Hysteresis effect on austenite-martensite interface in Ni-Mn-Ga single crystal

Coexistence of five domains at single propagating interface in single-crystal Ni Mn Ga shape memory alloy

“…9 shows a uniform region, which should be austenite. In fact, we can measure the mean strain field within each domain with DIC (Digital Image Correlation) to determine its state (austenite, single variant or twin) as discussed in details in (Qin et al, 2023;Zhang et al, 2023). On the other hand, we can also determine the domain's state by the combination of a simple compatibility analysis and the experimentally observed orientations of the domain walls (habit planes and the planes between different twins) and the twin-boundary orientation (the vertical lines in domains I and III) as shown in the following.…”

“…Martensite appears in the form of several variants with different orientations with respect to the austenite parent crystal, and therefore different characteristic transformation strains (Bain strains) are resulted (Ball and James, 1989; M. Pitteri and Zanzotto, 1998;James and Hane, 2000;Pitteri and Zanzotto, 2002;Bhattacharya, 2003). According to equilibrium thermomechanics (Ericksen, 1975;Falk, 1980;James, 1980;Abeyaratne and Knowles, 1991;He and Sun, 2009;Duval et al, 2011;Hallai and Kyriakides, 2013) and the experimental observations (Segui et al, 1996;Glatz et al, 2009;Seiner, 2015;Zhang et al, 2020;Qin et al, 2023;Zhang et al, 2023), the martensite variants and austenite with equal free energy can coexist during the phase transformation, among which there are twin boundaries (separating different martensite variants) and habit planes (separating austenite from martensite twins or variants). To guarantee the deformation reversibility of the phase transformation (avoiding plasticity), the twin boundaries and the habit planes must be compatible (coherent), meaning that the characteristic transformation strains of the different domains (martensite variants, twins, and austenite) must be accommodated without elastic strain (called "perfectly compatible" domain patterns) or with only small elastic strains (so-called "non-perfectly compatible" domain patterns).…”

“…Based on the pioneering work in understanding the basic kinematics and energetics in (Bowles, 1951;Wechsler et al, 1953;Basinski and Christian, 1954;Bowles and Mackenzie, 1954;Roitburd, 1978;Ericksen, 1980;Khachaturyan, 1983;Barsh and Krumhansl, 1984;Pitteri, 1984;Ball and James, 1989;Krumhansl and Gooding, 1989), various interfacial structures, especially the nonperfectly compatible domain patterns, have been intensively studied from 1990 until now (Bhattacharya, 1991;Bhattacharya, 1992;Ruddock, 1994;Shield, 1995;Ball and Carstensen, 1997;Hane and Shield, 1998;M. Pitteri and Zanzotto, 1998;Hane, 1999;Hane and Shield, 1999b;Hane and Shield, 1999a;Hane and Shield, 2000a;Hane and Shield, 2000b;Balandraud and Zanzotto, 2007;Stupkiewicz et al, 2007;Seiner et al, 2008;Balandraud et al, 2010;Levitas et al, 2010;Stupkiewicz and Górzyńska-Lengiewicz, 2012;Seiner et al, 2014;Seiner, 2015;Bronstein et al, 2019;Seiner et al, 2020;Stupkiewicz et al, 2021;He, 2023;Qin et al, 2023;Zhang et al, 2023).…”

“…Particularly, the domain patterns in single-crystal SMAs can clearly indicate the material's crystallographic relations and the associated compatibility requirements. For example, in clean single-crystals with little defects (such as annealed specimens in (Chang and Read, 1951)), the martensitic phase transformation can occur via a single interface propagation passing through a single-crystal specimen under thermal loadings such as a temperature gradient (Basinski and Christian, 1954;Salzbrenner and Cohen, 1979;Christian, 1982;Seiner et al, 2008;He, 2023;Qin et al, 2023;Zhang et al, 2023). The propagating interface can have different structures as classified in Fig.…”

“…By contrast, three-domain coexistence is more common in experiments; see Fig. 1(b) where two basic patterns are shown: (1) Planar interface (one habit plane) involving the austenite, a twin laminate and a single martensite variant, whose detailed evolutions in experiments can be found in the movies of (Qin et al, 2023;Zhang et al, 2023); it has been verified by compatibility analysis that this planar-interface domain pattern is energy-minimizing (Ball and James, 1989;Bhattacharya, 2003;Bronstein et al, 2019;Seiner et al, 2020). ( 2) "Wedge" pattern involving an austenite domain and two different martensite twins (Otsuka and Shimizu, 1974;Saburi and Wayman, 1979;Shusong Tan and Xu, 1990;Bhattacharya, 1991;Otsuka and Wayman, 1998;Bhattacharya, 2003).…”