V12 p5
Quenching had strengthened the axe, yes, but it has also made it more brittle. By heating it back up and slowly cooling it, the axe would retain it's toughness but also become more flexible and less prone to breakage. In not sure if this was an error of the original author (there have been many in this series) or an error in translation, but there are a few incorrect uses of technical terms here.
In metallurgy, strength can refer to several different properties. Quenching does not improve all of them and in fact reduces some.
Quenching increases hardness (the resistance to abrasion and ability to hold a fine cutting edge) in steel(but not in most other metals), at the cost of dramatically reducing toughness, which is the opposite of brittleness and describes the ability to survive impact without damage or deformation.
A more technically correct way to describe the process is that quenching hardened the steel, making it more brittle, and tempering (the process of reheating to a lower temperature after quenching) allows the steal to regain lost toughness while retaining most of the hardness gained through quenching.
There are a handful of other inaccuracies on the forging process but they seem unlikely to be the result of a translation error, whole sentences are wrong rather than one technical term being swapped for a different one with a similar meaning.