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Elastic moduli of TiB2 and C layers in a fiber reinforced glass ceramic composite
Scripta h4etaUqica et Matuialia, Vol. 33, No. 5, pp. 789-7%-t,1995 Etier Science Ltd 1995A!AMaallurgicaIIlC. F’rhtedinthcUSAAllri#srcscrvcd 0956-7lw95 $9.50 + .oo
Pergamon
0956-716x(95)00302-9
ELASTIC MODULI OF TiBz AND C LAYERS IN A FIBER REINFORCED GLASS CERAMIC COMPOSITE R. Berriche and R. Dutton’ Institutefor Aerospace Research National Research Council of Canada Ottawa, Ontario, Canada KlA OR6 Wright Laboratory/Materials Directorate Wright-Patterson AFB, OH 45433-7750, USA l
(Received March 19,1995) (Revised April 19,1995) Introduction
The interfaces between fibers and their matrices, in fiber reinforced composites, are usually modified such as by coating the fibers prior to embedding them in the matrix. The purpose of the coatings can be to reduce the strength of the interface, to reduce the mismatch in coefficient of thermal expansion between the fiber and the matrix, or to prevent any reactions from occurring at the interface. For mcxlelling purposes, there is a need to determine the elastic modulus values of any layers that exist at the interface between the fibers and their matrix. Obviously,conventional methods, such as the resonant frequency test, cannot be used to perform these me8surements because the layers are usually very thin and are sandwiched between the fiber and the matrix. A more suitable technique is the depth sensing indentation (DSI) method using the Nanomechanical Probe (NMP), whereby the material is indented with a Vickers diamond stylus, while monitoring the load and depth of penetration (1). The elastic module can then be calculated from the slope of the unloading segment of the load-depth plot (2). In this investigation DSI tests have been performed on a SIC fiber reinforced borosilicate composite near the inter&&l region to measum the elastic modulus values of TiB, and C layers. These layers were deposited on the Sic fibers prior to embedding them in the borosilicate matrix. The results of these DSI tests are presented and discussed in this paper. ExDerimental Procedure
The sample cons&d of a borosilicate matrix containing coated sigma (silicon carbide, SIC) fibers. The SIC fibers of diameter about 102 l.anwere coated with a C layer and an outer TiB, layer. Details on the processing of the composite can be found in a previous publication (3). A high magnification SEM cross section micrograph showing the interfacial region between the SIC fiber and the borosilicate matrix is presented in Figure 1. It indicates that the thickness of the C layer is about 1.5 pm and that of the TiB, layer is 0.5 pm. DSI tests were conducted in radial, circumferential or tangential rows at five of these interfacial regions, using the NMP. Each DSI test consisted of a loading-unloading triangular cycle in the displacement control mode with a period of 100 seconds. A Vickers (four sided pyramid) indenter was used for all the tests. The
790
FIBER-REINFORCED GLASS CERAMIC COMPOSITE
Figure 1. A high magnification
SEM micrograph
Vol. 33, No. 5
showing the TiB, and C layers.
elastic modulus (E) in GPa was calculated from load-depth plots using the following equation which was derived (2) from the elastic punch model of Sneddon (4):
where, dP/dh is the slope of the unloading segment (see Figure 2), & is the plastic depth (see Figure 2), v and v0 are the Poisson’s ratios and E and E, are the elastic moduli for the sample being indented and the indenter material (diamond), respectively; and AC is the contact area. The values of v that were used during the calculation of the elastic moduli for the various materials are listed in Table 1 along with corresponding E values determined by conventional methods. For diamond, v,, and E, were taken to be equal to 0.2 and 965 GPa, respectively (5).
Depth, h
hp
hmax
Figure 2. A typical load-depth plot from a DSI test using the NMP.
