due to addition of the athermal component Δσ0y* to σ0y, in the manner described by Hull and Mogford [21], thus raising the ambient temperature yield strength up to that of steel “B”. The danger indicated in the figure, which was deemed important at the time, was that steels “B” and “A*” could have the same ambient yield strengths and temperature dependencies of them while exhibiting appreciably different values of the dbtt [23]. A historical note is that Orowan had drawn attention to the condition of the yield stress being raised to the level of the cleavage fracture stress as a criterion for the onset of brittleness in steel; and, this consideration, taken together with a plastic constraint factor for the notch in a Charpy impact test [24], provided for a quantitative description of the dbtt in the same vein as described by Cottrell and Petch [25]. Wessel reported at ICF1, in Sendai, on the correlation of changes in TC associated with changes in σ0y and ky for a structural pressure vessel steel [26]. 3. The Cottrell crack-forming dislocation reaction In the seminal article by Cottrell on the dbtt [9], a breakthrough explanation was provided for the crystal structure dependent observation of cleavage occurring on cube-face {001} crystal planes in steel and related body-centered cubic (bcc) metals. On the basis of the bcc slip systems having lattice parameter, “a”, focus was placed on the [uvw] direction- and (hkl) planardislocation reaction for two (mixed-type) dislocation lines mutually oriented along the [010] crystal axis as: (a/2)[11-1](101) + (a/2)[-1-1-1](-101) = a[00-1](001) (3) The (001) plane is not a slip plane in the bcc lattice and under an [001] directed tensile axis, the thus-formed [00-1] edge type dislocation with line direction along [010] would anyway be a sessile dislocation. Cottrell proposed that the reacted dislocation could form a cleavage crack nucleus. Chou, Garofalo and Whitmore, followed up Cottrell’s model proposal with a quantitative analysis of arrested dislocation pile-ups which would be blocked at such intersection in alpha-iron [27]. And experimentally, Hahn et al. reported observations of initiated cleavage micro-cracks at temperatures centered on the dbtt for a number of polycrystalline iron and steel materials [28]. The observations relate to the Cottrell-Petch dbtt descriptions in that it had been proposed that break-out of cracking from within individual grains was required for material failure. Antolovich and Findley have reported on a re-examination of the Cottrell model [29]. Nevertheless, the importance of Cottrell’s mechanism of crack initiation also took hold for other observations of cracking in single crystal experiments. Most notably, Keh, Li and Chou applied the Cottrell model to explaining the occurrence of cleavage cracking observed on otherwise unfavorable {110} type planes at aligned diamond pyramid hardness impressions put into rocksalt-type structure MgO (001) crystal surfaces [30]. Figure 2 shows a schematic view of the dislocations distributed among the indentation-activated {110}<1-10> slip systems [31]. For this crystal geometry, the Cottrell-type reaction is specified [32] as (a/2)[10-1](101) + (a/2)[0-11](011) = (a/2)[1-10](112) (4) The line direction of the reacted dislocation of Eq. (4) lies along the [11-1] direction. The square “picture frame” structure immediately encompassing the residual indentation is formed by volume accommodating slip on secondary <110>{1-10} slip systems. The sub-surface interaction of dislocation pile-ups at the intersection of conjugate slip systems, for example in the second quadrant of the (001) picture frame, produces the sessile Cottrell-type dislocation reaction described in Eq. (4).
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