Using eigenmoduli and eigenstates to evaluate the possibility of martensitic phase transformations

The possibility of phase transitions (martensitic transformations) in shape-memory alloys is evaluated using the concept of eigenmoduli and eigenstates from the linear theory of elasticity. For alloys with cubic and hexagonal lattices, the matrices of elastic moduli and compl are given and expressions for their eigenmoduli and eigenstates are written. For cubic and hexagonal phases, the specific strain energy is presented as the sum of six independent terms corresponding to six orthogonal eigenstates. It is shown that depending on the ratio of eigenmoduli, there are six types of materials (alloys) with cubic and hexagonal symmetry. The specific strain energies in the cubic and hexagonal phases are compared. If the strain energy is greater in the hexagonal phase than in the cubic phase, the alloy can tend to return to its original state with lower energy. In addition, the strain energies in different phases can be compared using the formulas of the tensors closest in the Euclidean energy norm to cubic and hexagonal tensors. The energies are compared for some values of elastic constants.