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Crack Bridging. Lecture 2
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:
- The process of separation of the body is modeled by a traction-separation curve;
- The process of deformation in the body is modeled by a field theory, such as the linear elastic theory.
For a body of a given configuration and traction-separation curve, the model results in a boundary-value problem. A large number of such boundary-value problems have been solved. These problems can also be solved by commercial finite element software, such as ABAQUS. The limited time in this course will only allow us to describe a few examples.
Lecture 1 focused on small-scale bridging, when the body contains a pre-existing crack, and the size of the bridging zone is much smaller than the characteristic length of the body (e.g., the length of the crack and of the ligament). Under the small-scale bridging condition, the external boundary conditions of the body can be represented by a single parameter, the energy release rate. Consequently, the Griffith (1921) approach—as extended by Irwin, Orowan, Rivlin and Thomas in 1950s—can be used to determine the fracture energy. Once determined, the fracture energy of a material can be used to predict the failure of bodies of the same material but different configurations.
This lecture is devoted to large-scale bridging. When the size of the bridging zone is comparable to, or even larger than, the characteristic length of a body, the external boundary conditions cannot be represented by the energy release rate alone. The Griffith approach fails.
The crack-bridging model, however, applies under the large-scale bridging conditions. Within the crack-bridging model, the traction-separation curve characterizes the resistance of a material to fracture. The traction-separation curve can be determined by a combination of computation and experimental measurement. Once determined, the traction-separation curve of a material can be used to predict failure of specimens of the same material but different configurations.