Final answer:
Cold working an alloy after it has been precipitation hardened does not increase the peak hardness from the age hardening process; actually, it can negatively affect the material's properties. The statement is therefore false.
Step-by-step explanation:
The statement that cold working of an alloy that has been precipitation hardened increases the peak hardness obtained from age hardening heat treatment is false. Precipitation hardening, or age hardening, involves heating the alloy to a certain temperature and allowing it to cool, causing the precipitation of tiny particles within the metal matrix. These particles hinder the movement of dislocations and enhance the strength and hardness. Cold working after precipitation hardening can actually lead to additional dislocation structures, which might slightly increase hardness initially but at the cost of the beneficial effects of the previous heat treatment, like reduced ductility and possibly initiating cracks. It's essential to understand the sequence and balance of metalworking processes to obtain desired material properties.