Smart Materials and Structures

V. L. Sateesh CSIR- National Aerospace Laboratories

Pravartana 2016 IIT Kanpur

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Introduction • It can be described as one that mimics biological

functions

Morphing Health monitoring Active vibration control Self Healing

• This can be achieved by using

Flexible skins/special skins Distributed actuators Sensors Suitable control law

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Active Vibration Control using Piezo / Magneto materials

Health Monitoring

Smart / Intelligent Technologies

Morphing

Self Healing

Introduction (cont’d)

Advantages: • Enhance Performance • Extend Service Life • Reduce Costs

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Actuators /Sensors (Smart Materials)

• Shape Memory Alloys

• Piezo Electric Materials

• Shape Memory Polymers

• Magneto/Electrorheological Fluids

• Magnetostrictive Materials

• Electro Active Polymers

• Fiber Optic Sensors

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Shape Memory Alloys

Super elastic

T > Af

T < Mf

Shape memory

Elastic Behavior

0 2 4 6 8 10

200

400

600

Stre

ss in

MPa

Strain in %

Application of heat

• Phase transformation (A M)

with the application of

mechanical load (Pseudo-elastic

effect (SESMA)) / change

temperature (Shape memory

effect)

• Forward transformation (A to M) is exothermic and reverse transformation (M to A) is endothermic

• There is strong coupling between thermal and mechanical phenomenon

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Schematic of the Shape Memory Phenomenon

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SMP can undergo deformation at high temperatures, retain the deformed shape when cooled & return to original, unaltered configuration upon heating above the transition temperature

Shape Memory Polymers (SMP)

Schematic representation of shape memory cycle

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Phase Transitions

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First order transition Eg: Shape Memory Alloys

Second order transitions Eg: Shape Memory Polymers

G G

Phase A

Phase B

T T

Phase A Phase B

First Derivative

T T

Change of slope

Second Derivative

Discontinuity

G = Gibbs Free Energy T = Temperature P = Pressure S = Entropy Cp = Specific Heat

Discontinuity

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Piezoelectric Material

Direct piezoelectric effect • Electric field is developed when mechanical loading (pressure) is applied

Indirect piezoelectric effect • Piezo material undergo mechanical strain when field is applied

Temperature effect on crystal structure

Phase transformation takes place from

Cubic → Tetragonal → Orthorhombic → Rhombohedral

As a result of these structural changes material properties also change considerably

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Piezo Electric Materials

Relation between polarization-electric field

Relation between strain-electric field

→

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• When electric field is reversed, the polarization orients in that direction

• Delay in response of polarization leads to hysteresis

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Parameters Influencing Hysteresis Loop

– Amplitude of electric field

– Frequency of oscillation of electric field

– Mechanical stress

– Temperature

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SMA Actuated Leading Edge Segment of RTA Wing

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• To develop the technology for flexing LE (fused to main wing body) capable of undergoing large elastic deformations (drooping).

• Drooping of leading edge during take off and landing to increase the lift and thus reduce the runway distance.

• CFRP UD (0.17mm) • Load applied : 120 kg

10o Drooped

undrooped

0 500 1000 15000

2

4

6

8

10

Time in Sec

Ang

le in

o

• Angle obtained : 100 (approx)

Design, analysis and testing of SMA actuated LE segment droop system is completed

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Before droop After droop

• SMA actuators developed at NAL were used to droop the compliant leading edge Ground

Transmitter

SMA actuator board

MAV Receiver

Droop enabled

LE

SMA Actuated Leading Edge of MAV

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• CTFD analysis & wind tunnel tests have shown an increase in lift coefficient on LE droop

• Preliminary flight trials have shown some increase in lift. Need to ensure consistency.

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SMA based trim tab actuation

Horizontal Tail Elevator Trim tab

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SMA Mechanism

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SMP tool (Original shape)

Heat and deform to circular shape

Composite layup on the SMP tool

After curing, reheating tool for shape recovery

Easy release of the tool

SMP TOOLING – CONCEPT RT HT

HT

RT

RT

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Prediction of delamination in CRFP beams

Testing

150

Locations of De-lamination

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Frequencies of damaged and undamaged beams

Frequencies Undamaged

Frequencies 20% @ root

Middle Tip

Analysis Exp. Analysis Exp. Analysis

Exp. Analysis

Exp.

