On a simple lathe cut, what happens to the energy? Energy being force time distance and both are happening.
...
I guess some energy must go to shearing.
That's true; you have (at least) to break the chemical bond that holds the material together,
and the amount of energy must be at least the area of the newly created surface
times the energy per square inch that is the 'shear strength' of the material.
The Charpy shear test is intended to determine this energy.
There's also reformation of the bonds near the surface (cold working) especially
if the tool is dull... and plows rather than shearing.
That surface energy is why heavy cuts and coarse grinding is preferred for fast
material removal: it's more energy efficient, makes the least new surface.
On really tough materials, any fracture, rather than parting cleanly, takes a forked
path (forced sideways by inclusions like glass in fiberglass, or by vanadium
carbide needle crystals in tool steel) so that much additional energy can be
absorbed. Deformation like that causes local heating, so sharp hard tools
that slice clean are energy-savers; sharp abrasive grains are very effective. Accidental adhesion
with the tool causes friction heating, so cutting 'lubricant' also lessens the
energy need (it poisons the surface sites that would form weld-like bonds
with the cutting tool). The TiN coatings also deter bonding with some
sticky metals (aluminum for one). The cutting tool relief angle, and any chip-breaker
grooves, lessen the energy cost by reducing such adhesion, too.
Some alloys and some tools are just TOO weld-prone, or worse. That's why
diamond wheels are less effective than CBN on steel.
Chemistry, and physics, are complex enough that it's easier to cut-and-try than to predict.
For well-understood physics and quick cuts, use shaped-charge explosives. There,
you want prediction rather than trial-and-error.