Characterization of PZT-Structure Interaction: PhD Presentaion Slides

Characterization of Smart PZT Transducer and Admittance Signatures using PZT-Structure Interaction Models for Structural Health Monitoring

Dr. Annamdas Venu Gopal Madhav M.E (IISc, Bangalore), PhD (NTU, Singapore)

[PhD Presentation Slides : NTU Singapore] (Actual Presentation Date: 30 Mar 07)

11 Dec1 2008

Characterization of Smart PZT Transducer and Admittance Signatures using PZT-Structure Interaction Models for SHM 1. Definition / Applications/ Types of SHM ……

2. Literature Review……

3. Motivations and Objectives…….

4. Interaction Models…… a) S PZT-Structure [2D Strain (LSI)] b) S PZT- Structure [3D (DSI)] c) M PZT-Structure d) M PZT-Adhesive-Structure.

5. Characterization of PZT 6. Originalities / Major conclusions 7. Acknowledgements 1

Characterization of Smart PZT Transducer and Admittance Signatures using PZT-Structure Interaction Models for SHM 1. Definition Structural Health Monitoring (SHM) Over millions of Years--------- Precaution-------- Prevention Earlier / begin of life (animal / birds) : Instinct of living entity to protect its living place, itself, off-springs from pray/ enemies and climate (act of precaution) Modern : Acquiring, validating and analyzing structural data to facilitate life cycle management decisions of the structure (act of prevention)

Cont‌2

1.Applications of SHM 1. Space / Air crafts

•

2.

Civil / Mechanical Structures

3.

Navy (Sea)

4.

Submersible / semi-submersible marine (Under sea)

Partially collapse of Air France Terminal 2E in DeGaul airport in Paris

Cont…3

1. Types of SHM 1. Visual Inspection Methods Personnel checkups, tedious, time consuming, dismantling of fitting

Cont‌4

1. Types of SHM

2. Low Frequency Vibration Techniques (<100Hz) {dynamic loading} Input: Harmonic or impulse, output: displacements, velocities and accelerations Fails in locating damages, noisy, less sensitive

Contâ&#x20AC;Ś4

1. Types of SHM

3. Statistical Structural Response Techniques {static loading} Input: Static forces, output : Displacements, strains Large loads for measurable deflection, huge machinery, power, tedious

Contâ&#x20AC;Ś4

1. Types of SHM

4. Localized NDE Techniques Ultrasonic, acoustic, magnetic field, impact echo testing, thermal field and X-ray analysis portion or whole of the structure is rendered unavailable during the inspection period, skilled man power, uneconomical

Contâ&#x20AC;Ś4

1. Types of SHM

5. Smart Material Based High Frequency Vibration Techniques (k Hz) Piezoelectric Elements – PZT (lead zirconate titanates), PVDF’s (polyvinylidene fluorides), Electrostrictive Elements- PMN (lead magnesium niobate), PMN-PT (enriched), Magnetostictive Transducers, Electrorheological Fluids, Shape memory alloys, Fiber optics Automated, economical, less man power and time

Cont…4

Characterization of Smart PZT Transducer and Admittance Signatures using PZT-Structure Interaction Models for SHM PZT based Electromechanical Impedance (EMI) principle in SHM PZT: surface bonded or embedded + Electric field along direction 3 Structure

PZT

2 3 1

ZÆ 1 / Admittance (Y)

ÅFinally obtain it

PZT: measures resistance of structure to vibrations

Cont…5

Characterization of Smart PZT Transducer and Admittance Signatures using PZT-Structure Interaction Models for SHM PZT based Electromechanical Impedance (EMI) principle in SHM Z (EMI) Æ 1 / Admittance (Y) {Y = Conductance + j (Susceptance)}

Healthy Structure

YH = G H + j B H

Comparison mechanism

Damaged Structure YD = GD + j BD

Cont…6

Characterization of Smart PZT Transducer and Admittance Signatures using PZT-Structure Interaction Models for SHM Experimental Setup Multiplexer

Specimen

Impedance Analyzer

Cont…7……

PZT

2. Literature review Liang et al., (1994) {as a tribute} Assumptions • Mechanical interaction between actuator and structure occurs only at the ends of the actuator.

