Materials & Manufacturing Directorate

1. Detailed Morphology Modeling and Residual Stress Evaluation in Tri-axial Braided Composites Multiscale Modeling of Composites Workshop Cleveland, OH, US 23-24 July, 2009 Materials & Manufacturing Directorate David Mollenhauer, Tim Breitzman Endel Iarve, Eric Zhou, & Tom Whitney  (AFRL/RXBC) (RXBC/UDRI)

2. Textile Composites Objective: To predict the behavior of composite materials with complex fiber architectures, geometry, and/or service loading.

3. Outline • Morphology • Simulated & Image Based • Stress Analysis • Methodology • Homogenization Results • Experimental / IMM Comparison on Triaxially Braided Composite • Preform Compaction • Moiré Interferometry • Description of Models • Results • Conclusions

4. Outline • Morphology • Simulated & Image Based • Stress Analysis • Methodology • Homogenization Results • Experimental / IMM Comparison on Triaxially Braided Composite • Preform Compaction • Moiré Interferometry • Description of Models • Results • Conclusions

5. Fiber Tow Morphology • Approaches: • Simulation-Based • Method of Digital Chains • Image-Based • Image reconstruction • Goal: • Geometry for mechanics model

6. Fiber Tow Morphology (simulated via “digital chains”) • A tow consists of many “digital chains” • Chains • interact through contact elements

7. Fiber Tow Morphology (simulated via “digital chains”) • A tow consists of many “digital chains” • Chains • interact through contact elements

8. Fiber Tow Morphology (simulated via “digital chains”) • A tow consists of many “digital chains” • Chains • interact through contact elements virtual compaction

9. Fiber Tow Morphology (image-based) x-ray tomography optical microscopy Image reconstruction involves characteristic function computation, integration, & surface extraction. Image segmentation involves noise removal, histogram, edge detection, line segmentation, region segmentation, and edge smoothing

10. Outline • Morphology • Simulated & Image Based • Stress Analysis • Methodology • Homogenization Results • Experimental / IMM Comparison on Triaxially Braided Composite • Preform Compaction • Moiré Interferometry • Description of Models • Results • Conclusions

11. Morphology & Analysis Certification by analysis Combined Voxel Methods Stress Concentrations, Fracture Analysis Fidelity Stiffness Homogenization models Direct FEM Analytical Morphology representation Processing Based Fiber Tow Topology Simulation Idealized (sinusoidal) Fiber Tow Topology Directional Volume Fraction Distribution Image reconstruction Based morphology D. Mollenhauer, T Breitzman, E. Iarve, E. Zhou, & T. Whitney, “Three-Dimensional Stress Analysis in Complex Fiber Architecture Composites by Using Independent Mesh Method”

12. Computational Methods Direct FE discretization Voxel Methods Combined methods 3D MOSAIC, Bogdanovich et al., 1993 Binary Model, B. N. Cox et al., 1994 xFEM, Belytchko, et al., 2003 A-FEM, Q. Young, B.N. Cox ,2008 Independent Mesh Method, Iarve, E.V., Mollenhauer, D.H., Zhou, E., and Whitney, T.J.,, 2007 Mesh Superposition Methods, Fish, J, et al., 1999 Nakai, H., Kurashiki, T., and Zako, M.,, 2007 Domain Superposition Methods, Jiang,W.-G., Hallett, S.R., 2007 D. Mollenhauer, T Breitzman, E. Iarve, E. Zhou, & T. Whitney, “Three-Dimensional Stress Analysis in Complex Fiber Architecture Composites by Using Independent Mesh Method”

13. 1 0 1 Independent Mesh Method 1. Parametric geometry representation for each yarn 2. Independent mesh modeling of matrix D. Mollenhauer, T Breitzman, E. Iarve, E. Zhou, & T. Whitney, “Three-Dimensional Stress Analysis in Complex Fiber Architecture Composites by Using Independent Mesh Method”

14. Independent Mesh Method, Matrix Model • Yarn deformation modeled directly • Yarn-matrix connection modeled by penalty minimization • Matrix domain meshed independently • Shape functions truncated • Volume integration cubes Figure 3: Schematic of matrix displacement approximation function definitions, boundary interval integration, and extra degree of freedom elimination. D. Mollenhauer, T Breitzman, E. Iarve, E. Zhou, & T. Whitney, “Three-Dimensional Stress Analysis in Complex Fiber Architecture Composites by Using Independent Mesh Method”

15. Independent Mesh Method, Oval Fiber RVE IM7- fiber, epoxy matrix FEM IMM D. Mollenhauer, T Breitzman, E. Iarve, E. Zhou, & T. Whitney, “Three-Dimensional Stress Analysis in Complex Fiber Architecture Composites by Using Independent Mesh Method”

16. Independent Mesh Method, Textile RVE IMM FEM GRP fiber tow, Epoxy matrix D. Mollenhauer, T Breitzman, E. Iarve, E. Zhou, & T. Whitney, “Three-Dimensional Stress Analysis in Complex Fiber Architecture Composites by Using Independent Mesh Method”

