A Dislocation Model for the Directional Anisotropy of Grain-Boundary Fracture
- PDF / 178,137 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 92 Downloads / 197 Views
for the Directional Anisotropy of GrainBoundary Fracture Glenn E. Beltz and Don M. Lipkin
Introduction That fracture is governed by processes occurring over a wide range of length scales has been recognized since the earliest developments of modern fracture mechanics. Griffith’s study of the strength of cracked solids1,2 is perhaps the earliest example of such multiscale thinking, predating by several decades the first attempts to apply atomistically grounded traction-separation laws to fracture (e.g., the Orowan–Gilman model3,4). Griffith recognized the critical condition for crack extension to be a statement of thermodynamic equilibrium of a cracked solid, representing a balance between the mechanical energy decrease upon crack extension and the corresponding increase in energy due to the newly created crack surface. Griffith determined the elastic strain energy of the cracked body using the continuum solution of the stress field about an ellipse5 and recognized that the potential energy associated with the cleavage surfaces of the crack was directly proportional to the surface energy, the latter deriving from the cohesive molecular forces of the solid. The Irwin–Orowan extension of Griffith mechanics to include plastic dissipation,6–9 which is known to occur on the mesoscopic length scale (1–100 m), provides yet a further example of multiscale thinking in the early community of fracture researchers. In fact, the interaction of length scales is of central importance in most problems of fracture. At first glance, it may seem that combining continuum and discrete (atomistic and/or dislocation) approaches to model fracture over a large range of length scales would be difficult to realize because of the significant differences in the domain sizes and characteristic constitutive properties
MRS BULLETIN/MAY 2000
of the respective phenomena. However, such approaches have been successfully integrated by a number of investigators in recent years.10–23 Presently, we provide an additional example of how discrete dislocation theories can be exploited to explain certain fracture phenomena in a way that links theories appropriate for vastly differing length scales.
Fracture Anisotropy: A Departure from Griffith Mechanics? It is generally recognized that a material’s intrinsic resistance to fracture need not be isotropic, depending on the crystallographic orientation of the fracture plane,24,25 as discussed in additional detail in the article by Gumbsch and Cannon in this issue. The anisotropy of brittle fracture is easily incorporated into Griffith fracture mechanics by allowing the surface energy s to be a function of the crystallographic cleavage plane (see, for example, Reference 26). Upon further inspection, however, Griffith fracture mechanics appears to dictate that the resistance to fracture must be a scalar property and, as such, must not exhibit any anisotropy within a given cleavage plane. The fundamental measure of a material’s resistance to brittle fracture—the work of cohesion of the solid (or the work of a
Data Loading...
