Crushing and fragmentation of brittle spheres under double impact test

Brittle spheres are crushed and fragmented between two rigid platens dynamically. More than 140 plaster spheres with two different strengths (37 and 59 MPa) and three different sizes (50, 60 and 75 mm) were tested. The impact energies varied from 10 J to over 300 J with impact velocities ranging from 1 to 9 m/s. Twelve different failure patterns are identified, depending on the number of fragments and severity of crushing around the axis of compression. In general, fragments resulted from the double dynamic impact are of two different sizes, namely larger fragments resulted from primary fractures (mainly passing through a diameter of the sphere) and smaller fragments resulted from secondary fractures (do not pass through a diameter of the sphere). The number of smaller fragments increases with the impact energy. The cumulative mass of all fragments of size larger than d [i.e. R(d)] can be fitted into a power law of d (or the so-called Gates-Gaudin-Schuhmann distribution), but there are two distinct slopes of the double-log scale plot of R(d) versus d. The power index n of the larger-fragment-fit is, in general, larger than that of the smaller-fragment- fit. Typically, n ranges from 0.8 to 1.6 and decreases with the impact energy and strength of the sphere. The diameter of the end crushing zone is found approximately proportional to m1/4r1/4v1/2, where m is the mass of the impactor, r is the radius of the sphere and v is the impact velocity. In addition, taking into account of kinetic energy loss, crushing modulus as well as specific fracture energy were obtained for the spheres.