Multi-Scale Dynamics of Twinning in SMA

Abstract

The mechanical response of shape memory alloys (SMA) is determined by the dynamics of discrete twin boundaries, and is quantified through constitutive material laws called kinetic relations. Extracting reliable kinetic relations, as well as revealing the physical characteristics of the energy barriers that dictate these relations, are essential for understanding and modeling the overall twinning phenomena. Here, we present a comprehensive, multi-scale study of discrete twin boundary dynamics in a ferromagnetic SMA, NiMnGa. The combination of dynamic-pulsed magnetic field experiments, in conjunction with low-rate uniaxial compression tests, leads to the identification of the dominant energy barriers for twinning. In particular, we show how different mechanisms of motion for overcoming the atomic-scale lattice potential give rise to several kinetic relations that are valid at different ranges of the driving force. In addition, a unique statistical analysis of the low-rate loading curve allows distinguishing between events at different length scales. This analysis leads to the identification of a characteristic length scale (*15 lm) for the distance between barriers that are responsible for the twinning stress property. This characteristic distance is in agreement with the typical thickness of the internal micro-twin structure, which was recently found in these materials.

Highly mobile interfaces in shape memory alloys

“…For pulse-like magnetic field loads, a detailed study of mobility of Type 1 and Type 2 interfaces can be found in the above mentioned papers by Faran and Shilo [25][26][27][28][29]. The main conclusion from this study is that the dynamic behavior of the interfaces exhibits some kind of bimodal behavior: for low driving forces, the interfaces move by a nucleationand-growth mechanism, which involves thermal activation.…”

“…However, it is hard to decide whether such pinning is in any relation with the experiments and at which of the spatial scales it can be expected. The characteristic spacing between the obstacles (∼10−50μm) resulting from the analysis of mobility given in [25][26][27][28][29] seem to relate to the characteristic thickness of the a−b lamina observed by Chulist et al [41]. However, the differences between the Type 1 and Type 2 interfaces were observed also for alloys with a ≈ b [48], which proves that such a pining is not a dominant mechanism.…”

“…This assumption is further supported by the fact that the stress-strain curves for crystals with Type 1 interfaces show more pronounced jerkiness [10], which may correlate with stronger pinning of the Type 1 interface on the defects. Faran and Shilo [25][26][27][28][29] studied this jerkiness in more details, and showed that fine oscillation of the stress-strain response may correspond to pinning on obstacles with a characteristic spacing of approximately 10−50 μm; see also [30] for the analysis of this jerkiness by acoustic emission measurements. However, these fine oscillations were reported by Faran and Shilo [27] for both Type 1 and Type 2 interfaces (for the latter, this effect was also confirmed by observations by Barabash et al [31]), and so the relation between these 'obstacles' and the difference in thermal dependences of Type 1 and Type 2 twinning stresses becomes questionable.…”

“…The micro-morphology of such interfaces was shown to have a multi-scale hierarchical character by Barabash et al [42] for the case of 10 M martensite of NiMnGaFeCu. Typically, this complex structure is not discussed in the theoretical models of motion, including those of the mobility of the twins by Faran and Shilo [25][26][27][28][29] as well as continuum mechanics or phase field models of MIR [43,44]. Nevertheless, the theoretical twinning stress calculated for the symmetric Type 1 interface as for a perfect twinning plane by first-principles atomistic simulations [45] (3.5 MPa) is significantly higher than the experimentally observed values (0.5-1 MPa); this discrepancy may indicate that the finer structure may destabilize the interface and affect the twinning stress.…”

A discrete twin-boundary approach for simulating the magneto-mechanical response of Ni–Mn–Ga

“…This region is marked by a gray background in figure 1. The second parameter, g , 0 is related to the lattice barrier that resists twin boundary motion, and defines the transition value between slower thermally activated kinetics and faster a-thermal motion (see detailed discussion on this issue in [29][30][31][32]43]). For driving force values that fall between g ts and g 0 the velocity of a twin boundary follows an exponential type relation (equation ( 4)).…”