Finite Element Simulation of Woven Fabric Composites

B.H. Le Page*, F.J. Guild+, S.L. Ogin* and P.A. Smith*

*School of Engineering, University of Surrey, UK

+Department of Mechanical Engineering, University of Bristol, UK

University of Bristol

Collaborative project supported by EPSRC

Introduction• Woven fabric composites - why modelling?

• Development of the models– Modelling approach

– Layer/phase shift

• Predictions of Stiffness– Compliance calculation

• Predictions of energy release rate for cracks

• Comparison of results– Effect of layer/phase shift

– Comparison with equivalent cross-ply laminates

• Conclusions

University of Bristol

Woven Fabric Composites

• Increasingly chosen for semi-structural applications

• Improved impact performance

• Damage mechanisms not well understood

• Damage morphologies observed to depend on layer position

• We are seeking to understand that dependence using FE simulations

University of Bristol

Edge section of damage in two layer PW GFRP laminates at 1.6 % strain

Development of the Models

• 2-dimensional model drawn in the axial-thickness plane

• Out-of-plane direction is the specimen width

• Generalised plane strain elements - impose equal out-of-plane strain – Neglecting width-wise microstructural variability

– Not imposing severe plain strain constraint

• Use boundary conditions in the thickness direction to simulate different number of layers

• Use boundary conditions (and multi-point constraints) to model axial continuum

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Plane of mesh

load

Development of the Mesh

• The modelled shape of the fibre tow was matched to microstructural measurements

• The tow shape was found to be sinusoidal

• All the meshes were developed from this half-wave of the tow

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Micrograph

Model

Longitudinal tow

Single Layer Model

• Model contains 1712 6-noded generalised plane strain triangular elements

• Material properties for the Longitudinal Tow were input into the analysis separately for each element according to its orientation

• Material properties for the Transverse Tow Regions were input directly using transformation of the orthotropic tow properties

• Meshes for all models were developed using this mesh

• All analyses used non-linear geometry– Bending and fibre straightening taken into account

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2-Layer Models

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In-phase

Out-of-phase

Staggered

4-Layer Models

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In-phase

Out-of-phase

Staggered

Infinite Plate Models

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In-phase

Infinite Plate Models

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Out-of-phase

Infinite Plate Models

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Staggered

Boundary Conditions for Axial Continuum

• Staggered mesh requires boundary conditions and multi-point constraints along edges to impose axial continuum

• Further check that axial load is continuous

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Deformation of 2-Layer Staggered Mesh

• Conditions imposed on ends of in-phase and out-of-phase models

• Additional conditions along edges required for staggered mesh

Continuity of Axial Stress in Staggered Mesh

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No. of Layers Mesh Lay-up Stiffness (GPa)1 Plain Weave 44.662 Cross-ply [0/90]s 73.62 Plain Weave In-phase 50.562 Plain Weave Out-of-phase 48.882 Plain Weave Staggered 50.174 Cross-ply [0/902/0]s 73.64 Plain Weave In-phase 50.914 Plain Weave Out-of-phase 48.884 Plain Weave Staggered 50.64Infinite plate Cross-ply [0/902/0]ns 73.6Infinite plate Plain Weave In-phase 51.0Infinite plate Plain Weave Out-of-phase 48.95Infinite plate Plain Weave Staggered 50.72

Stiffness of Laminates

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Stiffness of Laminates

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0

10

20

30

40

50

60

70

80

1-layer 2-layer 4-layer Infinite

Cross-ply In-phase Out-of-phase Staggered

•Single layer is least stiff

•Cross-ply is most stiff•No change with thickness

•For woven•In-phase is most stiff

•Staggered has intermediate stiffness

•Small increase with thickness

•These results appear consistent

E (GPa)

Cracked 2-Layer Models

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In-phase

Out-of-phase

Staggered

Cracked 4-Layer Models

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In-phase

Out-of-phase

Staggered

• Analyse all models for 1% applied strain

• Compare compliance for uncracked and cracked models

• Use the well known compliance relationship to calculate G:G = P2 c

2b a

Calculation of Energy Release Rate, G

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Where: P = Load (at 1% strain) b = specimen width (out-of-plane) c = compliance change a = crack length

No. of Layers Mesh Lay-up Crack location G (Jm-2)1 Plain Weave Edge 343.12 Cross-ply [0/90]s Centre 134.22 Plain Weave In-phase Edge 352.92 Plain Weave Out-of-phase Centre 144.02 Plain Weave Staggered Edge 170.04 Cross-ply [0/902/0]s Centre 133.44 Plain Weave In-phase Centre 215.64 Plain Weave Out-of-phase Centre 146.34 Plain Weave Staggered Centre 158.2Infinite plate Cross-ply [0/902/0]ns Centre 133.8Infinite plate Plain Weave In-phase Centre 215.6Infinite plate Plain Weave Out-of-phase Centre 146.6Infinite plate Plain Weave Staggered Centre 151.7

Energy Release Rate (G)

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Energy Release Rate

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0

50

100

150

200

250

300

350

400

1-layer 2-layer 4-layer Infinite

Cross-ply In-phase Out-of-phase Staggered

•Single layer has high G

•Cross-ply has lowest G•No significant change with thickness

•For woven•In-phase has highest G

•Staggered has intermediate G

•Overall decrease with thickness

•High value for 2-layer in-phase arises from bending

G (Jm-2)

Comparison of Deformation for Centre and Edge Cracks

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2-layer out-of-phase: Centre Crack

2-layer in-phase: Edge Crack

G = 144.0 Jm-2

G = 352.9 Jm-2

Conclusions

University of Bristol

• We have successfully developed finite element models to investigate failure processes in woven fabric composites

• Predictions of stiffness show a small but expected dependence on layer shift

• Values of fracture energy for transverse crack growth in the 90o tows can be calculated

• Fracture energy is far higher - crack growth is more preferred - when the crack growth causes bending

• Fracture energy for cracks that preserve symmetry and in thicker laminates is close to the predicted (and measured) fracture energy for transverse cracking in cross-ply laminates