0
Technical Brief

Wave Propagation in a Shape Memory Alloy Bar Under an Impulsive Loading

[+] Author and Article Information
Pingping Zhu

Department of Mathematics,
City University of Hong Kong,
83 Tat Chee Avenue,
Kowloon Tong, Hong Kong
e-mail: ppzhu2-c@my.cityu.edu.hk

Hui-Hui Dai

Department of Mathematics,
City University of Hong Kong,
83 Tat Chee Avenue,
Kowloon Tong, Hong Kong
e-mail: mahhdai@cityu.edu.hk

1Corresponding author.

Manuscript received June 6, 2016; final manuscript received July 6, 2016; published online July 27, 2016. Assoc. Editor: Daining Fang.

J. Appl. Mech 83(10), 104502 (Jul 27, 2016) (6 pages) Paper No: JAM-16-1280; doi: 10.1115/1.4034115 History: Received June 06, 2016; Revised July 06, 2016

We analyze wave propagation in a semi-infinite shape memory alloy (SMA) bar under a rectangular impulsive loading. Different trilinear up–down–up nominal stress–strain curves for loading and unloading processes are adopted to complete the dynamical system. The chord criterion (equivalent to maximally dissipative kinetics) is employed to single out the unique solution for the impact problem. The interactions among discontinuities (loading/unloading elastic shock waves and phase boundaries) can yield some complicated wave structure. In particular, it is found that the encounter of the unloading elastic shock wave and the loading phase boundary can yield three different wave patterns depending on the level of impact stress, which are different from those for a hardening response studied in the literature. Solutions in the whole temporal and spatial domain are obtained, which reveal interesting wave structures induced by two different levels of impact. Phase transformation regions and tension/compression regions are also determined. The results also suggest that the SMAs can be used for impact-protection purpose effectively.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Your Session has timed out. Please sign back in to continue.

References

Dai, X. , Tang, Z. P. , Xu, S. , Guo, Y. , and Wang, W. , 2004, “ Propagation of Macroscopic Phase Boundaries Under Impact Loading,” Int. J. Impact Eng., 30(4), pp. 385–401. [CrossRef]
Chen, Y. , and Lagoudas, D. C. , 2005, “ Wave Propagation in Shape Memory Alloy Rods Under Impulsive Loads,” Proc. R. Soc. A, 461(2064), pp. 3871–3892. [CrossRef]
Song, Z. , Dai, H. H. , and Sun, Q. P. , 2013, “ Propagation Stresses in Phase Transitions of an SMA Wire: New Analytical Formulas Based on an Internal-Variable Model,” Int. J. Plast., 42, pp. 101–119. [CrossRef]
Hallai, J. F. , and Kyriakides, S. , 2013, “ Underlying Material Response for Lüders-Like Instabilities,” Int. J. Plast. 47, pp. 1–12. [CrossRef]
Făciu, C. , and Molinari, A. , 2006, “ On the Longitudinal Impact of Two Phase Transforming Bars. Elastic Versus a Rate-Type Approach. Part I: The Elastic Case,” Int. J. Solids Struct., 43(3–4), pp. 497–522. [CrossRef]
Pham, K. , 2014, “ An Energetic Formulation of a One-Dimensional Model of Superelastic SMA,” Continuum Mech. Thermodyn., 26(6), pp. 833–857. [CrossRef]
Abeyaratne, R. , and Knowles, J. K. , 1992, “ On the Propagation of Maximally Dissipative Phase Boundaries in Solids,” Q. Appl. Math., 1(1), pp. 149–172.
Abeyaratne, R. , and Knowles, J. K. , 2000, “ On a Shock-Induced Martensitic Phase Transition,” J. Appl. Phys., 87(3), pp. 1123–1134. [CrossRef]
Făciu, C. , and Molinari, A. , 2006, “ On the Longitudinal Impact of Two Phase Transforming Bars. Elastic Versus a Rate-Type Approach. Part II: The Rate-Type Case,” Int. J. Solids Struct., 43(3–4), pp. 523–550. [CrossRef]
Tobushi, H. , Tanaka, K. , Hori, T. , Sawada, T. , and Hattori, T. , 1993, “ Pseudoelasticity of Tini Shape Memory Alloy (Dependence on Maximum Strain and Temperature),” Int. J. Series A: Mech. Mater. Eng., 36(3), pp. 314–318.
Escobar, J. C. , Clifton, R. J. , and Yang, S.-Y. , 2000, “ Stress-Wave-Induced Martensitic Phase Transformations in NiTi,” AIP Conf. Proc., 505, pp. 267–270.
Lagoudas, D. C. , Ravi-Chandar, K. , Sarh, K. , and Popov, P. , 2003, “ Dynamic Loading of Polycrystalline Shape Memory Alloy Rods,” Mech. Mater., 35(7), pp. 689–716. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

The nominal stress–elongation response of a single NiTi strip and the up–down–up material response (Fig. 4 reprinted from Ref. [4] with permission from Elsevier)

Grahic Jump Location
Fig. 2

The trilinear up–down–up stress–strain curves for tensile/compressive loading and unloading processes

Grahic Jump Location
Fig. 3

Wave structure of the SMA bar under a rectangular impulsive loading for 0≤t≤t1

Grahic Jump Location
Fig. 4

Three possible wave patterns generated by the interaction of the unloading elastic shock wave and the loading phase boundary; the corresponding stress–strain states ahead and behind the discontinuity

Grahic Jump Location
Fig. 5

Wave structure of the SMA bar under a rectangular impulsive loading for σ*=−700 MPa

Grahic Jump Location
Fig. 6

Wave structure of the SMA bar under a rectangular impulsive loading for σ*=−1200 MPa

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In