IIc -Initial stiffness -Transverse strength - Shear strength -Mode I critical ERR -Mode II critical ERR -Mixed Mode test - Cohesive Model Used for Delamination and MIC Propagation  K Turon, et al. Composites: Part A, 2007

13. Laminates Under Tensile Loading Model Verification 1.Scaled Laminates Hallett, et al. Composites Science and Technology(2008) 2. Stacking sequence and ply Orientation effects [45 2 /-45 2 /90 2 ] s vs. [60 2 /-60 2 ] s Johnson and Chang, J Composite Mat. (2002) 3. Ply thickness effects [25/-25/90 n ] s Wang and Crossman, STP 775, 1982

14. Ply Thickness and Crack Density "Reprinted, with permission, from ASTM STP 775 Damage in Composite Materials, copyright ASTM International, 100 Barr Harbor Drive, West Conshohocken, PA 19428." T300/914 Wang, ASD and Crossman, STP 775, 1982, Reifsnider, Ed.

15. Ply Thickness and Crack Density Effect [±25/90 8 ] s [±25/90 3 ] s Delamination shape at the time step prior to global delamination

16. Tensile Strength Scaling in Quasi- Isotropic Composite Laminates Wisnom et al, Strength Scaling Studies Quasi-Isotropic laminates with various numbers of sub- laminates (n) and blocked plies (m) All with same scaled dimensions W/D = 5, L/D = 20 [45 m /90 m /-45 m /0 m ] ns x y

17. Experimental Data Pull-out BrittleDelamination Fiber Failure As hole size increases, failure stress decreases Delamination Failure As hole size increases, failure stress increases BG Green, MR Wisnom and SR Hallett, Composites Part A (2007)

18. Table of Models and Results These cases were selected for study because they failed in delamination mode. All cases contained only one sub-laminate (n=1) CASE No. Blocked Plies Ply Thickness Overall thickness Hole Diameter Failure Stress (MPa) mTply (mm)T (mm)D (mm)Experiment Coarse “C” Fine “F” B220.2523.175 396 469 448 C2 40.54 3.175275308 C3 6.35285318297 12.7362387(344) C4 25.4417466(424) C5 D2 81.08 3.175202211 D525.4232276(239)

19. 4-Blocked Ply 6.35 mm Hole

20. Meshes

21. Hole Size Effect (4-Blocked Ply Cases)

22. Hole Size Effects (4-Blocked plies)

23. Ply Thickness Effect (3.175mm Hole)

24. Response (4 blocked ply – 6.35 mm Hole)

25. Early Damage Progression Red = [45/90] interface, Green = [90/-45] interface, Blue = [-45/0] interface

26. Early Damage Progression Red = [45/90] interface, Green = [90/-45] interface, Blue = [-45/0] interface

27. Start of Delamination Interaction Red = [45/90] interface, Green = [90/-45] interface, Blue = [-45/0] interface

28. Late Damage Red = [45/90] interface, Green = [90/-45] interface, Blue = [-45/0] interface

29. Late Damage Red = [45/90] interface, Green = [90/-45] interface, Blue = [-45/0] interface

30. Near Failure Red = [45/90] interface, Green = [90/-45] interface, Blue = [-45/0] interface

31. Peak Traction Red = [45/90] interface, Green = [90/-45] interface, Blue = [-45/0] interface

32. Post Failure Red = [45/90] interface, Green = [90/-45] interface, Blue = [-45/0] interface

33. Conclusions A finite element method and software implementing regularized X-FEM approach and allowing modeling of complex interactive networks of matrix cracks and delamination has been developed. Effects of Hole Size and Ply Thickness have been simulated –Simulation without preconceived knowledge of damage evolution –Strength produced with coarse and fine mesh agreed with the experimental hole size effect trend –Delamination strength is proportional to the ligament width, which explains the apparent strength increase for larger specimens

34. Acknowledgements NASA AAD-2 contract number NNX08AB05A-G Special thanks to Dr. Cheryl Rose, Dr. Carlos Davila at NASA Langley