According to the Al and Cu simulations, the slip events adhering to the incipient slip domain entail local activations of a small number of dislocations ( = 1 or occasionally = 2) gliding ≈ 10Ž40 atomic planes (/ < 20 nm). Such a short-range glide suggests the attainment of fractional slips (7 < ) within the Q„-regime in the (7) distributions (Fig. 6.7). The minimum slip magnitude detected in the simulations (7 ≈ 0.1 ) is produced by a sudden expansion of a dislocation arm across ≈ 10 atomic spacings. Since the simulations enable detection of such small slip events, the computational noise (periodic fluctuations in V, see Appendix A7.3) is much smaller than the experimental fluctuations in the measured ∆V levels, the Q„-domain is therefore probed with smaller slip values than those obtained from the micropillar compression experiments [50]. In the Al [110] simulation (Fig. 6.7), the incipient slip domain tentatively spans from 7 89 ≈ 0.1 to 7 ≈ , thus validating the power-law scaling of the incipient slip regime with Q„≈ 0.5, which in accord with Fig. 6.7, spans over ≈1.5 decades of slip sizes when Al experiments and simulations are brought together in a single (7) representation. Although a straight line in the log( (7)) Žlog(7) representations over less than two slip decades is not a solid proof of power-law behavior [164], assertion of a robust power- law scaling in the present (7) distributions would require measurement of plastic events that produce much smaller slip sizes than the above 7 89, which arguably surpasses the physical limit for the onset of plastic intermittencies.
Large slip events characterized by 7 > 7 in the (7) distributions described through the exponent Q (Fig. 6.7) are produced by the collective glide of dislocation segments. As elucidated in the periodic Cu and Al simulations, the motion of 3 ≤ ≤ 6 leads to the emission of large dislocation avalanches. Development of these avalanches implies depinning of the dislocation network, where the initially-activated dislocation segment triggers additional unzipping of further segments gliding a distance of / ≈ 10 nm Ž 40 nm. The sequence of Figs 6.10(b)-(e) shows a dislocation avalanche in Al at 300 K carrying a slip size of 7 ≈ 2 . The activation of dislocation “1” revolving around “j1” (Fig. 6.10(b)) mobilizes (i) three pinned segments in Fig. 6.10(d), and (ii) an additional dislocation in Fig. 6.10(e). The dense dislocation forest (Fig. 6.10(a)) secures the motion of the active dislocations (see the pinned dislocations (*) marked in cyan in Fig. 6.10(f)) as the dislocation configuration approaches a steady
(subcritical) state, when the applied stress is lower than the critical stress [34, 44]. The strain evolution is drawn in Fig. 6.10(g) in terms of the effective V and U. In this figure, it is observed that the sudden mobilization of the dislocation segments (unzipping and bowing) leads to discrete increases in density (•U/•O > 0) during the avalanche development. The eventual avalanche arrest determines the initiation of a pinned stage in the dislocation network where the active segments are immobilized (see segment “5” in Figs. 6.10(e) and 6.10(f)). Although the dislocation segments may glide a few atomic distances within a pinned state [45], quasi- elastic periods (pinning) lying between two successive avalanche events entail ∆V ≈ ∆O and an effective ∆U/∆O ≈ 0, see Fig. 6.10(g).
CHAPTER 6. DISLOCATION AVALANCHE EMISSIONS IN INTERMITTENT PLASTICITY
97 Figure 6.10. Large avalanche event in the Al [110] simulation at 300 K. (a) The periodic dislocation network (ù ≈ •¸•Û ¿ƒ”) is mainly comprised by short-range multi-junctions of dislocations and SFT (see Fig. 6.8(c)). (b)-(f): Sequence of a dislocation avalanche carrying ≈ ” . The avalanche involves sudden expansions of dislocation segments pinned at junctions “j”. The mobile segments are marked in yellow while the arrested (*) dislocations are colored in cyan. Atoms are visualized with OVITO (Appendix A6). (g) Evolution of stress and dislocation density ù as a function of strain during the avalanche event. Segment mobilization due to unzipping produces a net increment in ù at the beginning of the avalanche (depinning). Avalanche termination (pinning) is characterized by a mild decrease in density due to eventual segment unbowing.
