T-stress solution of penny-shaped cracks in transversely isotropic elastic media

• T-stress of a penny-shaped crack in transversely isotropic infinite media is examined.
• Closed-form T-stress Green’s function for a pair of self-equilibrated normal point forces is derived.
• General formulae for computing T-stress under general loading condition is developed.
• Explicit dependence of T-stress on material properties is demonstrated.
• Closed-form solutions for T-stress is derived for certain loading conditions.

This paper presents explicit formulae of the T-stress for a penny-shaped crack in a transversely isotropic, linearly elastic, infinite medium under remote triaxial stress and crack-face normal traction. The T-stress Green’s function for a pair of opposite unit point forces is established first in a closed-form and these results are then utilized to derive the integral formulae of the T-stress for a penny-shaped crack under general loading conditions. The explicit dependence of the T-stress on material properties for both isotropic and transversely isotropic solids is presented. The closed-form expressions of the T-stress for uniform remote triaxial stresses and uniform, linear, and axisymmetric normal tractions are also reported.