Surface cracks contrast theory

The transmitted field to the right of the crack can be calculated similarly, with a change of sign in eqn (12.38) and in the x-dependence of wc(x, () and wsc(x). In this way approximate values of 1r and Rr can be found for the two-dimensional crack contrast theory, and possibly for the three-dimensional theory as well. The calculated field is reasonably good near the free surface but not near the crack tip, so the approximations are better the deeper the crack is compared with the wavelength. 

Theories of the oxidation of tantalum in the presence of suboxide have been developed by Stringer. By means of single-crystal studies he has been able to show that a rate anisotropy stems from the orientation of the suboxide which is precipitated in the form of thin plates. Their influence on the oxidation rate is least when they lie parallel to the metal interface, since the stresses set up by their oxidation to the pentoxide are most easily accommodated. By contrast, when the plates are at 45° to the surface, complex stresses are established which create characteristic chevron markings and cracks in the oxide. The cracks in this case follow lines of pores generated by oxidation of the plates. This behaviour is also found with niobium, but surprisingly, these pores are not formed when Ta-Nb alloys are oxidised, and the rate anisotropy disappears. However, the rate remains linear it seems that this is another case in which molecular oxygen travels by sub-microscopic routes. 

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