13th International Conference on Fracture June 16–21, 2013, Beijing, China -7- estimated load is used to calculate the displacement corresponding to a + Δaeff, from the theoretical compliance. Considering the scatter of individual load-displacement traces, the prediction up to maximum load is excellent. Thus, this very simple power law K-R procedure can be used to predict the non-linearity in concrete and stone structures up to maximum load. 0 20 40 60 80 100 0 50 100 150 200 250 300 350 400 Bažant KIeff = 17.8⋅Δa0.25 eff Pmax [N] W [mm] Bažant, Indiana limestone SE(B), S/W = 4 B = 13 mm, a0/W = 0.4 a) 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0 20 40 60 80 100 120 140 160 b) Bažant, Indiana limestone SE(B), S/W = 4 B = 13 mm, a0/W = 0.4 W = 25 mm P [N] Δ [mm] 0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0 50 100 150 200 250 c) KIeff = 17.8⋅Δa0.25 eff Bažant, Indiana limestone SE(B), S/W = 4 B = 13 mm, a0/W = 0.4 W = 51 mm P [N] Δ [mm] 0.00 0.05 0.10 0.15 0.20 0 100 200 300 400 d) KIeff = 17.8⋅Δa0.25 eff Bažant, Indiana limestone SE(B), S/W = 4 B = 13 mm, a0/W = 0.4 W = 102 mm P [N] Δ [mm] Figure 7. The prediction of load displacment dependence up to maximum load, based on simple effective K-R curve fitting to maximum load data. Data taken from [13]. Beyond maximum load, the connection between the effective crack length and the fracture process zone size breaks up. This is highlighted in Fig. 8. The load-displacement data was extracted from [1], so that for each specimen size representative upper and lower bound load-displacement traces were digitized. The effective crack length was estimated directly from the individual load-displacement data pairs, assuming that all the non-linearity is due to effective crack growth. Fig. 8a shows the effective crack driving force versus absolute effective crack growth and Fig. 8b shows the effective crack driving force versus proportional crack growth. Also included in the plots is the effective K-R curve estimated for the maximum load values. It is seen that for crack growth up to maximum load and slightly beyond, the effective K-R curve follows the absolute effective crack growth, whereas for large crack growths the effective K-R curve follows the proportional effective crack growth. This is a direct result of the fracture process zone evolution. Prior to maximum load, the fracture process zone is controlled by the fracture mechanical loading introduced by the crack. At some point, the connection between process zone size and the effective crack length breaks up. Finally, when the facture process zone has fully engulfed the crack and possibly extended to the free surface, the fracture process zone size develops as if there was no single crack in the structure.
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