Surface cracks, rice

Cracking to damage the surface of rice or wheat grains to make the interior more accessible. 

The solution constructed above provides the necessary tools from elasticity theory in order to consider nucleation of a dislocation at a crack tip. The philosophical perspective adopted here is that due to Rice (1992) in which a comparison is made between the work needed to create new free surface and that needed to create a slip distribution corresponding ultimately to a dislocation. We present this model not so much with the hope that it will deliver quantitative insights but on the grounds that it is highly instructive concerning the atomic-level processes near a crack tip. In particular, the model is appealing because the treatment of dissipative processes such as dislocation nucleation is endowed with atomic-level realism, while still maintaining an overall continuum description. 

Energy required to create unit area of crack surface for adhesive failure Rice contour integral Inverse spring constant Sgdv... 

A number of additional trends can be noted. For example, if the stress concentration factor is larger than 2 - it is approximately 3 for a circular groove in a tension field - then the site is more effective as a source of dislocations. If the configuration of the stress concentrator is a notch with a very high curvature of the notch surface at its root, then the stress concentration factor can be very large compared to 2, but the spatial extent of the localized stress field is significantly reduced from that of the circular stress concentrator. For the case of a planar crack, which is the ultimate sharp notch, the issue of dislocation nucleation has been modeled by Rice and Thomson (1973) and Rice and Beltz (1994). Similar techniques have been adapted for the study of dislocation nucleation at the edge of an epitaxial island (Johnson and Freund 1997). 

In heterogeneous catalysis, nth-order kinetics may be the result of adsorption on a nonideal catalyst surface. In homogeneous systems, nth-order kinetics may represent the overall rate of the underlying elementary reactions, e.g., the classical Rice-Herzfeld mechanism for thermal cracking of hydrocarbonsFor simplicity, n is assumed to be constant for all species. This is not a strong assumption for many petroleum processes. 

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