PSI - Issue 2_A

Solveig Melin et al. / Procedia Structural Integrity 2 (2016) 1351–1358 S Melin, P Hansson, A Ahadi / Structural Integrity Procedia 00 (2016) 000–000

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Table 2 Strain at plastic initiation: ε i , ε i e , ε iv for geometries Fig. 1 (a-c), at rupture : ε f , ε fe , ε f v for geometries Fig. 1 (a-c), and closure strain ε cv for geometry Fig. 1c.

s [orient] Solid Beam ε i

6 a 0 [100] 12 a 0 [100] 18 a 0 [100] 6 a 0 [110] 12 a 0 [110] 18 a 0 [110]

0.092 0.270 0.050 0.135 0.053 0.068 0.125

0.089 0.555 0.055 0.228

0.087 0.378 0.053 0.248

0.064 0.235 0.030 0.148 0.030 0.060 0.103

0.063 0.353 0.027 0.275

0.064 0.578 0.027 0.265

ε f

Beam with edge defect ε ie Beam with through void ε iv ε fe

0.068

0.065

0.040

0.035

-

-

-

-

ε cv ε fv

0.203

0.295

0.298

0.565

3.1 Solid beams Plasticity is forced along {111}-planes as expected, and rupture occurs through necking somewhere along the beam. From Table 2 and Fig. 3, solid lines, it is noticed that the strain at plastic initiation, ε i , seems practically independent of cross section size for each orientation. But the [110]-orientation initiates first, in the interval 0.70 < ε i [110] / ε i [100] < 0.74. Also failure occurs first for the [110]-orientation for the two smallest cross section sizes; with ε f [110] / ε f [100] ≈ 0.87 for s = 6 a 0 and ε f [110] / ε f [100] ≈ 0.64 for s = 12 a 0 . The exception is the case of s = 18 a 0 in the [100]-orientation which ruptures before s = 18 a 0 in the [110]-orientation, with ε f [110] / ε f [100] ≈ 1.5. A closer investigation shows that this is due to the placement of the necking region. All beams, with the exception of the case s = 18 a 0 in the [100]-orientation, necks away from the clamped ends of the beams. For s = 18 a 0 in the [100]-orientation, however, the neck forms close to one end where the constraint influences its vicinity and speeds up the necking process. 3.2 Beams with edge crack-like defects By introducing an edge defect the beam is weakened in the sense that both the strain at plastic initiation, ε ie , and at rupture, ε fv , are lowered for both orientation, cf. Table 2 and Fig. 3, dashed lines. Again, initiation of the first slip event seems independent of s . The [110]-orientation initiates plasticity first, with 0.49 < ε ie [110] / ε ie [100] < 0.60, like for the solid beams. Here, however, the [100]-orientation ruptures first, with 1.1 < ε fe [110] / ε fe [100] < 1.2, opposite to what applies to solid beams that necked away from the clamped ends. The invers rate becomes ε fe [100] / ε fe [110] ≈ 0.87, so that the orientations now behave conversely. Comparing to the solid beams, the strain at initiation drops more for the [110]-orientation than for the [100]- orientation, with 0.43 < ε ie [110] / ε i [110] < 0.47 and 0.54 < ε ie [100] / ε i [100] < 0.62, respectively. The opposite applies to the failure strain, where 0.46 < ε fe [110] / ε f [110] < 0.78 and 0.41 < ε fe [100] / ε f [100] < 0.50 with exclusion of the case s = 18 a 0 , respectively. The events during deformation are illustrated in Fig. 4 by snapshots showing the CSP for the case s = 6 a 0 and both orientations. Slip occurs along {111}-planes first emerging from the defect corners, and rupture eventually occurs through necking in this, initially defect, region. Final failure takes place due to sliding along the weakest slip planes. Thus, the edge crack-like defects do not in any of the cases show a mode I crack-like behavior, breaking atomic bonds. Only shear mechanisms are active. As seen from Figs 3a),d), showing the states after relaxation but prior to load application, the cavities are somewhat expanded due to lack of interatomic bonds across the free defect surfaces, causing the beams to bend slightly. This is most pronounced for the [100]-orientation. This is due to that, for the [110]-orientation, the surfaces are somewhat rougher than for the [100]-orientation, giving higher attraction over the void in the [110]-orientation due to slightly shorter interatomic distances.