《复合材料 Composites》课程教学资源（学习资料）第五章 陶瓷基复合材料_role of residual stress in A-Z

Journal of the European Ceramic Society 19(1999)255-262 C 1998 Elsevier Science Limited Printed in Great Britain. All rights reserved PII:S0955-2219(98)00189-7 0955-2219/98/S--see front matter The role of Residual Stresses in Layered Composites of Y-ZrO2 and AlO3 Henryk Tomaszewski, Jan Strzeszewski" and Wojciech Gebicki "nstitute of Electronic Materials Technology, Wolczyriska 133, 01-919 Warsaw, Poland Institute of Physics, Warsaw University of Technology, Koszykowa 75. 00-662 Warsaw, Poland (Received 6 March 1998; accepted 31 July 1998) abstract knowledge of the residual stresses is important for a number of reasons. One is that the stresses across Laminar composites, containing layers of Y-TZP grain boundaries can be sufficiently large that grain and either Al2O3 or a mixture of Al203 and Y-ZrO2 boundary microcracking can occur. The impor technique of water solutions containing suspended of work analyzing the mps s led to a large body have been fabricated using a sequential centrifuging tance of this phenomenon h particles. Controlled crack growth experiments with ing -A second, related, reason is that the local notched beams of composites were done and showed residual stress affects the path of a crack as it pro- the significant effect of barrier layer thickness and agates through the microstructure and is believed composition on crack propagation path during fre by many to lead to R-curve behaviour. b ,/In a ture. Distinct crack deflection in alumina layers was result, crack deflection and the increase in tough observed. The increase of crack deflection angle with ness of ceramics can be observed.8.9 The aim of this the alumina layer thickness was also found In the work was to investigate laminar composites con case of the barrier layer made of a mixture, crack taining layers of Y-ZrO2 and either Al2O3 or a deflection did not occur independently on layer mixture of AlO3 and Y-ZrO2 fabricated by thickness. The observed changes have been corre- sequential centrifuging of aqueous particle suspen lated with the radial distribution of residual stresses sions. The source of distinct stresses found here in barrier layers created during cooling of sintered were the difference in thermal expansion and composites from fabrication temperature. The stres- shrinkage between zirconia and alumina and the ses found were the result of the difference in the crystallographically anisotropic thermal expansion thermal expansion and sintering shrinkage of alu- of the Al2O3 phase. The distribution of compressive and zirconia and the crystallographically ani- stresses in barrier layers of composites occured to be sotropic thermal expansion of the alumina. The dependent on layer thickness and composition residual stress distribution has been measured by (alumina only or a mixture)and to be regarded as a piezo-spectroscopy based on the optical fuorescence factor responsible for observed toughness increase of Crt3 dopants in alumina. C 1998 Elsevier Sci- ence Limited. All rights reserved 2 Experimental Procedure Keywords: composite, thermal expansion, tough- ness, Zro2, AlO3. Laminar composites of Y-TZP and Al2O3 with layers with thicknesses of 10 to 60 um (equal for both type of materials) were fabricated by the 1 Introduction sequential centrifuging(Z382 Hermle) of powder suspensions. Aqueous slurries containing 5 to In cooling sintered polycrystalline ceramics from 10 wt% zirconia powder (ZrO2+ 3. 4 mol%Y2O3 their fabrication temperature residual stresses are 0-6 um median particle size obtained from Unitec created as a result of the difference in thermal Ceramics) or alumina powder (AKP-53 type, expansion between the phases present. The 0.29 um median particle size obtained from Sumitomo) were prepared by ultrasonicating the *To whom correspondence should be addressed. Fax: +48 powders in deionized water at pH 4. Cast samples 22-834-9003: e-mail: tomasz h(@sp itme. edu. pl were dried, additionally isostatically pressed at

