Crack nucleation from a wedge disclination dipole with shift of rotation axes

Abstract

This paper analyzes crack nucleation from a wedge disclination dipole in the presence of a remote stress, accounting for the shift of the rotation axes within the dipole arm of the disclinations. A Zener–Griffith crack is assumed and an energy method is employed for the analysis. A single energy equation determines the equilibrium crack lengths and the crack head opening. Uniaxial and biaxial dipoles are compared: in the former the disclinations share a common rotation axis while in the latter the axes are separate. The results show that stable and unstable cracks can nucleate from the positive disclination of the dipole, but some of them are energetically unfavorable. A uniaxial dipole is stable against crack nucleation when the axis is located away from the positive disclination. Biaxial dipoles are more stable when the rotation axis of each disclination approaches the defect line of the other disclination. If the negative disclinations of a uniaxial dipole and a biaxial dipole have the same axis shift, the critical nucleation stress of the biaxial dipole is larger if its positive disclination shift is more than that of the uniaxial dipole. Stable crack lengths generally increase, while the crack head openings decrease, with the axis shift of the positive disclination. The crack head opening to crack length ratio is of the order of 0.001–0.01, and can be higher if an applied stress is present.