In Eq. (7), the quantity in square brackets is Petch’s relationship for the cleavage fracture stress [20]. A compilation of cleavage fracture stress measurements was reported at ICF4 [50]. At constant plastic zone size, as appears to generally obtain in engineering fracture mechanics tests, a Hall-Petch type of dependence is obtained for KIc. Figure 5 shows a compilation of results reported for mild steel and related steel materials [51-55]. An unusual aspect of Fig. 5 is that an increase in fracture toughness is shown for materials obviously exhibiting an increase in yield stress (according to the corresponding H-P relationship for σy). In such a fracture mechanics test, however, yielding begins at the H-P determined σy at the root of the notch and the induced plastic zone strain hardens until a higher grain size dependent value of the cleavage stress, σC, is reached [56]. Knott provided an important review of the science and engineering aspects of fracture mechanics at ICF8 [57]. 6. Slip band intrusions and extrusions There is grain size dependence in the fatigue strength of metals also [25] but the situation is more complex, in no small part because of the occurrence of persistent slip bands (PSBs) and their increasingly pronounced behavior under cyclic loading [16, 17, 58]. Fig. 6. Cyclically-induced slip intrusions/extrusions and internal dislocation structures. Cottrell and Hull had produced a seminal description of surface intrusions/extrusions produced during fatigue testing [59]. Figure 6 provides a schematic illustration of the surface relief and internal dislocation structure accompanying cyclic loading [60]. Cottrell gave emphasis to the mechanical aspect of the nucleation and growth of cracking in a PSB as compared with the importance of mass transport by diffusion because of
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