The Role of Residual Stresses in Layered Composites of Y±ZrO2 and Al2O3 Henryk Tomaszewski,a * Jan Strzeszewskib and Wojciech Ge,bickib a Institute of Electronic Materials Technology, WoÂlczynÄska 133, 01-919 Warsaw, Poland b Institute of Physics, Warsaw University of Technology, Koszykowa 75, 00-662 Warsaw, Poland (Received 6 March 1998; accepted 31 July 1998) Abstract Laminar composites, containing layers of Y±TZP and either Al2O3 or a mixture of Al2O3 and Y±ZrO2 have been fabricated using a sequential centrifuging technique of water solutions containing suspended particles. Controlled crack growth experiments with notched beams of composites were done and showed the signi®cant e€ect of barrier layer thickness and composition on crack propagation path during frac￾ture. Distinct crack de¯ection in alumina layers was observed. The increase of crack de¯ection angle with the alumina layer thickness was also found. In the case of the barrier layer made of a mixture, crack de¯ection did not occur independently on layer thickness. The observed changes have been corre￾lated with the radial distribution of residual stresses in barrier layers created during cooling of sintered composites from fabrication temperature. The stres￾ses found were the result of the di€erence in the thermal expansion and sintering shrinkage of alu￾mina and zirconia and the crystallographically ani￾sotropic thermal expansion of the alumina. The residual stress distribution has been measured by piezo-spectroscopy based on the optical ¯uorescence of Cr+3 dopants in alumina. # 1998 Elsevier Sci￾ence Limited. All rights reserved Keywords: composite, thermal expansion, tough￾ness, ZrO2, Al2O3. 1 Introduction In cooling sintered polycrystalline ceramics from their fabrication temperature residual stresses are created as a result of the di€erence in thermal expansion between the phases present. The knowledge of the residual stresses is important for a number of reasons. One is that the stresses across grain boundaries can be suciently large that grain boundary microcracking can occur. The impor￾tance of this phenomenon has led to a large body of work analyzing the mechanics of microcrack￾ing.1±5 A second, related, reason is that the local residual stress a€ects the path of a crack as it pro￾pagates through the microstructure and is believed by many to lead to R-curve behaviour.6,7 In a result, crack de¯ection and the increase in tough￾ness of ceramics can be observed.8,9 The aim of this work was to investigate laminar composites con￾taining layers of Y-ZrO2 and either Al2O3 or a mixture of Al2O3 and Y±ZrO2 fabricated by sequential centrifuging of aqueous particle suspen￾sions. The source of distinct stresses found here were the di€erence in thermal expansion and shrinkage between zirconia and alumina and the crystallographically anisotropic thermal expansion of the Al2O3 phase. The distribution of compressive stresses in barrier layers of composites occured to be dependent on layer thickness and composition (alumina only or a mixture) and to be regarded as a factor responsible for observed toughness increase. 2 Experimental Procedure Laminar composites of Y±TZP and Al2O3 with layers with thicknesses of 10 to 60m (equal for both type of materials) were fabricated by the sequential centrifuging (Z382 Hermle) of powder suspensions. Aqueous slurries containing 5 to 10 wt% zirconia powder (ZrO2+3.4 mol%Y2O3, 0.6m median particle size obtained from Unitec Ceramics) or alumina powder (AKP-53 type, 0.29m median particle size obtained from Sumitomo) were prepared by ultrasonicating the powders in deionized water at pH 4. Cast samples were dried, additionally isostatically pressed at Journal of the European Ceramic Society 19 (1999) 255±262 # 1998 Elsevier Science Limited Printed in Great Britain. All rights reserved PII: S0955-2219(98)00189-7 0955-2219/98/$Ðsee front matter 255 *To whom correspondence should be addressed. Fax: +48- 22-834-9003; e-mail: tomasz_h@sp.itme.edu.pl

H. Tomaszewski et al 120 MPa and then sintered at 1600C. The larger The tests of controlled crack growth were per- shrinkage of the Y-ZrO2 during sintering caused formed using Zwick machine of 1446 type. The that in some layered composites the mixed compo- notched beams were loaded in three-point bending sition of 50 vol% AlO3 and Y-ZrO2 was used with I um/min loading speed and 40 mm bearing instead of a pure AlO3 to minimize this mismatch distance. The crack was initiated and slowly grown ( Table 1) Micrographs of composite samples with step by step in a controlled way by permanent both types of barrier layers were shown in Fig. 1. loading and remowing of the load. This procedure The samples after sintering were cut and ground to results in less than 100 um increase of crack length the dimensions of 45x4x 1.5 mm and one surface by one step. The path of the crack during fracture perpendicular to the layers was polished. The