PSI - Issue 13

Per Hansson / Procedia Structural Integrity 13 (2018) 837–842 Per Hansson/ Structural Integrity Procedia 00 (2018) 000 – 000

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Also in the case of an edge defect in the beam, three different δ xmax , the same as used for the centrally placed void, where considered. The results in Fig. 5 show that initiation of plasticity (first drop of the curve) occurs at higher values than for the case of a centrally placed void, cf. Fig. 4, as also seen from Table 1. However, it is in the case of an edge defect only in the case with the lowest load steady state was found. For the two higher loads, the stress drops in the following load cycles, due to increased plasticity. The beams eventually rupture after five and eight cycles, respectively.

Fig. 5. Stress, σ x versus time, t for beams with an edge defect at T = 300K for three different values of δ xmax .

3.3 Atomic configurations and events during the first load cycle For the solid beams events during the first load cycle are illustrated in Fig. 6, which zooms in the first part of Fig. 3, together with atomic snapshots at key events in the case of δ xmax ,=15.36Å (blue curve), with atoms color coded by the CSP parameter. The first snapshot (1) is directly after relaxation, the second (2) is at the initiation of plastic deformation and the third (3) at zero displacement after the first load cycle. It can clearly be seen that the plastic initiation results in a large drop in σ x and that the deformation consists of slip along several close packed [110] directions in the material. At this highest applied displacement, marked * in Fig. 6, the plasticity has spread out over a larger portion of the beam.

Fig. 6. Events during the first load cycle a solid beam with δ xmax =15.36Å, cf. Fig. 3. The atomic snapshots are color coded by the CSP with blue corresponding to 0 and red above 30.* Denotes δ xmax . In the case of a centrally placed void the events during the first load cycle are illustrated in Fig. 7, which zooms in the first part of Fig. 4, for the case of δ xmax =10.85Å (red curve). The first drop in the curve (2) is a result of the collapse of the void, due to plastic deformation in the vicinity of the void. The second drop (3) corresponds to the formation of new slip planes, similar to what was observed for the solid beam, over a larger portion of the beam. The third drop, at maximum displacement (4), also corresponds to further formation of new slip planes. An observed difference is that in the case of a void all slip planes have the same directions whereas in the case of a solid beam a sick sack pattern of planes was observed. Lastly, in the case of an edge defect the events during the first load cycle is illustrated in Fig. 8 , which zooms in the first part of Fig. 5, for the case of δ xmax =9.941Å (blue curve). Here it can be seen that after the initial relaxation (1) the beam is already bent due to the non-symmetric geometry. The first drop in the stress curve (2) is explained by initiation of plastic deformation in the vicinity of the defect. The second drop (3) occurs as a result of spread of the plasticity to a larger area of the beam, just before reaching maximum displacement. Compared to the case of a void and solid beam, the plasticity is more local around the defect, and not spread out over a large part of the beam as in the other cases. Here also a picture describing the beam at zero displacement is shown (4). Here it can clearly be seen that the beam is bent, due to the increased length of the beam through plasticity in the loading part of the load cycle.