We have modeled a body by using the linear elastic theory. We have modeled a crack in the body by a flat plane, and the front of the crack by a straight line. Within this idealized model, the field around the front of the crack is singular. The singular field is clearly an artifact of the idealized model, but Irwin and others made the singular field a centerpiece of fracture mechanics.

The mathematics of this singular field had been known long before Irwin entered the field. We will focus on the mathematics in this lecture, and will describe Irwin’s way of using the singular field in the following lecture.

In previous lectures, we have described the work of Griffith (http://imechanica.org/node/7470), and the reinterpretation of Irwin and Orowan (http://imechanica.org/node/7507). The descriptions centered on two quantities: energy release rate and fracture energy. This energy-based approach leads us into applications of fracture mechanics (http://imechanica.org/node/7531). Before showing you more applications, I’d like to tell you about a basic concept, possibly also due to Irwin, concerned with the modes of fracture.

The concept of the modes appeals to our intuition, but this concept is absent in the energy-based approach. Energy release rate by itself does not differentiate the modes of fracture. To describe the modes of a crack will require us to talk about the field around the front.