See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/267195545
Simulation for Thermomechanical Behavior of Shape Memory Alloy (SMA) using COMSOL Multiphysics Conference Paper · September 2006
CITATIONS
READS
2
565
1 author:
Shamit Shrivastava University of Oxford 20 PUBLICATIONS 291 CITATIONS SEE PROFILE
Some of the authors of this publication are also working on these related projects:
Consequences of shock waves and unltrasound in duced cavitation near lipid interfaces and its implications for drug delivery and neuromodulation View project
Biological Signaling via Nonlinear Sound Waves in Cellular Membranes View project
All content following this page was uploaded by Shamit Shrivastava on Shrivastava on 26 July 2015. The user has requested enhancement of the downloaded file. All in-text references underlined in blue are blue are added to the original document and are linked to publications on ResearchGate, letting you access and read them immediately.
Excerpt from the Proceedings of the COMSOL Users Conference 2006 Bangalore
Simulation for Thermomechanical Behavior of Shape Memory Alloy (SMA) using COMSOL Multiphysics Shamit Shrivastava Department of Mechanical Engineering, Indian Institute of Technology Guwahati, Assam, India
[email protected]
Abstract: Finite Element Method (FEM) is applied for numerical analysis of SMA beam fixed at both the ends. Shape memory alloys (SMAs) like Nitinol (Nickel-Titanium alloy) are well known materials capable of recovering extremely large inelastic strain (of the order of 10%) by the Martensite-Austenite phase transformation. The shape memory effect (SME), pseudoelasticity and martensite deformability are typical thermomechanical behaviors of SMAs. A Nitinol (Nickel - 45%) beam fixed at the both ends is modeled using a thermodyanamic constitutive model. The material properties of SMAs are dependent upon the stress-strain values generated during runtime. The wire is heated through resistive heating by providing controlled potential at the ends of the beam. Due to the SME, the beam tends to return to its original position and the curvature of the beam is simulated. A Micro Pump action is then simulated with the modeled SMA beam and a few Nanobioscience applications are highlighted.
and temperature. Formation of martensitic phase under stress results in the desired crystalline variant orientation which leads to large induced strain [2,3]. Dependent upon the temperature of the system, the strain is recovered either in a hysteresis loop upon unloading or upon heating the material. This capability of reversible, controllable large strain is the basis for use of SMAs as control materials. Large shape changes can be induced easily and reproducibly with these materials.
1. Introduction
1.1 Methods Since shape memory material behavior depends on stress and temperature and is intimately connected with the crystallographic phase of the material and the thermodynamics underlying the transformation process, formulation of adequate macroscopic constitutive law is necessarily complex. A variety of constitutive models have been developed, most aimed at one dimensional description of the material behavior [2,3,4,5]. One feature of many of the constitutive models of the shape memory behavior can generally be separated into a mechanical law governing stress-strain behavior and a kinetic law governing transformation behavior. These two relationships are coupled because stress is an input for the kinetic law and the dynamic phase fraction in turn affects the stress-strain behavior.
Smart Materials are receiving unprecedented attention in recent years for their great potential to revolutionize the engineering of actuation and control. Shape Memory Alloys (SMAs) are one such ‘smart material’ that is currently being studied with great enthusiasm as they hold the promise for many engineering advancements in the near future. They are capable of recovering very large strains due to crystallographic transformations between the highly symmetric parent phase of austenite and low symmetry product phase of martensite [1]. The phase change that occurs is a function of both stress
1.2 Theory In this paper we are going to use the recently developed thermo-elastic model, that makes use of the engineering property measurement, by Turner et. Al.[6]. The effective coefficient of thermal expansion model (ECTEM) is relatively simplified and easily integrated into commercial structural analysis softwares such as COMSOL Multiphysics. As opposed to approach of the different models discussed in previous paragraph, in ECTEM, the stress in a SMA material is based purely on the elastic component and an effective thermal strain component. This
Keywords: Shape Memory Alloy (SMA), Nitinol, Finite Element Method (FEM), MEMS, Actuation, Micropump, Computation and Modeling.
