1. 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 School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK University of Bristol Collaborative project supported by EPSRC

2. 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 School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK University of Bristol

3. 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 School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK University of Bristol Edge section of damage in two layer PW GFRP laminates at 1.6 % strain

4. 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 School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK University of Bristol Plane of mesh load

5. 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 School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK University of Bristol Micrograph Model Longitudinal tow

6. 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 School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK University of Bristol

7. 2-Layer Models School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK University of Bristol In-phase Out-of-phase Staggered

8. 4-Layer Models School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK University of Bristol In-phase Out-of-phase Staggered

9. Infinite Plate Models School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK University of Bristol In-phase

10. Infinite Plate Models School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK University of Bristol Out-of-phase

11. Infinite Plate Models School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK University of Bristol Staggered

12. 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 University of Bristol School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK 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

13. Continuity of Axial Stress in Staggered Mesh University of Bristol School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK

14. Stiffness of Laminates School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK University of Bristol

15. Stiffness of Laminates University of Bristol School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK 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 )

16. Cracked 2-Layer Models School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK University of Bristol In-phase Out-of-phase Staggered

17. Cracked 4-Layer Models School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK University of Bristol In-phase Out-of-phase Staggered

18. Analyse all models for 1% applied strain Compare compliance for uncracked and cracked models Use the well known compliance relationship to calculate G: G = P 2  c 2b  a Calculation of Energy Release Rate, G School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK University of Bristol Where: P = Load (at 1% strain) b = specimen width (out-of-plane)  c = compliance change  a = crack length

19. Energy Release Rate (G) School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK University of Bristol

20. Energy Release Rate University of Bristol School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK 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 )

21. Comparison of Deformation for Centre and Edge Cracks University of Bristol School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK 2-layer out-of-phase: Centre Crack 2-layer in-phase: Edge Crack G = 144.0 Jm -2 G = 352.9 Jm -2

22. Conclusions School of Mechanical & Materials Engineering University of Surrey Guildford, Surrey GU2 5XH, UK 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 90 o 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