The central aim of this work is to investigate energy input required for initiation of fracture within quasibrittle media with existing defects. As a model problem, a solution for a central crack in a plane subjected to load applied at infinity is considered. Density of energy that should be introduced into the plane in order to create conditions leading to fracture in the tip of the existing central crack is studied. Situations corresponding to fracture created by purely compressive loading, fracture created by pure shear and fracture created by combination of compressive and shearing load with different intensity ratios are investigated. It is found, that combination of compressive and shearing load is resulting in significantly lower energies spent for creation of fracture as compared to energies corresponding to purely compressive loading. These estimates are qualitatively coinciding with phenomena observed experimentally for processes connected with grinding and fragmentation of quasibrittle heterogeneous media with existing defects (cracks). Earlier it was shown that for grinding of rocks and other similar materials, addition of shear component to compressive impact loading applied to the fractured media results in significant reduction of the process energy consumption. The results received in this paper can be used for prediction of optimal energy saving parameters for industrial machines working for grinding and fragmentation of quasibrittle materials.