Material stability criteria for a plane stress asymptotic solution for steady mode I crack growth in an elastic/perfectly plastic solid

In a recent plane stress asymptotic solution for a mode I steadily moving crack in an elastic/perfectly plastic material, an exact solution for the proportionality function of the flow rule was not determined. Here, an exact solution is found for this function in the fan region of mathematical characteristics. The exact proportionality function of the flow rule is useful in determining the extent of radial distance from the crack tip for which the material remains stable. Although the plastic proportionality function is itself a function of Poisson’s ratio, the limiting value of maximum radius for a stable solution is independent of this material parameter.