What happens to the semiconductor in an LED when it is given voltage that it cannot handle?
what will happen to the material?


The LED may experience an incident of Electrical Overstress (EOS).  This depends upon if the supply can source more current than the LED's maximum allowed current. And if the LED can tolerate the supply's maximum current whether the supply's voltage output will reduced itself to the LED's forward voltage. Over current and over voltage (i.e. over driven) will result in an EOS event.

EOS damage in LEDs can be catastrophic in that the 
LED is permanently non-functional immediately after the EOS event; alternatively there may be just partial damage whereby a significant degradation in performance or the complete failure of the LED only occurs later on. Partial EOS damage in LEDs might manifest itself as reduced light output, poor thermal performance, and/or a shorter service life.

When an LED is overdriven the failures here include the thermal overstressing of the semiconductor or a fused wire bond.  Notice in the photo below the stress is greatest where the bond wire is attached to the semiconductor material. 

Example of a fused wire bond
In this experiment, an LED with a 250 mA max was driven with 1000 mA, four times the data sheet 
maximum current.   Failure occurred in about 
10–20 seconds.




X-Ray of the above LED failure mode



In the image below the same LEDs were driven with a single pulse of 3000 mA for 300 ms. Due to the higher power load, the bond wire melted.



Source: The Basic Principles of Electrical Overstress (EOS) App Note