Shape Memory Alloys in Structural Vibration Control ...docentes.fct.unl.pt/cornel/files/c60.pdfShape Memory Alloys (SMAs) Metallic alloys exhibiting two peculiar thermo-mechanical

Shape Memory Alloys in Structural Vibration ControlResearch at UNIC/DEC/FCT/UNL

Corneliu Cismasiu & Filipe Pimentel Amarante dos Santos

Centro de Investigacao em Estruturas e Construcao - UNICFaculdade de Ciencias e Tecnologia

Universidade Nova de Lisboa

C60 - CONFERINTA INTERNATIONALA “Constructii 2013”

C. Cismasiu & F.P. Amarante dos Santos (C60, 2013) SMAs in Structural Vibration Control 1 / 30

Shape Memory Alloys (SMAs)

Metallic alloys exhibiting two peculiar thermo-mechanical properties:

◮ shape memory effect – allows the material to recover its original geometrythrough a heat cycle, after withstanding large deformations;

◮ superelasticity – enables the material to recover from large nonlinear strainsduring a mechanical cycle of loading and unloading, while dissipating aconsiderable amount of energy through hysteresis.

Five primary alloy families are of interest in civil engineering aplications: the nickel-titanium family (Nitinol), the iron-magnesium-silicon alloys, two copper-based families,the cooper-zinc-aluminum-nickel and the copper-aluminium-nickel, and some specialstainless steel formulations.


Shape memory effect

The sample is deformed (A to B) and unloaded (B to C) at a temperature below Mf.The residual deformation is restored during heating to a temperature above Af.

(Mf – martensite finish temperature, Af – austenite finish temperature, Mf < Af )


Shape memory effect - civil engineering applications

Smart prestressing of the bridge carrying

Sherman Road over US-31 [NCHRP-96-IDO29]

Shear cracks on beam stem Heating of SMA rods

Rehabilitation of a concrete structure using

intelligent materials [Soong et al ., 2006]

During loading After heating the crack closes up

Self-repairing performance of concrete elements using superelastic SMA wires, smartprestressing, RC beams with variable stiffness and strength, health monitoring andrehabilitation of concrete structures, self actuating fuse for auto-adaptive compositestructures.


Superelasticity

The sample is strongly deformed at relatively low stresses (A to B) at a temperatureabove Af. During subsequent unloading a complete shape recovery occurs (B to C).


Superelasticity - civil engineering applications

Seismic protection of cultural heritage structures

Basilica of St. Francis of Assisi [Croci, 2001]

S.Giorgio Church Bell-Tower [Indirli et al., 2001]

St. Feliciano Cathedral [Castellano et al., 2000]

Research project:

◮ ISTECH - Shape Memory Alloy

Devices for Seismic Protection of

Cultural Heritage Structures


Superelasticity - civil engineering applications

Superelastic restrainers and connectors

[Johnson et al., 2008]

[Padgett et al., 2009] [Ocel et al., 2004]

Research projects:

◮ NEES Payload Project - Large-scaleexperimental evaluation of shape

memory alloy bridge cable restrainers

◮ MANSIDE - Memory Alloys for New

Seismic Isolation and Energy

Dissipation Devices

◮ SUPERB - Seismic Unseating

Prevention. Elements for Retrofitting

of Bridges


Superelasticity

σ

εA

D

B

C

Transformations in the crystaline structure:

◮ forward transformation (A → M) – curve ABC

◮ inverse transformation (M → A) – curve CDA

hysteretic cycle null residual deformations⇓ ⇓

energy dissipation repositioning capability⇓ ⇓

Vibration control devices based on superelastic SMAs


SMA - temperature and strain rate independent constitutive models

The constitutive model is characterised by the austenitic elastic modulus, the strainassociated with the transformation process and the starting and final stresses duringthe forward and inverse transformations.

ε [%]

σ [MPa]

ExperimentalNumerical

0

50

100

150

200

250

300

350

400

450

70 1 2 3 4 5 6

Complete cycle followed by a small inner cycle

ε [%]

σ [MPa]

70 1 2 3 4 5 60

50

100

150

200

250

300

350

400

450

ExperimentalNumerical

Three complete cycles of decreasing amplitude


SMA - temperature and strain rate dependent thermo-mechanical models

As the strain rate increases, the SMA wires can no longer expel the internal heatgenerated during the loading phase and absord heat from its environment duringthe unloading phase and therefore the constitutive model must relate stress, strain,austenite fraction and the temperature in the material.

