This is for you to find out after fabricating the questionable alloy by mechanical alloying whether the fabricated alloy exhibits the property of shape memory and pseudoelasticity. It is an excellent research idea!.
usually for heat treatment of shape memory alloys, particularly NiTi alloy, vacuum furnace is mandatory, otherwise oxide is diffused on material. I also don't recommend mechanical alloying for NiTi alloy based on same problem. Properties are very sensitive to oxide phases.
I have produced Copper based shape memory alloys by mechanical alloying. You may go to my profile and download several papers about powder metallurgy of Copper based SMA, including by mechanical alloying (MA). In particular Cu-Al-Ni SMA.
Just two points. First: I have not startet from pure metals, because Al powder becomes easily oxidized during MA. So I started by a pre-alloyed powder atomized by gas. Second: MA have a tendency to introduce oxide particles inside the material, this is good for hardening structural alloys, but is not good for the functional properties of SMA. So try to avoid oxidation during MA. I used hermetically closed cans, with an o-ring and doing vacuum previously the MA, to avoid oxidation, and eventually after that you may introduce inside pure Ar gas under presion, once the can for MA is mounted in the planetary machine.
After MA you have a powder and you still need to do a compaction. I used Hot Isostatic Pressing (HIP), it works much better than the clasical sintering methos.
Look for the papers on SMA produced by powder metallurgy in my profile.
I forgot to answer your first question. Basically the question is if we need to use vacuum or not during the melting. The answer is YES.
In case of Ti-Ni, the Ti is too reactive with oxigen and vacuum must be used.
In case of Copper based SMA, the main alloys contain also Aluminium, and it becomes also oxidized during melting, because you should go above the melting temperaute of copper. Then, you risk to introduce in the material particles of Al2O3, and in addition the oxidation of Al (Mn) during melting will produce a lost in the effective Al concentration in the alloy. Consequently the transformation temperatures of the SMA become very difficult to be precisely controlled.
In case of using Mn as alloying element, I recommend you to use initially vacuum to degas the material at medium temperature, and introduce Ar gas for the final melting, in order to avoid evaporation of Mn.
In Induction Melting, oxidation will occurs, whereas in Vacuum induction melting no chances of oxidation because of inert gas atmosphere.
For Cu-Al based SMA, you can use induction melting with inert gas setup. For Ni-TI shape memory alloys, must to use vacuum induction melting or vacuum arc melting, because Ti easily reacts with oxygen.