791
Vol. 33, No. 5
TABLE 1 v and E Values for Bomsilicate, Sic, TB2 and C
Results and Discussion
Examples of load vs. depth plots obtained for tests on SIC and borosilicate are shown in Figure 3. The two tests were conducted at the same displacement amplitude. The higher maximum load (J’_) and lower maximum depth of per&&ion (h_) for the SIC load-depth plot reflect much higher elastic and plastic properties for Sic than for borosihcate. The elastic modulus values calculated from these two plots are 32 1 GPa for SIC and 54 GPa for the borosilicate. The E values obtained from tests on these two materials at higher loads are 327 GPa at P-=0.14 N for Sic and 5 1 GPa at P-4.1 1 N for the borosilicate. These results are in excellent agreement with published values for these two materials listed in Table 1. This establishes that the DSI method using the NMP is an accurate method for measurin g the elastic properties of small volumes of materials. A previous study on hot &statically pressed S&N.,(10) also found that the DSI method using the NMP yielded results which were in excellent agreement with results corn conventional methods, such as the resonant frequency method. Obviously, one of the advantages of the DSI technique is that it does not need large and accurately machined samples to conduct the measurements. A large number of DSI tests were perhormed at loads of about 0.02 N at the inter-facialregions between the Sic fibers and the borosilicate matrix in order to determine the elastic moduli of the TiB, and C layers. An example of a row of indentations that spans the region from the borosilicate matrix to the Sic/C interface is shown in the SEM micrograph of Figure 4 along with a plot of the elastic modulus values calculated from corresponding load-depth plots. The indentations are spaced about 2 pm apart. In tbis case, indentations 1 to 3 can be seen in the SEM micrograph, and are clearly in the borosilicate matrix. The calculated E values
z
0.08
-
0.06
-
z _z:
0.3
0.6
Depth (pm) Figure 3. Load-depthplotsfiumDSI tests cmthe Sic fiber and the borosili~
matrix
792
Vol. 33, No. 5
FIBER-REINFORCED GLASSCERAMICCOh4POSITE
200 150 100 50 1
2
3
4
5
6
7
6
Indent number Figure 4. SEM miaqqph of and elastic modulus vs. indent number (or position) for indentations at the interfacial region between Sic and borosilicate. Spacing between consecutive indentatior~~ is 2 pm. Indentations 1,2 and 3 are in the matrix.
for indentations 1 and 2 are 64.3 and 62.1 GPa, respectively. Indentation 3, on the other hand, has a slightly higher calculated E value (82.6 GPa) possibly because it is too close to the more rigid TiEl, layer. The rest of the indentations could not be seen in the SEM micrograph. However, since the spacing between the indentationsis known, it is possible to pinpoint their positions relative to the indentations in the borosilicate matrix. Using this method, indentation4 is right in the middle of the TiB, layer, indentation 6 is in the middle of the C layer, while number 5 is somewhere in between. For these three indentations, the calculated E values am 150.6,117.1 and 91.9 GPa, respectively. Therefore, the elastic modulus of the TiB, layer should be close to 150 GPa and that of the C layer should be about 92 GPa. Indentations 7 and 8 have E values that are much higher than that of indentation 6 because they are at the interface between the C layer and the SIC fiber. Another example of a series of indentations is shown in Figure 5. Indentations 9 and 10 are clearly in the Sic fiber. The E values calculatedt?om the corresponding load-depth plots are 387.5 and 33 1.8 GPa, respectively The reason the latter value is lower than that for indent 9 is that indentation 10 is too close to the less rigid carbon layer. Indentation 12 is in the borosilicate matrix, and its calculated E value is 55.6 GPa. Indentation 11, on the other hand, cannot be seen in the SEM micrograph of Figure 5, but is half way between indentations 10 and 12, i.e. it falls within the TiD, layer. The calculated E value in this case is 117.3 GPa, which is lower than the value of 150 GPa for TiB, because the indentation is too close to either the C layer and/or the borosilicate matrix. Since it is very difkult and time consuming to find the indentations when the sample is examined under the SEM, for the rest of the indentations the method adopted to determine on which material a particular test was performed is as follows. The load-depth plot for any indentation was compared to the plots of the indentations discussed above, namely 1,2 or 12 for borosilicate, 9 or 10 for Sic, 4 for TiB, and 6 for C. Loaddepth plots of tests on the same material must have overlapping loading parts. This selection process indicated
Vol. 33, No. 5
FIBER-REINFORCED GLASS CERAMIC COMPOSITE
793
400 ?? s
300
2 3E
200
CJ 'E 4 w
100 0 10
11