•

1D Model

L

Actuator Impedance Z a = F / V at end points (No electric field) Structure Impedance Z s = − F / V (electric field) F is actuator force V is drive point velocity 8

Suresh Bhalla(2004) …..cont…2D model of Zhou (1996) Assumptions •

Mechanical interaction between a bonded actuator and its host structure occurs along entire boundary of the patch.

•

Plane X-Y

2L

2L Cont…9

Effective displacement and effective velocity terms Instead of drive point velocity (Liang et al (1994)) Za= F / eff. Vel. (No elec. Field)

L

Zs= -F/ eff. Vel. (Elec. Field)

2L

Contâ&#x20AC;Ś10

Researchers --Liang et al (1994) --Zhou et al (1996) --Park et al (2001) --Naidu (2003) --Bhalla and Soh (2004) have one thing in common………

Cont…11

2

or Y

Only Extensional Actuation 1 or X Cont…12…..

3. Motivation and Objectives Specific: Limitations in existing models

1. Extensional actuations only 2. Lack of mathematical definitions for PZT

2D

3. No interaction models for general PZT 4. Limitations in statistical models 5. Mechanical and electrical isotropy 6. Surface bonded PZT 13â&#x20AC;Śâ&#x20AC;Ś.

3D

EMBEDDED PIEZO-IMPEDANCE TRANSDUCERS IN LAMINATED BEAMS

2D in plane 1-3 (proposed in year 2004) Longitudinal Actuation

3

1

Extensional Actuation

Extension in direction 1 is supplemented by contraction in direction 3

14

EMBEDDED PIEZO-IMPEDANCE TRANSDUCERS IN LAMINATED BEAMS

Assumptions • PZT patch is mechanically isotropic • Plane strain • Force transmission between the PZT patch and the structure is distributed along both length and thickness directions Limitations addressed • Electrically isotropic/ anisotropic • Embedded PZT • Longitudinal actuation (direction 3)

Cont…15

EMBEDDED PIEZO-IMPEDANCE TRANSDUCERS IN LAMINATED BEAMS

Average Sum Impedance (PZT Actuator) Distribution points

3

1 2 3 ………………………

n 1

T3

2H

T1

1

T3

w

Distribution points

T3

T1 T3

m

L m

Za =

∑ Dist. force = F

H

1

m

.

1 u m1 ∑ m 1

n

+

2∑ Dist. force =2 FV 1

n

.

1 u n3 ∑ n 1

Za =

T1W 2 H .

u1( X = L )

+

2T3WL .

u 3( Z = H ) Cont…16

EMBEDDED PIEZO-IMPEDANCE TRANSDUCERS IN LAMINATED BEAMS

Mechanical Impedance of structure Zs (ASI)

− Zs =

FHS .

+

FT .

+

FB .

u1 ( X =L) u3 (Z=H) u3 (Z=H)

=

FHS .

u1 ( X = L )

+

2F .

u3 ( Z = H )

Cont…17

EMBEDDED PIEZO-IMPEDANCE TRANSDUCERS IN LAMINATED BEAMS

Admittance Formula for a sandwiched PZT E

d 31Y jωW {(2a sin kL − bα P kL cos kH ) A0 + L(d 33b − d 31a)} ( L ε 33 + 2 Y at = 2 a −b E H d 33 Y {(α P akL cos kH − 2b sin kL) A0 + L(d 31b − d 33 a)}) + a2 − b2 __

Semi_Analytical

AXY 2H

Z

X

L Cont…18

EMBEDDED PIEZO-IMPEDANCE TRANSDUCERS IN LAMINATED BEAMS

Admittance Formula of a free PZT.

Y at − fr

E

d 31Y jωW {(2a sin kL − bα P kL cos kH ) A0− fr + L(d33b − d31a)} = ( L ε 33 + 2 2 a −b H __

E

d 33 Y + 2 2 {(α P akL cos kH − 2b sin kL) A0− fr + L(d 31b − d 33a)}) a −b

AXY 2H

Z

X

L

Cont…19

Experimental Specimens Specimen 1

Exp 2.6 cm AL AL

5 mm

23 cms Contâ&#x20AC;Ś20

Specimen 1 - Few typical modes

Click1

Click5

Click20

Contâ&#x20AC;Ś21

Specimen 2

Exp 2.6 cm 5.2 mm 14 cm

Contâ&#x20AC;Ś22

2D Stress Model (Bhalla and Soh 2004)

• Very small structure • Poor peak matching • A difficult correction factor (practically not possible) • MIT Fellowship awarded formulation

23

Why 3D Model ?

