Summary: Consider a crack propagating in a plane according to a loading that results in anti-plane shear deformation. We show here that if the crack path consists of two straight segments making an angle \(\varphi \neq 0\) at their junction, examples can be provided for which the value of the stress-intensity factor (SIF) actually depends on the previous history of the motion. This is in sharp contrast with the rectilinear case (corresponding to \(\varphi = 0\)), where the SIF is known to have a local character, its value depending only on the position and velocity of the crack tip at any given time.