Spring 2010

These notes belong to a course on fracture mechanics

A body consists of two materials bonded at an interface. On the interface there is a crack. The body is subject to a load, causing the two faces of the crack to open and slide relative to each other. When the load reaches a critical level, the crack either extends along the interface, or kinks out of the interface.

These notes belong to a course on fracture mechanics

A crack pre-exists in a body. When the body is loaded, the two faces of the crack may simultaneously open and slide relative to each other. The crack is said to be under a mixed-mode condition. When the load reaches a critical level, the crack starts to grow, and usually kinks into a new direction. Subsequently the crack often grows along a curved path.

These notes belong to a course on fracture mechanics

Lecture 1 introduced the crack bridging model. The model is also known as the cohesive-zone model, the Barenblatt model, or the Dugdale model. The model consists of two main ingredients:

These notes belong to a course on fracture mechanics

Following Griffith (1921), we distinguish two processes: deformation in the body and separation of the body. Up to this point, the process of deformation has been described by field theories of various kinds, such as

These notes belong to a course on fracture mechanics

Lecture 1 described the Begley-Landes experiment, and the blunting of a crack due to large deformation. Lecture 2 is motivated by the following considerations.

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.

A glass may withstand a static load for a long time (days, weeks, or years) and then, without warning, breaks suddenly. Here are salient empirical observations:

These notes were prepared when I taught fracture mechanics in 2010, and were updated when I taught the course again in 2014.

Notes on other parts of the course are also online.