The relative stability of dislocations embedded in the β phase matrix and in martensite phases in copper based alloys

Dislocations are observed in many shape memory alloys after thermal or stress cycling. The amount of dislocations (with Burgers vector $\text{b}{}_{\mathrm{\beta }}\text{= a}{}_0\text{〈010〉}$ and 〈1̄11〉 line direction in the β phase) increases with the number of cycles. The dislocations are accumulated in the sample and are incorporated in the corresponding growing phase. The relative energy of the dislocations when embedded in the parent phase or in one or another variant of martensite is evaluated in this work. The crystallographic changes of the dislocations provide a primary selection rule for those martensite variants in which the dislocations have the lowest energy. In order to proceed more quantitatively a full calculation of the dislocation energies has to be performed using the anisotropic theory. In this work these calculations have been made on the basis of measured elastic constants of the β and 2H phases of a Cu-Al-Ni alloy. It is found that a given dislocation could indeed have different energies depending whether it is embedded in the β phase or one or another oriented variant of martensite. In particular, those dislocations with Burgers vector lying on the basal plane of the 2H martensite show the lowest energy as compared to their self energy when embedded in other oriented variants (Burgers vector out of the basal plane) or in the β phase.