fracture mechanics

These notes belong to a course on fracture mechanics

Decouple elastic deformation of the body and inelastic process of separation. Up to this point we have been dealing with the following situation. When a load causes a crack to extend in a body, a large part of the body is elastic, and the inelastic process of separation occurs in a zone around the front of the crack. Inelastic process of separation includes, for example, breaking of atomic bonds, growth of voids, and hysteresis in deformation.

For a crack in an elastic body subject to a load, the elastic energy stored in the body is a function of two independent variables: the displacement of the load, and the area of the crack. The energy release rate is defined by the partial derivative of the elastic energy of the body with respect to the area of the crack.

Fracture mechanics without invoking any field theory. In Lecture 1 on Fracture of Rubber, we considered the extension of a crack in an elastic body subject to a load. Following Rivlin and Thomas (1953), we regarded the elastic energy stored in the body as a function of two independent variables: the displacement of the load, and the area of the crack. The partial derivative of the elastic energy with respect to the area of the crack defined the energy release rate.

A rubber band can be stretched several times its original length. This large deformation may hide its brittleness: the strain to rupture can be markedly reduced by the presence of a crack. This lecture describes fracture mechanic of highly deformable materials, such as rubbers and gels.