When a material is subjected to irradiation, many primary defects are created at the atomic level by sequences of ballistic collision events to form highly disordered regions defined as displacement cascades. The long term evolution of materials under irradiation is dictated by the number and the spatial distribution of the surviving defects in the displacement cascade. The peculiar power law shape of collision cross sections is responsible for the fractal feature of atomic trajectories set and then the fragmentation of a displacement cascade into smaller subcascades. We present a criterion to describe the fragmentation of a displacement cascade into subcascades and to calculate the volume fraction of subcascades in the overall cascade due to this fragmentation. Such a volume fraction then provides a natural framework to estimate the efficiency of different projectiles to induce phase transformation or amorphisation in solids under irradiation. From this definition of the fragmentation of a displacement cascade, this work gives some new insights to compare different irradiations performed with different particles.