sharp of layered composite was registered by SEM using notch in the center of the beams was prepared with of OPTON DSM 950 microscope. All experiments two diamond saws: 0.200 and 0-025 mm(Fig. 2) were done at room temperature in normal air environments The spatial distribution of residual stresses Table 1. Shrinkage of materials used for Y-ZrO2/Al2O3 com- within the alumina and a mixture of alumina and posite preparation in a sintering temperature zirconia layer of the composites was measured Material used Shrinkage after sintering using the piezospectroscopic technique. The inl600°C(%) method is based on the photostimulated fluores- Y-ZrO, cence from trace Cr+3 ions in alumina Al,O The frequency shift Av of the two lines in the R Mixture of 50 vol% Al,O3 and Y-Zro doublet is a measure of the elastic strain within the volume of material excited by the laser, following where: Ili are the piezospectroscopic coefficients 100 Fm and oi are the stress components The made using an optical microscope with an attached spectrometer(DILOR X4800) An argon ion laser ing at wavelength of 514.5 nm was used the excitation source. In each experiment a region of 5968 interest in the sample was first selected using the microscope then the laser beam was focused to a spot BShoNse on that feature. This way the alumina or a mixture layer of composite were scanned by 5 to 10 um steps (a The intensities of the stimulated R, and R fluores- cence lines were typically collected by scanning the 时的 25k 188pm M35 Fig. 1. Microstructure of layered composite with Y-TZP natrix and barrier layers(darker regions) consisted of (a) Fig. 2. An example of notched beam used in controlled crack alumina and(b) a mixture of alumina and zirconia propagation tests

120 MPa and then sintered at 1600C. The larger shrinkage of the Y±ZrO2 during sintering caused that in some layered composites the mixed compo￾sition of 50 vol% Al2O3 and Y±ZrO2 was used instead of a pure Al2O3 to minimize this mismatch (Table 1). Micrographs of composite samples with both types of barrier layers were shown in Fig. 1. The samples after sintering were cut and ground to the dimensions of 4541.5 mm and one surface perpendicular to the layers was polished. The sharp notch in the center of the beams was prepared with two diamond saws: 0.200 and 0.025 mm (Fig. 2). The tests of controlled crack growth were per￾formed using Zwick machine of 1446 type. The notched beams were loaded in three-point bending with 1m/min loading speed and 40 mm bearing distance. The crack was initiated and slowly grown step by step in a controlled way by permanent loading and remowing of the load. This procedure results in less than 100m increase of crack length by one step. The path of the crack during fracture of layered composite was registered by SEM using of OPTON DSM 950 microscope. All experiments were done at room temperature in normal air environments. The spatial distribution of residual stresses within the alumina and a mixture of alumina and zirconia layer of the composites was measured using the piezospectroscopic technique. The method is based on the photostimulated ¯uores￾cence from trace Cr+3 ions in alumina. The frequency shift
 of the two lines in the R￾doublet is a measure of the elastic strain within the volume of material excited by the laser, following tensorial relation:10
 ˆ ijij where: ij are the piezospectroscopic coecients and ij are the stress components. The piezospectroscopic measurements were made using an optical microscope with an attached spectrometer (DILOR X4800). An argon ion laser operating at wavelength of 514.5 nm was used as the excitation source. In each experiment a region of interest in the sample was ®rst selected using the microscope then the laser beam was focused to a spot on that feature. This way the alumina or a mixture layer of composite were scanned by 5 to 10m steps. The intensities of the stimulated R1 and R2 ¯uores￾cence lines were typically collected by scanning the Fig. 1. Microstructure of layered composite with Y±TZP matrix and barrier layers (darker regions) consisted of (a) alumina and (b) a mixture of alumina and zirconia. Fig. 2. An example of notched beam used in controlled crack propagation tests. Table 1. Shrinkage of materials used for Y-ZrO2/Al2O3 com￾posite preparation in a sintering temperature Material used Shrinkage after sintering in 1600C (%) Y±ZrO2 19.04 Al2O3 16.27 Mixture of 50 vol% Al2O3 and Y±ZrO2 18.47 256 H. Tomaszewski et al.

