PSI - Issue 13

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

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

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T =300K. In Fig. 3 the results for defect free solid beams are presented for four different values of δ xmax , three at T =300K and one, for comparison, at T =0.01K with higher value of δ xmax (red line). It can be seen that in the case of T=0.01K the stress is higher in the first load cycle than in the following cycles. This is because the beam undergoes plastic deformation already in the first load cycle, resulting in lower stress in the following cycles. The point of first plastic initiation can be seen as a large drop in stress. During the following cycles a steady state emerges, both regarding spread of plasticity in the beam and the maximum stress in each load cycle.

Fig. 3. Stress, σ x versus time, t for solid beams at T = 300K without any defects for three different values of maximum displacement δ xmax . For comparison also one simulation at T= 0.01K is included with δ xmax .=18.075Å (red line). For the three cases at T=300K different scenarios are found depending on δ xmax . For the lowest value, δ xmax =10.85Å, it can be seen that all stress cycles are almost identical. This is because in this case no plastic deformation of the beam takes place, resulting in fully elastic deformation with no accumulation of damage through the load cycles. For the two higher values of δ xmax plasticity occurs already in the first load cycle, resulting in lower stress amplitudes in the following load cycles. In the case of δ xmax =13.56Å only a very limited amount of plasticity accumulates, still this does not lead to a steady state in the following cycles, as seen in the case of T=0.01K. Instead the maximum stress in the load cycle continues to drop in each cycle, although failure never occurs during the ten applied load cycles. For the highest value of δ xmax =15.36Å, more extensive plasticity is formed in the first load cycle, with following reduction in maximum stress in the following cycles and rupture of the beam in the eight load cycle, seen as a flat portion of the curve in Fig. 3. Snapshot of these events are presented in section 3.3, together with a more detailed description of the events in the first load cycle. In the case of a centrally placed void in the beam, three different δ xmax where considered, lower than for the solid beam to avoid rupture already in the first load cycle, cf. Fig. 4. In this case it can be seen that for the two lowest values of δ xmax, a steady state was observed after the initial cycle in which massive plastic deformation occurred. Although there is a large difference in the amount of plastic deformation in the first cycle between the two simulations, no additional plasticity occurred in the following cycles. However, for the largest value of δ xmax, no steady state was observed and the stresses reduced rapidly already in the second cycle where additional plasticity occurred. This led to rupture of the beam already in the third load cycle, seen as a region of almost zero stress in the stress-time curve, cf. Fig 4.

Fig. 4. Stress, σ x versus time, t for beams with a centrally placed void at T = 300K for three different values of δ xmax .