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Materials & Manufacturing Directorate
Detailed Morphology Modeling and Residual Stress Evaluation in Tri-axial Braided
CompositesMultiscale Modeling of Composites WorkshopCleveland, OH, US
23-24 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
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
Ima
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on
str
uc
tio
n
Ba
sed
mo
rph
olo
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Analytical
Certification by analysis
Morphology representation
Morphology & Analysis
An
aly
sis
Fid
elit
yDirect FEM
Voxel Methods
Combined
Dir
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na
l Vo
lum
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Fra
ctio
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istr
ibu
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Idea
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sin
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Fib
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To
w T
op
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Pro
ces
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ase
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Fib
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Sim
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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. Independent mesh
modeling of matrix
0 1
1
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 FEMGRP 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 towshas 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
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• AS4/3501-6 Properties with T=-155°C• Only top layer modeled
• Modeling Sequence1.Free-expansion without cut2.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• AS4/3501-6 Properties with T=-155°C• Only top layer modeled
• Modeling Sequence1.Free-expansion without cut2.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• AS4/3501-6 Properties with T=-155°C• Only top layer modeled
• Modeling Sequence1.Free-expansion without cut2.Free-expansion with cut
Modeling Details
z
x
Moiré results Uncompacted results
zz
Full-Field Strain Results
-7000 zz () 1000
z
x zz
z
x
z
xzz zz
Moiré results Compacted results
Full-Field Strain Results
-7000 zz () 1000
z
x
z
xzz zz
Moiré results Compacted resultsVirtually “Sanded”
Full-Field Strain Results
-7000 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
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 AS4/3501-6 composite embedded in epoxy
Loaded in the z-directionNote: this triax ply model has not been
“virtually” compacted
z
Z
z
Z
tow 15Add 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)