Indent number Figure 5. SEM mierograph and elastic modulus vs. indent number for a row of indedtions that start in the SiC fibex and end in the borosilicab matrix. The magnification ofthe SEM picture can be obtained %nn the thickness ofthe C layer, which is 1.5 p that 10 indentations were performed on the Sic, 29 on the borosilicate matrix, 5 on the TB, and 4 on the C layer The average elastic modulus values calculatedfor the four materials, namely Sic, borosilicate, TiE$ and C, t?om their loaddepth plots after perhorming this selection process, are presented in Table 2. The average elastic modulus values obtained for the Sic fiber from indentations away from the interfacial region, at the load of about 0.025 N is 352 f 27 GPa. The error bar, representing f one standard deviation, indicates that there is a variation in E from one position to the other. Since the indentation test is a local&d test, probing a very small volume of the material, such a variation in measurements is expected, as the microstructure of the material is expected to vary from one position to the other. The values measured using the NMP for the present Sic fibers varied from about 320 to 390 GPa, which is within the range of the published
TABLE 2 Cakulated E Values for the Various Materials in the Fiber Reinforced Glass Ceramic Composite Calculated from Load-Depth Plots Material
BC Borosilicate TiB, C
Number of indentations 10 29 5 4
M,P 0 0.025 0.018 0.021 0.020
Average E (GPa) 352 f 27 62*6 143 * 7 91*6
794
FIBER-REINFORCED GLASSCERAMICCOMPOSITE
Vol. 33, No. S
value of 325 (6) to 400 GPa (7). It should be pointed out that measurement and calculation errors, such as errors in &term&g the slope of the linear region of the unloading segment, are of the order of *4 GPa. The average calculated E value for borosilicate is 62 f 6 GPa. The scatter in the data is very small in this case, and the value obtained is fairly close to the value of 50 GPa measured by a conventional method (6). For the C layer, the average elastic modulus value measured is 9 1 i 6 GPa, which is comparable to the published value of 80 GPa found in reference 9. For TiB,, on the other hand, there is a large difference betwcen the value measured by the DSI method and the published value of 489.5 GPa (8). The main reason for this di&rence is believed to be that the TiE3,layer has a different microstructure from that of bulk TiB, used to measure the value given in Table 1. In particular, as the SEM micrograph of Figure 1 shows, the TiH, layer appears to have a columnar structure with small gaps between the columns. Such intercohtmnar gaps are expected to reduce the elastic modulus of TiB, in the same way as porosity is found to decrease the elastic modulus of bulk ceramics (10). The reduction in E due to intercolumnar gaps has already been reported for electron beam physical vapour deposited zirconia coatings by Strangman (11). Another possible reason for the diIferenosbetween the E value measured for the TiB, layer and the published value is that the C layer and borosilicate matrix, which have lower E values, could have alfected the measurements. The sizes of the indentations in the TB, are expected to be only slightly lower than the thickness of this layer. Hence, the elastic zone could extend to either the borosilicate and/or C layer which would results in a slightly lower measured E value for the TB, layer.
DSI tests have been performed at the interfacial region between Sic fibers and their borosilicate matrix to determine primarily the elastic moduli of the TiB, and C layers found at this interface. Some tests were also performed on the Sic fibers and the borosilicate matrix, which gave E values that were in excellent agreement with published E values determined for these two materials using conventional methods. This establishes that the DSI method using the NMP is an accurate method for measuring elastic properties of materials. The average elastic modulus values obtained for the TiH, and the C layers are 143 f 7 and 9 1 f 6 GPa, respectively. The calculated value for TiB, is much lower than the published one due to the layer having a different microstructure and/or due to proximity to other layers. The E value for the C layer, on the other hand, is comparable to the published value. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
R Beniche, Canadian Aeronautics and Space Journal 40, 163 1994. J.L. Loubet, J.M. Georges, J.M. Marchesini andG. Meille, J. Tribol. 106,43 1984. N.J. Pagano, R.E. Dutton, RY. Kim, P. Karpur and T.E. Matikas, Proceedmgs of International Conference on Composite Engineering D. Hui ed, p.387, New G&am, USA, (1994). LA Sneddon,Int. J. Eng. Sci. 3,47 1965. R.W. Hertzberg, Deformation and Fracture. Me&auks of EngineeringMaterials, 3rd Edition, Wiley, p.7, (1989). RY. Kim, Wright Laboratoq, unpublishedresults. AL. Geiger and M. Jackson, Advanced Mate&Is & Recesses 136,24 1989. Anonymous, Machine Design, p.l1,1993. E. Fitzer aud M. Heym, High Temperature-HighPressure lo,29 1978. R Beniche and RT. Holt, Ceramic Engineeringand Science Proceed&, 14(7-S), 188 (1993). T.E. Straugman, Thiu Solid Films 127,93 1985.
