From Encyclopedia Awesomica
Breaking down is one of three options to get rid of an unwanted item. The others are selling it back to the equipment store and dropping it off in your guild repository. Breaking down an item yields a variety of materials, the amount of which depends on if the item has been previously upgraded at the blacksmith and the stats of the item, and the process completely and irrevocably destroys the item.
The amount of materials gained from breaking down can vary, and the calculation to determine the amount depends on whether the item has been upgraded at the blacksmith previously or not.
Previously Upgraded Items
If an item has been upgraded at the blacksmith, it will yield 50% of the materials used to upgrade when it is broken down, with the exception of unobtainium. In some cases, this could result in less material yield than if the item had never been upgraded.
If an item had never been upgraded at the blacksmith, it will yield the square root of the stat pertaining to each type of material, rounded down with a minimum of 1 for postitive stats. For example, if an item has 10 hit and 1 crit, it will yield 9 enchanted eyes and 1 basilisk venom.
Given the above information, and considering the relative scarcity of materials, breaking down an item is often a wise choice. However, breaking down stronger and stronger items suffers from diminishing returns. Therefore, it is always sensible to breakdown cheap items with low numbers, and rarely sensible to breakdown items with high stats across the board, unless the blacksmith was used to create those high stats.