13th International Conference on Fracture June 16–21, 2013, Beijing, China -5- Table 2. Outline of theoretical and numerical parameters for the strain energy density evaluation for the tested graphite specimens ρ [mm] β [°] a [mm] F [N] Fth [N] Δ [%] σmax [MPa] SED [MJ/m3] 0.25 0 10 3967 4146 4.31 87.0 0.1201 0.5 0 10 4060 4200 3.35 67.0 0.1225 1 0 10 3998 4483 10.82 51.8 0.1044 2 0 10 4967 5089 4.96 51.1 0.1251 4 0 10 4910 5434 9.64 45.1 0.1070 0.25 30 10 3991 3981 2.54 90.4 0.1317 0.5 30 10 4022 4030 4.41 67.7 0.1308 1 30 10 4125 4479 7.90 52.9 0.1111 2 30 10 4609 5080 9.26 47.8 0.1079 4 30 10 4775 5501 13.18 42.8 0.0991 0.25 45 10 3786 3857 2.98 89.4 0.1264 0.5 45 10 3893 4062 4.29 66.2 0.1205 1 45 10 4121 4309 4.36 56.5 0.1200 2 45 10 4972 5006 1.18 53.8 0.1293 4 45 10 4777 5243 8.90 45.6 0.1090 0.25 60 10 3995 4027 3.31 94.3 0.1291 0.5 60 10 3856 4066 5.18 68.1 0.1179 1 60 10 4114 4160 3.03 57.3 0.1283 2 60 10 4496 4669 3.71 50.7 0.1215 4 60 10 4553 5078 10.34 45.5 0.1055 The averaged strain energy density criterion (SED) as presented in Refs. [18-22] states that brittle failure occurs when the mean value of the strain energy density over a given control volume,W , is equal to a critical value Wc. This critical value varies from material to material but is not dependent on the notch geometry and sharpness. The control volume is considered to be dependent on the ultimate tensile strength and the fracture toughness KIc in the case of brittle or quasi-brittle materials subjected to static loads. Under plane strain conditions the critical length, Rc, can be evaluated according to the following expression [20]: 2 t Ic c σ K 4π 8 ) ν (1 )(5 R ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ + − ν ⎛ = (1) where KIc is the fracture toughness, ν the Poisson’s ratio and σt the ultimate tensile stress of a plain specimen that obeys a linear elastic behavior. This critical value can be determined from the ultimate tensile stress σt according to Beltrami’s expression 2E W 2 t c σ = (2)
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