On the all components of T-stress for an external circular crack under tension and bending

• Analytical solutions of T-stresses were derived for external circular cracks.
• Potential method and Hankel transformation were used.
• Full field solutions of all stress components on the crack plane were obtained.
• Asymptotic analyses were carried out to obtain the components of T-stress.
• Full field solutions were compared with asymptotic K-T and K fields.

External circular crack in an infinite body is a well-known problem for three-dimensional elasticity theory. Although previously studied extensively, main focus has been on the determination of stress intensity factors, and thus only the stress components normal to the crack plane have been derived analytically. In this paper, the external circular crack problem is further studied for the purpose of determination of all components of T-stress, under both the axisymmetric (tension) and asymmetric loading (bending) loading conditions. Complete analytical expressions of stress components on the crack plane are derived first; and based on which the asymptotic analyses are carried out to obtain the components of T-stress. Comparisons of the full field solutions in the near crack front regions with asymptotic stress fields based on both stress intensity factors K and T-stresses (K–T field), and with the ones based on stress K alone (K field) are carried out. It is demonstrated the K–T field provides approximations with better accuracy comparing to the K field. The present derived T-stress solutions can be used for advanced three-dimensional fracture mechanics analyses of external cracks in engineering components. They can also be used as benchmark problems for the verifications of computational/numerical methods for the analyses of 3D crack problems.