Evaluation of T-stress in an infinite plate with double-crack under compression and shear

Abstract

The T-stress at the crack tip under compression and shear has received more and more attention, but most of the theoretical researches have focused on single-crack, with little reported on the closed form solutions of T-stress at the double-crack or multi-crack tips. Therefore, the single-crack problem under compression and shear is first analyzed in this paper, the formulas for calculating the three components of T-stress (Tx, Ty and Txy) are obtained. According to the principle of superposition, the origins of the three components of T-stress are examined. Then the basic equations for solving the double-crack problems under compression and shear are established, leading to the formulas for calculating the three components of T-stress at the double-crack tips. Finally, the effects of the spacing between two cracks, the ratio of double-crack half-length, the dip angle of rock-bridge and the absolute angle between two cracks on the three components of T-stress are discussed. The results indicate that the Tx and Ty are unaffected by the friction on the crack surface, but the Txy is significantly correlated with it. Each component of T-stress at the inner and outer tips of double-crack is influenced by different geometrical factors and shows a different variation curve, which may be a potential factor contributing to the complexity of the double-crack or multi-crack problems under compression shear.