13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- highly localized at the notch root. A previous study by Butcher and Chen [15] using a Gurson-based constitutive model has shown that the only appreciable damage occurs within this region (Figure 5c). The resulting ligament and axial strains are extracted from the FE model upon the onset of element deletion. The simulations are repeated five times for particle fields denoted P1-P5 that were generated from the tomography data of Orlov [14]. (a) (b) (c) Figure 5: (a) Typical notch geometry. (b) 1/8th FE mesh showing percolation elements and (c) Porosity distribution obtained by Butcher and Chen (2011) using a traditional GT damage model. 5. Results and discussion The predictions of the percolation model for the axial and ligament strain with the experimental values are shown in Figures 6a and 6b. The fracture strains are presented as 95% confidence intervals due to the stochastic nature of the percolation model. Although only five particle fields were considered, the variation in the axial strain predicted by the percolation model is comparable to the experimental variation. The predicted porosity distributions of the five particle fields considered are shown in Figure 7a. All of the particle fields are in excellent agreement with the experimental porosity data of [14] at a plastic strain up to 0.10 and show generally good agreement at the higher strain levels. All of the particle fields considered, P1-P5, exhibit the same behaviour where deformation is relatively homogenous until the commencement of void nucleation at higher strains. The start of nucleation is followed by localized coalescence which promptly sweeps throughout the particle field causing failure. The fracture porosities are also in good agreement with the metallographic observations of Smerd et al. [17] who reported failure porosities on the order of 0.3%.
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