The role of residual stresses in layered composites of Y-ZrO2 and A120 257 spectrometer gratings using steps of 0.204 wave- numbers and integrating over 0.5s intervals. The Tensile stresses Zro collected data were subsequently analyzed with curve-fitting algorithms(double Lorentz function) The line position was identified by simultaneously Compressive stresses fitting the Ri and R2 peaks using Nice Fit software package. By using an objective lens of 100x mag- Tensile stresses zro nifying power, a minimum spot size of 3 um dia meter could be achieved. It is known that both Ri and R, lines shift to smaller wavenumber with Fig. 3. Expected stress distribution in layered zircon increasing temperature, so a consistent calibration alumina composites. for the ruby was performed. Instrumental fluctua tions were compensated by monitoring an external compressive stress in alumina layer will oppose the of a neon discharge opening the crack. This expectation was confirmed lamp. Although the volume of material probed in by the tests of crack initiation in notched beams o the experiments was unknown, it was estimated composite studied. It occured that for the same hat the spectroscopic information was obtained layer thickness and bearing distance, 25% higher from a depth equalled spot size. force had to be used to initiate the crack in the C For determining the stresses in alumina, the RI sample where notch ended at the beginning of alu ne and piezospectroscopic coefficient(7-59 cm-/ mina layer in comparison to the sample where it GPa), for hydrostatic stress state, found by He and ended in zirconia layer. The character of the crack Clarke have been used path during fracture was also different in these The same method was used for calculating the samples. In the case of second sample initiated the same type of alumina powder and at the same cularly to the layer Ough zirconia layer perpend esidual stresses in alumina pellet prepared from crack propagated thi temperature of sintering. Although the average In the case of first sample (notch ended at the stress over the pellet must be zero, variations in begining of alumina layer), crack was deflected at stress from one grain to another being a result of the begining of its way through the alumina layer the difference in thermal expansion coefficient (see Fig 4) along its (ae=9.5 Further observation of controlled crack (aa=86x 10-6oC-)cause both a line shift and a showed that deflection of crack takes place only in broadening of the line due to superposition of alumina layer. In zirconia layer the crack deflects spectra from individual fluorescing volumes. This back to its original direction. It was found that the way was possible to measure the everage value of magnitude of the crack deflection is dependent on the line shift and calculate subsequent everage alumina layer thickness of composite. The values value of local residual stresses in polycrystalline of crack deflection angle (understood as a deflec alumina tion angle from direction perpendicular to the lay- The critical stress intensity factor, Klc, of com- ers)in a function of layer thickness are listed in posites was measured on notched beams described Table 2. As can be seen, crack deflection angle earlier by the method and relation proposed by increases with layer thickness. In 60 um thick alu- Evans mina layers crack defects at 90(Fig. 5). In layers with thickness of 10 um and lower crack deflection does not take place(Fig. 6) 3 Results and discussion At the crack front, deflection process in alumina layers is more complicated than it was shown in Thermal expansion mismatch(azro,= 12 x 10 Figs 5 and 6. Crack not only deflects but branches 9x 10-6C-)and shrinkage mis- also(see Fig. 7)what distinctly enhances the length match(see Table 1) between zirconia and alumina of the crack way and energy release during fracture lead after cooling from fabrication temperature to through the alumina layer. After crack front mov residual stress distribution in layered composites ing farther, only one branch of the crack is widely shown at Fig. 3. In the layer with lower a and opened but the rest of them is getting less visible lower shrinkage, the biaxial compressive stress is for microscopic observations expected and similarly, biaxial tensile stress in the Described above crack behaviour was observed in layer with higher a and shrinkage. Such a distribu- the bulk of the material studied and it seems to be a tion indicates that expected tensile stress in zirconia result of residual stresses present in barrier layers layer should promote opening the crack in the not- As can be seen from Figs 8-ll, the frequency shift ched beam during bending. On the contrary, the Ri line and subsequent compressive stresses

