1. A Constitutive Model Based on Meso and Micro Kinematics for Impregnated Woven Continuous Fibre Reinforced Composites P. Harrison M.J. Clifford A.C. Long C.D. Rudd University of Nottingham

2. Contents Motivation Introduction to textile composite models Method Results

3. PAM-FORM ESI Software Motivation: Simulate forming process Shear angle

4. Specific aim Make force versus shear angle predictions using fibre diameter, fibre volume fraction, matrix viscosity and weave structure Reduce or eliminate the need for time- consuming and expensive characterisation experiments, e.g. picture frame and bias extension tests

5. Background: modelling textile composites Continuum models based on Ideal Fibre Reinforced theory (Spencer, 1972) Non-continuum approach: homogenisation methods

6. Proposed modelling approach Combine predictions of continuum and micromechanical models Incorporate observed meso-scale kinematics in model

7. Background: Continuum theory, uniaxial model Extra stress tensor, depends on rate of deformation tensor, D, and fibre direction, a Stress tensor Reaction stresses due to fibre inextensibility and material incompressibility

8. Background: Continuum theory, uniaxial model continued The form of  can be derived from the general property that  must be form invariant with respect to rigid rotations and is linear with D, thus Transverse viscosity Longitudinal viscosity (b)

9. Background: Continuum theory, biaxial model for textiles Biaxial models have been proposed to model textile composites hereusing general properties of tensors find Unfortunately, the five model parameters can no longer be related to micro-mechanical mechanisms, thus not accessible to micromechanical modelling

10. Current approach: Combine uniaxial theory with observed mesoscopic kinematics Inter-tow region Tow Layer 1 + Layer 2 = Textile Need effective viscosities of tow and inter-tow regions

11. Cross-section of tow showing fibres and kinematics d

12. Calculating effective tow viscosity Consider affine deformation

13. Unit cell gogo gogo d Before shear T g d After shear

14. Meso-scale kinematics: observation

15. Meso-mechanical observations Average strain profile across material Meso-scale strain profile

16. Effects of non-uniform meso- scale shear strain 1.New rate of deformation tensor, D, required for use in uniaxial continuum theory 2.Energy dissipation is produced between tow crossovers

17. Crossover kinematics Crossover area Low friction High friction

18. Energy dissipation due to crossover shear Y X Element

19. Comparison between picture frame test and model predictions: test conditions Glass/polypropylene 2 x 2 twill weave thermoplastic 180 o C

20. Meso-scale observations Material shear angle  = 90-42 = 48 o Tow shear angle  = 90 – 73 = 17 o

21. Viscosity of polypropylene matrix Carreau-Yassuda model

22. Results of uniaxial model Experiment Uniaxial model

23. Results of uniaxial model Experiment Uniaxial model Uniaxial model predicts similar form but wrong magnitude (viscosity predictions too low)

24. Results of crossover model Crossover model predicts right magnitude but wrong form Experiment Crossover model

25. Combine predictions of two models Use magnitude predictions from crossover model Use curve shape prediction from uniaxial continuum model

26. Result of combined model Experiment Combined model Combined model predicts right magnitude and similar form

27. Conclusions Produced predictions of similar magnitude and form as experimental data without use of fitting parameters Need more comparisons between experiment and theory to investigate to generality of the results

28. Acknowledgements We would like to thanks the following organisations for their support: EPSRC, BAE SYSTEMS, BP Amoco, ESI Software, Ford Motor Company, QinetiQ, Saint-Gobain Vetrotex, MSC Software Ltd., and the Universities of Cambridge and Leeds

29. Questions?