Mechanical behavior of a unidirectional TiNi shape memory alloy (SMA) fiber composite subjected to a single isothermal loading and unloading cycle is analyzed using a threedimensional micromechanical method of cells. The multiaxial rhombohedral and martensitic phase transformations of TiNi SMA fibers embedded in an elastic matrix are taken into account. Numerical simulations are performed for different fiber volume fractions and for different fiber orientation angles. It is clearly observed that a pseudoelasticity-like hysteretic behavior appears in the stress-strain relationships of the composite system of TiNi SMA fibers and an elastic matrix under the prescribed isothermal loading and unloading conditions. The shape and size of the hysteresis are significantly influenced by the volume fraction of TiNi SMA fibers. For a high volume fraction of fibers, in particular, the rhombohedral transformation of the embedded TiNi SMA fibers characterizes the overall hysteretic behavior of the TiNi SMA composite. The present simulations manifest the significance of the capability to predict the rhombohedral transformation of TiNi SMAs under multiaxial loading conditions, and also demonstrate the efficiency of the micromechanical composite model for evaluating the average characteristics of the TiNi SMA fiber composites.
Get full access to this article
View all access options for this article.
References
1.
Aboudi, J.1991. Micromechanics of Composite Materials, Elsevier, The Netherlands.
2.
Armstrong, W. D. and H. Kino. 1995. "Martensitic Transformations in a NiTi Fiber Reinforced 6061 Aluminum Matrix Composites,"Journal of Intelligent Material Systems and Structures, Vol. 6, pp. 809-816.
3.
Boyd, J. G. and D. C. Lagoudas. 1994. "Thermomechanical Response of Shape Memory Composites,"Journal of Intelligent Material Systems and Structures, Vol. 5, pp. 333-346.
4.
Bidaux, J. E. , N. Bernet, C. Sarwa, J. A. E. Manson and R. Gotthardt. 1995. "Vibration Frequency Control of a Polymer Beam Using Embedded Shape-Memory-Alloy Fibers,"J Physique, IV, Vol. 5, C8, pp. 1177-1182.
5.
Birman, V. , D. A. Saravanos and D. A. Hopkins. 1996. "Micromechanics of Composites with Shape Memory Alloy Fibers in Uniform Thermal Fields,"AIAA Journal, Vol. 34, No. 9, pp. 1905-1912.
6.
Birman, V.1997. "Review of Mechanics of Shape Memory Alloy Structures,"Applied Mechanics Reviews, Vol. 50, No. 11, 629-645.
7.
Boubakar, M. L. , S. Moyne and C. Lexcellent. 1999. "SMA Pseudoelastic Finite Strains, Theory and Numerical Application,"ASMEJ. Eng. Mater Technol., Vol. 121, No. 1, pp. 44-47.
8.
Bo, Z. , D. C. Lagoudas and D. Miller. 1999. "Material Characterization of SMA Actuators under Nonproportional Thermomechanical Loading," J. Eng. Mater Technol., Vol. 121, No. 1, pp. 75-85.
9.
Brinson, L. C. , M. S. Huang, C. Boller and W. Brand. 1997. "Analysis of Controlled Beam Deflections Using SMA Wires,"J. Intelligent Material Systems and Structures, Vol. 8, pp. 12-25.
10.
Christensen, R. M. and K. H. Lo. 1979. "Solutions for Effective Shear Properties in Three Phase Sphere and Cylinder Models,"J. Mechanics of Physics of Solids, Vol. 27, pp. 315-330.
11.
Chamis, C. C.1984. "Simplified Composite Micromechanics Equations for Hygral, Thermal and Mechanical Properties,"SAMPE Quarterly, Vol. 15, pp. 14-23.
12.
Culshaw, B.1996. Smart Structures and Materials, pp. 122-126, Artech House.
13.
Duerig, T. W. , A. R. Pelton and D. Stockel. 1996. "The Use of Superelasticity in Medicine,"Metall., Vol. 50, pp. 569-574.
14.
Evard, M. E. and A. E. Volkov. 1999. "Modeling of Martensite Accommodation Effect on Mechanical Behavior of Shape Memory Alloys,"ASME J. Eng. Mater Technol., Vol. 121, No. 1, pp. 102-104.
15.
