Is It Possible to Determine the Whole Crack Path at Once?

Abstract

A brief review of crack path calculation methods using integral principles of mechanics is presented. In twodimensional setting, a crack is considered as a geodesic line on the surface of a body with a metric that depends on the initial stress state. The possibility of approximate determination of crack path on the basis of integral principles is illustrated on a number of problems. In particular, crack paths in a half-plane under uniformly distributed load applied on its edge are determined. The calculations include the stress state of the half-plane taken from the solution for a body without a crack. The fruitfulness of the representation of displacements of crack edges using the Winkler’s hypothesis is shown. To study the subcritical behavior of the crack, the concept of cracon, a quasi-particle simulating the motion of the crack tip, can be introduced. The problem of determining the crack path on the basis of integral principles of mechanics is insufficiently investigated and requires further research.

Keywords

• fracture mechanics
• solid mechanics
• cracks path
• quasi-brittle fracture
• fracture stress
• composite material