There are two types of fracture found for most engineering materials, either ductile or brittle.
Ductile fracture is characterised by large amounts of plastic deformation before failure. This form of fracture involves large amounts of energy absorption (high toughness).
Brittle fracture is characterised by low plastic deformation and small amounts of energy absorption at failure (low toughness).
It takes a lot of force to deform a glass rod. With the load shown the rod is not broken.
But if the rod has a small notch, the force required to cause fracture is greatly reduced, and the rod breaks. Observe how the fracture originates from the notch.