We have measured the changes in the ultrasonic wave velocity, induced
by the application of uniaxial stresses in a Cu-Al-Ni single crystal.
From these measurements, the complete set of third-order elastic const
ants has been obtained. The comparison of results for Cu-Al-Ni with av
ailable data for other Cu-based alloys has shown that all these alloys
exhibit similar anharmonic behavior. By using the measured elastic co
nstants in a Landau expansion for elastic phase transitions, we have b
een able to give an estimation of the value of a fourth-order elastic
constants combination. The experiments have also shown that the applic
ation of a stress in the [001] direction, reduces the material resista
nce to a (110)[1(1) over bar0$] shear and thus favors the martensitic
transition.