Cracking in a loaded, brittle elastic half-space

An approximation giving the relation between the applied load and the crack density in a microscratch test is presented from considerations of sliding contact and fracture analysis. First, the three-dimensional problem of two interacting cracks, with arbitrary shape and configuration, in an elastic half-space is analyzed using the body force method. Then, the analysis is specialized to study the surface cracking which occurs due to the indenter sliding over the rough, brittle half-space. Numerical examples are given for point contact by a spherical indenter sliding over a zirconia ceramic and the shielding effects between two adjacent surface cracks with different spacings are discussed in the context of the determination of crack density.