Kinetics of materials with wiggly energies: Theory and application to the evolution of twinning microstructures in a Cu-Al-Ni shape memory alloy

Theory of phase transformation and reorientation in single crystalline shape memory alloys

“…A complex interior hysteresis loop was observed in uniaxial tensile tests in single crystalline shape memory alloys [47][48][49][50][51][52][53], and a similar phenomenon has been reported in martensite reorientation between two martensite lattice correspondence variants [34]. These interior hysteresis loops were given various names, such as internal elasticity, internal yield and internal recovery in the literature (for example figure 2 in [48], figures 1 and 4 in [49], figures 4, 5 and 8 in [50]).…”

“…It is obvious that if the habit plane variants are chosen as potential wells, martensite reorientation cannot be properly described, since reorientation happens among lattice correspondence variants, which are subunits of habit plane variants. A particular example is discussed in [34]. In some of the previous models [12,[36][37][38][39], lattice correspondence variants are chosen as potential wells instead of habit plane variants.…”

“…It uses the Cauchy-Born hypothesis, where minimum total free energy is required for any mechanical response. The total free energy usually comprises deformation energy (or elastic strain energy) and loading device energy (refer to equation (13) in [34], and equation (8) in [35]). The deformation energy is assumed to be a smooth function of temperature and deformation gradient.…”

The Simply Laminated Microstructure in Martensitic Crystals that Undergo a Cubic-to-Orthorhombic Phase Transformation

“…A typical example of such a crystal is the shape-memory alloy Copper-Aluminum-Nickel (Cu-Al-Ni) single crystal which is widely used for experimental studies of the shape-memory effect, see for example [2,16,22,23,38,42], and which has motivated various theoretical studies including [2,11,28,29]. A crystal capable of undergoing such a transformation has six variants of martensite, each pair of variants being rank-one connected.…”

“…This gives some rigorous justification for the assumption made in most of analytical and computational investigations of the Chu-James experiment (cf. [16]) that the deformation gradient can be modeled by a two-well problem [1,2,7,25,28,29].…”