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.

Theory of Crack Spacing in Concrete Pavements

“…As a result, one finds that 2L = 21 0 , This analysis shows that 10 is simply the ratio of the specific elastic strain energy to the fracture energy, which is why 10 is one of the main factors that determine the crack spacing. This minimum value of crack spacing was also obtained by Li et al (1995) in their study of spacing of parallel cracks initiated from the surface of an elastic half plane. For more general loading, the strain energy that can be stored, as well as the fracture energy needed, depend on the crack depth.…”

“…10330. fracture energy of the material. These two additional conditions were introduced in Li and Bazant's (1994) study of the initial spacing of radial bending through cracks in sea ice emanating from a penetrating object and in the subsequent Li et al (1995) study of parallel thermal cracks in a half-space. The purpose of this study is to apply these conditions to a pavement plate supported on an elastic foundation, taking at the same time into account that the material is not perfectly brittle but quasibrittle.…”

An Experimental Study on the Fracture Energy of Foamed Concrete Using V-Notched Beams

“…It can also be referred to as the energy required in the incarnation and formation of cracks as dissipated per unit area [7,8]. Fracture energy basically corresponds to the area of the softening phase at a stress-strain curve, as shown in Fig.…”

Size and boundary effects on desiccation cracking in hardened cement paste

“…The concrete may be attached to a substrate or experience no external restraint at all (Hong et al 1997;Yang et al 2002;Bolander and Berton 2004). Predictions of initial spacing and depth of desiccation cracks can be made using a half-plane model (Li et al 1995;Jagla 2002). However, the way desiccation cracks propagate during ongoing drying will be very much determined by the boundary conditions and slab thickness.…”

“…Different approaches have been used to predict universal characteristics of desiccation crack-patterns (Li et al 1995;Kitsunezaki 1999;Leung and Néda 2000;Jagla 2002;Jenkins 2005) or to simulate desiccation cracking in specific materials (Chertkov 2002;Bolander and Berton 2004). In modeling of desiccation cracking in concrete pavements or repair layers, the choice of boundary conditions are important.…”