January 1999 Radial variations in Modulus and Hardness in SCS-6 Silicon Carbide Fibers at brass wheel. This final stage was found to be the best way curves for the inner and outer sheaths ha steeper slopes to ensure an even surface across both the hard Sic outer sheath at the maximum load than that of the core and the soft carbon core. The indentations within each array The material in the inner and outer sheaths deforms elasti- were typically 10 um apart. However, when small arrays were cally and inelastically during indentation as shown by the used to examine the variation in properties across the edge of force-displacement curves in Fig. 3. The first unloading seg- the core, the indentation spacing was reduced to 2 or 3 um. ment is offset from the initial loading segment, and there is a Various indentation procedures were used during the testing; in anent indentation depth when all force is removed. The each case the indentations were performed by increasing the deformation on subsequent reloading and unloading, though, is d at a fixed rate up to a peak load in the range 3 to 40 m recoverable and therefore elastic as seen by the overlapping The indentations were unloaded at a fixed rate, and repeated curves. The indentations which are in the SiC but within a few loading/unloading cycles were utilized. Additionally, a hold micrometers of the carbon core exhibit greater permanent de egment was inserted into the final unload at 20% of the pea formation than those farther from the core. This suggests that load to enable a correction to be made for thermal drift. The the weakest part of the SiC sheath lies in very close proximity peated cycling of force was used to investigate the presence to the core of anelastic deformation The indentation curves for each fiber were analyzed To determine hardness and Youngs modulus from the force the method of oliver and Pharr 7 assuming a poisson rat tio of lacement data, the procedure outlined by oliver and Pharr 0.25, and then averaged so that variations in modulus and was followed. 7 Power law curves were fitted to the first 90% hardness could be plotted as a function of the radial distance of the unloading curves, and contact stiffnesses and contact from the fiber's center. The averaged results(based on over depths were obtained by differentiating and extrapolating these 300 individual data points) are shown in Fig. 4. The inner curves. Care was taken to remove the machine compliance that carbon core shows constant hardness (4.2 GPa)and modulus is associated with the tip shaft and the sample mounting. This (28 GPa) across its full width. The Sic also has approximatel was calibrated by performing a large array of indentations on a constant hardness(34 GPa) and modulus(360 GPa), though standard(fused silica) sample. The machine compliance was close to the core both the hardness and the modulus of the inner ermined to be 1.62 x 10-7 m/N. The data from the calibra SiC sheath fall dramatically. This drop in modulus and hard tion run were also utilized to evaluate the shape of the diamond ness begins gradually, as shown by Fig. 4, but close to the inner ip using the method outlined by Oliver and Pharr. The con- core this drop becomes very rapid In this region the averaged tact depths and the calibrated diamond tip shape were used to data are somewhat misleading as they show a gradual drop in calculate the contact area at peak load for each indentation. modulus and hardness. Individual indentations do not show Hardness was calculated by dividing the maximum applied such a gradual transition. Instead the modulus and hardness for ad by the contact area under load, and Youngs modulus was alculated using the relationship between contact area and con tact stiffness for a parabolic tip Pyrolytic SiC in IV. Results ore Outer siC Matri叉 e-displacement data from three indentations into ar 4联 CS-6 SiC fiber are shown in Fig. 3. The indentations were made in three separate positions across the fiber's face: the carbon core, the edge of the inner sheath(close to the core), and the outer sheath. The loading curves and the unloading curves are all parabolic in shape. The indentation into the carbon core is predominantly elastic in nature. The loading and unloading curves show little separation, and when force is cycled, the path of the first loading curve is repeated. This suggests there is little inelastic or nonrecoverable deformation in the carbon that under the diamond indenter. The shallow slope for this in- mentation shows clearly that the carbo is very compliant compared to the inner and outer sheaths. The indentation IlI it Fraction of Radius Fig 4. Avera Fig 3. Load-displacement data for indentations into three different fiber's radius. Ea regions of an SCS-6 SiC fibflat brass wheel. This final stage was found to be the best way to ensure an