Distribution Statement A: Approved for public release distribution is unlimited. (88ABW-2009-1482)

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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str

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tio

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Ba

sed

mo

rph

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Analytical

Certification by analysis

Morphology representation

Morphology & Analysis

An

aly

sis

Fid

elit

yDirect FEM

Voxel Methods

Combined

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Fra

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Pro

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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)