17. Outline • Morphology • Simulated & Image Based • Stress Analysis • Methodology • Homogenization Results • Experimental / IMM Comparison on Triaxially Braided Composite • Preform Compaction • Moiré Interferometry • Description of Models • Results • Conclusions

18. Virtual Preform Compaction Needed 3-layers vacuum bag side caul plate side Virtual Consolidation Needed!

19. Virtual Compaction of Preform Step 1: single layer relaxation by multi-chain digital simulation Step 2: nesting 5 layers upon measurement from image Step 3: applying vacuum pressure on digital net (rigid or flexible)

20. Virtual Compaction of Preform Step 4: cutting off boundaries after digital simulation of vacuum press Top view Front view Comparison between braided tows has to be at same exact location

21. Photomechanics Lab Moiré Interferometry Experimental Validation (general description of test & models) • Experiment: 5-layer Compacted triax-braid • Model 1: 1-layer Uncompacted triax-braid (i.e. resin rich) • Model 2a: 5-layer Compacted braid (only top layer modeled) • Model 2b: same as 2a except Virtually “Sanded”

22. Photomechanics Lab Moiré Interferometry Experimental Validation (general description of test & models) • Experiment: 5-layer Compacted triax-braid • Model 1: 1-layer Uncompacted triax-braid (i.e. resin rich) • Model 2a: 5-layer Compacted braid (only top layer modeled) • Model 2b: same as 2a except Virtually “Sanded” saw cut in specimen releases residual stresses

23. Comparison of Cross-Sections Uncompacted Morphology Compacted Morphology Cross-Section Location Virtually“Sanded” Morphology Cross-Section Location CT Image Cross-Section of Actual Specimen

24. Y X Z Modeling Details • Experimental Specimen: 5 layer Compacted braid • IMM Analysis: 1 layer Uncompacted & 5 layer virtually compacted braids • Slot cut completely from left free-edge to right free-edge • AS4/3501-6 Properties with DT=-155°C • Only top layer modeled • Modeling Sequence • Free-expansion without cut • Free-expansion with cut (1) Free then (2) Fixed BCs Virtual Saw Cut (modeled as a “tow”) (1) & (2) Fixed BCs

25. Y X Z Modeling Details • Experimental Specimen: 5 layer Compacted braid • IMM Analysis: 1 layer Uncompacted & 5 layer virtually compacted braids • Slot cut completely from left free-edge to right free-edge • AS4/3501-6 Properties with DT=-155°C • Only top layer modeled • Modeling Sequence • Free-expansion without cut • Free-expansion with cut (1) Free then (2) Fixed BCs Virtual Saw Cut (modeled as a “tow”) (1) & (2) Fixed BCs

26. Y X Z Modeling Details • Experimental Specimen: 5 layer Compacted braid • IMM Analysis: 1 layer Uncompacted & 5 layer virtually compacted braids • Slot cut completely from left free-edge to right free-edge • AS4/3501-6 Properties with DT=-155°C • Only top layer modeled • Modeling Sequence • Free-expansion without cut • Free-expansion with cut (1) Free then (2) Fixed BCs Virtual Saw Cut (modeled as a “tow”) (1) & (2) Fixed BCs Virtual “Sanding” Layer

27. z z x x ezz ezz -7000ezz (me)1000 Full-Field Strain Results Moiré results Uncompacted results

28. z z x x ezz ezz -7000ezz (me)1000 Full-Field Strain Results Moiré results Compacted results

29. z z x x ezz ezz -7000ezz (me)1000 Full-Field Strain Results Moiré results Compacted results Virtually “Sanded”

30. z x Extracted Strain Results Data plotted along a line 0.25 mm from the top edge of slot for… Data Line

31. z x Extracted Strain Results Data plotted along a line 0.25 mm from the top edge of slot for… Data Line

32. z x Extracted Strain Results Data plotted along a line 0.25 mm from the top edge of slot for… Data Line

33. z x Extracted Strain Results Data plotted along a line 0.25 mm from the top edge of slot for… Data Line

34. Outline • Morphology • Simulated & Image Based • Stress Analysis • Methodology • Homogenization Results • Experimental / IMM Comparison on Triaxially Braided Composite • Preform Compaction • Moiré Interferometry • Description of Models • Results • Conclusions

35. Conclusions • Research Conclusions • Textile morphology tool is on the right track • Independent Mesh Method allows modeling of otherwise intractable problems • Experimental investigation • critical step in understanding complex materials • validating new modeling methods

36. Uniaxial Loading of Triaxial Braid (3D X-ray tomography) • Cracks: • Matrix • Inter tow • Intra tow E. Zhou (UDRI), T. Whitney (UDRI), D. Daniels (UES), & D. Mollenhauer (AFRL)

37. Z Z ez ez Independent Mesh Method (unique capability) Single ply of triaxially braided AS4/3501-6 composite embedded in epoxy Loaded in the z-direction Note: this triax ply model has not been “virtually” compacted Add a “virtual hole” anywhere. Allows the examination of stress concentration due to a “structural” feature at various locations with respect to the fiber tow architecture. tow 15