Final answer:
Ductile materials fail at a 45-degree plane due to the presence of line defects called edge dislocations. These dislocations are responsible for the materials' ductility and malleability and their movement allows for plastic deformation. This weakening of the structure in a one-dimensional space is a key factor in the failure of ductile materials.
Step-by-step explanation:
When a ductile material fails at a 45-degree plane, it is due to the presence of line defects, specifically edge dislocations. Edge dislocations are responsible for the ductility and malleability of materials. Their movement allows for plastic deformation, such as hammering and stretching. Line dislocations typically form loops or end at the surface of a single crystal. These dislocations weaken the structure along a one-dimensional space and affect the mechanical properties of the material.