Ductile shear fracture mechanics

Doubly-notched ductile steel bars have been fractured in shear. From the punch load (F) - punch displacement (delta) relations at constant starting crack length, the fracture toughness at crack initiation (J(c)) is determined using non linear fracture mechanics. Since the shear load depends directly on the length of the ligament between notches, cracking is predicted to occur at the same punch displacement for ah starter crack lengths. Experimental results agree. The propagating crack runs ahead of the punch, and opening-up of partially-propagated sheared steel samples in liquid nitrogen reveals that propagation (Delta a) is not uniform across the testpiece. Such subsequent crack propagation is investigated in the traditional way by means of J(R) curves. Separate J(R) curves are found for different starter crack lengths. Analysis is also performed in novel terms separating the prastic flow in the shear band from the crack tip toughness work and including the 'extra work' required beyond the NLEFM/Hencky plasticity work caused by the fact that the process is not fully reversible. This approach shows that the local crack-tip toughness R follows a relation something like R = 50 + 200[1 - exp(- 2000 Delta a)]kJ/m(2) (Delta a in m) independent of starter crack length. The geometry-dependent J(R) curves may be predicted from this novel approach, and also the Delta a similar to delta relations.