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

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

Collaboration With IIMEC The British University in Egypt 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

IIMEC Egypt The British University in Egypt

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

Averaging Models Mori-Tanaka Hills SCM fiber Matrix M-T Composite SCM Periodic Array PHA Idealized RVE The British University in Egypt Multiscale Modeling (2/2)

Nye 1957 The British University in Egypt Multifunctionality

Constitutive Laws Of A Single Phase Electro-Thermo-Mechanical Coupling (1/5) Direct Mechanical Effect Stress σ (N/m 2 ) Strain ε Stiffness L (N/m 2 ) The British University in Egypt Compliance M (m 2 /N) Electrical Displacement Electrical Field Intensity D (C/m 2 ) E (V/m) Direct Electrical Effect Permittivity κ (C/Vm) Permittivity -1 κ -1 (Vm/C)

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

Constitutive Laws Of A Single Solid Electro-Thermo-Mechanical Coupling (3/5) The British University in Egypt Temperature Electrical ( o C) Displacement D (C/m 2 ) Pyroelectric constant q (C/m 2 / o C) Thermo-Electrical Coupling

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

Constitutive Laws of A Single Solid Electro-Thermo-Mechanical Coupling (5/5) 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 eigenstress eigenstrain The British University in Egypt

Microscopically Heterogeneous Multi Phase Materials Levins (1967) formula for thermal eigenstresses Generalized by Dvorak & Benveniste (1992) Stress concentration factor B depends on local elastic properties and geometry The British University in Egypt

Local Fields Multi Phase Materials, 1)Due to overall fields Hill (1967) The British University in Egypt

Local Fields Multi Phase Materials, 1)Due to overall fields 2)Self-Induced by eigen fields Eshilby (1956) Hill (1967) r The British University in Egypt

Local Fields Multi Phase Materials, r 1)Due to overall fields 2)Self-Induced by eigen fields 3)Transformed by eigen fields Dvorak (1992) s The British University in Egypt

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

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

Damage Criteria Failure CriterionDescription I Local Ply In-plane Phase Failure due to Tension or Compression Strength II Matrix Failure Due to Transverse Shear III Sliding Failure due to Local Longitudinal Shear The British University in Egypt

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

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

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

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

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

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

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

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

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

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

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

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

Conclusion The British University in Egypt 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