This may come in our mind that what exactly will happen if we operate a DC Motor at a speed more than the rated speed. In fact, the thermal capacity of the motor decides at what speed it can run and for how long. There is always a safety factor considered in the design which lets one to operate a motor for about 30% above its rated speed.
The diagram describes torque speed characteristics of a DC Motor. The knee point here gives the rated speed.
After the knee point the back EMF of the motor, which is directly proportional to the speed, increases such that the motor is no longer able to maintain the toruqe. Any increase in current would require a proportional increase in supply voltage, which is generally fixed. Hence after this point the motor operates in constant power mode as the back EMF keeps on increasing and the current keeps on reducing.
As the current is reducing continuously, the motor torque also reduces in proportion. Again, the back EMF produced in the windings is proportional to speed and at high speeds it can be so high that the windings may flashover and burn.
Also, High speed causes the rotor to experience high centrifugal forces and the shaft can break apart causing the motor to catastrophically explode. Thus motor shall only be operated within the safety margin.
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