Effect of T-stress on the fracture in an infinite two-dimensional decagonal quasicrystals of a cruciform crack with unequal arms

Abstract

The T-stress near the tips of a cruciform crack with unequal arms in the two-dimensional (2D) decagonal quasicrystals (QCs) are analyzed. The associated boundary value problems can transform to a system of singular integral equations by using the integral transformation technique. According to the stress difference method, T-stresses of phonon field and phason field can be expressed as the sum of an integral involving crack opening displacements (CODs) and applied loading at infinity. CODs play a leading role in determining T-stresses of phonon field and phason field. The role of the T-stresses in brittle fracture for 2D decagonal QCs is emphasized. Moreover, the influence of the ratio of two crack-arm lengths b/a and the CODs on the T-stresses of a cruciform crack is examined.