L x W x T (mm3) 1 2

10 x 10 x 0.5 10 x 10 x 2

3 4

15 x15 x 0.5 15 x 15 x 2

24a

Why 3D Model ?

24b

Raja et al (2004)

Shear actuation

d 24

d 33

Longitudinal actuation

(YZ Plane) Extensional actuation

d 32

E3

d15

E2

Z Y

Shear actuation

Face Y

(XZ Plane)

E1 L Face Z

Y

X 2H

d 31

Top

Extensional actuation

X

Face X

W Face Z

25 Bottom

Raja et al (2004)

d 24Shear actuation

d 33

Longitudinal actuation

(YZ Plane) Extensional actuation

d 32

E3

d15

E2

Z Y

Shear actuation

Face Y

(XZ Plane)

E1 L Face Z

Y

X 2H

d 31

Top

Extensional actuation

X

Face X

W Face Z

25 Bottom

3D actuation for embedded and surface bonded PZT

26

THREE DIMENSIONAL (3D) ELECTROMECHANICAL IMPEDANCE MODEL: FORMULATION OF DIRECTIONAL SUM IMPEDANCE (DSI)

-( Z S ) = (Linear impedances) + (Cross impedances)

FX σ X (2 LH ) = Z S1 = u&1 u&1

Z12 ≈ −

ZS2

FY σ Y (2WH ) = = u& 2 u& 2

Z 23

Z S3

FZ FT − FB = = u& 3 u& ZB − u& ZT

Z 31

Z S 1Z S 2 Z S1 + Z S 2 − Z S 3

≈

−

ZS 2ZS 3 Z S1 + Z S 2 − Z S 3

≈

−

Z S 3Z S1 Z S1 + Z S 2 − Z S 3

27

THREE DIMENSIONAL (3D) ELECTROMECHANICAL IMPEDANCE MODEL: FORMULATION OF DIRECTIONAL SUM IMPEDANCE (DSI)

Structural Impedance

− Z S = Z S1 + Z S 2 − Z S 3 + 2Z12 − 2Z 23 − 2Z13

− Z S = ( Z S 1λ1 + Z S 2 λ2 − Z S 3λ3 ) Response Factors ⎛ ⎞ Z S1 ⎟⎟ λ2 λ1 = ⎜⎜ ⎝ Z S1 + Z S 2 − Z S 3 ⎠

(1) (2)

⎞ ⎛ ZS2 ⎛ ⎞ ZS3 ⎟ ⎜ =⎜ ⎟⎟ λ3 = ⎜⎜ ⎟ ⎝ Z S1 + Z S 2 − Z S 3 ⎠ ⎝ Z S1 + Z S 2 − Z S 3 ⎠

Semi Analytical

Cont…28

THREE DIMENSIONAL (3D) ELECTROMECHANICAL IMPEDANCE MODEL: FORMULATION OF DIRECTIONAL SUM IMPEDANCE (DSI)

FX ,Y , Z = FIK

Linear Impedance FX σ X (2 LH ) Z S1 =

=

u&1

u&1

ZS2

FY σ Y (2WH ) = = u& 2 u& 2

Z S3

FZ FT − FB = = u& 3 u& ZB − u& ZT

Total Force on Face I of PZT

Net Total Force on Face I

N

u& I = ∑ u& IK K =1

Cont…29

THREE DIMENSIONAL (3D) ELECTROMECHANICAL IMPEDANCE MODEL: FORMULATION OF DIRECTIONAL SUM IMPEDANCE (DSI)

− Z S = ( Z S 1λ1 + Z S 2 λ2 − Z S 3λ3 )

σ

σ

(2)

σ

2σ X λ1 ∑ WK 2 H 2σ Y λ2 ∑ LK 2 H 2σ Z λ3 ∑ LKWK 2 3 = + + 1 u& v& w& Semi-analytical directional stresses

⎡λ1 0 ⎡σ 1 ⎤ ⎢0 λ ⎢σ ⎥ = 2 ⎢ ⎢ 2⎥ ⎢⎣σ 3 ⎥⎦ Semi _ analytical ⎢⎣ 0 0

(3)