4.26 4.89 (1st bend. freq)

4.26 4.89 4.26 4.89 4.26 4.89

146.67 158.04 (4th bend. freq)

145.1 151

146.43 142 146.3 143.5

242.95 240.81

241.5 220

240.78 239 242.3 239.7

Delamination at root

0% 13.3% 9.99% 6% FEM EXP. FEM Exp. FEM Exp FEM Exp

4.26 4.89 (1st bend. freq)

4.26 4.89 4.26 4.89 4.26 4.89

146.7 158.04 (4th bend. freq)

145. 151

146.2 146.2 146.47 146.6

242.8 240.8 241. 220

242.5 240.4 242.8 240.4

Material Modeling

• Empirical Models

• Microscopic Models

• Models based on thermodynamics

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Material Modeling Governing equations are developed by using

– Conservation laws Conservation of mass Conservation of linear momentum Conservation of angular momentum Conservation of charge

Constitutive relations are developed by using

– Thermodynamics Conservation of energy Second law of thermodynamics

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Thermodynamics based Smart material Modeling (SMA, SMP, Piezo, Magnetostrictive) Thermo dynamic modeling of SMA Energy Balance + Second law of T. D Free Energy

Clausius duhem inequality Free energy time der. into clausius duhem inequality Driving force for Transformation Kinetics Validation/Simulation

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Smart materials Modeling

Energy balance equation

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Tm m

V S V S

d v v U dV n v dS B v dV q v dSdt δ δ

ρ ρ σ ⋅ + = ⋅ + ⋅ − ⋅ ∫ ∫ ∫ ∫

m EV V

dV W dVδ δ

ρ γ+ +∫ ∫

Second law of thermodynamics

mm

V V S

d qdV dV n dSdt δ δ

ρ γρ ηθ θ

≥ − ⋅∫ ∫ ∫

Thermodynamic equations CSIR-NAL

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Hysteresis Modeling (in PZT) • Helmholtz free energy is a function of independent variables

• Introducing additional variable to represent the micro level phenomenon

Helmholtz free energy (per unit volume) can be written as

( ), , , ,j M iy E θΨ = Ψ Θ

,i My Deformation gradient

E Electric field

Internal variable Temperature

Θθ

Θ

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Hysteresis Modeling (cont’d)

Clausius-Duhem inequality

( ), ,,

ij M i j M i ij M i

dX y P E Sy dt E

σ θθ

∂Ψ ∂Ψ ∂Ψ − − + − + ∂ ∂ ∂

,1 0i iqθθ

∂Ψ− Θ− ≥∂Θ

Varying the rate terms independently, the constitutive relations can be written as

ij i jkl

PEσε∂Ψ

= −∂

ij

PE∂Ψ

= −∂

Sθ

∂Ψ= −

∂

0∂Ψ−Θ ≥

∂Θ Dissipation energy must be positive

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Higher order terms have been included to have a better fit of hysteresis loop (loading upto saturation)

Using above expression constitutive relations in workable form are obtained

Hysteresis Modeling (cont’d)

2 21 2 22 ijkl ij kl ij i j ijk i jk ij ijC b E E C e Eθε ε θ ξ ε α ε θΨ = − + + Θ − +

2 2 2 2i i ij ij i iE Eλ θ ε β ζ θ+ − Ω Θ− Θ+ Θ

ijkl i j k l ijklm ij k l m ijklmn ij kl m nQ E E E E H E E E f E Eε ε ε+ − − +

ijklmno ij kl mn o ijklmnop ij kl mn opg E Xε ε ε ε ε ε ε− +

Expressing Ψ as a quadratic in terms of all state variables and quartic in terms of strain and electric field

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Nonlinear Constitutive Relations

ijklm jk l m ijklmn jk lm n ijklmno jk lm noH E E f E gε ε ε ε ε ε+ − +

ij ijkl kl ijk k ij ij i j ijkl j k mC e E PE H E E Eσ ε α θ= − − −Ω Θ− −

i ij j ijk jk i i ijkl j k lP b E e Q E E Eε β λθ= + + Θ− +

ij ij i iS E Cθα ε λ θ ζ= + + − Θ

Constitutive relation for stress

Constitutive relation for polarization

Constitutive relation for entropy

ijklmn kl m n ijklmno kl mn ijklmnop kl mn opf E E g E Xε ε ε ε ε ε+ − +

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Nonlinear Constitutive Relations (cont’d)

1

1,3,5.. 2,4,6..

ji

i j ji j

−

= =

∂Ψ ∂Ψ ∂Ψ Θ = − Γ + Γ Γ ∂Θ ∂Θ ∂Θ ∑ ∑

Rate of internal variable evolution

Where i i ij ijEξ β ε ζθ∂Ψ= Θ− −Ω +

∂Θ

This relation ensures 0∂Ψ−Θ ≥

∂Θ

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Validation of Constitutive Relations

Piezo patch under varying electric field

Considering 1-D piezo patch (PZT-5H) Applying time varying electric field (sinusoidal) of amplitude 2 kV/mm Frequency of oscillation 0.0165 Hz

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Validation of Hysteresis and butterfly loop

