Abstract: Under the condition that all the perfectly plastic stress components at a crack tip are the functions of θ only, making use of the Tresca yield condition, steady-state moving equations and elastic perfectly-plastic constitutive equations, we derive the generally analytical expressions of perfectly palstic stress field at a rapidly propagating plane-stress crack tip. Applying these generally analytical expressions to the concrete crack, we obtain the analytical expressions of perfectly plastic stress field at the rapidly propagating tips of models I and II plane-stress cracks.

Key words: instantaneous point source, anomalous diffusion, fractional calculus, Fox function, Mellin transform