Distribution Statement A: Approved for public release distribution is unlimited. (88ABW ) Materials & Manufacturing Directorate Detailed Morphology Modeling and Residual Stress Evaluation in Tri-axial Braided Composites Multiscale Modeling of Composites Workshop Cleveland, OH, US July, 2009  (AFRL/RXBC)  (RXBC/UDRI) David Mollenhauer, Tim Breitzman Endel Iarve, Eric Zhou, & Tom Whitney

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

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

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

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

(simulated via “digital chains”) A tow consists of many “digital chains” Chains interact through contact elements

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

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

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

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

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

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 Computational Methods Direct FE discretization Voxel Methods Combined methods D. Mollenhauer, T Breitzman, E. Iarve, E. Zhou, & T. Whitney, “Three-Dimensional Stress Analysis in Complex Fiber Architecture Composites by Using Independent Mesh Method”

Independent Mesh Method 1. Parametric geometry representation for each yarn 2. I ndependent 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”

Figure 3: Schematic of matrix displacement approximation function definitions, boundary interval integration, and extra degree of freedom elimination. 1.Yarn deformation modeled directly 2.Yarn-matrix connection modeled by penalty minimization 3.Matrix domain meshed independently Shape functions truncated Volume integration cubes Independent Mesh Method, Matrix Model D. Mollenhauer, T Breitzman, E. Iarve, E. Zhou, & T. Whitney, “Three-Dimensional Stress Analysis in Complex Fiber Architecture Composites by Using Independent Mesh Method”

IMM FEM Independent Mesh Method, Oval Fiber RVE IM7- fiber, 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”

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

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

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

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

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 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” Photomechanics Lab Moiré Interferometry Experimental Validation (general description of test & models)

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

Virtual Saw Cut (modeled as a “tow”) X Z Y 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/ Properties with  T=-155°C Only top layer modeled Modeling Sequence 1.Free-expansion without cut 2.Free-expansion with cut (1) & (2) Fixed BCs (1) Free then (2) Fixed BCs Modeling Details

Virtual Saw Cut (modeled as a “tow”) X Z Y (1) & (2) Fixed BCs (1) Free then (2) Fixed BCs 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/ Properties with  T=-155°C Only top layer modeled Modeling Sequence 1.Free-expansion without cut 2.Free-expansion with cut Modeling Details

(1) & (2) Fixed BCs (1) Free then (2) Fixed BCs Virtual Saw Cut (modeled as a “tow”) Virtual “Sanding” Layer X Z Y 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/ Properties with  T=-155°C Only top layer modeled Modeling Sequence 1.Free-expansion without cut 2.Free-expansion with cut Modeling Details

z x Moiré resultsUncompacted results  zz Full-Field Strain Results  zz (  ) 1000 z x  zz

z x z x Moiré resultsCompacted results Full-Field Strain Results  zz (  ) 1000

z x z x  zz Moiré resultsCompacted results Virtually “Sanded” Full-Field Strain Results  zz (  ) 1000

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

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

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

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

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

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

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)

Single ply of triaxially braided AS4/ composite embedded in epoxy Loaded in the z-direction Note: this triax ply model has not been “virtually” compacted zz Z zz Z tow 15 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. Independent Mesh Method (unique capability)