PSI - Issue 5

Sameera Naib et al. / Procedia Structural Integrity 5 (2017) 1417–1424 Naib et al./ Structural Integrity Procedia 00 (2017) 000 – 000

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 Slip line trajectories agree to a fair extent with the theoretically predicted 45° lines for homogeneous bodies. Nonetheless, the trajectories show notable irregularities. The cause and implications of these irregularities deserve a profound further investigation, as discussed further in this paper. The discussion above relies on the validity of the finite element model. Therefore, numerically predicted slip line trajectories are evaluated by comparison with experiments. Figure 5(a) shows the points of maximum equivalent plastic strains eq,pl-max  when the notch is in OM region. Figure 5(b) shows the points of eq,pl-max  for notch located in UM region. The experimental points are shown by a black line and the points from simulation are shown as diamond markers. Obtained trajectories are depicted in conjunction with the hardness distribution.

20

20

45 0 line

45 0 line

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15

10

10

5

5

Y Distance (mm)

Y Distance (mm)

Notch

Notch

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0

-15

-10

-5

0

5

10

15

-15

-10

-5

0

5

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X Distance (mm)

X Distance (mm)

Simulation Experiment

Simulation Experiment

(a)

(b)

A first evaluation of the trend of deformation patterns indicates a satisfactory agreement between numerical simulations and experiments. The extracted locations of eq,pl-max  shows similar tendency in experiments and numerical study. The small variations observed between the two methods can be attributed to variety of reasons, either numerical (accuracy of the finite element model, transfer of hardness values to constitutive properties), experimental (scatter in optical strain measurement, variability of hardness map along the direction of welding) or analytical (significance of difference between total and plastic equivalent strain). Also, the disagreement between experimental and numerical slip lines can be related to the magnitude of strain and as the difference between total and plastic strain becomes more significant, the agreement decreases. A detailed analysis of the deformation bands shows that the points of eq,pl-max  are not straight as assumed by slip line theory. As Hertelé et al., 2016 points out, the deformation bands tend to avoid the harder regions and prefer relatively softer regions where there is less resistance to plastic deformation. Though the regions of maximum strains around the crack tip are at an angle of roughly 45 0 , deviations tend to become more pronounced in the plastic region away from the notch tip. This is due to the heterogeneous nature of the material, effect of ligament collapse and crack growth. Regarding the development of slip lines, Figures 6 and 7 shows the eq,pl-max  points at the beginning of plastic deformation and at maximum deformation. In order to maintain consistency with figures 4 and 5 , the points obtained from simulations are shown as diamond markers and experimental data are shown as lines. Most deviations between the theoretical 45° lines and observed patterns occur away from the notch tip. Hence, material heterogeneity tends to affect regions of smaller strains to a stronger extent. Related hereto, Ewing and Griffiths, 1971 showed that the applicability of slip line theory is strongest around the notch tip where highest degree of plasticity occurs. Likewise, we can see that the eq,pl-max  points invariably make an angle of 45 0 orientation around the notch tip and the deviations begin away from the notch as the influence of heterogeneity comes in to play. To confirm this observation, eq,pl-max  points were extracted at the initiation of plasticity and at maximum deformation from simulations and experiments. eq,pl-max  on SE(T) specimen surface at maximum applied deformation (a) deformation pattern for a notch located in the strength overmatching (OM) weld region and (b) deformation pattern for the notch in the strength undermatching (UM) region Figure 5: The points of