PSI - Issue 39

Mahsa Sakha et al. / Procedia Structural Integrity 39 (2022) 792–800 M. Sakha et al. / Structural Integrity Procedia 00 (2019) 000–000

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3

C

C

P/B

R

R

B

a

a

S 2

S 1 =0.8R

S 1 =0.8R S 2

Section CC

C

C

( a )

( b )

Fig. 1. Schematics of the SCB test setup for (a) K II / K I > 0 and (b) K II / K I < 0

of the fracture toughness in anisotropic solids are given by Nejati et al. (2020b); Bahrami et al. (2020). The crack tip parameters, including K I and K II and the T-stress, are calculated using the finite element method. In doing so, the SCB specimen was modeled in the finite element software ABAQUS, where K I and K II were determined using the domain integral method. In addition, the values of the T-stress were determined using the finite element over-deterministic method (FEOD) (Ayatollahi et al., 2020). Table 2 gives the T-stress values calculated in a dimensionless form as ¯ T = T √ 2 π L c / K 2 I + K 2 II in all the test configurations. Table 1. The mechanical properties values measured for the Grimsel Granite. Here, ξ = E / E is the anisotropy ratio of Young’s modulus, and η is defined as η = G / G sv , where the transverse shear modulus G sv is given by Nejati et al. (2019b) Elastic moduli [GPa] Dimensionless elastic properties Fracture toughness [MPa √ m] FPZ length [mm] E E G ν ν ξ η K Ic , 1 K Ic , 2 K IIc , 1 K IIc , 2 L c 36 18 10 0 . 3 0.15 2 1 0.78 1.35 1.90 2.88 10

Table 2. Dimensionless values of T-stress, ¯ T , measured for the four sets of experiments at different orientations of β . The loading ratio K II / K I of each set is also given. β ( ◦ ) K II / K I 0 15 30 45 60 75 90 Set I -0.4 -0.89 -1.01 -1.02 -0.96 -0.87 -0.78 -0.71 Set II 0.4 -0.90 -0.76 -0.64 -0.59 -0.60 -0.65 -0.72 Set III -1 -1.99 -2.13 -2.00 -1.88 -1.73 -1.59 -1.54 Set IV 1 -2.05 -1.85 -1.70 -1.58 -1..51 -1.51 -1.49

3. Fracture growth

Fracture growth is a process by which a pre-existing stressed crack propagates from the crack tip. There are several fracture criteria in the literature which can predict the onset of fracture propagation in anisotropic rocks. Among the theories proposed to predict fracture growth in anisotropic solids, maximum tangential stress (MTS) and maximum energy release rate (MERR) are notable. These fracture growth models are now adopted to predict the kink angle as well as the effective fracture toughness observed in 99 fracture toughness tests on the Grimsel Granite samples. To enhance the accuracy of the fracture growth predictions, the T-stress, a stress term parallel to the crack, is also included in the formulation.