description of cracking in thin sheet material [44]. The BCS analysis involved use of the method of continuous distributions of dislocations to model both the elastic stress state of the crack and extent of the plastic zone (as an inverted dislocation pile-up). Unstable growth of the crack was specified for a ratio of plastic zone size, s, to crack half-length, c, at fracture stress, σF, and yield stress, σy, in the transcendental equation (s/c) = [sec(πσF/2σy)] – 1 (5) In turn, Eq. (5) was shown to be well-approximated by the relationship [45] σF ≈ Aσy [s/(c + s)] 1/2 (6) The equation, with σy replaced by σC for crack-free material, was shown at ICF3 to describe the crack size dependence of the brittle fracture stress for several reference steel materials and for polymethylmethacrylate (PMMA) glass material. In Eq. (6), A = (π/2) for (s/c) < 1.0 and A = 1.0 for (s/c) → 1.0 [46]. Fig. 5. Compilation of fracture mechanics stress intensity, K, values for mild steel [47]. The BCS description provided very importantly for specification of fracturing in terms of a critical crack tip opening criterion that has proved to be very useful in fracture mechanics testing [47]. But in either case of the critical stress criterion in Eq. (6) or in terms of the BCS-described crack tip opening, a same dependence on grain size and plastic zone size was obtained for the plane strain fracture mechanics stress intensity, KIc [48]. For yielding in plane strain on a von Mises basis, a value of KIc was given [49] as KIc = (8/3π) 1/2[σ0C + kCℓ -1/2]s1/2 (7)
RkJQdWJsaXNoZXIy MjM0NDE=