In media-assisted machining, thermal and mechanical properties of a high-pressure

jet of water or emulsion are directed into the cutting zone to ameliorate conventional machining of difficult-to-cut materials such as advanced Ni and Ti alloys for aerospace. High-pressure coolant can provide benefits such as efficient chip break-ability and reduction in cutting forces, especially in difficult-to-cut materials. It can also improve lubrication and reduce thermal loads on the cutting tool. 

You can read:

1. Current status and applications of hybrid micro-machining processes: A review

2. Surface integrity in cryogenic machining of nickel based alloy—Inconel 718

During machining, energy evolves at the chip-tool interface. The cutting temperature in case of advanced tool materials can be as high as 800 - 1000 C (The temperature is so high because to extract the benefit of advanced tool materials, the material removal rate is increased intentionally). During cryogenic cooling (say with liquid nitrogen jet), the jet is directed towards the cutting zone and it may bring down the temperature from 900 C to 650 C. It does not bring down the temperature to cryogenic temperature and thus embrittlement under cryogenic cooling does not take place.

You may refer to the following papers on the application of cryogenic cooling machining Ti-alloys:

Article Growth of tool wear in turning of Ti6Al4V alloy under cryoge...

Article Tool wear in cryogenic turning of Ti-6Al-4V alloy

Article Turning of titanium alloy with TiB 2 -coated carbides under ...