Why at low temperatures ductile material fails in brittle manner? (What changes takes place at low temperatures in ductile material that they fail in brittle manner?)

This is actually a very restricted question in the manner that not all materials show this, not all conditions suit this, and not every time we are gonna observe this situation.

First, for briefing, there is temperature known as ductile to brittle transition below which the ductile material starts to slowly behave as a brittle material. The energy than absorbed is less and the fracture occurs at lower stress values.

But this is only fixed to some crystals like BCC where The yield stress is a strong function of temperature and usually not observed in FCC since the yield stress is not a strong temperature function. The fracture is stress is not a strong temperature function.

So in BCC when Temperature is lower than the intersection(see fig) of the fracture and yield stress the yield stress being more supports the brittle fracture.

This can be interpreted by the fact that BCC has more number of slip systems but most of them are inactive. The strain produced by the solute atoms is more in BCC as the distortion is larger in the Octa voids, Also, due to less close pack planes and less diffusion and other dislocations movement being restricted to the materials stores lots of strains.  This usually makes the crystals harder and harder as we go on decreasing the temperature and a temperature limit comes when no more sufficient movement and deformation are seen and the materials can’t deform as ductile and slowly becomes brittle. But at higher temperatures, more slip systems and processes like climb are active which increases the motion ad ductile behavior is prominent.

On the contrary, The FCC metals which have more mechanism of slipping are usually not dependent much on temperature. the Slip system in FCC is close pack one and there are methods like Cross slip which readily occurs so that dislocation can move and ductility is maintained. So they don’t show such transitions.

So you see that not always it is the nature of ductile materials to have brittle fractures it’s only certain conditions like BCC crystals, notches or higher strain rates which can trigger them.