spectrometer gratings using steps of 0.2±0.4 wave￾numbers and integrating over 0.5 s intervals. The collected data were subsequently analyzed with curve-®tting algorithms (double Lorentz function). The line position was identi®ed by simultaneously ®tting the R1 and R2 peaks using NiceFit software package. By using an objective lens of 100 mag￾nifying power, a minimum spot size of 3m dia￾meter could be achieved. It is known that both R1 and R2 lines shift to smaller wavenumber with increasing temperature, so a consistent calibration for the ruby was performed. Instrumental ¯uctua￾tions were compensated by monitoring an external reproducible spectral line of a neon discharge lamp. Although the volume of material probed in the experiments was unknown, it was estimated that the spectroscopic information was obtained from a depth equalled spot size. For determining the stresses in alumina, the R1 line and piezospectroscopic coecient (7.59 cmÿ1 / GPa), for hydrostatic stress state, found by He and Clarke10 have been used. The same method was used for calculating the residual stresses in alumina pellet prepared from the same type of alumina powder and at the same temperature of sintering. Although the average stress over the pellet must be zero, variations in stress from one grain to another being a result of the di€erence in thermal expansion coecient along its c-axis (c ˆ 9
5 10ÿ6Cÿ1) and a-axis (a ˆ 8
6 10ÿ6Cÿ1) cause both a line shift and a broadening of the line due to superposition of spectra from individual ¯uorescing volumes. This way was possible to measure the everage value of the line shift and calculate subsequent everage value of local residual stresses in polycrystalline alumina. The critical stress intensity factor, KIc, of com￾posites was measured on notched beams described earlier by the method and relation proposed by Evans.11 3 Results and Discussion Thermal expansion mismatch (ZrO2 ˆ 12 10ÿ6 Cÿ1; Al2O3 ˆ 9 10ÿ6Cÿ1) and shrinkage mis￾match (see Table 1) between zirconia and alumina lead after cooling from fabrication temperature to residual stress distribution in layered composites shown at Fig. 3. In the layer with lower  and lower shrinkage, the biaxial compressive stress is expected and similarly, biaxial tensile stress in the layer with higher  and shrinkage. Such a distribu￾tion indicates that expected tensile stress in zirconia layer should promote opening the crack in the not￾ched beam during bending. On the contrary, compressive stress in alumina layer will oppose the opening the crack. This expectation was con®rmed by the tests of crack initiation in notched beams of composite studied. It occured that for the same layer thickness and bearing distance, 25% higher force had to be used to initiate the crack in the sample where notch ended at the beginning of alu￾mina layer in comparison to the sample where it ended in zirconia layer. The character of the crack path during fracture was also di€erent in these samples. In the case of second sample initiated crack propagated through zirconia layer perpendi￾cularly to the layers. In the case of ®rst sample (notch ended at the begining of alumina layer), crack was de¯ected at the begining of its way through the alumina layer (see Fig. 4). Further observation of controlled crack growth showed that de¯ection of crack takes place only in alumina layer. In zirconia layer the crack de¯ects back to its original direction. It was found that the magnitude of the crack de¯ection is dependent on alumina layer thickness of composite. The values of crack de¯ection