The Fracture Mechanics of materials is very important because it can tell you how a material will likely break before it does.  It can tell you if there will be medical problems if the titanium rod breaks in an artificial hip.  It is able to do this by using the crystallographic make-up to predetermine how the atoms or molecules in a material will slide and deform when a stress is applied.

For example, in the picture above, a deformed region is definitely visible as the jagged edge between the two more ordered looking areas.  You can obviously ascertain that the break happened between the two pieces.  However, with a greater knowledge of Material Science & Engineering, you could also venture to guess that this sample was also a brittle metal (most likely a brass or a cast iron) purely based upon the shape and look of the fracture. 

Every type of material breaks in a certain way.  It is the way these materials break that makes them better or worse for certain application.  Polymers break differently than metals, metals break differently than ceramics, and ceramics break differently than polymers.  These breaks in deformations can give the engineer or scientist a very good clue as to what is causing the breakage.