ADVANCED METALIC ENGINEERING

Advanced Metallic Engineering

Advanced Metallic Engineering

1. Introduction

In fracture mechanics, there are two fundamental failure theories proposed by Griffith and Barenblatt . Griffith realized that brittle fracture happens as a result of competition between strain energy release and surface energy required to create new fracture surfaces. In the Griffith's theory it is predicted that for a given crack length there is a unique critical stress above which crack grows and below which crack remains in equilibrium. Barenblatt proposed the cohesive theory of fracture in which one assumes that there is a nonlinear region in the vicinity of the crack tip. The interesting thing here is that there is no stress singularity. Increasing applied loads causes the separation between crack faces to increase in the cohesive region and when the opening displacement is large enough the crack propagates.

The interest in understanding brittle fracture on a more fundamental level has led many researchers to study it in the lattice scale. Thomson et al. showed that in a very simplified 1D model for a range of stresses above and below Griffith's stress a crack becomes lattice trapped. Later Hsieh and Thomson extended their results to 2D. Esterling using a lattice statics method, studied similar problems for three-dimensional cracks in a cubic lattice with nearest-neighbor interactions. Masudajindo et al. and studied fracture of crystalline materials using the lattice Green's function method. In particular, they showed that mode I and II crack problems are coupled in the lattice scale. There have been some very recent atomic-scale fracture studies in the literature (see , , and and references therein) and it seems that even after a few decades of research in fracture mechanics, some physics/mechanics coupled problems remain to be resolved.

Search for some novel mathematical tools that would remove the physically unacceptable singularities predicted by the classical mechanics of fracture began soon after the publication of the seminal work by Griffith . Orowan and Irwin proposed the “plasticity correction” term that was added in the equations describing the stress intensity factors for fracture of various modes, so that for the crack length approaching zero a finite stress resulted. This outcome described the intrinsic strength of the undamaged material, while the associated stress at the crack tip could now be identified with a finite stress level corresponding to the local yield stress. Similar effort was undertaken in Russia by Novozhilov , who suggested that the very nature of the crack propagation is discrete, and who for the first time introduced the concept of the minimum admissible growth step a0. According to Novozhilov this entity, named by him a “fracture quantum”, must be included in the energy Griffith criterion - or an equivalent local stress criterion for fracture. Initially, the fracture quantum was identified with the interatomic distance b0 (in a cubic lattice). Similar concepts were proposed independently by Eshelby (see also ). In recent years, similar ideas have been pursued mainly in , where “Quantized Fracture Mechanics” (QFM) was introduced and was later used in several ...