New analytical model of expansion of spherical cavity in brittle material based on the concepts of mechanics of compressible porous and powder materials

In this paper, the concepts of mechanics of porous and powder media are applied for development of new analytical model of expansion of spherical cavity in brittle materials. The model is based on the approach that recognizes the existence of three regions with different rheology: region of comminuted and compacted material; region of pore formation formed by radial cracks; elastically deformed region. Strain–stress state in each region is determined and analyzed. Cavity expansion pressure is determined. Energy losses on elastic deformation, fracture and compaction of material are calculated and compared for a number of ceramic materials. It is shown that the contribution of compaction and fracture in total energy losses is considerable. The presented model avoids the use of rheological characteristics that are difficult to determine and uses instead the porosity of the material.