Rate-dependent domain spacing in a stretched NiTi strip. (English) Zbl 1196.74162
Summary: Superelastic fine-grained Nickel-Titanium (NiTi) polycrystalline shape memory alloys under tensile loading deform collectively via the nucleation and growth of macroscopic martensite domains. Recent experiments on a stretched NiTi strip showed that the number of nucleated domains (or the domain spacing) increased (decreased) with increasing applied stretching rate. It is also shown that the rate dependence of the domain formation is due to the coupling between the transfer of the locally released heat and the temperature dependence of the transformation stress. In this paper, a simple one-dimensional model is developed to quantify this effect of thermo-mechanical coupling on the observed domain spacing. Analytical relationship between the domain number, thermo-mechanical properties of the material, heat transfer boundary conditions and the externally applied strain rate is established. It is found that for the case of strong heat convection the domain spacing is inversely proportional to the applied stretching rate, while for the case of weak convection, the domain spacing is dictated by a power-law scaling with exponent - 0.5. The latter theoretical prediction agrees well quantitatively with the experimental data in stagnant air.
MSC:
| 74N05 | Crystals in solids |
| 74F05 | Thermal effects in solid mechanics |
| 80A22 | Stefan problems, phase changes, etc. |
| 80A20 | Heat and mass transfer, heat flow (MSC2010) |
Keywords:
rate-dependent domain spacing; power-law scaling; thermo-mechanical coupling; martensitic phase transition; NiTi polycrystalline shape memory alloy; self-organized domainsReferences:
| [1] | Abeyaratne, R.; Knowles, J. K.: A continuum model of a thermoelastic solid capable of undergoing phase transitions, J. mech. Phys. solids 41, 541-571 (1993) · Zbl 0825.73058 · doi:10.1016/0022-5096(93)90048-K |
| [2] | Amalraj, J. J.; Bhattacharyya, A.; Faulkner, M. G.: Finite-element modeling of phase transformation in shape memory alloy wires with variable material properties, Smart mater. Struct. 9, 622-631 (2000) |
| [3] | Bruno, O. P.; Leo, P. H.; Reitich, F.: Free boundary conditions at austenite – martensite interfaces, Phys. rev. Lett. 74, 746-749 (1995) |
| [4] | Brinson, L. C.; Schmidt, I.; Lammering, R.: Stress-induced transformation behavior of a polycrystalline niti shape memory alloy: micro and macro-mechanical investigations via in situ optical microscopy, J. mech. Phys. solids 52, 1549-1571 (2004) · Zbl 1159.74300 · doi:10.1016/j.jmps.2004.01.001 |
| [5] | Churchill, C. B.; Shaw, J. A.; Iadicola, M. A.: Tips and tricks for characterization shape memory alloy wire: part 3: localization and propagation phenomena, Exp. tech. 33, 70-78 (2009) |
| [6] | Delaey, L.; Krishnan, R. V.; Tas, H.; Warlimont, H.: Review thermoelasticity, pseudoelasticity and the memory effects associated with martensitic transformations, part 1. Structural and microstructural changes associated with transformations, J. mater. Sci. 9, 1521-1535 (1974) |
| [7] | Favier, D.; Louche, H.; Schlosser, P.; Orge’as, L.; Vacher, P.; Debove, L.: Homogeneous and heterogeneous deformation mechanisms in an austenitic polycrystalline ti – 50.8 at.% ni thin tube under tension. Investigation via temperature and strain fields measurements, Acta mater. 55, 5310-5322 (2007) |
| [8] | Feng, P.; Sun, Q. P.: Experimental investigation on macroscopic domain formation and evolution in polycrystalline niti microtubing under mechanical force, J. mech. Phys. solids 54, 1568-1603 (2006) |
| [9] | Feng, P., He, Y.J., Sun, Q.P., in press. Strain rate effects on morphology and temperature evolution of NiTi shape memory alloys strips subject to uniaxial tensile loading. In: Proceeding of 20th International Conference on Adaptive structure and Technologies. |