Excerpt from the Proceedings of the COMSOL Users Conference 2006 Bangalore
effective thermal strain term represents both the thermal and transformational components of other models. As a consequence, the ECTEM model is limited to thermally activated transformations, but is particularly attractive for SMA because it only requires the experimental measurement of fundamental engineering properties. Direction 1 is along the axis of the fixed beam while 2 represent the direction transverse to it. The following constitutive relation is the fundamental equation of the ECTEM developed by Turner [9] for SMA element along direction 1 T
= E(T)[ε 1-
σ1
∫
( )dτ ]
α1 τ
To
where, E is the Young’s modulus of the SMA, ε1 is the strain in direction 1 and α1 is the coefficient of thermal expansion (CTE). The key feature of the constitutive relation is the term T
–E(T)
∫
( )dτ ]
α1 τ
To
and this embodies the effect of both the thermal strain and transformational strain of the SMA. In the constrained recovery application, the term is related to recovery stress and elastic modulus of SMA i.e. σ r (T , ε p ) and E(T), still capturing the nonlinear effects when the temperature is above austenitic start ( T>As). T
–E(T)
∫
( )d τ = σ r or
α1 τ
To T
∫ To
( )d τ =
α1 τ
−σ r (T , ε p) E (T )
When the temperature is below austenitic start (T < As) the thermoelastic relation remains the same, and the ECTE of the SMA is due to thermal expansion only, and can be measured experimentally. Therefore, the temperature dependent constitutive relation in the 1-direction for the SMA actuator specific to constrained recovery can be expressed as
(a) For T < As T
∫
= E(T)[ε 1-
σ1
( )dτ ]
α1 τ
To
(b) For T > As
= E(T)[ε 1 +
σ1
σr
(T , ε p )
Ea (T )
]
Only the engineering properties of
α1(τ)
for
T < A s and σr , E for T ≥ As need to be measured in experimental setups that imitate the application (pre-strain ε p=4% and boundary Conditions = clamped) to implement the model. A similar constitutive relation results for principle material direction-2 (transverse) T
σ2
= E(T)[ε 2-
∫
( )dτ ]
α2 τ
To
In this case the transverse CTE α2(τ) is not related to the recovery stress, σr , and elastic modulus E(T), but is still nonlinear due to the changing of the martensite and austenite phases.
2. Computation and Modeling The ECTEM requires measurement of material properties viz coefficient of thermal expansion, α (table 1), recovery stress, σr and young’s modulus, E as a function of temperature [7]. This data was then interpolated using fourth degree polynomials. To obtain temperature dependent functions for E, σr and α. The (2.6x10-3x1.2x10-5) m, nitinol beam with 138 boundary elements and a total of 260 elements was then simulated for midspan deflection versus central line temperature. The temperature range was set between the experimentally obtained values and the deflection was simulated for three different values of transverse pressure (Figure 4).
Excerpt from the Proceedings of the COMSOL Users Conference 2006 Bangalore
Figure 2. Total displacement variation with the temperature.
Figure 3. Design of the Micropump. Figure 1. X and Y displacements variation with the temperature.
3. Results and Discussion As expected x and y displacements (Figure 1) and hence the total displacement (Figure 2) was found to decreases in magnitude with increase in temperature. The deformation was simulated for two different values of external force on concave surfaces viz 15N/m and 20 N/m and the obtained shapes can be observed in figure 4. This shows that such a device can function over a wide range of pressure. Since its a 2-d model of a diaphragm surface, the unit is force per unit length. This ‘forced return’ to the mean position after initial buckling can find many applications in micro as well as nano-scale devices such as micropumps and squeezers. One such design was suggested by Benard and Kahn [10]. We suggest one more such design in figure 3 and this has the advantage of being able to induce motion at microlevels, a property that is not possible in the
model suggested by Benard and Kahn. The two diaphragms will bulge out due to initial heating and inlet valve will operate during this period. As temperature increases the shape memory effect will come into picture and this will create stress within the SMA that will drive the diaphragms back to the original positions. Such a device can find applications in a number of fields [8,9,10,11]; from microhearts which are electrically controlled, to cell membranes reaction with microvolt stimulation, to fluid absorption retention and release in tissue samples, to lung simulators and diaphragm support structures[12,13,14]. Inflammation causes a temperature gradient to develop in tissues and this gradient can be used effectively for optimized drug delivery. This will work with the same principal as that of the micropump.
Excerpt from the Proceedings of the COMSOL Users Conference 2006 Bangalore
Figure 4 Force=15 N/m Temperature,T=298 K and T=343 K. Force =20/N/m Temperature, T=298 and T=343 K respectively.
