Elastic-Plastic Fracture Mechanics. Lecture 2

These notes belong toa course on fracture mechanics

Lecture 1描述了Begley-Landes试验t, and the blunting of a crack due to large deformation. Lecture 2 is motivated by the following considerations.

When a rubber containing a crack is loaded, before the crack extends, strain everywhere in the rubber can be large. By contrast, when a metal containing a crack is loaded, before the crack extends, strain in the metal is typically small, except near the tip of the blunted crack. Consequently, to analyze deformation in the metal, at a distance a few times the crack opening displacement away from the crack tip, we can use the field theory of infinitesimal deformation.

When a metal strains far beyond the elastic limit, the stress-strain relation is often fit to a power law.

When a metal undergoes homogeneous deformation subject to proportional loading, the stress-strain behavior of plastic deformation is indistinguishable from that of elastic deformation.

The above idealizations are used to formulate a field theory of infinitesimal deformation and power-law material model. Within this theory, a large class of boundary-value problems has solutions of a remarkably simple form. This result, the Ilyushin theorem, generalizes the linearity in the linear elastic theory into a scaling relation for the power-law material.

The power-law material and the Ilyushin theorem are described in the present lecture. We then apply these ideas to elastic-plastic fracture mechanics. In particular, we will describe the HRR field.