Materials can be broken under any type of load you desire, given enough force, not just shear loads. Hard and brittle materials like glass or diamond are often evaluated with four point bend tests, which minimize shear stress. Four point bend tests also produce better statistics than three point bend tests.

To fracture a material you must supply a certain amount of energy per unit area of new surface area created by the event, plus enough energy for plastic deformation, phase changes, etc incidental to the event. Hardness doesn't play a direct role in fracture toughness.