4. Conclusion Shape memory alloy based micropump can operate over a wide range of temperatures and pressures and micropumps based on SMA promise a lot for futuristic microdevices. Large deformations that are recovered leads to a high volume of fluid pumped per stroke as compared to micropumps based on other mechanisms. Owing to properties like high resistance to corrosion and very low reactivity they are very much compatible with bio-sytems and hence there is a lot of scope for pragmatic biomedical applications.
References [1] Rogers C A 1993 Intelligent material systems—the dawn of a new material age J. Intell. Mater. Syst. Struct . 4 4–12. [2] Brinson L C 1993 One dimensional constitutive behavior of shape memory alloys: thermo-mechanical derivation with non-constant material functions J. Intell. Mater. Syst. Struct .4 229–42. [3] Brinson L C and Lammering R 1993 Finite element analysis of the behavior of shape memory alloys and their applications Int. J. Solids Struct 30 3260-80. [4] Brinson L C and Huang M S 1996 Simplifications and comparisons of shape memory alloy constitutive models J. Intell. Mater. Syst. Struct . 7 108–14. [5]. O. Heintze, S. Seelecke, Interactive WWW page for the simulation of shape memory alloys, http://www.mae.ncsu/homeages/seelecke, 2000. [6] T.L. Turner, “Experimental Validation of a Thermoelastic Model for SMA Hybrid Composites, “ Smart Structures and Materials 2001; Modeling, Signal Processing, and Control in Smart Structures, SPIE Vol. 4326, Paper No. 4326-24, Newport Beach, CA, 2001. [7] Brian A. Davis, North Carolina State University, North Carolina, Investigation of the Thermomechanical Response of Shape Memory Alloy Hybrid Composite Beams, NASA/CR2005-213929.
Excerpt from the Proceedings of the COMSOL Users Conference 2006 Bangalore
[8] S. Shoji and M. Esashi, “Microflow devices and systems,” J. Micromech. Microeng ., vol. 4, pp. 157–171, 1994. [9] P. Gravesen, J. Braneberg, and O. S. Jensen, “Microfluidics a review,” J. Micromech. Microeng., vol. 4, pp. 168–182, 1993. [10] William L. Benard, Harold Kahn, Arthur H. Heuer, and Michael A. Huff, “Thin-Film ShapeMemory Alloy Actuated Micro-pumps”, Journal of Microelectromechanical Systems, Vol. 7, No. 2, June 1998. [11] M. Mehregany, W. H. Ko, A. S. Dewa, C. C. Liu, and K. Markus,“Introduction to microelectromechanical systems and the multiuser MEMS process activities,” Case Western Reserve Univ., Cleveland, OH, Aug. 8– 10, 1993. [12] H. T. G. Van Lintel, F. C. M. Van De Pol, and S. Bouwstra “A piezoelectric micropump based on micromachining of silicon,” Sens.Actuators , vol. 15, pp. 153–167, 1988. [13] S. Shoji, S. Nakagawa, and M. Esashi, “Micropump and sample-injector for integrated chemical analyzing systems,” Sens. Actuators , vol. A21- 23, pp. 189–192, 1990. [14] E. Stemme and G. Stemme, “A novel valveless fluid pump,” in IEEE Transducers Conf. 1993 , pp. 110–113.
Acknowledgement I am indebted to Dr. Arun Chattopadhyay, Indian Institute of Technology,Guwahati, who gave me valuable advice and motivation and was good enough to find time for fruitful discussion. My deepest and most sincere thanks to Mr. Ramakrishnan, Centre for Nanotech IIT and Guwahati, Mr. Venkataramanan Soundararajan, Sasisekharan Lab, MIT who inspite of their busy schedule, were able to spare time to help and guide me in doing my project. A special thanks to Mr. Arun Prasad, Comsol Multiphysics, Banglore who provided all possible help.
Appendix Table 1. Data used for simulation to obtain interpolated function.[7]
CTE Temp(K) E (Gpa) *(10^6) 294.25 27.17 6.606 299.85 24.82 6.606 305.35 22.41 6.606 310.95 20.06 6.606 316.45 25.72 6.606 322.05 31.37 7.236 327.55 36.96 7.866 333.15 42.61 8.496 338.75 48.27 9.108 344.25 54.88 9.738 349.85 61.43 10.37 355.35 64.19 11 360.95 63.16 11 366.45 62.06 11 372.05 63.92 11 377.55 65.78 11 383.15 67.64 11 388.75 69.5 11 394.25 71.36 11 399.85 70.81 11 405.35 70.33 11 410.95 69.78 11 416.45 69.29 11 422.05 68.74 11
