Asymptotic Field Near the Tip of a Debonded Anticrack in an Anisotropic Elastic Material

Abstract

We use the sextic Stroh formalism to study the asymptotic elastic field near the tip of a debonded anticrack in a generally anisotropic elastic material under generalised plane strain deformations. The stresses near the tip of the debonded anticrack exhibit the oscillatory singularities $r^{-3/4\pm i\varepsilon }$ and $r^{-1/4\pm i\varepsilon }$ (where $\varepsilon $ is the oscillatory index) as well as the real power-type singularities $r^{-3/4}$ and $r^{-1/4}$ . Two complex-valued stress intensity factors and two real-valued stress intensity factors are introduced to respectively scale the two oscillatory and two real power-type singularities. The corresponding three-dimensional analytic vector function is derived explicitly, and the material force on the debonded anticrack is obtained. Our solution is illustrated using an example involving orthotropic materials.