Fischer, F. D. , Q. P. Sun and K. Tanaka. 1996. "Transformation-Induced Plasticity (TRIP),"Applied Mechanics Reviews, Vol. 49, No. 6, pp. 317-364.
16.
Funakubo, H. ed. 1987. Shape Memory Alloys, New York, Gordon and Breach Science Publishers.
17.
Furuya, Y. , A. Sasaki and M. Taya. 1993. "Enhanced Mechanical Properties of TiNi Shape Memory Fiber/Al Matrix Composites,"Materials Transactions, JIM, Vol. 34, No. 3, pp. 224-227.
18.
Furuya, Y. 1995. "Design and Experimental Verifications of Intelligent Materials Using Shape Memory Alloy,"Proc. Int. Symp. Micromachine, Intelligent Materials and Robots, MIMR'95, pp. 313-318.
19.
Gandhi, M. V. and B. S. Thompson. 1992. Smart Materials and Structures, pp. 192-215, Chapman & Hall.
20.
Graesser, E. J. and F. A. Cozzarelli. 1994. "A Proposed Three-Dimensional Constitutive Model for Shape Memory Alloys,"Journal of Intelligent Material Systems and Structures, Vol. 5, pp. 78-89.
21.
Hashin, Z. and B. W. Rosen. 1964. "The Elastic Moduli of FiberReinforced Materials,"J. Applied Mechanics, Vol. 31, pp. 223-232.
22.
Hurlbut, B. J. and M. E. Regelbrugge. 1996. "Evaluation of a Constitutive Model for Shape Memory Alloys Embedded in Shell Structures,"J. Reinforced Plastics and Composites, Vol. 15, pp. 1249-1261.
23.
Liang, C. and C. A. Rogers. 1993."Design of Shape Memory Alloy Springs with Applications in Vibration Control,"ASME Journal of Vibration and Acoustics, Vol. 115, pp. 129-135.
24.
Lim, T. J. and D. L. McDowell. 1999. "Mechanical Behavior of an Ni-Ti Shape Memory Alloy under Axial-Torsional Proportional and Nonproportional Loading,"ASME J. Eng. Mater Technol., Vol. 121, No. 1, pp. 9-18.
25.
Lin, P. , H. Tobushi, K. Tanaka, T. Hattori and K. Uchino. 1994. "Deformation Properties Associated with Martensitic and R-Phase Transformation in TiNi Shape Memory Alloy,"Transaction of JSME, Vol. 60A, No. 569, pp. 126-133.
26.
Lagoudas, D. C. , J. G. Boyd and Z. Bo. 1994. "Micromechanics of Active Composites with SMA Fibers,"ASME Journal of Engineering Materials and Technology, Vol. 116, pp. 337-347.
27.
Lagoudas, D. C. , Z. Bo and A. Oidwai. 1994. "Micromechanics of Active Metal Matrix Composites with Shape Memory Alloy Fibers,"InelasticityandMicromechanics of Metal Matrix Composites, ed. Voyiadjis, G. Z. and Ju, J. W., pp. 163-190, Elsevier Science.
28.
Lagoudas, D. C. , D. Moorthy, M. A. Qidwai and J. N. Reddy. 1997. "Modeling of the Thermomechanical Response of Active Laminates with SMA Strips Using the Layerwise Finite Element Method,"J. Intelligent Material Systems and Structures, Vol. 8, pp. 476-488.
29.
Liu, Y. , Z. Xie, J. V. Humbeeck and L. Delaey. 1998. "Asymmetry of StressStrain Curves under Tension and Compression for NiTi Shape Memory Alloys,"Acta Mater, Vol. 46., No. 12, pp. 4325-4338.
30.
Miyazaki, S. , T. Imai, Y. Igo and K. Otsuka. 1986. "Effect of Cyclic Deformation in the Pseudoelasticity Characteristics of Ti-Ni Alloys,"Metallurgical Transactions, Vol. 17A, pp. 115-120.
31.
Mori, T. and K. Tanaka. 1973. "Average Stress in Matrix and Average Energy of Materials with Misfitting Inclusions,"Acta Metallurgica et Materialia, Vol. 21, pp. 571-574.
32.
