13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- at which it nucleated as shown in Figure 8b. All of the particle fields display the well-known behaviour that small voids will nucleate only at high strains while larger particles display a negligible size effect and have a near constant nucleation stress or strain. Orlov [14] experimentally observed that no particles that had a volume smaller than 17.8 μm3 nucleated a void and this is in accordance with the predictions of the model. 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 True axial strain Average particle nucleation stress (MPa) P1 P2 P3 P4 P5 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0 10 20 30 40 50 60 70 80 90 100 110 120 Average volume of a broken particle (μm3) Equivalent plastic strain at nucleation1 P1 P2 P3 P4 P5 Figure 8: (a) Comparison of the average maximum principal stress in the particles at nucleation and (b) equivalent plastic strain in the matrix upon nucleation. 6. Summary The complete damage percolation model was used to predict fracture and damage evolution in a notched tensile sheet specimen of AA5182 sheet. Representative particle distributions were created and mapped to the percolation elements located at the notch root where fracture initiates in the sample. The fracture strain, porosity, and nucleation predictions of the model are in very good agreement with the experiment data of Orlov [14]. No calibration or adjustable parameters were employed in the model and its good predictions of the experiment data attest to the strong physical foundation of the model. Fracture is a sole consequence of the stress state, material composition and the particle distribution. The main advantages of the present percolation model are that it is directly coupled into a finite-element code, contains a particle field generator as a preprocessor, and rests upon a minimum of assumptions regarding void evolution. At present, the main limitation of the model is its significant computational cost. The next phase of development of the percolation model will address this limitation and involve a large-scale application to a practical metal forming operation. References [1] Gurson, A.L. (1977). Continuum theory of ductile rupture by void nucleation and growth – Part I. Yield criteria and flow rules for porous ductile media. J. Eng. Mech. Tech. 99, 2-15. [2] Butcher, C. (2011). A multi-scale damage percolation model of ductile fracture. Ph.D. thesis, University of New Brunswick, Canada: http://dspace.hil.unb.ca:8080/handle/1882/35391
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