2596 N. Eswara Prasad et al. Engineering Fracture Mechanics 71(2004) 2589-2605 E 1.5 Crack Divider Orientation J.=1.36kJm2 Crack arrester orie Crack Length(a Fig. 5. Variation of elastic-plastic fracture toughness o) with crack length for the CFCC in crack divider and crack arrester ori- event that the material undergoes first fibre bundle fracture. As discussed earlier, these events include matrix microcracking and fibre/matrix debonding: but, do not include the fibre bundle failure and fibre pull-out. However, it is well accepted now that the last two events too contribute significantly to the overall fracture resistance of CFCC materials and the energy absorbed during these two processes is also con siderable. Hence, an alternative method of total (elastic-plastic) fracture energy release rate is adopted to evaluate the fracture resistance that accounts for all the fracture events of the present material( described in details in the next section). Hence, the Jie values evaluated and reported in the present section are valid materials' fracture resistance properties; however, they are conservative in nature 3.4. Total fracture energy release rate (e) Li and coworkers [26-29] have successfully extended the J-integral concept to brittle materials, first for concrete materials and later for inhomogeneous and discontinuous materials, a preliminary review of which was provided by Mai [30]. Later, these methodologies were successfully employed for CFCCs by Li and coworkers themselves [29]and Nair and Wang 31]. Homogeneous materials exhibit a parabolic decrease in the stress with radial distance (r) from the crack tip(Fig. 6a). Such a gradual decrease in the stress denotes stable crack extension, which is one of the basic requirements for applying J-integral. The discontinuous, heterogeneous CFCCs also exhibit such crack tip stress singularity. But these materials, in addition, exhibit events of unstable crack extension. This is despite the fact that the material, in general, exhibits parabolic decrease in the stress with radial distance, r(Fig. 6b). Each of the load excursions and sudden load drops in the failure of a fibre bundle and the subsequent load excursion is due to gradual build up of the local stref o ig. 6b represent the local crack tip fracture event. A sudden load drop in the crack tip stress level is due In such cases, the overall or global fracture energy (a or the total fracture energy release rate, Je)represents the fracture resistance of the materialevent that the material undergoes first fibre bundle fracture.As discussed earlier, these events include matrix microcracking and fibre/matrix debonding; but, do not include the fibre bundle failure and fibre pull-out.However, it is well accepted now that the last two events too contribute significantly to the overall fracture resistance of CFCC materials and the energy absorbed during these two processes is also con￾siderable.Hence, an alternative method of total (elastic–plastic) fracture energy release rate is adopted to evaluate the fracture resistance that accounts for all the fracture events of the present material (described in details in the next section).Hence, the JIc values evaluated and reported in the present section are valid materials’ fracture resistance properties; however, they are conservative in nature. 3.4. Total fracture energy release rate (Jc) Li and coworkers [26–29] have successfully extended the J-integral concept to brittle materials, first for concrete materials and later for inhomogeneous and discontinuous materials, a preliminary review of which was provided by Mai [30].Later, these methodologies were successfully employed for CFCCs by Li and coworkers themselves [29] and Nair and Wang [31].Homogeneous materials exhibit a parabolic decrease in the stress with radial distance (r) from the crack tip (Fig.6a).Such a gradual decrease in the stress denotes stable crack extension, which is one of the basic requirements for applying J-integral.The discontinuous, heterogeneous CFCCs also exhibit such crack tip stress singularity.But these materials, in addition, exhibit events of unstable crack extension.This is despite the fact that the material, in general, exhibits parabolic decrease in the stress with radial distance, r (Fig.6b).Each of the load excursions and sudden load drops in Fig.6b represent the local crack tip fracture event.A sudden load drop in the crack tip stress level is due to the failure of a fibre bundle and the subsequent load excursion is due to gradual build up of the local stress. In such cases, the overall or global fracture energy (Ja or the total fracture energy release rate, Jc) represents the fracture resistance of the material. 0.5 1.0 1.5 2.0 2 5 Crack Length (a), mm Elastic Plastic Fracture Toughness (JQ), k /m2 3 4 6 7 Crack Divider Orientation Crack Arrester Orientation JIc= 0.66 k /m2 J JIc= 1.36 k /m2 J J Fig.5.Variation of elastic–plastic fracture toughness (JQ) with crack length for the CFCC in crack divider and crack arrester ori￾entations. 2596 N. Eswara Prasad et al. / Engineering Fracture Mechanics 71 (2004) 2589–2605