A dislocation model for the directional anisotropy of grain-boundary fracture
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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. Griffitha's study of the strength of cracked solids 1,2 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 (~1100 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.