even surface across both the hard SiC outer sheath and the soft carbon core. The indentations within each array were typically 10 mm apart. However, when small arrays were used to examine the variation in properties across the edge of the core, the indentation spacing was reduced to 2 or 3 mm. Various indentation procedures were used during the testing; in each case the indentations were performed by increasing the load at a fixed rate up to a peak load in the range 3 to 40 mN. The indentations were unloaded at a fixed rate, and repeated loading/unloading cycles were utilized. Additionally, a hold segment was inserted into the final unload at 20% of the peak load to enable a correction to be made for thermal drift. The repeated cycling of force was used to investigate the presence of anelastic deformation. To determine hardness and Young’s modulus from the force displacement data, the procedure outlined by Oliver and Pharr was followed.17 Power law curves were fitted to the first 90% of the unloading curves, and contact stiffnesses and contact depths were obtained by differentiating and extrapolating these curves. Care was taken to remove the machine compliance that is associated with the tip shaft and the sample mounting. This was calibrated by performing a large array of indentations on a standard (fused silica) sample. The machine compliance was determined to be 1.62 × 10−7 m/N. The data from the calibra￾tion run were also utilized to evaluate the shape of the diamond tip using the method outlined by Oliver and Pharr.17 The con￾tact depths and the calibrated diamond tip shape were used to calculate the contact area at peak load for each indentation. Hardness was calculated by dividing the maximum applied load by the contact area under load, and Young’s modulus was calculated using the relationship between contact area and con￾tact stiffness for a parabolic tip.17 IV. Results Force–displacement data from three indentations into an SCS-6 SiC fiber are shown in Fig. 3. The indentations were made in three separate positions across the fiber’s face: the carbon core, the edge of the inner sheath (close to the core), and the outer sheath. The loading curves and the unloading curves are all parabolic in shape. The indentation into the carbon core is predominantly elastic in nature. The loading and unloading curves show little separation, and when force is cycled, the path of the first loading curve is repeated. This suggests there is little inelastic or nonrecoverable deformation in the carbon that is under the diamond indenter. The shallow slope for this in￾dentation shows clearly that the carbon core is very compliant compared to the inner and outer sheaths. The indentation curves for the inner and outer sheaths have much steeper slopes at the maximum load than that of the core. The material in the inner and outer sheaths deforms elasti￾cally and inelastically during indentation as shown by the force–displacement curves in Fig. 3. The first unloading seg￾ment is offset from the initial loading segment, and there is a permanent indentation depth when all force is removed. The deformation on subsequent reloading and unloading, though, is recoverable and therefore elastic as seen by the overlapping curves. The indentations which are in the SiC but within a few micrometers of the carbon core exhibit greater permanent de￾formation than those farther from the core. This suggests that the weakest part of the SiC sheath lies in very close proximity to the core. The indentation curves for each fiber were analyzed using the method of Oliver and Pharr17 assuming a Poisson ratio of 0.25, and then averaged so that variations in modulus and hardness could be plotted as a function of the radial distance from the fiber’s center. The averaged results (based on over 300 individual data points) are shown in Fig. 4. The inner carbon core shows constant hardness (4.2 GPa) and modulus (28 GPa) across its full width. The SiC also has approximately constant hardness (34 GPa) and modulus (360 GPa), though close to the core both the hardness and the modulus of the inner SiC sheath fall dramatically. This drop in modulus and hard￾ness begins gradually, as shown by Fig. 4, but close to the inner core this drop becomes very rapid. In this region the averaged data are somewhat misleading as they show a gradual drop in modulus and hardness. Individual indentations do not show such a gradual transition. Instead the modulus and hardness for Fig. 3. Load–displacement data for indentations into three different regions of an SCS-6 SiC fiber. Fig. 4. Average Young’s modulus and hardness as a function of the fiber’s radius. Each average data point includes data for indentations performed to a number of different peak loads. January 1999 Radial Variations in Modulus and Hardness in SCS-6 Silicon Carbide Fibers 113