Antiplane shear crack in a prestressed elastic medium based on the couple stress theory

Abstract

A prestressed elastic medium containing a mode-III crack is studied by means of the couple stress theory (CST). Based on the CST under initial stresses, a governing differential equation along with a mixed boundary value problem is established. The singularities of the couple stress and force stress near the crack tips are analyzed through the asymptotic crack-tip fields resulting from the characteristic expansion method. To determine their intensity, a hypersingular integral equation is derived and numerically solved with the help of the Chebyshev polynomial. The obtained results show a strong size-dependence of the out-of-plane displacement on the crack and the couple stress intensity factor (CSIF) and the force stress intensity factor (FSIF) around the crack tips. The symmetric part of the shear stress has no singularity, and the skew-symmetric part related to the couple stress exhibits an r^−3/2 singularity, in which r is the distance from the crack tip. The initial stresses also affect the crack tearing displacement and the CSIF and FSIF.