Acids are usually corrosive but what determines this? Is it the concentration of the acid or strength of the acid ($K_a$ value)?
Corrosiveness of an acid is a more complex concept, of course the concentration of the acid and the strength of the acid are two main factors that determinate the success of the corrosion reaction. For example this is the Pourbaix diagram of iron both concentration and $K_a$ determine the pH of the solution so if this is higher then about 9 the metal is passivate and you can't have any corrosion.
I add to these another important factor: temperature.
In some case the corrosiveness is due to a more complex interaction that is directly linked to the material you are dealing. One example is acqua regia in this case the strong corrosiveness is due to the couple effect of two different acid that are able to de-passivate the metal allowing an enhanced corrosive effect on noble metals. However acqua regia is not the best choice for an organic material in this case Piranha Solution has a greater corrosive effect.