Issue 40

K. Kaklis et alii, Frattura ed Integrità Strutturale, 40 (2017) 1-17; DOI: 10.3221/IGF-ESIS.40.01 5             n 2i 2 ΙI i i i 1 N 2sin 2 B θ S (9) where the first five values of i T , i S and the corresponding   i A θ ,   i B θ are given in Tabs. 1 and 2 in Ref. [4], respectively. Fig. 3 presents the variation of the dimensionless coefficients Ι Ν , IΙ Ν with respect to the inclination angle θ for dimensionless notch lengths    0.1 0.6 . (a) (b) Figure 3: The dimensionless coefficients (a) Ι Ν and (b) IΙ Ν for    0.1 0.6 . In the ISRM suggested methods [6] the mode I fracture toughness IC K of CCNBD specimens [6, 14, 15, 16] can be calculated by the following equation:    * max IC min P K Y B D (10) where max P is the maximum load that can be sustained by the specimen and * min Y is the minimum (critical) dimensionless stress intensity factor which is determined by the specimen geometry parameters   0 1  ,  and  B only, and is given by:     *  v 1 min Y u e (11) where u and v are constants determined by  0  and  B only [6]. Changing the angle between loading direction and chevron notch orientation (i.e. angle θ in Fig. 1b), fracture toughness tests can be performed under mode II and mixed mode I-II loading conditions. Thus, for pure mode I loading, the crack direction should be exactly along the applied diametral force (i.e.,  o θ 0 ), while a pure mode II condition in CCNBD specimen is achieved when the dimensionless SIF * I Y in relationship (5b), is equal to zero. According to Fig. 3a,  * I Y 0 when the crack inclination angle θ is about o 23 . Several researchers have also determined this angle to range between 20 and 24 degrees using numerical models [11, 14]. Markides et al. [17] and Markides and Kourkoulis [18] through analytical solutions of short straight through cracks and bigger cracks obtained from elliptic holes respectively, calculated, also, this angle as a function of the dimensionless crack length from a maximum value of about 29 degrees for  α / R 0.1 (very short crack) to about 22 degrees for  α / R 0.5 . Calculation of the Critical crack length Different dimensionless values for the critical crack length have been proposed in the literature. In the ISRM Suggested methods [6] it is stated that the critical crack length is   * m 0.5149 (for a specimen geometry given by Eq. (2)) without any explanation of how this value was calculated. For the exact same specimen geometry, Wang et al. [7] proposed to use a critical crack length of 0.49, while a value of 0.4915 is derived in the present paper, by minimizing the dimensionless Stress