Terms Upto 7th Order power in internal variable equation have been used

Comparison of theoretical and experimental hysteresis loop (Kamlah)

Butterfly loop

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Effect of Frequency of Electric Field

E < Ec max E > Ec max

• and are found to be frequency dependent • Dissipation of energy is high with decrease in frequency when E < Ec max • Dissipation of energy is high with increase in frequency when E > Ec max (similar

observation can be found in Viehland et al.)

cE rP

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Analysis of Smart Composite Plates

• Static Analysis – Linear analysis Effective lay-up of piezo patches Effective ply-orientation of core of the plate

– Nonlinear analysis • To study the effect of P-E interaction

• nonlinear force in equilibrium eqn., and • Antisymmetric stress term in constitutive relations

• Dynamic Analysis – Nonlinear analysis

• To study the dissipation due to P-E hysteresis effect

Layer-by-layer finite element method is used for the analysis

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Finite Element Formulation

Nonlinear Equilibrium equations Maxwell equation

Principle of virtual work

Simplified form

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Finite Element Formulation (cont’d)

Ni Inplane shape functions (Triangular Elements)

lΦ Out of plane shape functions (Line elements)

Nodal displacements

Layerwise Displacement Field (Prismatic elements)

• Cubic approximation has been used for inplane and out of plane shape functions

∑∑= =

Φ=ΦuN

ilil

n

li ztqyxNtzyxq

1 1)()(),(),,,(

Twvuq ,,,, Θ= φilq

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Finite Element Formulation (cont’d)

Evolution of internal variable equation is

Where, q Displacement vector ( ) [K] Linear stiffness matrix [K1] Stiffness matrix due to nonlinear force term [K2] Stiffness matrix due to nonlinear stress [K3] Stiffness due to higher order terms in constitutive relations F Force vector

Nonlinear governing equation in matrix form

Twvu ,,, Θ,φ

1

1,3,5.. 2,4,6..

ji

i j ji j

−

= =

∂Ψ ∂Ψ ∂Ψ Θ = − Γ + Γ Γ ∂Θ ∂Θ ∂Θ ∑ ∑

)]([)]([)]([][][ 321 FqqKqqKqqKqKqM =++++

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Static Analysis (cont’d)

Schematic representation of plate with piezo patches (all dimensions are in mm)

[0 / 45]s±

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Static Analysis (cont’d)

Linear and nonlinear longitudinal bending (200980 unknowns)

Nonlinear effect shows softening trend

Exp. Crawley and Lazarus 1991 CSIR-NAL

CSIR

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Static Analysis (cont’d)

Linear and nonlinear transverse bending deflection

Nonlinear effect shows hardening trend

Exp. Crawley and Lazarus 1991 CSIR-NAL

CSIR

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Dynamic Analysis (cont’d)

• Problem Description (free vibration analysis by Heyliger and Saravanos.)

• Lamina sequence (Graphite-epoxy)

• Thickness of each composite lamina: 0.00267 m • Single piezo layer either side of the plate (PZT-4)

• Thickness of piezo patch: 0.001 m

• Length to thickness ratio: 50

• L1=L2=L

]0/90/0[

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Response for Mechanical Loading

• Transverse displacement at center of the plate with applied mechanical impulse load of 100 kPa

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Low Cycle fatigue life estimation of SESMA

Relation between total dissipated energy and no. of cycles

Frequency Amplitude Ed for 500 Cyc

Fact. Engy.

Predicted no of cyc.

Actual No.

% of error

1 1 Hz 3% to 6% 1409 2114 2300 2775 17

2 5 Hz 3% to 6% 1196. 1794 2000 2400 16.6

3 1 Hz 2% to 5% 1692 3045 3400 3156 7

Factorizing the energy for strain

Where, Et Energy of the test specimen εBmax Maximum strain of bench mark specimen ( here 6 %) εtmax Maximum strain of test specimen εBmin Minimum strain of bench mark specimen (1.5%) εtmin Minimum strain of test specimen

Estimation of Low Cycle Fatigue Life Cycles

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Smart Material Based Aircraft

Fibre Optic Sensors PZT

SMA

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Concluding Remarks

• Special Thanks to Prof. C. Venkatesan Prof. C. S. Upadhyay

Deep condolence to Prof N G R Iyanger

Acknowledgements • Mr. Shyam Chetty, Director, NAL • Dr. G N Dayananda, HOD, CSMST, NAL • Prof. C Venkatesan • Prof. C S Upadhyay • Prof. P M Mohite • Prof. V Laxman • Dr. Senthil Kumar P, NAL • Jayasankar, NAL • Kavitha V Rao, NAL • Dr. Sandhya Rao • National Programme on Smart Materials (NPSM) • Aeronautics Research and Development Board

(AR&DB)

Thank You