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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2.3. Analysis of plastic deformations

The analysis of plastic deformations is the initial step to extract slip lines originating from the crack tip. In this study, plastic deformations are expressed in terms of equivalent plastic strains ( ) eq,pl  . These strains are obtained at the nodes in the finite element model and using DIC in experiments. The experimental technique is based on equivalent elastic-plastic strains rather than equivalent plastic strains as DIC cannot differentiate between linear-elastic and plastic components of strain. Hence the linear elastic part is neglected. The full field strain distributions are obtained at the surface of the specimen, making it a 2D analysis on a 3D model. The maximum strains in experiments and simulations are obtained by creating a series of grid points parallel to the notch on the surface of the specimen. The maximum values of eq,pl  is extracted from each of the lines. The process is explained in detail in Hertelé et al., 2016. It should be noted that the theoretical slip line analysis relates to the Tresca’s criterion for plastic flow upon attainment of a critical value of maximum shear stresses, in an isotropic 2D elastic-perfectly plastic material (Hill, 1950). Instead, equivalent plastic strain eq,pl  rather relates to von Mises’ plasticity criterion.  eq,pl relates to the von Mises equivalent stress through the material’s uniaxial true stress -true strain behavior. The link between theoretical slip lines (trajectories of maximum shear stress) and observed ones through strain analysis will be evaluated in the next section. The starting point of this section is a finite element analysis based evaluation of the relevance of maximum strain analysis with respect to slip line field theory, as questioned in the previous paragraph. Points of maximum shear stress max  ( related to Tresca’s criterion ) and of maximum equivalent plastic strain eq,pl-max  (related to von Mises’ criterion) were extracted from the analysis grid ( refer Section 2.3 ) at maximum applied deformation in both numerical simulations. Trajectories of max  and eq,pl-max  originating from the notch are shown in Figure 4 . This graph is plotted at highest deformation rate. Fig. 4(a) shows the points of max  and eq,pl-max  for the specimen having the notch located in the OM region and Fig. 4(b) shows the points for the notch located in UM region of SE(T) specimens. Shown as a reference are 45° oriented straight lines, predicted to act as slip lines within the severe assumptions of slip line field theory. 3. Results and discussions

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45 0 line

45 0 line

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Y distance (mm)

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Notch

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X Distance (mm)

X Distance (mm)

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eq,pl-max  and max  obtained from simulations of two configurations – Notch located in OM (a) and

Figure 4: The comparison between

notch located in UM (b)

Two observations are made from Figure 4:

 Omitting marginal differences, trajectories of eq,pl-max  and max  are similar. This confirms that strain analysis (e.g. facilitated by means of DIC) may serve to investigate the influence of weld heterogeneity on the development of (shear stress based) slip lines.