Chapter 2 - Linear Elastic and Nonlinear Fracture Mechanics

Abstract

This chapter introduces fundamental concepts from both linear fracture mechanics (LEFM) and nonlinear fracture mechanics (NLFM) of concrete that are essential for understanding the subsequent development of the computational theories on multiple-crack analysis. The theory of the fracture mechanics of concrete, which is a branch of NLFM with its governing law for crack propagation drawn from the inelastic material behavior exhibited in an extensive fracture process zone (FPZ) ahead of an open crack, is largely developed from the theory of linear elastic fracture mechanics (LEFM). The chapter introduces the elastic theories of the crack-tip stress fields. Under the assumption of elasticity, the crack-tip stresses have an invariant form of distribution with an inverse-square-root singularity at the tip of the crack. A crack may be subjected to three different types of loading that cause displacements of the crack surfaces. In Mode I loading, the load is applied normal to the crack plane. Mode II loading refers to in-plane shear and causes the two crack surfaces to slide against each other. In Mode III loading, out-of-plane shear is applied which tends to tear the two crack surfaces apart. After defining the crack-tip fields in terms of the stress intensity factor, an energy description of the fracture process needs to be explained using Griffith's fracture theory, whose innovative concept of introducing fracture energy into the study of cracked materials laid a solid foundation for the later development of fracture mechanics. The fracture energy required for creating a unit surface of an open crack has a close relationship with the stress intensity factor. Consequently, the stress intensity factor loses its physical significance as a fracture parameter. This implies that LEFM is no longer valid, and the problem has to be analyzed based on NLFM.