13th International Conference on Fracture June 16–21, 2013, Beijing, China -9- (a) (b) (c) (d) Figure 12. Static crack growth in the CT geometry. Loading–pin displacements of (a) 24Å, (b) 40Å, (c) 60Å, and (d) 70Å are shown. Plots are colored according to element values of σyy in units of GPa as shown in the legend 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 loading pin reaction force (KN) loading pin displacement (Å) Figure 13. Reaction force versus loading-pin displacement for CT specimen The crack opening behavior due to displacement of the top and bottom pins is observed in Fig.12. Before crack propagation begins to occur, the cohesive zone begins to form, as seen in Fig.12(a) and (b). Once a critical displacement is reached, crack propagation is seen in Fig.12(c) and (d). We can further verify our analysis by taking the value of peak load in Fig.13, 68.06 kN, and combining it with geometric dimensions of the system to obtain the stress intensity factor. We obtain a value for fracture toughness of Jc=0.42 MPa·m. This value lies close to experimental result in literature [19]. Our study shows that the estimated fracture toughness coincides with test value from experiment. It shows the expected linear relationship between loading-pin displacement and reaction force. More complex fracture mechanics problems can be analyzed through combining the cohesive law derived from MD simulations and finite element method. 6. Conclusion
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