Introduction

The treatment of fracture in Chapter 9 was descriptive and qualitative. In contrast, fracture mechanics provides a quantitative treatment of fracture. It allows measurements of the toughness of materials and provides a basis for predicting the loads that structures can withstand without failure. Fracture mechanics is useful in evaluating materials, in the design of structures, and in failure analysis.

Early calculations of strength for crystals predicted strengths far in excess of those measured experimentally. The development of modern fracture mechanics started when it was realized that strength calculations based on assuming perfect crystals were far too high because they ignored pre-existing flaws. Griffith reasoned that a pre-existing crack could propagate under stress only if the release of elastic energy exceeded the work required to form the new fracture surfaces. However, his theory based on energy release predicted fracture strengths that were much lower than those measured experimentally. Orowan realized that plastic work should be included in the term for the energy required to form a new fracture surface. With this correction, experiment and theory were finally brought into agreement. Irwin offered a new and entirely equivalent approach by concentrating on the stress states around the tip of a crack.

Theoretical Fracture Strength

Early estimates of the theoretical fracture strength of a crystal were made by considering the stress required to separate two planes of atoms. Figure 10.1 shows schematically how the stress might vary with separation.