Asymptotics of stresses and strain rates near the tip of a transverse shear crack in a material whose behavior is described by a fractional-linear law

An approximate solution of the problem of determining the fields of stresses and strain rates due to creep near the tip of a transverse shear crack in a material whose behavior is described by a fractional-linear law of the theory of steady-state creep is given. It is shown that the strain rates have a singularity of the type $\dot{\varepsilon}\sim r^{-\alpha}$ near the crack tip; the order of singularity $\alpha$ changes discretely, depending on the polar angle, and takes the values 1, 2/3, and 1/2.