Issue 75

R. Ince et alii, Fracture and Structural Integrity, 75 (20YY) 435-462; DOI: 10.3221/IGF-ESIS.75.30

Figure 12: Test details of limestone specimens a) fractured flexural and compressive specimens b) notched beam test setup c) fractured notched beams d) SNCB specimen test setup e) fractured SNCB specimens. As stated above, the peak load method based on TPM is an optimization-based technique since the number of unknowns (three or more distinct specimens must be tested to ensure statistically valid results) is greater than the number of equations (Eqns. (1) and (2)). The objective function of the optimization problem is to minimize Eqn. (6), while the constraints of the problem are the critical crack lengths, which must be greater than initial crack lengths and smaller than specimen depth as detailed below. Fig. 13 indicates the implementation of the peak load method to beams and SNCB specimens with Elazig limestone. The K s Ic and CTOD c plots of the beams are demonstrated at the top, and those of the SNCB specimens are at the bottom, while the s - K s Ic plots based on Eqn. (6) are illustrated in the middle in Fig. 13. For the dimensionless functions used in drawing the K s Ic and CTOD c plots, Eqns. (3)-(5) were used for beams, while Eqns. (16), (19), and (21) derived in this study were employed for SNCB specimens. This figure shows that there is a strong correlation between the unstable fracture toughness of Elazig limestone for both specimen types. To compute the initiation fracture toughness based on the double- K , Eqns. (9) and (27) were employed for beams and SNCB specimens, respectively. The fracture quantities corresponding to each   value were reported for two different bending specimens in Tab. 8. In the last column of Tab. 8, the relative crack extension values (  c ) are also presented for each specimen and each   value. These values demonstrate that the effect of the FPZ on the fracture quantities of rocks cannot be ignored, as it is in other quasi-brittle civil engineering materials such as concrete and asphalt concrete. Although both specimen types are subjected to three-point bending loading, the  c values of beams are smaller than those of SNCB specimens. The most important reason for this is that SNCB specimens behave like deep beams, where the depth of the compression zone is larger than that of the beam under three-point bending loading. On the other hand, it is well known that the depth of crack extension at the peak load is not a fracture parameter and varies depending on specimen type and specimen size in quasi brittle materials [2].

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