PSI - Issue 13

Guiyun Gao / Procedia Structural Integrity 13 (2018) 51–56 Guiyun Gao/ Structural Integrity Procedia 00 (2018) 000 – 000

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For the Mode I, Mode II and mixed Mode in plane problems, the displacement fields can be expressed as function of stress intensity factor (Gao et al., 2015a; Gao et al., 2015b). If the displacement u x and u y within a certain distance from crack tip could be determined, the mode I and mode II stress intensity factor K I and K II could be determined by using a least square method. Here a virtual extensometer technique was used to assist the dynamic fracture analysis. By setting the virtual digital extensometer along the crack path, the crack open displacement of each frame could be determined(Shah and Kishen, 2011). The crack tip position and the crack propagation velocity could also be calculated by combining the least square method and the virtual extensometers. The dynamic loading was exerted with a 25 mm diameter SHPB system, which contains a gas pressure gun, a striker bar and an incident bar. Using a modified hydraulic press, the uniaxial compression was exerted at the top and bottom ends of the rock plate (Fig. 1). An adapter was introduced here to ensure uniform pressure exerted at the top end of the plate. The hydraulic pressures were changed from 0 MPa to 30 MPa, while the confining stress exerted on the specimen were about 0 to 10.6 MPa. An ultra-high speed framing camera (model: Ultra UHSi 12/24 IVV Imprint™) was utilized in our tests. The frame rate used in our tests was 50000 f ps. 3. Experiments

Fig. 1 Experimental setups

The Young’s modulus is 32.5 GPa and the Poisson’s ratio of the granite is 0.24. And the tensile strength is 5.34MPa. The size of the granite specimen is about 305 mm × 305 mm × 10.5 mm. A notched crack, with about 10 mm in length and 0.9 mm in width, was fabricated using a diamond impregnated saw. 4. Results and discussion The displacement fields’ evolution during the dynamic facture process could be calculated using DIC method. Typical vertical displacement u y field evolutions are shown in Fig. 2. The vertical opening displacement increases with loading time. And the crack initiates at 120s when the open displacement near the crack tip increases to the critical value. For this typical specimen (ps2), the crack propagation velocity is about 843.6 m/s. The fracture toughness K Ic is 1.39 MPa∙m 1/2 . The crack propagation velocities and fracture toughness under different incident velocities were calculated using DIC method combined with facture mechanics analysis. As the loading speed increases, the fracture toughness increases from 1.39 MPa∙m 1/2 to 2.25 MPa∙m 1/2 , while the crack propagation velocity increases from 843.6 m/s to 1148.3 m/s (shown in Fig. 3). These results reveal the so-called loading rate dependency for rock materials(Gao et al., 2015b). The crack propagation velocity change from 0.42 C r to 0.57 C r , which is higher that obtained using small specimens(Gao et al., 2015b)..