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SIMULATION OF SMA BEHAVIOUR IN FEA SOFTWARE FOR TRAILING EDGE CONTROL SURFACE ACTUATION

Mr. D. DwarakanathanScientist, Dynamics and Adaptive Structures GroupStructural Technology division

ByBharath Shekar H. R.Reg. No 100922011M.I.T Manipal

Under the guidance of

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Dr. S. RajaSenior Principal Scientist & Group HeadDynamics and Adaptive Structures GroupStructural Technology division

Dr. N. Yagnesh SharmaProfessor, Dept. of Mech & Mfg EnggMIT, Manipal

Carried out at National Aerospace Laboratories, Bangalore

CONTENTS

• Introduction• Literature review• Problem definition and objective• Methodology• Finite element implementation• MATLAB simulation• Implementation to 1D truss structure• Implementation to Flap actuation• Results and discussions• Conclusion• Scope for future work• References

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SHAPE MEMORY ALLOY• A Swedish physicist Arne Olander discovered “the

Shape Memory Effect” (SME) in goldcadmium (AuCd) alloy in 1932.

• Shape Memory Alloy (SMA) wires are attractive materials for use in adaptive structures because of their superelastic and actuation capabilities.

• Shape memory alloys can be trained to remember their shape and size in both martensite and austenite phases.

• Shape memory alloys have wide engineering and biomedical application

• Shape Memory Alloys (SMAs) are a class of metal alloys that can recover apparent permanent strains when they are heated above a certain temperature

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BASIC WORKING PRINCIPLE

• SMAs have two stable phases - the high-temperature phase, called austenite and the low-temperature phase, called martensite.

• the martensite can be in one of two forms: twinned and detwinned, as shown in Figure (b),(c).

• A phase transformation which occurs between these two phases upon heating/cooling is the basis for the unique properties of the SMAs.

Two different types of behaviour

The shape memory effect is a property by which very large mechanical strains can be recovered by heating the material above a critical temperature. This strain recovery property produces large contractions in the shape memory materials and enables their use as thermo-mechanical actuators.The pseudoelastic effect, is a property by which the material exhibits a very large strain upon loading that is recovered fully when the material is unloaded.

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Shape memory effect Pseudoelastic effect

LITERATURE REVIEW

• Tanaka [1] developed a constitutive law by assuming that the strain, temperature and the martensite volume fraction are the only state variables, and developed the equations for the martensite volume fraction in terms of stress and temperature. Tanaka modeled the martensite volume fraction as an exponential function.

• Liang and Roger [2] used the same constitutive relationship that Tanaka has used. But the main difference arises in the development of the martensite volume fraction. In this the martensite volume fraction is modeled using cosine function.

• Brinson [3] presented an internal variable approach to derive the constitutive law for shape memory alloys. Included the phase transformation effects by introducing two separate variables for martensite fraction. Also conducted the experimental tests to validate the theoretical results. The phase transformation equations were derived on the basis of these tests.

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LITERATURE REVIEW

• Turner et.al [10] implemented the SMA hybrid composite structures in the commercial finite element codes MSC.Nastran and ABAQUS. The effective coefficient of thermal expansion (ECTE) model has been used. The mechanical properties were determined first by using the ECTE model and then given as input in tabular form to the FEM tools.

• P.D Mangalgiri [12] has implemented the Buravalla and Khandelwal model into the UMAT for ABAQUS. In the work the author has established an algorithm to generate user material code.

Summary of literature review: The shape memory alloys can produce 8% of strain in martensite phase and it can be

recovered upon heating above the austenite finish temperature. SMA’s have high power to weight ratio. Hence this can be applied in aerospace domain. Many researchers have developed various constitutive material models. But still now none of the commercial tools have released a module which can completely capture the behaviour of shape memory alloy. Shape memory alloys can be used in various domains like biomedical, aerospace, automobile, aerospace etc

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OBJECTIVEPrimary Objective:• Development of FORTRAN codes for the SMA truss element using a constitutive

model developed by L.C Brinson [2]• Analysis using ABAQUS Secondary Objective:• Conceptual design of mechanism for the deployment of flap, which converts the

linear motion in to rotational motion and it has to be placed in the main structure.

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PROBLEM DEFINITIONTo simulate the SMA behaviour in FEA software for trailing edge control surface actuation

MOTIVATIONThe time and cost required to build and test SMA structures can be very large, but finite element software has the ability to simulate and analyze structures without being very expensive and time consuming, which makes them valuable tools in the design process. Unfortunately, commercially available FEA software does not currently include built-in models that accurately simulate both the pseudoelastic and actuation behavior of SMA materials.

