The molecular wedge in a brittle crack: A simulation of mica/water
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This paper presents an atomic calculation of the wedging effect which occurs in a brittle crack when molecules of a chemisorbing species of molecules of sufficient size enter the crack mouth. A surface tension develops at the tip of the wedge caused by the difference between the covered and vacuum surface energies. This force draws the chemisorbing molecules toward the crack tip and distorts the crack faces, causing, in turn, a compensating elastic force on the molecules which tends to eject the molecules. We calculate the equilibrium penetration of the wedging molecules and the configuration of the crack and wedge by an atomistic calculation. We simulate mica/water chemistry by means of a simplification of the mica lattice and calculate interactions between the water and mica on the basis of Born-Mayer. Water is found to form a wedge tongue of two or three molecular thicknesses and a length of about 20 molecular distances, which penetrates into the crack tip cohesive zone. When strong wedging action occurs at a crack tip, crack advance near threshold loadings will be limited by molecular diffusion through the wedge tongue.
I. INTRODUCTION
In the literature on chemically enhanced brittle fracture, one often finds questions about the penetration of the external molecular species to the crack tip, where they might affect the bond breaking process in the classical mechanism1 for crack growth. Lawn,2'3 however, was the first to question seriously molecular accessibility to the crack tip, noting that a crack loaded at the threshold value in a typical active environment is often too narrow near its tip to allow penetration of the molecules, assuming linear elastic crack displacements. He has also emphasized the crucial importance of the interactions of the external molecules with the cleavage surfaces in determining the overall crack behavior. For example, if penetration to the crack tip cannot occur, then crack advance must, instead, primarily involve the transport of the molecules in the highly constrained region near the wedge tip. Furthermore, he has noted the close connection between the "surface forces" acting during cracking and those measured directly, using the surface force balance.4 Thus, the issues associated with the accessibility of reacting molecules to the crack tip have opened up an entirely new set of interesting questions about crack structure and phenomena which need further theoretical exploration. In a previous short paper,5 we introduced the idea of a "chemical wedge" which acts when strongly chemisorbing external molecules enter the mouth of a brittle crack. The chemical wedge mechanism arises from the difference between the surface tensions for a chemisorbed surface and a vacuum surface, and the 524
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result of the wedging action is a complete change in the structure of the crack. In Ref. 5, we derived a rough rule of thumb for the degree of penetration, using essentially continuum ideas. However, since the property under discussion is so intimately tied up with th
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