Abstract
A phase transformation constitutive relation including the effect of strain gradient is introduced to examine the extension of a thin wire. The resulting equilibrium equation in terms of strain is a nonlinear (even for small strain deformation) third order differential equation while that of the conventional elasticity theory is only first order and linear for small strain. Additional boundary conditions over those of the conventional theory are needed to make the solution unique and can be derived from a variational functional. The solutions show necking, bulging and periodic striation. We have established the closed form solution for phase transformation with trilinear stress-strain relation and examined the phase transformation behavior in details.
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References
Shaw, J.A. and Kyriakides, S., Thermomechanical Aspects of NiTi, J. Mech. Phys. Solids, 43(1995), pp. 1243–1281.
Sun, Q. P., and Hwang, K. C, Micromechanics modeling for the constitutive behaviors of polycrystalline shape memory alloys, J. Mech. Phys. Solids, 41 (1993) 1–33.
Coleman, B. D., Necking and drawing in polymeric fibers under tensions, Arch. Ration. Mech. Analysis, 83 (1983), pp. 115–137.
Sun, Q. P., Li, Z. Q. and Tse, K. K. (2000), On superelastic deformation of NiTi shape memory alloy micro-tubes and wires, in Proceedings of IUTAM Symposium on Smart Structures and Structronic Systems (Gabbert and Tzou Eds.), Kluwer Academic Publisher, pp. 113–120.
Zhong, Z., Sun, Q. P. and Tong, P.: On the elastic axisymmetric deformation of a rod containing a single cylindrical inclusion, Int. J. of Solids and Struct., 37 (2000), pp. 5943–5955.
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© 2002 Springer Science+Business Media Dordrecht
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Tong, P., Lam, D.C.C., Sun, Q.P. (2002). Phase Transformation of Thin Wires in Tension. In: Sun, Q.P. (eds) IUTAM Symposium on Mechanics of Martensitic Phase Transformation in Solids. Solid Mechanics and Its Applications, vol 101. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0069-6_27
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DOI: https://doi.org/10.1007/978-94-017-0069-6_27
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6071-6
Online ISBN: 978-94-017-0069-6
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