METHODOLOGY

• Modeling of wing structure• Selection of suitable Constitutive model• Matlab coding to plot the behaviour• Implementation of constitutive model for Abaqus user subroutine using Fortran

programming.• Implementation for a 1D truss element• Selection of suitable mechanism for flap actuation• Implementation of SMA wire for flap actuation

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WING MODEL

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Wing span = 800mmChord length = 600mm

BRINSON CONSTITUTIVE MODEL• The constitutive equation can then be written as

• The Young’s modulus D and the phase transformation coefficient Ω are the functions of the total Martensitic volume fraction expressed as

where =stress induced =Phase Transformation co.eff =Thermal expansion co.eff =Stress induced Martensitic = Total strain volume fraction = Max. allowable strain =Temperature induced , , , are the intial conditions Martensitic volume fraction =Total martensitic vol.fraction

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0 0 0 0 0 0( ) ( ) ( ) ( ) ( )S SD D T T

( ) ( )M A MD D D D ( ) ( )LD

0

( )S

S T

T

00 0( )

L

For Conversion to Detwinned Martensite If T>Ms and < <

• If T<Ms and

For Conversion to Austenite• If T>As and

Calculation of Martensitic volume fraction:

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( )crf M sC T M ( )cr

s M sC T M

0 01 1cos{ [ ( )]}

2 2crS S

S f M scr crs f

C T M

00 0

0

( )1

TT T M M

M

cr crs f

( ) ( )A f A sC T A C T A

0 {cos[ ( )] 1}2 A s

A

a T AC

00 0

0

( )SS S

00 0

0

( )TT T

ASSUMPTIONS

• The transformation temperatures are in the following order Mf<Ms<As<Af.

• At any temperature T such that Ms<T<As, there is no phase change.

• At any temperature T such that Mf<T<Af, both Martensite and Austenite coexist.• The internal variables such as the internal stress and initial phase condition are

considered when setting up a relation between transformation temperature and applied stress.

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References• Tanaka, K. “A Thermomechanical Sketch of shape memory effect one dimensional tensile behaviour”, Res Mechanica,

Elsevier publishers, vol.2, issue.3,1986, pp59-72.• Liang, C. “One-dimensional Thermomechanical Constitutive Relations for shape memory materials”, Ph.d thesis, 1990,

Virginia Tech.• L.C. Brinson, “one-dimensional constitutive behaviour of shape memory alloys: Thermomechanical derivation with non-

constant material functions and redefined martensite internal variable”, Journal of Intelligent Material Systems and Structures, vol.4, April-1993, pp 229-241.

• Boyd, J.D, Lagoudas, D.C, “A thermodynamical constitutive model for shape memory materials. Part I. The monolithic shape memory alloy”, International Journal of Plasticity, vol.12, issue.6, 1996, pp 805-842

• Boyd, J.D, Lagoudas, D.C, “A thermodynamical constitutive model for shape memory materials. Part II. The SMA composite material”, International Journal of Plasticity, vol.12, issue.7,1996,pp 843-873

• Michael, J.M, Constantinos Mavroidis, Charles Pfeiffer, “Design and dynamics of shape memory alloy wire bundle actuator”, Proceedings of the ANS, 8th Topical meeting on Robotics and Remote Systems, 1999

• Dimitris C. Lagoudas, Zhonghe Bo & Muhammad A. Qidwai “A unified thermodynamic constitutive model for sma and finite element analysis of active metal matrix composites”, Mechanics of composite materials and structures, Taylor & Francis group,vol.2, issue.2, 1996, pp 153-179

• Jardine, AP, Bartley-Cho,JD, Flanagan,JS, “Improved design and performance of the SMA torque tube for the DARPA smart wing program” proceedings SPIE 3674,270, Newport Beach, CA, USA, Tuesday 02 March 1999

• Benoit Berton, “Shape memory application: Trailing edge shape control”, Multifunctional structures/Integration of sensors and antennas, proceedings RTO-MP-AVT-141, France, 2006, pp 13.1-13.16

• Travis L. Turner, Hemant D. Patel, “Analysis of SMA hybrid composite structures using commercial codes”, smart structures and materials: Model, Signal Processing, and Control, Proceedings of SPIE vol.5383, paper no. 12, San Diego, CA, 14-18 March 2004

• Casper van der Eijk, Jim Stian Olsen, Zhiliang Zang, “Applications of NiTi shape memory alloy dampers in civil structures”, proceedings of the First International Conference on Self Healing Materials, Springer publications, Noordwijk aan Zee, the Netherlands, 18-20 April

• P.D Mangalgiri, A.G Thakare, B.Dattaguru, “Use of SMA constitutive model in finite element analysis of wire-based actuators”,IUTAM Symposium on Multi-Functional Material Structures and Systems, IUTAM Book series 19, 2010

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THANK YOU

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