The stress is unbounded, and that is the point
Linear elasticity at a sharp crack gives Williams’ field: stress of order r−½ multiplied by a stress intensity factor K. Mode I opens the faces, mode II slides them in plane, mode III tears them out of plane. The singularity is not a material fact; it is the price of an infinitely sharp tip in a linear solid. Griffith’s energy release G = KI²/E′ is finite. The theory holds while the process zone is small compared with the crack.
σ along the ligament · log r
σij = K / √(2π r) · fij(θ)
Colour is the leading Williams stress: opening, sliding, or antiplane shear. On a log–log plot the ligament stress has slope −½. At r = 0 the linear field is infinite; a cohesive zone or a yield zone cuts that off.