The U Ž O evolution from the Al simulation (Fig. 6.11(a)) indicates that increments in dislocation density (see the inset to Fig. 6.11(a)) are due to the proliferation of stair-rod segments in the dislocation network (pink line in Fig. 6.11(a)). Despite the fact that the emitted mobile dislocations predominantly exhibit the conventional Shockey partial dissociation (red
98
arrows in Fig. 6.11(a) mark the onset of large avalanche events), the Shockey density remains at a relatively constant level from O ≈ 0.035 to O ≈ 0.07, see Fig. 6.11(a). The simulation reveals that the increments in the stair-rod density are associated with the recurrent formation of SFTs [97], which produce intermittent slip events by means of specific unzipping processes which are illustrated in the sequence of Figs. 6.11(b)-(f), where the activation of segment “1” leads to junction formation with segment “2” (Fig. 6.11(c)) and “3” (Fig. 6.11(f)). Notice how the progressive SFT formation [97] that results from the interaction with segment “3” (Fig. 6.11(d)) leads to avalanche emission due to the unzipping of segments “2” and “3” in Fig. 6.11(e). Although the FCC simulations exhibit occasional formation of dual dislocation junctions during the emission of dislocation avalanches (e.g., the Lomer-Cottrell junction in Fig. 6.11(g) in the Al simulation (Fig. 2.8(a))), the above construction is found to evolve to one of the multi-segment type (Figs. 2.8(e)-(g)). In this regard, it is noted in the periodic simulations that the dense dislocation configurations favor multi-junction formation in FCCs (Fig. 6.8(c)) due to the small atomic distances between neighbor segments (≈ 10–30 nm).
Figure 6.11. Development of dense dislocation network in the MD simulation of Al at 300 K. (a) Dislocation populations of 1/2<110> (full), 1/6<112> (Shockley) and 1/6<110> (stair-rod) segments during the simulation. (b)-(f): The interplay of segments “1”, “2” and “3” leads to the formation of stair-rod arrangements which result in the onset of a SFT and a complex multi-junction. (g) Lomer-Cottrell junction detected in the MD simulation. The dislocations are labelled in accord with the corresponding slip plane. Segments in red, blue, and magenta correspond to full, Shockley, and stair-road dislocations, respectively. Orange atoms denote SF planes.
CHAPTER 6. DISLOCATION AVALANCHE EMISSIONS IN INTERMITTENT PLASTICITY
99 In the Cu simulation at 400 K, the depinning of dislocation segments from the network is also mediated through the aforementioned mechanisms involving SFT formation. The U Ž O evolutions in Fig. 6.12(b) show that the intermittent development of the dislocation entanglement is distinguished by (i) mild increases in the stair-rod populations (indicating SFT formation, see the circles in Fig. 6.12(a)) and (ii) a gradual reduction in Shockley density due to dislocation annihilation. At higher temperatures (e.g. at 650 K), the U Ž O curves from Fig. 6.12(d) show that the stair-rod density (pink curve) remains at a relatively fixed level during the simulation, indicating that SFT-mediated unzipping becomes inconsequential to the emission of the avalanches (red arrows in Fig. 6.12(b)). On the other hand, dislocation annihilation and cross-slip processes associated with Shockley partial dissociation play a much more important role in the development of the dislocation network (see red arrows in Fig. 6.12(d)). In this sense, it is noted that the enhancement of cross slip processes implies the arrangement of a defect configuration with much more intricate dislocation segments (cf. Figs. 6.8(a) and 6.8(b)). Finally, the greater KLM of Shockley partials in Cu (compare Fig. 6.8(a) with 6.8(c)) arguably hinder dislocation dissemination across the periodic volumes, leading to the attainment of smaller dislocation densities in the periodic simulation cell at 650 K in comparison with that obtained in the Al simulation at 300 K (cf. Figs. 6.11(a) and 6.12(c)).
Figure 6.12. Development of the defect networks in the Cu simulations. Fully-fledged dislocation networks (á ≈ 0.05) at 400 K and 650 K are given in (a) and (c), respectively. Circles in (a) denote large-sized SFT arrangements. Segments in red, blue, and magenta correspond to full, Shockley, and stair-road dislocations, respectively. Orange atoms denote SF planes. The serrated evolution of the ù Ž á curves from (b) and (d) are indicative of the intermittent development of the dislocation populations at 400 K and 650 K, respectively. Red arrows mark the onset of large avalanche events. See text for further details.
100