Generally, the T-N and T-I characteristics of DC motors can be expressed by two straight lines as shown below when the supply voltage is constant.
Basic performance is that when torque (load) becomes higher then speed becomes lower and current becomes higher. On the other hand, when torque (load) becomes lower then speed becomes higher and current becomes lower.
And when supply voltage is changed, T-N, T-I curves move parallel.
DC motors have a rated speed and rated current. Please note these parameters. If the motor is used higher than them, commutator and brush might ware out then shorter life time or get a trouble due to over heating.
In addition, performance of DC motors change by operation temperature.
If the motor operated under higher temperature, winding resistance gets higher and magnet performance gets lower. Finally, DC motor has lower starting torque and higher no-load speed