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The stress field of an elliptically blunted crack under remote antiplane shear loading and its interaction with a nearby screw dislocation are investigated with the complex variable method. The Gurtin-Murdoch model is adopted to characterize the surface stress effect of the nano blunt crack. It is found that the surface stress effect can influence the stress field of the nano blunt crack, the critical load for dislocation emission and the shielding effect of the dislocation significantly.

Asymptotic approximations to the waves guided by a curved, elastic waveguide, whose curvature is small and changes slowly over a wavelength are discussed using the JWKB method. The antiplane shear problem is treated. The asymptotic method is carefully explained and a brief comparison with similar and contrasting asymptotic approaches made. The conclusions reached are: (1) Provided the caustic is outside the guide, the presence of the curvature affects the mode shape and modulates the amplitude, but leaves the dispersion relation almost unchanged from that of a guide having no curvature. (2) A caustic can often form inside the guide. Its presence alters the modes, the modulated amplitude and the dispersion rather dramatically. The region of guided propagation becomes that between the caustic and the upper concave surface, though the lower convex surface continues to influence the propagation, and the wavenumber becomes dependent on the curvature.

The problem of a semi-infinite crack suddenly arising in a loaded strip of finite width and then propagating with a constant velocity is considered. The analysis is carried out within the realm of the classical theory of elasticity and a state of antiplane shear is assumed. By using integral transform methods the problem is reduced to an equation of the Wiener—Hopf type, which can be solved by a standard technique involving the infinite product theory. In order to determine the stress state in the vicinity of the crack tip, i.e. the stress intensity factor, asymptotic expansions are employed. The time-dependence of this quantity is calculated numerically and exposed in diagrams. The influence of various parameters is discussed and it is shown that the stress intensity factor oscillates with a decreasing amplitude and tends to a steady-state value.