From crystallographic properties to macroscopic detwinning strain and magnetisation of Ni-Mn-Ga magnetic shape memory alloys

Abstract
In this present work, all the known crystallographic structures of Ni-Mn-Ga alloys (i.e. 5M, 7M and NMT martensitic structures) are considered and their properties are used to deduce the macroscopic detwinning strain and magnetisation of a single crystal by a change of scale. The microstructure configurations of twin martensitic bands in a single crystal are worked out using the nonlinear kinematic theory. The process of rearrangement (or detwinning) of twin martensites is rigorously studied. Detwinning strain, material rotation induced by detwinning and orientation between twin martensitic structures are investigated for a single crystal. Numerical applications shows that results are very sensitive to lattice parameters. A comparison with estimated values shows slight difference, as bigger as, lattice parameter a is greater (or smaller) than c. Magnetic properties are also examined. In order to deduce macroscopic physical quantities from microscopic ones, a Representative Volume Element (RVE) which is representative of the whole material is introduced. By a change of scale, partial detwinning strain and magnetisation are expressed as functions of microstructure parameters, such as, volume fraction of one of twin martensites, length ratio of two consecutive magnetic domains and lattice parameters. These results will be used to performed modeling of magneto-mechanical behavior of Ni-Mn-Ga alloys initially proposed by authors.