Pergamon
0956-716x(95)00302-9
ELASTIC MODULI OF TiBz AND C LAYERS IN A FIBER REINFORCED GLASS CERAMIC COMPOSITE R. Berriche and R. Dutton’ Institutefor Aerospace Research National Research Council of Canada Ottawa, Ontario, Canada KlA OR6 Wright Laboratory/Materials Directorate Wright-Patterson AFB, OH 45433-7750, USA l
(Received March 19,1995) (Revised April 19,1995) Introduction
The interfaces between fibers and their matrices, in fiber reinforced composites, are usually modified such as by coating the fibers prior to embedding them in the matrix. The purpose of the coatings can be to reduce the strength of the interface, to reduce the mismatch in coefficient of thermal expansion between the fiber and the matrix, or to prevent any reactions from occurring at the interface. For mcxlelling purposes, there is a need to determine the elastic modulus values of any layers that exist at the interface between the fibers and their matrix. Obviously,conventional methods, such as the resonant frequency test, cannot be used to perform these me8surements because the layers are usually very thin and are sandwiched between the fiber and the matrix. A more suitable technique is the depth sensing indentation (DSI) method using the Nanomechanical Probe (NMP), whereby the material is indented with a Vickers diamond stylus, while monitoring the load and depth of penetration (1). The elastic module can then be calculated from the slope of the unloading segment of the load-depth plot (2). In this investigation DSI tests have been performed on a SIC fiber reinforced borosilicate composite near the inter&&l region to measum the elastic modulus values of TiB, and C layers. These layers were deposited on the Sic fibers prior to embedding them in the borosilicate matrix. The results of these DSI tests are presented and discussed in this paper. ExDerimental Procedure
The sample cons&d of a borosilicate matrix containing coated sigma (silicon carbide, SIC) fibers. The SIC fibers of diameter about 102 l.anwere coated with a C layer and an outer TiB, layer. Details on the processing of the composite can be found in a previous publication (3). A high magnification SEM cross section micrograph showing the interfacial region between the SIC fiber and the borosilicate matrix is presented in Figure 1. It indicates that the thickness of the C layer is about 1.5 pm and that of the TiB, layer is 0.5 pm. DSI tests were conducted in radial, circumferential or tangential rows at five of these interfacial regions, using the NMP. Each DSI test consisted of a loading-unloading triangular cycle in the displacement control mode with a period of 100 seconds. A Vickers (four sided pyramid) indenter was used for all the tests. The
790
FIBER-REINFORCED GLASS CERAMIC COMPOSITE
Figure 1. A high magnification
SEM micrograph
Vol. 33, No. 5
showing the TiB, and C layers.
elastic modulus (E) in GPa was calculated from load-depth plots using the following equation which was derived (2) from the elastic punch model of Sneddon (4):
where, dP/dh is the slope of the unloading segment (see Figure 2), & is the plastic depth (see Figure 2), v and v0 are the Poisson’s ratios and E and E, are the elastic moduli for the sample being indented and the indenter material (diamond), respectively; and AC is the contact area. The values of v that were used during the calculation of the elastic moduli for the various materials are listed in Table 1 along with corresponding E values determined by conventional methods. For diamond, v,, and E, were taken to be equal to 0.2 and 965 GPa, respectively (5).
Depth, h
hp
hmax
Figure 2. A typical load-depth plot from a DSI test using the NMP.