| [10] | Grabe, C.; Bruhns, O. T.: On the viscous and strain rate dependent behavior of polycrystalline niti, Int. J. Solids struct. 45, 1876-1895 (2008) · Zbl 1149.74015 · doi:10.1016/j.ijsolstr.2007.10.029 |
| [11] | He, Y. J.; Sun, Q. P.: Effects of structural and material length scales on stress-induced martensite macro-domain patterns in tube configurations, Int. J. Solids struct. 46, 3045-3060 (2009) · Zbl 1167.74526 · doi:10.1016/j.ijsolstr.2009.04.005 |
| [12] | He, Y. J.; Sun, Q. P.: Scaling relationship on macroscopic helical domains in niti tubes, Int. J. Solids struct. 46, 4242-4251 (2009) · Zbl 1176.74073 · doi:10.1016/j.ijsolstr.2009.08.013 |
| [13] | He, Y. J.; Sun, Q. P.: Macroscopic equilibrium domain structure and geometric compatibility in elastic phase transition of thin plates, Int. J. Mech. sci. 52, 198-211 (2010) |
| [14] | He, Y. J.; Yin, H.; Zhou, R. H.; Sun, Q. P.: Ambient effect on damping peak of niti shape memory alloy, Mater. lett. 64, 1483-1486 (2010) |
| [15] | Holman, J. P.: Heat transfer, (2010) |
| [16] | Iadicola, M. A.; Shaw, J. A.: Rate and thermal sensitivities of unstable transformation behavior in a shape memory alloy, Int. J. Plast. 20, 577-605 (2004) · Zbl 1134.74345 · doi:10.1016/S0749-6419(03)00040-8 |
| [17] | Leo, P. H.; Shield, T. W.; Bruno, O. P.: Transient heat transfer effects on the pseudoelastic behavior of shape-memory wires, Acta metall. Mater. 41, 2477-2485 (1993) |
| [18] | Li, Z. Q.; Sun, Q. P.: The initiation and growth of macroscopic martensite band in nano-grained niti microtube under tension, Int. J. Plast. 18, 1481-1498 (2002) |
| [19] | Muller, I.; Villaggio, P.: A model for an elastic – plastic body, Arch. ration. Mech. anal. 65, 25-46 (1977) · Zbl 0366.73038 · doi:10.1007/BF00289355 |
| [20] | Ng, K. L.; Sun, Q. P.: Stress-induced phase transformation and detwinning in niti tubes, Mech. mater. 38, 41-56 (2006) |
| [21] | Pieczyska, E. A.; Gadaj, S. P.; Nowacki, W. K.; Tobushi, H.: Investigation of nucleation and propagation of phase transitions in tini SMA, Qirt j. 1, 117-128 (2004) |
| [22] | Pieczyska, E. A.; Gadaj, S. P.; Nowacki, W. K.: Phase-transformation fronts evolution for stress- and strain- controlled tension tests in tini shape memory alloy, Exp. mech. 46, 531-542 (2006) |
| [23] | Puglisi, G.; Truskinovsky, L.: Thermodynamics of rate-independent plasticity, J. mech. Phys. solids 53, 655-679 (2005) · Zbl 1122.74318 · doi:10.1016/j.jmps.2004.08.004 |
| [24] | Shaw, J. A.; Churchill, C. B.; Iadicola, M. A.: Tips and tricks for characterization shape memory alloy wire: part I — differential scanning calorimetry and basic phenomena, Exp. tech., 55-62 (2008) |
| [25] | Shaw, J. A.; Kyriakides, S.: Thermo-mechanical aspects of niti, J. mech. Phys. solids 43, 1243-1281 (1995) |
| [26] | Shaw, J. A.; Kyriakides, S.: On the nucleation and propagation of phase transformation fronts in a niti alloy, Acta mater. 45, 683-700 (1997) |
| [27] | Shaw, J. A.; Kyriakides, S.: Initiation and propagation of localized deformation in elasto-plastic strips under uniaxial tension, Int. J. Plast. 13, 837-871 (1998) |
| [28] | Shaw, J. A.: Simulations of localized thermo-mechanical behavior in a niti shape memory alloy, Int. J. Plast. 16, 541-562 (2000) · Zbl 1043.74525 · doi:10.1016/S0749-6419(99)00075-3 |
| [29] | Sun, Q. P.; Li, Z. Q.: Phase-transformation in superelastic niti polycrystalline microtubes under tension and torsion? from localization to homogeneous deformation, Int. J. Solids struct. 39, 3797-3809 (2002) |
| [30] | Sun, Q. P.; He, Y. J.: A multiscale continuum model of the grain-size dependence of the stress hysteresis in shape memory alloy polycrystals, Int. J. Solids struct. 45, 3868-3896 (2008) · Zbl 1169.74519 · doi:10.1016/j.ijsolstr.2007.12.008 |
| [31] | Zhang, X. H.; Feng, P.; He, Y. J.; Yu, T. X.; Sun, Q. P.: Rate dependence of macroscopic domain patterns in stretched niti strips, Int. J. Mech. sci. (2010) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