Response Factors

0⎤ ⎡σ X ⎤ ⎢σ ⎥ 0 ⎥⎥ ⎢ Y⎥ λ3 ⎥⎦ Numerical ⎢⎣σ Z ⎥⎦ Analytical

Final Admittance

YA = G + j B Cont…30

THREE DIMENSIONAL (3D) ELECTROMECHANICAL IMPEDANCE MODEL: FORMULATION OF DIRECTIONAL SUM IMPEDANCE (DSI)

Analytical + Numerical

Cont…31

(3D Single PZT- host structure model)

(Surface bonded PZT on a aluminium plate of dimension 10 cm x 10 cm x 2 mm)

(PZT embedded inside epoxy adhesive, which is sandwiched between two aluminium plates) Contâ&#x20AC;Ś32

•Surface bonded PZT • Small size • difficult correction

Summary of dimensions used

• peaks missing • only ext. actuation

• X-Y plane: 4.8 cm x 4.8 x10 mm

• Embedded PZT

•X-Z plane: 23 cm x 2.6 cm x 5 mm • 3D :

• Longer size

10 cm x 10 cm x 2 mm (mostly predicted) 5 cm x 5 cm x 5 mm (mostly predicted)

• Some peaks miss • Ext. + Long.

• Reasonably large structures •Surface +Emb.

Next challenge

•Ext. + Long. act •Good peak pred.

Increasing dimensions Æ real application

•Rec / sq PZT •Elec. Iso / anisotrophy 33

3D EMI MODEL FOR MULTIPLE PZT-STRUCTURE INTERACTION

34

3D EMI MODEL FOR MULTIPLE PZT-STRUCTURE INTERACTION

N PZT of different dimensions

Y

A

N

= G+ Bj = ∑ Y K =1

A K

N

=∑

K =1

jωLK WK 2H K

[ ε 33 + YR {

d 31λ1{[ A0 sin kLK − d31 ] + R[C0 sin kWK − d 32 ] + R[ E0 k cos k 2H K − d 33 ]} + d 32 λ2 {R[ A0 sin kLK − d 31 ] + [C 0 sin kW K − d 32 ] + R[ E0 k cos k 2 H K − d 33 ]} +

d 33λ3 {R[ A0 sin kLK − d 31 ] + R[C0 sin kWK − d 32 ] + [ E0 k cos k 2 H K − d 33 ]}}]

Cont…35

3D EMI MODEL FOR MULTIPLE PZT-STRUCTURE INTERACTION

Case 1

Multiple PZT Specimen

Cont…36

3D EMI MODEL FOR MULTIPLE PZT-STRUCTURE INTERACTION

case2

Multiple PZT Specimen

Cont…36

3D EMI MODEL FOR MULTIPLE PZT-STRUCTURE INTERACTION

Case 3

Multiple PZT Specimen

Cont…36

3D EMI MODEL FOR MULTIPLE PZT-STRUCTURE INTERACTION

Results Case 1

Case 2

Case 3

Cont…37

3D EMI MODEL FOR MULTIPLE PZT-STRUCTURE INTERACTION

Conclusions of Multiple PZT-Structure • 3D Structures • Extensional + Longitudinal actuations of PZT • Global monitoring of structure • Generic : no constrains on Electric isotropy of PZT on PZT shape /size (Thick, thin, square, rectangular) • Reduction to Single PZT – Structure model Next challenge

Protected or wrapped PZT Cont…38

Characterization of PZT Any ‘changes’ in the mechanical and electrical properties of PZT due to 1.

2.

3.

4.

Deterioration of the PZT Atmospheric factors Acidic or alkaline attacks Presence of electrical or magnetic zone

Æ Defective admittance signatures, which may lead to over or under estimation

39

Characterization of PZT Variation No.

Changed

property

Property type

1

None

(say base line )

-

2

Dielectric loss factor

3

Mechanical loss factor

4

Electric permittivity

5

Young’s Modulus

6

Piezoelectric Strain Coefficients

d31 , d32

δ

Electrical

ε 33

Electrical

η

N / m2

7 signatures

Mechanical

Mechanical Electrical

and d 33

(m/V) along directions X, Y and Z 7

Poison ratio

Mechanical

Cont…40

Characterization of PZT

Contâ&#x20AC;Ś41

Characterization of PZT

Contâ&#x20AC;Ś42

43

EMI MODEL OF PZTâ&#x20AC;&#x201C; ADHESIVE - STRUCTURE Epoxy adhesive mm3

Al

1

Negligible

100 x 100 x 2

2

10 x 10 x 0.5

3

10 x 10 x 1

Finite element mesh of one-quarter 1

mm3

PZT mm3 10 x10 x 0.3

Finite element mesh of one quarter 2

Results

EMI MODEL OF PZT– ADHESIVE - STRUCTURE

Experimental

Experimental

Cont…44

Originalities •

The use of longitudinal actuation of PZT transducer.

