Crack deflection in a biaxial stress state

Cotterell and Rice theory (Int J Fract 16(2):155-169, 1980) on the kinking of a crack submitted to a biaxial loading in a homogeneous material is revisited. Using both an energetic and a stress fracture criteria (Leguillon, Eur J Mech A/Solids 21:61-72, 2002) allows defining a positive threshold of the T-stress Tc below which no branching can occur (Selvarathinam and Goree, Eng Fract Mech 60(5-6):543-561, 1998) provided the inhomogeneities size is small compared to the Irwin length. The absence of such a threshold would definitely condemn experimental procedures like the double-cantilever beam (DCB) or compact tension (CT) tests, which result in a positive T-stress at the crack tip. The stress intensity factors KI and T are computed using a contour integral. Calculations provide a very good agreement with the analytical results of the infinite Centrally Notched (CN) plate in tension for instance. An asymptotic analysis makes it possible to define the branching angle as a discontinuous function of T with a jump from 0◦ to some significant positive value as T reaches Tc. Furthermore, for non vanishing KII , a similar analysis is carried out, a positive T-stress increases the kinking angle due to KII alone.