13th International Conference on Fracture June 16–21, 2013, Beijing, China 11 ' a f K c π σ =− Ι (10) where 12 11 11 8 3 2 1 1 c c f = + + . It is clear, for 0=θ τ r ， 0 ' = ΙΙ K . 2.3 Stress intensity factors under both confining pressure and diametrical forces loading condition The cracked disk subjected to a pair of diametral-compressive forcePand ambient confining pressure cσis shown in Fig.3. ais the half length of the crack, the disk radius is R and thickness is B, θ is the loading angle (the angle of inclination of the crack relative to the line of loading). The stress intensity factors for cracked Brazilian disk subjected to a pair of diametral-compressive P have been given as [2] ] [ 2 2( 1) 1 1 1 11 '' − = Ι ∑ + = i i n i i A f a f K α π σ （11） 2( 1) 2 1 2 '' 2 − = ΙΙ ∑ = i i n i i a A f K α π σ （12） where BR P π σ= , coefficients ji f and angle coefficients ji A (j=1,2; i=1,2,…...n) are shown in the literature[2]. Fig.3 Cracked Brazilian Disk under both confining pressure and diametrical forces loading Now, based on the diametral-compressivePload, the confining pressure ( cσ) was applied. By employing the superposition principle of stress intensity factors [12], the stress intensity factors for cracked Brazilian disk under both confining pressure cσand diametrical forcesPcan be obtained '' ' Ι Ι Ι = + K K K ] [ 2 2( 1) 1 1 1 11 11 − = ∑ + + =− i i n i i c A f a f a f α π σ π σ 2( 1) 1 1 1 11 2 ) ( − = ∑ + = − i i n i i c a A f a f α π σ π σ σ （13） By letting / c t σ σ= , then c t σ σ = . Where t is a dimensionless scaling factor (simply called confining pressure coefficient) and different confining pressure coefficients are correspond to different confining pressures. Then IK can be written as 2( 1) 1 1 1 11 2 (1 ) − = Ι ∑ + = − i i n i i a A f t a f K α π σ π σ （14 ） The normalized stress intensity factor, IF may be written as 2( 1) 1 1 1 11 (1 ) 2 − = Ι Ι ∑ = = − + i i n i i t f A f a K F α π σ （15）
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