Ortiz, M. and J. C. Simo. 1986. "An Analysis of a New Class of Integration Algorithms for Elastoplastic Constitutive Relations,"Int. J. Num. Methods. Engng., Vol. 23, pp. 353-366.
33.
Paley, M. and J. A. Aboudi. 1992. "Micromechanical Analysis of Composites by the Generalized Cells Model,"Mechanics of Materials, Vol. 14, pp. 127-139.
34.
Paine, J. S. N. , C. A. Rogers and R. A. Smith. 1995. "Adaptive Composite Materials with Shape Memory Alloy Actuators for Cylinders and Pressure Vessels,"Journal Intelligent Material Systems and Structures, Vol. 6, pp. 210-219.
35.
Sullivan, B. J.1994. "Analysis of Properties of Fiber Composites with Shape Memory Alloy Constituents,"Journal of Intelligent Material Systems and Structures, Vol. 5, pp. 825-832.
36.
Simamoto, A. , Y. Furuya and M. Taya. 1995. "Active Control of Crack-Tip Stress Intensity by Contraction of Shape Memory TiNi Fibers Embedded in Epoxy Matrix Composite,"Proc. Int. Symp. Micromachine, Intelligent Materials and Robots, MIMR'95, pp. 463-466.
37.
Santis, S. De ., F. Trochu, G. Ostiguy, H. Sol and J. M. Berthelot. 1997. "Material and Structural Characterization of the Dynamic Behavior of Shape Memory Alloy Reinforced Composites,"J. Composite Materials, Vol. 31, No. 19, pp. 1985-1998.
38.
Srinivasan, A. V.1997. "Multiplexing Embedded NiTiNOL Actuators to Obtain Increased Bandwidth in Structural Control,"J. Intelligent Material Systems and Structures, Vol. 8, pp. 202-214.
39.
Shahin, A. R.1997. "Modeling of SMA Tendons for Active Control of Structures,"J. Intelligent Material Systems and Structures, Vol. 8, pp. 51-70.
40.
Song, G. Q. , Q. P. Sun and M. Cherkaoui. 1999. "Role of Microstructure in the Thermomechanical Behavior of SMA Composites,"ASME J. Eng. Mater Technol., Vol. 121, No. 1, pp.86-92.
41.
Tanaka, K.1986. "A Thermomechanical Sketch of Shape Memory Effect: One-Dimensional Tensile Behavior,"Res Mechanica, Vol. 18, pp. 251-263.
42.
Tanaka, K. , S. Kobayashi and Y. Sato. 1986. "Thermomechanics of Transformation Pseudoelasticity and Shape Memory Effect in Alloys,"International J. Plasticity, Vol. 2, pp. 59-72.
43.
Tanaka, K. , 1988. "A Phenomenological Description on Thermomechanical Behavior of Shape Memory Alloys,"Elastic-Plastic Failure Modelling of Structures with Applications, ed. Hui, D. and Kozik, T. J., PVP-Vol. 141, pp. 163-170.
44.
Tanaka, K. , H. Tobushi and S. Miyazaki. 1993. Mechanical Properties of Shape Memory Alloys (in Japanese), Yokendo.
Taya, M. , Y. Furuya, Y. Yamada, R. Watanabe, S. Shibata and T. Mori. 1993. "Strengthening Mechanism of TiNi Shape Memory Fiber/Al Matrix Composite,"Proc. Smart Materials (ed. V. K. Varadan), SPIE, pp. 373-383.
47.
Umezaki, E. , H. Ikebe, E. Kawahara and E. Watanabe. 1995. "Time Dependence of Crack Closure in Epoxy Matrix Composite Material with Embedded SMA,"Proc. Int. Symp. Micromachine, Intelligent Materials and Robots, MIMR'95, pp. 330-333.
48.
Venkatesh, A. , J. Hilborn, J. E. Bidaux and R. Gotthardt. 1992. "Active Vibration Control of Flexible Linkage Mechanisms Using Shape Memory Alloy Fiber-Reinforced Composites,"Proc. Ist European Conf. on Smart Structures and Materials, Glasgow, pp. 185-188.
49.
Yamada, Y. , M. Taya and R. Watanabe. 1993. "Strengthening of Metal Matrix Composite by Shape Memory Effect,"Materials Transactions, JIM, Vol. 34, No. 3, pp. 254-260.
