B G. Nair et al. Materials Science and Engineering 4300 (2001)68-79 matrix cracks extending almost along the length of the -52D:20°/-70° specimen that would have made a contribution to the bulk strain: careful examination of the data indicates 6.0 that the 20/-70o composites showed an increase in n 不 with a,(in other words, a deviation from the laminate model), which could be an effect of the volume strain introduced due to crack-growth. Another observation that seemed to question the validity of the lamellar approximation is the relative lack of interfacial cavita- tion in the 90 plies of the 0/-90 composite. The predictable interfacial cavitation seen in the =900 specimens in this work and in CAS-lll/SiC ID con 1,2 1.5 1.6 posites [9] scales with accumulated total strain in the Log [-,( MPa) composite and arises due to the development of tensile tractions along the fiber-matrix interface perpendicular 2D:40°/-50° to the direction of the applied stress. However, the T=1300c presence of microcracks, would relieve some of these tensile tractions due to opening of these cracks in 巧.5 directions perpendicular to that of the applied stress i.e. they affect the stress distribution in the(y-90) plies. Such crack opening reduces the 'effective viscos- ity of the(y-90%) plies and thus acts as a limitation to Data the universal applicability of the laminate model. A 一-a=4opr more comprehensive model would take into account modifications in the viscoelastic response of the (y 90)plies due to crack opening by the Poisson effect. 1.2 1.6 Log F-o, (MPa) Despite the limitations of the laminate model in cases where large scale crack-growth affects the overall com- Fig. 13. Comparison of the data for 2D composites to predictions of posite creep response, the good agreement for 0/-90 simplified model that assumes that the composite plies with differ. and 40/-50% composites paints an optimistic picture for ent fiber orientations behave as lamella (i.e.. thin sections of ID composites), accommodated by flow of a matrix layer of thickness a the eventual feasibility of continuum modeling of creep between the plies. (a)20/-70%(b)40/-500. of multi-directionally reinforced composites with com- plex lay-up of plies. The prediction of the rheologic be a fairly common feature in multidirectional com- behavior of such 2D composites would be relatively posites [5,6, 24]. Further, crack initiation and growth in simple using the lamellar approach, and is expected to cross-plies has been frequently observed during tensile be accurate at least for small levels of total strain.The and flexural creep of 2D ceramic composites [7, 8]. Some key(and the limiting factor, at present) to such model work has been done on modeling the effects of crack ing is the generation of a comprehensive data set for creep of ID composites in off-axis geometries. The growth on creep of 0/90 cross-ply laminates under demonstration of independence of plies in off-axis ge- tensile loading [25]. The authors concluded that the ometries indicates that such a data set can be almost majority of strain in the 90. plies resulted from the directly applied to predict the response of 2D com opening and growth of initial matrix cracks along planes perpendicular to the direction of the applied posites under complex loading geometries tensile stress. This crack growth results in the deforma ion of the composite being controlled by creep of fibers 5. conclusions n the 0 plies. Under compressive loads, however, it is expected that the effects of these microcracks would not Theon-axis'andoff-axis' compressive creep behav be quite as drastic. Some extent of crack opening in a ior of 2D composites was studied in the temperature expected due to the Poisson effect and indeed confi- steady-state strain-rates of 2D composites was, in gen rmed through optical microscopy. But at least in the eral, intermediate to that of the ID composites with 0/-90% and 40/-50 composites, the extent of crack orientations to the applied stress corresponding to that opening is not nearly enough to cause a significant of the constituent plies in the 2D material. The behav- contribution to the bulk strain of these plies. The 70 ior of the 0/-90% composites was still rate-limited by plies in the 20/-700 composite, however, showed large fiber-creep despite 50/ of the fibers being in the trans-78 B.G. Nair et al. / Materials Science and Engineering A300 (2001) 68–79 Fig. 13. Comparison of the data for 2D composites to predictions of a simplified model that assumes that the composite plies with differ￾ent fiber orientations behave as lamella (i.e., thin sections of 1D composites), accommodated by flow of a matrix layer of thickness a between the plies. (a) 20/–70°; (b)40/–50°. matrix cracks extending almost along the length of the specimen that would have made a contribution to the bulk strain: careful examination of the data indicates that the 20/–70° composites showed an increase in n with s1 (in other words, a deviation from the laminate model), which could be an effect of the volume strain introduced due to crack-growth. Another observation that seemed to question the validity of the lamellar approximation is the relative lack of interfacial cavita￾tion in the 90° plies of the 0/–90° composite. The predictable interfacial cavitation seen in the c=90° specimens in this work and in CAS-III/SiCf 1D com￾posites [9] scales with accumulated total strain in the composite and arises due to the development of tensile tractions along the fiber-matrix interface perpendicular to the direction of the applied stress. However, the presence of microcracks, would relieve some of these tensile tractions due to opening of these cracks in directions perpendicular to that of the applied stress, i.e. they affect the stress distribution in the (c−90°) plies. Such crack opening reduces the ‘effective’ viscos￾ity of the (c−90°) plies and thus acts as a limitation to the universal applicability of the laminate model. A more comprehensive model would take into account modifications in the viscoelastic response of the (c− 90°) plies due to crack opening by the Poisson effect. Despite the limitations of the laminate model in cases where large scale crack-growth affects the overall com￾posite creep response, the good agreement for 0/–90° and 40/–50° composites paints an optimistic picture for the eventual feasibility of continuum modeling of creep of multi-directionally reinforced composites with com￾plex lay-up of plies. The prediction of the rheologic behavior of such 2D composites would be relatively simple using the lamellar approach, and is expected to be accurate at least for small levels of total strain. The key (and the limiting factor, at present) to such model￾ing is the generation of a comprehensive data set for creep of 1D composites in off-axis geometries. The demonstration of independence of plies in off-axis ge￾ometries indicates that such a data set can be almost directly applied to predict the response of 2D com￾posites under complex loading geometries. 5. Conclusions The ‘on-axis’ and ‘off-axis’ compressive creep behav￾ior of 2D composites was studied in the temperature range 1275–1325°C at stresses of 15–50 MPa. The steady-state strain-rates of 2D composites was, in gen￾eral, intermediate to that of the 1D composites with orientations to the applied stress corresponding to that of the constituent plies in the 2D material. The behav￾ior of the 0/–90° composites was still rate-limited by fiber-creep despite 50% of the fibers being in the trans￾be a fairly common feature in multidirectional com￾posites [5,6,24]. Further, crack initiation and growth in cross-plies has been frequently observed during tensile and flexural creep of 2D ceramic composites [7,8]. Some work has been done on modeling the effects of crack￾growth on creep of 0/90° cross-ply laminates under tensile loading [25]. The authors concluded that the majority of strain in the 90° plies resulted from the opening and growth of initial matrix cracks along planes perpendicular to the direction of the applied tensile stress. This crack growth results in the deforma￾tion of the composite being controlled by creep of fibers in the 0° plies. Under compressive loads, however, it is expected that the effects of these microcracks would not be quite as drastic. Some extent of crack opening in a direction perpendicular to that of the applied stress is expected due to the Poisson effect and indeed confi- rmed through optical microscopy. But at least in the 0/–90° and 40/–50° composites, the extent of crack opening is not nearly enough to cause a significant contribution to the bulk strain of these plies. The 70° plies in the 20/–70° composite, however, showed large