Damage tolerant ceramic matrix composites 1055 damage Unstable (displacemen control) 合P Distributed Elastic (undamage Localized pull out △=EL △=EnL (1)m Fig. 6. Schematic illustration of overall load-displacement curve, distributed and localized energy dissipation during loading, frac- ture and separation of a tensile cn. The solid line is the load-displacement curve that would occur if the experiment was conducted under crack opening( 8)control, while the dotted line indicates the unstable fracture that takes place under control of the displacement of the specimen. The deformation during loading is due to distributed phenomena, while the down-going par comprises distributed deformation EL and localized crack opening 8. Thus, regarding fu and (D)max as material con- distributed energy dissipation and localized pull stants,a tail(stable fracture)will only appear if out energy dissipation. During loading the energy the specimen length is sufficiently short. Using the dissipation per unit volume by distributed mecha material data for SiC/CAS Il and SiC/LAS III nisms is the non-recoverable part of the tough (Table 1)and(D)max =0 4 mm for the Sic-fibres, ness, i. e. Ume Uab, and ws. During unloading the the critical length is calculated to be L s 50 mm. reverse sliding that takes place along the fibre The experimental results of Cao et al.were matrix interface dissipates additional energy, wsl obtained with a gauge length of 15 mm, and a small per unit volume (superscript* indicate unloaded tail was measured by extensometer. The experi- state). When the composite is completely free of ments of Sorensen and Talreja were also con- external forces, residual stresses exist in fibre and ducted in displacement control, but on specimens matrix due to interfacial friction, such that strain with longer gage section(80 mm). The fracture oc- energy is stored in fibre and matrix. Therefore the curred unstably (i.e. no tail), although fibre pull total energy dissipation, from initial undamaged out occurred. These results are in agreement with state until the specimen is fully separated, can be eqn(25). There are examples in the literature calculated as the sum of distributed energy dissi- where a tail, the down-going part of the load- pation and localization displacement curve, has been termed as a tough behaviour, contrasting materials that did not show a down-going tail (unstable fracture). Such interpre P4)d△=LAW+AW (26) tation is incorrect and should not be accepted. as described above there is no correlation between U and the fracture stability, since fracture stability is where WD is the energy absorbed per unit volume not a material property, but depends on speci- of the composite by distributed mechanisms length and loading condi uggest that attention should be focused on W=Ume+b+W+W+φ+φ*-φ"-φ whether amaterial is damage tolerant or flaw (27) As indicated in Fig. 6, the total energy dissipa- and wp is the pull-out energy per unit area. The tion(the area under the quasi-static load-displace- energy dissipation due to reverse sliding( full slip ment curve(solid line) comprises two sources, per unit volume of the composite isDamage tolerant ceramic matrix composites 1055 Distributed damage Unstable Localized pull out 6 Distributed Localized qAl,x energy energy dissipation dissipation Fig. 6. Schematic illustration of overall load-displacement curve, distributed and localized energy dissipation during loading, frac￾ture and separation of a tensile specimen. The solid line is the load-displacement curve that would occur if the experiment was conducted under crack opening (8) control, while the dotted line indicates the unstable fracture that takes place under control of the disnlacement of the snecimen. The deformation during loading is due to distributed phenomena, while the down-going part comprises distributed deformation EL and localized crack oiening 6. Thus, regarding E, and (I,),,, as material con￾stants, a tail (stable fracture) will only appear if the specimen length is sufficiently short. Using the material data for SiCKAS II and SIC/LAS III (Table 1) and (I,),,, = 0.4 mm for the Sic-fibres, the critical length is calculated to be L = 50 mm. The experimental results of Cao et al.32 were obtained with a gauge length of 15 mm, and a small tail was measured by extensometer. The experi￾ments of Sorensen and Talreja” were also con￾ducted in displacement control, but on specimens with longer gage section (80 mm). The fracture oc￾curred unstably (i.e. no tail), although fibre pull out occurred. These results are in agreement with eqn (25). There are examples in the literature where a tail, the down-going part of the load￾displacement curve, has been termed as a tough behaviour, contrasting materials that did not show a down-going tail (unstable fracture). Such interpre￾tation is incorrect and should not be accepted. As described above there is no correlation between U and the fracture stability, since fracture stability is not a material property, but depends on speci￾men length and loading condition. Instead, we suggest that attention should be focused on whether amaterial is damage tolerant or flaw sensitive. As indicated in Fig. 6, the total energy dissipa￾tion (the area under the quasi-static loaddisplace￾ment curve (solid line)) comprises two sources, distributed energy dissipation and localized pull out energy dissipation. During loading the energy dissipation per unit volume by distributed mecha￾nisms is the non-recoverable part of the tough￾ness, i.e. U,, U,,. and IV,,. During unloading the reverse sliding that takes place along the fibre/ matrix interface dissipates additional energy, IV,,* per unit volume (superscript* indicate unloaded state). When the composite is completely free of external forces, residual stresses exist in fibre and matrix due to interfacial friction, such that strain energy is stored in fibre and matrix. Therefore, the total energy dissipation, from initial undamaged state until the specimen is fully separated, can be calculated as the sum of distributed energy dissi￾pation and localization A max s P(A)dA = L A F-J’, + A Wp, 0 (26) where IV,, is the energy absorbed per unit volume of the composite by distributed mechanisms, (27) and Wr is the pull-out energy per unit area. The energy dissipation due to reverse sliding (full slip) per unit volume of the composite is