Transformedphase

M A

Mechanical law Exponential kinetic law

10

20

40

60

80

100

30

50

70

90

Heat balance equation

The model couples the constitutive relations, a kinetic law that describes the volumefraction of austenite and a balance equation that considers the thermal effects on thematerial ⇒ reliable constitutive model even for high strain rates.


SMA - temperature and strain rate dependent thermo-mechanical models

T = 10◦C f = 0.02Hz

Experimental

Numerical

100

200

300

400

500

600

700

800

00 1 2 3 4 5 6 7 8

ε [%]

σ [MPa]

T = 20◦C f = 0.02Hz

0 1 2 3 4 5 6 7 8

100

200

300

400

500

600

700

800

0

Experimental

Numerical

ε [%]

σ [MPa]

T = 10◦C f = 0.1Hz

Experimental

Numerical

100

200

300

400

500

600

700

800

00 1 2 3 4 5 6 7 8

ε [%]

σ [MPa]

T = 20◦C f = 0.1Hz

Experimental

Numerical

0 1 2 3 4 5 6 7 8

100

200

300

400

500

600

700

800

0ε [%]

σ [MPa]


Strain rate analysis using thermo-mechanical model

10000 200 400 600 800 10000 200 400 600 800 10000 200 400 600 8000

10

20

30

40

50

0

10

20

30

40

50

0

10

20

30

40

50

σ [MPa]

f = 0.001 Hz

time [s]

ε [%]

T [◦C]

ε [%]

σ [MPa]

f = 10 Hzf = 0.1 Hz

σ [MPa]

ε [%]

T [◦C]

time [s]

T [◦C]

time [s]

0 1 2 3 4 5 76 0 1 2 3 4 5 76 0 1 2 3 4 5 760

100

200

300

400

500

600

0

100

200

300

400

500

600

0

100

200

300

400

500

600

Dissipated energy

f [Hz]

W /W0.001

0.95

0.90

0.85

0.80

0.75

1.00

0.001 100.01 0.1 1

Pseudostatic load → Dynamic load

Room Temperature = 20◦C


Cycling effects - experimental tensile tests

Evolution of:

◮ Cummulative creep deformation;

◮ Critical stress to inducemartensite;

◮ Strain associated to thetransformation.


Cycling effects - experimental validation of the numerical model


Superelastic SMA based oscillators

u(t)

p(t)

m

SE

m

u(t)

p(t)

SE1 SE2

m

u(t)

p(t)

SE1

SE2

SE3

◮ simple SMA wire

◮ two pre-tensioned wires working inphase oposition

◮ two pre-tensioned wires withre-centring element


Simple SMA wire (T = 20◦C, f = 2 Hz)

Exhibits:

◮ self-recentring

◮ low energydissipation(ζeq ≃ 8%)


Two pre-tensioned wires working in phase oposition (T = 20◦C, f = 2 Hz)

Exhibits:

◮ good energydissipation(ζeq ≃ 15%)

◮ noself-recentring


Two pre-tensioned wires with re-centring element (T = 20◦C, f = 2 Hz)

Exhibits:

◮ good energydissipation(ζeq ≃ 15%)

◮ self-recentring

↓

appealing propertiesfor seismic control

devices


Drawbacks of SMA based passive control devices

◮ Re-centring capabiliy implies a third elastic element;

◮ Relaxation can not be avoided, as the use of permanent pre-strained SE wires isa must in order to obtain competitive damping ratio;

◮ Cumulative creep can be avoided by keeping the strains inside a so calledpseudo-elastic window, which ensures appropriate material behaviour, but this isa very challenging task when dealing with arbitrary seismic excitations.


Proposed semi-active device

1 2 3 4 5 6 87 9

t

u

SE2

SE1

General behaviour of the proposed semi-active control system


Sao Martinho railway viaduct

Legend: 1. SMA device, 2. Abutment, 3. Transverse girder, 4. Main girder

For the longitudinal analysis, the viaduct is assimilated to a 1DOF dynamic system:4650 ton mass, 355×103 kN/m stiffness and 5% structural damping.

Two passive control devices are placed at the two ends of the viaduct, one for eachmain girder. The devices consist of two sets of 1.0 m SMA wires, each set with atotal area of 1963 mm2 (bars or a set of smaller wires laid parallel in strands, to forma cable).


