13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- Butcher et al. [11] adapted the volume-based criterion of Moulin et al. [12] for the break-up of irregularly shaped particles during rolling to ellipsoidal particles for void nucleation as: * 1c * 1c 1c 6 1 1 N p K K K V σ α α π = = ≈ (12) where * 1C K is the effective critical toughness of the particle material, Vp is the average particle volume and α is a geometry parameter in the Griffith mode I crack criterion to account for various effects such as crack blunting. This criterion contains only one physically-based parameter, K1c, and captures the particle size-effect where small particles nucleate at high strains while large particles nucleate at low stresses [13]. The nucleation model also predicts that brittle phases are more likely to crack than more ductile phases. 3. Generation of representative particle fields A particle field generator was developed and implemented into LS-DYNA [6] as a pre-processor for the percolation model. The measured probability distributions from micro-tomography studies were then re-created using rejection-sampling techniques. In this work, the distributions obtained by Orlov [14] were adopted for the semi-axes, orientations, volume fractions, and spacings of the voids and particles found in AA5182. The coupling of the percolation model with a particle field generator can enable stochastic predictions of fracture by performing multiple percolation model simulations. A typical particle field with a volume of 200 μm x 200 μm x 200 μm is shown in Figure 4 where the clustering of the voids and particles is evident along with their preferential orientation along the rolling direction. The respective number of voids, Mg2Si and Fe-rich particles in this volume are 447, 616, 5273, corresponding to volume fractions of 0.053%, 0.049% and 0.483%. Figure 4: Generated particle field of AA5182 with a volume of 200 µm x 200 µm x 200 µm.
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