Change in Young's modulus associated with martensitic transformation in shape memory alloys

Martensitic transformations in Cu-Zn-Al, Cu-Al-Ni, and Ti-Ni alloys are accompanied by so-called elastic anomaly. The values of elastic constant decreases considerably in the transformation temperature range. The magnitude of Young's modulus in parent and martensite phases is then almost equal to each other for single-phase alloys. They are, however, not equal for the particular Cu-Al-Ni-Ti dual-phase alloy containing a large number of small dispersed particles of x-phase. The addition of titanium was aimed to suppress the grain growth of the alloy. The addition of titanium to the alloy will produce precipitates of x-phase which may contribute to give a higher Young's modulus in the parent phase matrix than in the martensite matrix. To interprete this profound difference, the authors proposed a model with varying behavior of interface between x-phase particles and the matrix. According to the law of mixing, Young's modulus should approach the upper bound when the interface is coherent (for the beta(1)-matrix). On the contrary, it should approach the lower bound, when the interface is incoherent (for the beta(1)'-matrix).