A dislocation shielding model for the fracture of semibrittle polycrystals

Using a dislocation mechanics-based crack-tip shielding model, a zeroth-order estimate of the grain size and yield strength dependence of fracture toughness is made for mild steel. This model, appropriate to cleavage fracture in the lower shelf regime, is shown to predict the fracture toughness determined over a temperature regime of 100 to 240 K in both quasi-static and dynamic tests and for two different grain sizes. Two grain size terms in the proposed model result. One is associated with grain boundary blockage effects on crack-tip shielding, while the other is proposed to affect the far-field stresses and, indirectly, the local crack-tip stress field. Differences between the present approach and the classic Cottrell-Petch model are in how the friction stress and grain size affect local stresses at the crack tip rather than at a carbide or a grain boundary.