791
Vol. 33, No. 5
TABLE 1 v and E Values for Bomsilicate, Sic, TB2 and C
Results and Discussion
Examples of load vs. depth plots obtained for tests on SIC and borosilicate are shown in Figure 3. The two tests were conducted at the same displacement amplitude. The higher maximum load (J’_) and lower maximum depth of per&&ion (h_) for the SIC load-depth plot reflect much higher elastic and plastic properties for Sic than for borosihcate. The elastic modulus values calculated from these two plots are 32 1 GPa for SIC and 54 GPa for the borosilicate. The E values obtained from tests on these two materials at higher loads are 327 GPa at P-=0.14 N for Sic and 5 1 GPa at P-4.1 1 N for the borosilicate. These results are in excellent agreement with published values for these two materials listed in Table 1. This establishes that the DSI method using the NMP is an accurate method for measurin g the elastic properties of small volumes of materials. A previous study on hot &statically pressed S&N.,(10) also found that the DSI method using the NMP yielded results which were in excellent agreement with results corn conventional methods, such as the resonant frequency method. Obviously, one of the advantages of the DSI technique is that it does not need large and accurately machined samples to conduct the measurements. A large number of DSI tests were perhormed at loads of about 0.02 N at the inter-facialregions between the Sic fibers and the borosilicate matrix in order to determine the elastic moduli of the TiB, and C layers. An example of a row of indentations that spans the region from the borosilicate matrix to the Sic/C interface is shown in the SEM micrograph of Figure 4 along with a plot of the elastic modulus values calculated from corresponding load-depth plots. The indentations are spaced about 2 pm apart. In tbis case, indentations 1 to 3 can be seen in the SEM micrograph, and are clearly in the borosilicate matrix. The calculated E values
z
0.08
-
0.06
-
z _z:
0.3
0.6
Depth (pm) Figure 3. Load-depthplotsfiumDSI tests cmthe Sic fiber and the borosili~
matrix
792
Vol. 33, No. 5
FIBER-REINFORCED GLASSCERAMICCOh4POSITE
200 150 100 50 1
2
3
4
5
6
7
6
Indent number Figure 4. SEM miaqqph of and elastic modulus vs. indent number (or position) for indentations at the interfacial region between Sic and borosilicate. Spacing between consecutive indentatior~~ is 2 pm. Indentations 1,2 and 3 are in the matrix.
for indentations 1 and 2 are 64.3 and 62.1 GPa, respectively. Indentation 3, on the other hand, has a slightly higher calculated E value (82.6 GPa) possibly because it is too close to the more rigid TiEl, layer. The rest of the indentations could not be seen in the SEM micrograph. However, since the spacing between the indentationsis known, it is possible to pinpoint their positions relative to the indentations in the borosilicate matrix. Using this method, indentation4 is right in the middle of the TiB, layer, indentation 6 is in the middle of the C layer, while number 5 is somewhere in between. For these three indentations, the calculated E values am 150.6,117.1 and 91.9 GPa, respectively. Therefore, the elastic modulus of the TiB, layer should be close to 150 GPa and that of the C layer should be about 92 GPa. Indentations 7 and 8 have E values that are much higher than that of indentation 6 because they are at the interface between the C layer and the SIC fiber. Another example of a series of indentations is shown in Figure 5. Indentations 9 and 10 are clearly in the Sic fiber. The E values calculatedt?om the corresponding load-depth plots are 387.5 and 33 1.8 GPa, respectively The reason the latter value is lower than that for indent 9 is that indentation 10 is too close to the less rigid carbon layer. Indentation 12 is in the borosilicate matrix, and its calculated E value is 55.6 GPa. Indentation 11, on the other hand, cannot be seen in the SEM micrograph of Figure 5, but is half way between indentations 10 and 12, i.e. it falls within the TiD, layer. The calculated E value in this case is 117.3 GPa, which is lower than the value of 150 GPa for TiB, because the indentation is too close to either the C layer and/or the borosilicate matrix. Since it is very difkult and time consuming to find the indentations when the sample is examined under the SEM, for the rest of the indentations the method adopted to determine on which material a particular test was performed is as follows. The load-depth plot for any indentation was compared to the plots of the indentations discussed above, namely 1,2 or 12 for borosilicate, 9 or 10 for Sic, 4 for TiB, and 6 for C. Loaddepth plots of tests on the same material must have overlapping loading parts. This selection process indicated
Vol. 33, No. 5
FIBER-REINFORCED GLASS CERAMIC COMPOSITE
793
400 ?? s
300
2 3E
200
CJ 'E 4 w
100 0 10
11