•

Applicability for both thick and thin PZT

• Characterization of the PZT : to efficiently monitor real life structures to avoid misleading variations which may under or over estimate the damages.

• Study of uniplexing and multiplexing.

45

Major Contributions Characterization of PZT properties

Multiple PZT- Adhesive â&#x20AC;&#x201C; host structure Multiple PZT â&#x20AC;&#x201C;host structure Single PZT- host structure

Characterization of Admittance signatures

46

Major Contributions

Yr 3

Yr 2 Yr 2

3D : M-PZT + adhes+host str

3D : M-PZT + host str, larger structures

3D : Single PZT + host str., rect or sq, Embedded or surface,

Yr 1

Existing models

Rect. or sq, Embedded, both ext & long. act

Square, surface, only ext. act, elec. isotropy PZT + small str, 2D 46

Path forwarding â&#x20AC;˘ steps needed for implementing all the developed models in practical cases 1.

Damage analysis

2.

Under ground

3.

Other surfaces (curvilinear)

4.

non-permanent way of bonding PZT on host structures

46

Publications in Journals Published 1.

2.

3.

4.

5.

Annamdas V. G. M and Soh C. K (2006) "Embedded piezoelectric ceramic transducers in sandwitching beams", Volume 15, Issue 2: 538-549, Smart Materials and Structures [based on chapter 3 of my thesis].

Annamdas V. G. M and Soh C. K (2007) "Three Dimensional Electromechanical Impedance Model I: Formulation of Directional Sum Impedance ", Volume 20, Issue 1:5362, Journal of Aerospace Engineering, ASCE [based on chapter 4].

Annamdas V. G. M and Soh C. K (2007) "Three Dimensional Electromechanical Impedance Model II: Damage analysis and PZT characterization", Volume 20, Issue 1:6371, Journal of Aerospace Engineering, ASCE [based on chapter 5].

In Press Madhav A. V. G and Soh C. K (2007) "Multiplexing and uniplexing of PZT transducers for structural health monitoring", Volume 18, Issue 5, Journal of Intelligent Material systems and structures [based on chapter 6] (May issue) Madhav A. V. G and Soh C. K (2007) "Electromechanical Impedance Model of Piezoceramic Transducer -Structure in Presence of Thick Adhesive Bonding ", Volume 16, Smart Materials and Structures, SMS/238344/PAP [based on chapter 8].

(Scheduled for April) 47

6.

Madhav A. V. G and Soh C. K (2006+) "Multiple PZT-Structure Interaction Model", Journal of Aerospace Engineering, ASCE (Under review since march 06), [based on chapter 7].

7.

Madhav A. V. G , Yang .Y and Soh C. K (2007+) â&#x20AC;&#x153; Structural health monitoring of concrete using embedded PZT transducersâ&#x20AC;?, (ready for submission) [based on first year PhD report].

Publication in conference

1.

Annamdas V. G .M and Soh C. K (2006) "Multiple PZT-Host structure interaction model" SPIE symposium, San Diego, California, USA, 26 Feb-2 Mar. Proc. of SPIE Vol. 6174, 61743G1-G12, [based on chapter 7].

(25th July 2003 - 21st July 2006) 48

ACKNOWLEDGEMENTS 1. To my Parents, 2. Prof. Soh Chee Kiong [PhD supervisor] 3. Prof. Yang Yaowen 4. Prof. Rama Krishna (FYP supervisor, Osmania University, India) [1997-98] 5. Prof. Chandra Kishen (M.Engg supervisor, Indian Institute of Science )[2000-01] 6. Seniors / Juniors / Friends (esp. Zhang Lei) 7. Indian Institute of Science (IISc) and Osmania University 8. Singapore, a perfect host city ……….. and many more..

49

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