Y-F. Liu et al./ Mechanics of Materials 29(1998)111-121 Table 2 oG;=20.0N/m Basic microstructural parameter set for numerical study G;=12.0N Debonding toughness, Gic (N/m) C/c=0.5 =1000MPa △G;=6.0N/m Frictional stress, T(MPa) Temperature change, AT(K) Fiber volume fraction, f bE Altered parameters are indicated in the corresponding figure 4.1. Composite fracture criterion 0.0 Considering the plane-strain condition for a Normalized position, x/c Mode-I crack lying in the plane of transverse Fig. 8. Influences of G on the distribution of bridging stress. sotropy, Budiansky and Cui (1994)obtained the following expression of critical Mode-I stress inten- sity factor, Kic, on the basis of energy balance KIc is obtained from Eq (13). Then, a crack growth length of Ac is extended, leaving intact fibers be- E(1-m(1-f (13) bridging, the value of K, is reduced (d K/dc <0)so that gradually increasing loading is required to sat isfy KI=Kic. The newly obtained loading stress, where Kme is the critical Mode-I stress intensity t is used to describe fracture process of fiber-rein- factor for monolithic matrix. A criterion K,=Kic is used to simulate crack growth, where KI is the stress forced ceramics in the form of R-curve or g-c intensity factor calculated in Section 2 curve, where c=Co Ac. The R-curve approach is utilized in the current study and fracture resistance 4.2. Matrix crack growth analysis Kg, is defined as KR=20VC/T Fig. 13 shows the flow chart for crack growth simulation carried out in the present study. Firstly, Cracking extension becomes unstable under the cracking initiation stress, oo, for a given initial flaw following two situations while the relation KI-Mic size, co, is calculated as do=Kc/(2/c/T), where is satisfied. One is due to initiation of fiber fracture at the largest fiber stress obtained for each loading increment and this leads to next fiber fracture. and hen catastrophic cracking follows. Fiber fracture is x上 G:=200N/m o=100. 0MPa Fig. 7. Influences of G on the distribution of coD Fig. 9. Influences of G on the distribution of debond lengthY.-F. Liu et al.rMechanics of Materials 29 1998 111–121 ( ) 117 Table 2 Basic microstructural parameter set for numerical study Debonding toughness, Gic Ž . Nrm 6.0 Frictional stress, t Ž . MPa 50.0 Temperature change, DT Ž . K 500 Fiber volume fraction, f 0.20 Altered parameters are indicated in the corresponding figure. 4.1. Composite fracture criterion Considering the plane–strain condition for a Mode-I crack lying in the plane of transverse isotropy, Budiansky and Cui 1994 obtained the Ž . following expression of critical Mode-I stress inten￾sity factor, K , on the basis of energy balance IC arguments: 2 bEŽ . 1ynm KIC mc sK ) Ž . Ž. 1yf , 13 2 EmŽ . 1yn where Kmc is the critical Mode-I stress intensity factor for monolithic matrix. A criterion K sK is I IC used to simulate crack growth, where K is the stress I intensity factor calculated in Section 2. 4.2. Matrix crack growth analysis Fig. 13 shows the flow chart for crack growth simulation carried out in the present study. Firstly, cracking initiation stress, s0 , for a given initial flaw size, c , is calculated as s sK rŽ . 2'crp , where 0 0 IC Fig. 7. Influences of G on the distribution of COD. ic Fig. 8. Influences of G on the distribution of bridging stress. ic K is obtained from Eq. 13 . Then, a crack growth Ž . IC length of Dc is extended, leaving intact fibers be￾hind to bridge the matrix crack. Owing to the fiber bridging, the value of KI is reduced dŽ . KrdcF0 so that gradually increasing loading is required to sat￾isfy K sK . The newly obtained loading stress, I IC s , is used to describe fracture process of fiber-rein￾forced ceramics in the form of R-curve or syc curve, where csc qDc. The R-curve approach is 0 utilized in the current study and fracture resistance, K , is defined as: R KRs2s'crp . 14 Ž . Cracking extension becomes unstable under the following two situations while the relation KI IC sK is satisfied. One is due to initiation of fiber fracture at the largest fiber stress obtained for each loading increment and this leads to next fiber fracture, and then catastrophic cracking follows. Fiber fracture is Fig. 9. Influences of G on the distribution of debond length. ic