B G. Nair et al. /Materials Science and Engineering 4300(2001)68-79 4.2. 2D Composite rheology 900-y) yielded strain-rates significantly different (too low) from those observed for the 2D specimens experi Creep behavior of the 0/-90% 2D composites is con- mentally. Microstructural investigation of undeformed trolled by creep of fibers in the 0 plies- values of n 2D composites, however, suggests that there are very ind Oapp for 0/-90o composites correspond well with few areas where direct contact between the fibers of the data available for of fully crystallized adjacent plies is seen. Rather, a discrete layer of matrix Nicalon"fibers [ 19, 20] and also with our data for creep material exists between the plies. This layer is of thick of lD composites with =00. If all the applied stress ness a 10-50 um(cf Fig. 13a), which is about 5-25% arried by the fibers in the 0o plies, the expected strain of the thickness of the individual plies. Thus, it is rate for the stresses employed in our experiments reasonable to assume that this matrix layer acts as a 10-7s, which compares very favorably with the third lamellar constituent in the composite and observed strain-rates for the 0/-90o composite tributes to the bulk creep strain according to its The creep behaviors of 40/-50 and 20/700 composites effective viscosity. are strikingly similar, although the 40/-50% composites Fig. 12 presents a highly simplified schematic of a show much higher strain-rates in the temperature range 2-ply section of the 2D composite along with the inter 1275-1300oC. The strong dependence of gnn on G,, spersed layers of unreinforced matrix. The constitutive and the unusually high values of ann observed bear equations for the rheology of each of the plies and the testament to an increase in the matrix von-Mises poten- manx layer at constant temperature can De exp tials with temperature due to thermally activated vis- cous flow of the interphase [15]. At higher differentia stresses, the expected flow mechanism of the matrix non-Newtonian(n- 3)dislocation creep [21, 22]. Thus, In addition to these three constitutive equations, for constant al, more volume of the matrix exhibits Isostrain conditions demand that, at steady state, the dislocation creep at a higher T, resulting in a higher strain-rates in all three plies are the same A straightforward application of laminate theory to where the three terms correspond to the steady-state he rheology of 2D material, with each of the plies strain-rates of the two sets of plies and the unreinforced characterized as having the viscoelastic properties of matrix, respectively. Finally, if the thickness of each set the corresponding ID composites(i.e, with o=y and of plies is d (cf Fig. 12), equilibrium imposes the following constraint 2am+(d-a)ow+(d-a)ow-90-y where om, oy and o(v-goo)are the partitioned stresses in the matrix layer and the two sets of constituent plies y90° respectively. Numerical solution of these equations em- ploying different values of a with the viscosity of this layer being that of the unreinforced matrix nicely fit the data for 2D composites using a 20-30 um for the 0/-90 and 20/-70 composites and a 30-40 um for the 40/-500 composites(see Fig. 13). As this result is consistent with the microstructural observations. the analysis seems to support the initial assumptions, spe- cifically regarding the behavior of the 2D composite a plastic laminate. Similar behavior has been observed in glass-fiber-reinforced polymers [23], where axis composites with an orientation v/-y(fibers in adjacent plies not perpendicular to each other except for when y= 45%) had creep compliances similar to that of unidirectional composites with =y, which indi- cates that the plies behaved as ID composite sections The presence of a network of matrix microcracks Fig 12 Highly simplified schematic of the lamellar structure of a 2D some questions regarding the applicability of the simple composite. The matrix regions included at the ends are to model described above. A study of the literature ever suggests that such a network of microcracksB.G. Nair et al. / Materials Science and Engineering A300 (2001) 68–79 77 4.2. 2D Composite rheology Creep behavior of the 0/–90° 2D composites is con￾trolled by creep of fibers in the 0° plies — values of n and Qapp for 0/–90° composites correspond well with the data available for creep of fully crystallized Nicalon® fibers [19,20] and also with our data for creep of 1D composites with 8=0°. If all the applied stress is carried by the fibers in the 0° plies, the expected strain￾rate for the stresses employed in our experiments is 10−7 s−1 , which compares very favorably with the observed strain-rates for the 0/–90° composite. The creep behaviors of 40/–50 and 20/70° composites are strikingly similar, although the 40/–50° composites show much higher strain-rates in the temperature range 1275–1300°C. The strong dependence of Qapp on s1, and the unusually high values of Qapp observed bear testament to an increase in the matrix von-Mises poten￾tials with temperature due to thermally activated vis￾cous flow of the interphase [15]. At higher differential stresses, the expected flow mechanism of the matrix is non-Newtonian (n3) dislocation creep [21,22]. Thus, for constant s1, more volume of the matrix exhibits dislocation creep at a higher T, resulting in a higher ‘average’ n. A straightforward application of laminate theory to the rheology of 2D material, with each of the plies characterized as having the viscoelastic properties of the corresponding 1D composites (i.e., with 8=c and 90°−c) yielded strain-rates significantly different (too low) from those observed for the 2D specimens experi￾mentally. Microstructural investigation of undeformed 2D composites, however, suggests that there are very few areas where direct contact between the fibers of adjacent plies is seen. Rather, a discrete layer of matrix material exists between the plies. This layer is of thick￾ness a10–50 mm (cf. Fig. 13a), which is about 5–25% of the thickness of the individual plies. Thus, it is reasonable to assume that this matrix layer acts as a third lamellar constituent in the composite and con￾tributes to the bulk creep strain according to its own effective viscosity. Fig. 12 presents a highly simplified schematic of a 2-ply section of the 2D composite along with the inter￾spersed layers of unreinforced matrix. The constitutive equations for the rheology of each of the plies and the matrix layer at constant temperature can be expressed as o; ss=Csn (3) In addition to these three constitutive equations, isostrain conditions demand that, at steady state, the strain-rates in all three plies are the same: o; c=o; (c−90$) =o; m (4) where the three terms correspond to the steady-state strain-rates of the two sets of plies and the unreinforced matrix, respectively. Finally, if the thickness of each set of plies is d (cf Fig. 12), equilibrium imposes the following constraint: 2asm+(d−a)sc+(d−a)s(c−90$) =2ds1 (5) where sm, sc and s(c−90°) are the partitioned stresses in the matrix layer and the two sets of constituent plies, respectively. Numerical solution of these equations em￾ploying different values of a with the viscosity of this layer being that of the unreinforced matrix nicely fit the data for 2D composites using a20–30 mm for the 0/–90 and 20/–70° composites and a30–40 mm for the 40/–50° composites (see Fig. 13). As this result is consistent with the microstructural observations, the analysis seems to support the initial assumptions, spe￾cifically regarding the behavior of the 2D composite as a plastic laminate. Similar behavior has been observed in glass-fiber-reinforced polymers [23], where 2D off￾axis composites with an orientation c/–c (fibers in adjacent plies not perpendicular to each other except for when c=45°) had creep compliances similar to that of unidirectional composites with 8=c, which indi￾cates that the plies behaved as 1D composite sections. The presence of a network of matrix microcracks in the as-fabricated, undeformed 2D composites raises some questions regarding the applicability of the simple model described above. A study of the literature, how￾ever, suggests that such a network of microcracks could Fig. 12. Highly simplified schematic of the lamellar structure of a 2D composite. The matrix regions included at the ends are to ensure symmetry.