Multiscale Modelling of Multifunctional Composites

1. Multiscale Modelling of Multifunctional Composites Yehia Bahei-El-Din & Amany Micheal Center of Advanced Materials CAM The British University in Egypt BUE Third Annual Meeting of IIMEC College Station, Texas, January 18-19, 2012

2. SPONSORS • International Institute for Multifunctional Materials for Energy Conversion IIMEC • Air Force Office of Scientific Research AFOSR The British University in Egypt

3.  Collaboration With IIMEC • Participation of IIMEC affiliates in International Workshop on • Advanced Materials for Wind Turbine Blades organized by • CAM • IIMEC offered summer internships to BUE students • Collaboration with Drs. Zoubeida Ounaies and Pradeep • Sharma The British University in Egypt

4. IIMEC Egypt The British University in Egypt

5. Multiscale Modeling (1/2) Laminate Analysis & Composite (Ply) Model Phase Scale Laminate Scale The British University in Egypt

6. Multiscale Modeling (2/2) Idealized RVE • Periodic Array • PHA • Averaging Models • Mori-Tanaka • Hill’s SCM fiber Matrix M-T Composite SCM The British University in Egypt

7. Multifunctionality The British University in Egypt Nye 1957

8. Constitutive Laws Of A Single PhaseElectro-Thermo-Mechanical Coupling (1/5) Direct Mechanical Effect Stress σ (N/m2 ) Strain ε Stiffness L (N/m2 ) Compliance M (m2/N) Direct Electrical Effect Electrical Displacement Electrical Field Intensity D (C/m2) E(V/m) Permittivity κ (C/Vm) Permittivity-1κ-1(Vm/C) The British University in Egypt

9. Constitutive Laws Of A Single SolidElectro-Thermo-Mechanical Coupling (2/5) Thermo-Mechanical Coupling Strain ε Temperature (oC) Coeff.of thermal expansion α /oC Piezoelectric constant e (C/m2) Electrical Displacement D Strain ε (C/m2) Electro-Mechanical Coupling Piezoelectric constant d T (m/V) Strain ε Electrical Field E (V/m) The British University in Egypt

10. Constitutive Laws Of A Single SolidElectro-Thermo-Mechanical Coupling (3/5) Thermo-Electrical Coupling Temperature Electrical (oC) Displacement D (C/m2) Pyroelectric constant q (C/m2/oC) The British University in Egypt

11. Constitutive Laws Of A Single SolidElectro-Thermo-Mechanical Coupling (4/5) Direct Effect Coupling Effect The British University in Egypt

12. eigenstress eigenstrain • Remain in the system following mechanical loading/unloading • Lump up of induced thermal, electrical and damage effect • Function of mechanical and/or physical properties of material Constitutive Laws of A Single SolidElectro-Thermo-Mechanical Coupling (5/5) The British University in Egypt

13. Levin’s (1967) formula for thermal eigenstresses • Generalized by Dvorak & Benveniste (1992) • Stress concentration factor B depends on local elastic properties and geometry Microscopically HeterogeneousMulti Phase Materials The British University in Egypt

14. s, e Local FieldsMulti Phase Materials • Due to overall fields • Hill (1967) The British University in Egypt

15. lr s, e Local FieldsMulti Phase Materials • Due to overall fields • Self-Induced by eigen fields • Eshilby (1956) • Hill (1967) The British University in Egypt

16. lr s, e ls Local FieldsMulti Phase Materials • Due to overall fields • Self-Induced by eigen fields • Transformed by eigen fields • Dvorak (1992) The British University in Egypt

17. ؟ Transformation Field Analysis • Dvorak (1992) • Local eigen fields caused by deformation mechanisms are known functions of stress, temperature, Electric Field, internal parameters • Damage ? The British University in Egypt

18. ؟ Transformation Field Analysis of Damage • Bahei-El-Din (2004) The British University in Egypt

19. Damage Criteria The British University in Egypt

20. Examples (0/90)s Laminate (0/±45/90)s Laminate The British University in Egypt

21. Electrical Field Intensity E versus Electrical Displacement D for Different Layup The British University in Egypt

22. Temperature-Electric Displacement for Different Layup The British University in Egypt

23. Stress-Electric Field Intensity Path for a (0/90)s Laminate The British University in Egypt

24. Stress-Strain Response for a (0/90)s Laminate Under Overall Stress in X1 Direction The British University in Egypt

25. Stress-Electric Displacement for the 0 Ply in a (0/90)s Laminate Under Overall X1 Stress The British University in Egypt

26. Stress-Electric Displacement for the 90 Ply in a (0/90)s Laminate Under Overall X1 Stress The British University in Egypt

27. Electric Field Intensity-Electric Displacement at Different X1 Tension Stress Levels on a (0/90)s Laminate The British University in Egypt

28. Stress-Strain Response of a Sym. (0/±45/90)s Laminate Under Tension in Overall X1 Direction The British University in Egypt

29. Stress-Electric Displacement for a (0/±45/90)s Under Overall X1 Stress The British University in Egypt

30. Stress-Strain Response for a (0/±45/90)s Laminate Under Overall Shear Stress The British University in Egypt

31. Stress-Electric Displacement for a (0/±45/90)s Under Overall Shear Stress The British University in Egypt

32. Conclusion • A Multiscale Study is conducted on a Laminate composite • Constituents are multifunctional materials with electro-thermo- • mechanical coupling • All effects other than mechanical , including damage, are • lumped up and treated as transformation or eigen effects • Laminate layup affects the direct electric response of PZT • fibers in a certain ply due to confinement caused by other plies • It is concluded that local damage due to all effects in a certain • ply changes the electric response of piezoelectric fibers in all • plies with different aspects The British University in Egypt

33. The British University in Egypt