Y-F. Liu et al./ Mechanics of Materials 29(1998)111-121 During the above simulation process, partic care was taken regarding selection of Ac.Exces- Maximum K ively large step sizes should be avoided to catch Initial slopes of R-curves ding stresses that satisfy Ki=Kic, while fairly small ones may hinder efficient computation. In the 29.0 current study, Ac=Co/12 was used at initial incre- ments of loading stress, however, a finer cracking increment, Ac=Co/60, was taken to obtain accurate loading stresses leading to matrix cracking(Eq (16) latrix cracking Fiber fracture 43. R-curve results Fig. 14 shows typical R-curves for three different values of Gic. In the case of large Gic, initial slope Fig. 15. Influences of G on the maximum fracture resistance and of the r-curve is large, however fiber failure occurs nitial R-curve slope. at an early stage and the maximum resistance cannot be expected. Meanwhile, for small fiber failure or matrix cracking. Fig. 15 reveals that case of weakly bonding composite, the composite the larger the debonding toughness, the larger the fracture pattern is matrix cracking alone and only a initial slope, however the maximum Kg possesses a small maximum resistance is achieved. It is an inter- peak value at an intermedium debonding toughness medium value of interfacial debonding toughness The maximum Kg increases initially, then decreases that yields the largest fracture resistance, while an with the increase of Gic. Accompanied with the appropriate initial slope of the R-curve is obtained as increase of Gic, the underlying fracture mechanism well. Thus, the toughest composite is obtained in of the composite is dominated by matrix cracking at such a case. In addition to the results shown in Fis first but then changed to fiber fracture(Figs. 14 and 14, interfacial toughness was changed over a wide 15). The analytical results demonstrate that there investigate its influence on the R-curve and exists an appropriate debonding toughness to achieve slopes of the curve. Fig. 15 shows the ob- maximum fracture resistance. Thus, G results. In this figure, the initial slope is important role in determining fracture resistance, defined as slope of the line connecting the first two crack growth stability and fracture mechanism transi- points of crack extension in Fig. 14, with the maxi- tions. As G may be changed by heat treatment mum fracture resistance obtained as the larger one at conditions of the composite and introduction of the point of composite unstable cracking, namely, terphases between matrix and fiber using interlayers of different types, control of processing conditions, on para phases( Gupta et al., 1993), such a R-curve tendency Fiher fracture Fiber fracture身 shown in Fig. 14 has important significance in mate A→ Matrix cracking Altering interfacial frictional stress, T, the ob- shown in Fig. 16. Like the debonding toughness, larger T results in a larger initial slope of R-curve but a maximum fracture resistance appears at an G;=12.0Nm Kg=20vc/T intermediate level of T. Although not shown here. it has been revealed that smaller residual stresses and larger fiber volume fraction yield the same effect on the initial slope of R-curve and maximum fracture Fig. 14. R-curve results for three different values of G resistance as that of larger G and T(Liu. 1995). AllY.-F. Liu et al.rMechanics of Materials 29 1998 111–121 ( ) 119 During the above simulation process, particular care was taken regarding selection of Dc. Exces￾sively large step sizes should be avoided to catch loading stresses that satisfy KI IC sK , while fairly small ones may hinder efficient computation. In the current study, Dcsc r12 was used at initial incre- 0 ments of loading stress, however, a finer cracking increment, Dcsc r60, was taken to obtain accurate 0 loading stresses leading to matrix cracking Eq. 16 . Ž Ž .. 4.3. R-curÕe results Fig. 14 shows typical R-curves for three different values of G . In the case of large G , initial slope ic ic of the R-curve is large, however fiber failure occurs at an early stage and the maximum resistance cannot be expected. Meanwhile, for small G , i.e., in the ic case of weakly bonding composite, the composite fracture pattern is matrix cracking alone and only a small maximum resistance is achieved. It is an inter￾medium value of interfacial debonding toughness that yields the largest fracture resistance, while an appropriate initial slope of the R-curve is obtained as well. Thus, the toughest composite is obtained in such a case. In addition to the results shown in Fig. 14, interfacial toughness was changed over a wide range to investigate its influence on the R-curve and initial slopes of the curve. Fig. 15 shows the ob￾tained results. In this figure, the initial slope is defined as slope of the line connecting the first two points of crack extension in Fig. 14, with the maxi￾mum fracture resistance obtained as the larger one at the point of composite unstable cracking, namely, Fig. 14. R-curve results for three different values of G . ic Fig. 15. Influences of Gic on the maximum fracture resistance and initial R-curve slope. fiber failure or matrix cracking. Fig. 15 reveals that the larger the debonding toughness, the larger the initial slope, however the maximum K possesses a R peak value at an intermedium debonding toughness. The maximum K increases initially, then decreases R with the increase of G . Accompanied with the ic increase of Gic , the underlying fracture mechanism of the composite is dominated by matrix cracking at first but then changed to fiber fracture Figs. 14 and Ž 15 . The analytical results demonstrate that there . exists an appropriate debonding toughness to achieve maximum fracture resistance. Thus, Gic plays an important role in determining fracture resistance, crack growth stability and fracture mechanism transi￾tions. As G may be changed by heat treatment ic conditions of the composite and introduction of in￾terphases between matrix and fiber using interlayers of different types, control of processing conditions, and also varying deposition parameters for inter￾phases Gupta et al., 1993 , such a Ž . R-curve tendency shown in Fig. 14 has important significance in mate￾rial design and application. Altering interfacial frictional stress, t , the ob￾tained relationship between K and crack length, is R shown in Fig. 16. Like the debonding toughness, larger t results in a larger initial slope of R-curve but a maximum fracture resistance appears at an intermediate level of t . Although not shown here, it has been revealed that smaller residual stresses and larger fiber volume fraction yield the same effect on the initial slope of R-curve and maximum fracture resistance as that of larger G and t Ž . Liu, 1995 . All ic