Initiation of parallel cracks from surface of elastic half-plane

Abstract

The paper deals with the problem of initiation of thermal or shrinkage cracks from the surface of a half plane. Linear elastic fracture behavior is assumed. The initial spacing and initial stable equilibrium length of parallel equidistant cracks emanating from the surface is determined from three conditions formulated in a preceding study of penetration of sea ice plate: (1) The stress at the surface reaches a given strength limit. (2) After the initial cracks form, the energy release rate equals its given critical value. (3) The finite energy release due to the initial crack jump equals the energy needed to form the crack (according to the given fracture energy of the material or fracture toughness). The problem is reduced to a singular integral equation which is solved numerically by Erdogan's method. The results of analysis appear to be compatible with the experimental evidence on thermal cracking in glass, and appear to give also reasonable predictions for thermal cracking on top of sea ice plates and shrinkage cracking in concrete.