13th International Conference on Fracture June 16–21, 2013, Beijing, China -2- Crack in rock test specimens are usually created either with a straight front or a chevron shape, as shown in Figure 1. The chevron notched SCB specimen in the static mode has been rarely studied and only a limited SIF calibration was done by Kuruppu using a 3D finite element method [7–9]. The fracture toughness values of SCB with straight crack are calculated from [10]: ( , ) 2 π = f IC I P a K Y a R S R Rt (1) where fP is the maximum failure load, I Y is the dimensionless stress intensity factor, t, R and a are the thickness, radius of SCB specimen and crack length, respectively. I Y , also known as geometry factor, is a function of the ratio of crack length over the semi-disc radius (a R ) and the ratio of half-distance between the two bottom supports over the semi-disc radius (S R ) [11]. Lim et al. [10] found SIFs in terms of a R and S R . Their results can be summarized by the following relation: ( ) 2 3 4 5 2.91 54.39 391.4 1210.6 1650 875.9 α α α α α = + − + − + I Y S R (2) where α is a R . If a standard CCNBD specimen is cut into two equal parts, two pieces of CCNSCB are obtained. Figure (1-c) shows the chevron notched SCB specimen and its geometrical coefficients. 0 0 ( ) α =a R , 1 1 ( ) α =a R and ( ) α = m a R are the dimensionless initial crack length, dimensionless final crack length and dimensionless critical crack length, respectively. αs is a coefficient obtained from dividing sR (radius of rotary saw) by R. Also ( ) α = B B R is the normalized thickness. Similar to the equation suggested by ISRM for the CCNBD specimen [4], the initiation fracture toughness IC K of CCNSCB specimen can be determined as: min * max = IC P K Y B D (3) where max P is the measured maximum load, B and D are the thickness and diameter of the disc respectively, min * Y is the minimum value of * Y , which is the dimensionless stress intensity factor (SIF). It should be noted that all the restrictions and the geometrical relationships for the CCNBD is assumed to be applicable to CCNSCB too. So far, several approximate analytical methods have been used to determine * Y , although applicability and accuracy of any of these methods have not been evaluated in CCNSCB. In this paper a slice synthesis method (SSM) is presented to evaluate the minimum dimensionless stress intensity factor in the CCNSCB specimen. Then, its accuracy is examined using both experimental test and finite element method. Experimental results show that the CCNSCB specimen can be employed for measuring rock fracture toughness. 2. Slice synthesis method in CCNSCB specimen Slice synthesis method, proposed first by Bluhm [12], is a semi-analytical method for solving fracture problems with curved crack fronts. Wang et al. [13] used the SSM to calculate the stress intensity factor of CCNBD. In this method, the thickness of the sample is cut into a number of slices each with a thickness Δt as shown in Fig. 2. The analysis of a single slice is easier than analyzing the whole specimen. First, analytical equations are written for each slice. Then, by combining these equations, an equation for the entire sample can be achieved according to the
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