Indent number Figure 5. SEM mierograph and elastic modulus vs. indent number for a row of indedtions that start in the SiC fibex and end in the borosilicab matrix. The magnification ofthe SEM picture can be obtained %nn the thickness ofthe C layer, which is 1.5 p that 10 indentations were performed on the Sic, 29 on the borosilicate matrix, 5 on the TB, and 4 on the C layer The average elastic modulus values calculatedfor the four materials, namely Sic, borosilicate, TiE$ and C, t?om their loaddepth plots after perhorming this selection process, are presented in Table 2. The average elastic modulus values obtained for the Sic fiber from indentations away from the interfacial region, at the load of about 0.025 N is 352 f 27 GPa. The error bar, representing f one standard deviation, indicates that there is a variation in E from one position to the other. Since the indentation test is a local&d test, probing a very small volume of the material, such a variation in measurements is expected, as the microstructure of the material is expected to vary from one position to the other. The values measured using the NMP for the present Sic fibers varied from about 320 to 390 GPa, which is within the range of the published
TABLE 2 Cakulated E Values for the Various Materials in the Fiber Reinforced Glass Ceramic Composite Calculated from Load-Depth Plots Material
BC Borosilicate TiB, C
Number of indentations 10 29 5 4
M,P 0 0.025 0.018 0.021 0.020
Average E (GPa) 352 f 27 62*6 143 * 7 91*6
794
FIBER-REINFORCED GLASSCERAMICCOMPOSITE
Vol. 33, No. S
value of 325 (6) to 400 GPa (7). It should be pointed out that measurement and calculation errors, such as errors in &term&g the slope of the linear region of the unloading segment, are of the order of *4 GPa. The average calculated E value for borosilicate is 62 f 6 GPa. The scatter in the data is very small in this case, and the value obtained is fairly close to the value of 50 GPa measured by a conventional method (6). For the C layer, the average elastic modulus value measured is 9 1 i 6 GPa, which is comparable to the published value of 80 GPa found in reference 9. For TiB,, on the other hand, there is a large difference betwcen the value measured by the DSI method and the published value of 489.5 GPa (8). The main reason for this di&rence is believed to be that the TiE3,layer has a different microstructure from that of bulk TiB, used to measure the value given in Table 1. In particular, as the SEM micrograph of Figure 1 shows, the TiH, layer appears to have a columnar structure with small gaps between the columns. Such intercohtmnar gaps are expected to reduce the elastic modulus of TiB, in the same way as porosity is found to decrease the elastic modulus of bulk ceramics (10). The reduction in E due to intercolumnar gaps has already been reported for electron beam physical vapour deposited zirconia coatings by Strangman (11). Another possible reason for the diIferenosbetween the E value measured for the TiB, layer and the published value is that the C layer and borosilicate matrix, which have lower E values, could have alfected the measurements. The sizes of the indentations in the TB, are expected to be only slightly lower than the thickness of this layer. Hence, the elastic zone could extend to either the borosilicate and/or C layer which would results in a slightly lower measured E value for the TB, layer.
DSI tests have been performed at the interfacial region between Sic fibers and their borosilicate matrix to determine primarily the elastic moduli of the TiB, and C layers found at this interface. Some tests were also performed on the Sic fibers and the borosilicate matrix, which gave E values that were in excellent agreement with published E values determined for these two materials using conventional methods. This establishes that the DSI method using the NMP is an accurate method for measuring elastic properties of materials. The average elastic modulus values obtained for the TiH, and the C layers are 143 f 7 and 9 1 f 6 GPa, respectively. The calculated value for TiB, is much lower than the published one due to the layer having a different microstructure and/or due to proximity to other layers. The E value for the C layer, on the other hand, is comparable to the published value. References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11.
R Beniche, Canadian Aeronautics and Space Journal 40, 163 1994. J.L. Loubet, J.M. Georges, J.M. Marchesini andG. Meille, J. Tribol. 106,43 1984. N.J. Pagano, R.E. Dutton, RY. Kim, P. Karpur and T.E. Matikas, Proceedmgs of International Conference on Composite Engineering D. Hui ed, p.387, New G&am, USA, (1994). LA Sneddon,Int. J. Eng. Sci. 3,47 1965. R.W. Hertzberg, Deformation and Fracture. Me&auks of EngineeringMaterials, 3rd Edition, Wiley, p.7, (1989). RY. Kim, Wright Laboratoq, unpublishedresults. AL. Geiger and M. Jackson, Advanced Mate&Is & Recesses 136,24 1989. Anonymous, Machine Design, p.l1,1993. E. Fitzer aud M. Heym, High Temperature-HighPressure lo,29 1978. R Beniche and RT. Holt, Ceramic Engineeringand Science Proceed&, 14(7-S), 188 (1993). T.E. Straugman, Thiu Solid Films 127,93 1985.