Response of the structure to “El Centro” earthquake

DISPLACEMENT TIME HISTORYUNCONTROLLED

[s]

[cm] DISPLACEMENT TIME HISTORYPASSIVE CONTROL

[s]

[cm] DISPLACEMENT TIME HISTORYSEMI−ACTIVE CONTROL

[s]

[cm]

ACCELERATION TIME HISTORYPASSIVE CONTROL

[s]

[m/s2] ACCELERATION TIME HISTORYSEMI−ACTIVE CONTROL

[s]

[m/s2]ACCELERATION TIME HISTORYUNCONTROLLED

[s]

[m/s2]

−8

−6

−4

−2

0

2

4

6

8

0 10 20 30 40 50−8

−6

−4

−2

0

2

4

6

8

0 10 20 30 40 50−8

−6

−4

−2

0

2

4

6

8

0 10 20 30 40 50

−8

−6

−4

−2

0

2

4

6

8

0 10 20 30 40 50−8

−6

−4

−2

0

2

4

6

8

0 10 20 30 40 50−8

−6

−4

−2

0

2

4

6

8

0 10 20 30 40 50


Response of the structure to “El Centro” earthquake

STRAIN TIME HISTORYPASSIVE CONTROL

21

[%]

[s]

STRAIN TIME HISTORYSEMI−ACTIVE CONTROL

21

[%]

[s]

SE SE

0

1

2

3

4

5

6

7

8

0 10 20 30 40 50 0

1

2

3

4

5

6

7

8

0 10 20 30 40 50

SE SE


Response of the structure to “Kobe” earthquake

DISPLACEMENT TIME HISTORYUNCONTROLLED

[s]

[cm]

2

DISPLACEMENT TIME HISTORYPASSIVE CONTROL

[s]

[cm] DISPLACEMENT TIME HISTORYSEMI−ACTIVE CONTROL

[s]

[cm]

ACCELERATION TIME HISTORYUNCONTROLLED

[s]

[m/s2]

2

[s]

[m/s2] ACCELERATION TIME HISTORYPASSIVE CONTROL

ACCELERATION TIME HISTORYSEMI−ACTIVE CONTROL

[s]

[m/s2]

−20

−10

0

10

20

0 10 20 30 40 50 60

failure in SE

−20

−10

0

10

20

0 10 20 30 40 50 60

−20

−10

0

10

20

0 10 20 30 40 50 60

−20

−10

0

10

20

0 10 20 30 40 50 60

failure in SE

−20

−10

0

10

20

0 10 20 30 40 50 60

−20

−10

0

10

20

0 10 20 30 40 50 60


Response of the structure to “Kobe” earthquake

STRAIN TIME HISTORYSEMI−ACTIVE CONTROL

21

STRAIN TIME HISTORYPASSIVE CONTROL

21

[%]

[s][s]

[%]

2

0

2

4

6

8

10

0 10 20 30 40 50 60

SE SE

SE SE

0

2

4

6

8

10

0 10 20 30 40 50 60

failure in SE


Experimental prototype


Experimental prototype under harmonic load

30

25

20

15

10

5

00 10 20 30 40 50 60 70 80 90

Setpoint highPID threshold highPID threshold low

Setpoint lowForce

Accumulated force

CONTROL-ONCONTROL-OFF

PID-ON

PID-OFF

PID-ON

F[%Fmax ]

t[s]

Force time-history in a SMA wire


Experimental prototype under harmonic load

20

15

10

5

0

-5

-10

-5 0 5 10 15

1

2

F[%Fmax ] Initial cycle

Final cycleu[mm]

Force-displacement diagram


Conclusions regarding the proposed semi-active device

◮ The strain accumulation in the wires is a result of the motion of the structureitself, with no need of external energy input in the system;

◮ With no need of initial pre-strain calibration, the device responds well to virtuallyany level of dynamic excitation;

◮ It presents important damping capabilities, is able to confine the strains in theSE wires inside recoverable limits to minimise the rheological effects related tocumulative creep, and finally, at the end of the action, is able to recover the SEwires strain free condition exhibiting efficient re-centring capabilities andavoiding relaxation problems;

◮ Is able to confine force values throughout the entire duration of the seismicaction, meaning that the force the semi-active device transmits to the structurecan be conveniently bounded.


Shape Memory Alloys in Structural Vibration ControlResearch at UNIC/DEC/FCT/UNL

Corneliu Cismasiu & Filipe Pimentel Amarante dos Santos

Centro de Investigacao em Estruturas e Construcao - UNICFaculdade de Ciencias e Tecnologia

Universidade Nova de Lisboa

C60 - CONFERINTA INTERNATIONALA “Constructii 2013”


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Shape Memory Alloys in Structural Vibration Control ...docentes.fct.unl.pt/cornel/files/c60.pdfShape Memory Alloys (SMAs) Metallic alloys exhibiting two peculiar thermo-mechanical