13th International Conference on Fracture June 16–21, 2013, Beijing, China -8- 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.16 Axial strain at failure 1 Experiment Percolation model -0.08 -0.07 -0.06 -0.05 -0.04 -0.03 -0.02 -0.01 0.00 True ligament strain Experiment Percolation model Figure 6: (a) Comparison of the experimental and predicted 95% confidence intervals for the true axial strain at failure and (b) true ligament strain. The number of voids in the particle field is representative of void nucleation and the experimental and numerical predicted values are presented in Figure 7b. The predicted number of voids in each of the particle fields are in are in very good agreement with the experimental measurements of Orlov [17]. The convergence of the nucleation predictions demonstrates that only several particle fields are required to obtain the general trends. The porosity and fracture strains in the previous figures are expected to exhibit the most variation because they are related to coalescence which is strongly dependent upon the local microstructure. This agreement with the experimental nucleation trends is very encouraging for the physical foundation of both the percolation and the nucleation models. 0.0% 0.1% 0.2% 0.3% 0.4% 0.5% 0 0.1 0.2 0.3 0.4 0.5 0.6 Equivalent plastic strain Porosity Exp. - Surface and Center Exp. - Surface Exp. - Center P1 P2 P3 P4 P5 50000 60000 70000 80000 90000 100000 110000 120000 130000 0 0.1 0.2 0.3 0.4 0.5 0.6 Equivalent plastic strain Total number of voids and cracks per mm 3 1 Exp. - Surface and Center Exp. - Surface Exp. - Center P1 P2 P3 P4 P5 Figure 7: (a) Comparison of the predicted porosity and (b) total number of voids and cracks in the center of the notch root. The experimental tomography data is from [17] using a standard tensile specimen. The average principal stress in the particles upon cracking (void nucleation) is shown in Figure 8a. Large particles crack at low stresses early in the deformation process while the smaller particles do not nucleate until the later in the deformation process. From this result, the stress required to fracture an Fe-rich particle is about 950 MPa. A strain-based nucleation criterion can also be developed by comparing the average volume of a broken particle to the global plastic strain
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