angle (understood as a de¯ec￾tion angle from direction perpendicular to the lay￾ers) in a function of layer thickness are listed in Table 2. As can be seen, crack de¯ection angle increases with layer thickness. In 60m thick alu￾mina layers crack de¯ects at 90 (Fig. 5). In layers with thickness of 10m and lower crack de¯ection does not take place (Fig. 6). At the crack front, de¯ection process in alumina layers is more complicated than it was shown in Figs 5 and 6. Crack not only de¯ects but branches also (see Fig. 7) what distinctly enhances the length of the crack way and energy release during fracture through the alumina layer. After crack front mov￾ing farther, only one branch of the crack is widely opened but the rest of them is getting less visible for microscopic observations. Described above crack behaviour was observed in the bulk of the material studied and it seems to be a result of residual stresses present in barrier layers. As can be seen from Figs 8±11, the frequency shift of the R1 line and subsequent compressive stresses in Fig. 3. Expected stress distribution in layered zirconia± alumina composites. The role of residual stresses in layered composites of Y±ZrO2 and Al2O3 257

1000 R35/4 sxS 25 kv Fig. 5. The crack path in 55 um thick alumina layer of Y-ZrO2/ Al2O3 composite (inverted image) 8§°封 Fig. 4. Y-ZrO 一= of crack path during fracture of layered posite dependent on the type of layer where notch ha one:(a)the end of the notch in zirconia layer tes perpendicularly to the layer, (b)the end of the notch in alumina layer-the crack immediately deflects Table 2. mean value of crack o n angle a gradient of 1888 compressive stresses in alumin of Y-ZrO2/Al2O3 com- posite as a function of na layer thickness Thickness of alumina layer(un Mean value of crack 022±562±890 deflection angle°) Gradient of c 13-250-81581188-4 stresses,△a(MPa) sR28/1叫 alumina layers are not only a function of barrier 85H layer thickness but a position across the layer also Maximum of compressive stress equalled 280 MPa is observed at the interface and it is independent on Fig. 6. The crack path in alumina layer of Y-ZrO2/Al2O3 alumina layer thickness. The minimum of stress is composite as a function of layer thickness: (a)19. 5 um and (b) achieved in the center of the layer. However the stres 8.2 um(inve in minimum is dependent on alumina layer thickness ( see Table 2). In the case of 60 um thick barrier layer type of alumina powder and at the same tempera the stress minimum equals 88.3 MPa. As it was said ture of sintering and caused by crystallographically earlier, this value is exactly equal the residual stresses anisotropic thermal expansion of the alumina only measured in alumina pellet prepared from the same It means also that the presence of compressive

alumina layers are not only a function of barrier layer thickness but a position across the layer also. Maximum of compressive stress equalled 280 MPa is observed at the interface and it is independent on alumina layer thickness. The minimum of stress is achieved in the center of the layer. However the stress in minimum is dependent on alumina layer thickness (see Table 2). In the case of 60m thick barrier layer the stress minimum equals 88.3MPa. As it was said earlier, this value is exactly equal the residual stresses measured in alumina pellet prepared from the same type of alumina powder and at the same tempera￾ture of sintering and caused by crystallographically anisotropic thermal expansion of the alumina only. It means also that the presence of compressive Fig. 4. Character of crack path during fracture of layered Y±ZrO2/Al2O3 composite dependent on the type of layer where notch has been done: (a) the end of the notch in zirconia layerÐ the crack propagates perpendicularly to the layer, (b) the end of the notch in alumina layerÐthe crack immediately de¯ects. Table 2. Mean value of crack de¯ection angle and gradient of compressive stresses in alumina layer of Y±ZrO2/Al2O3 com￾posite as a function of alumina layer thickness Thickness of alumina layer (mm) 10 25 40 60 Mean value of crack de¯ection angle () 0 22‹5 62‹8 90 Gradient of compressive stresses,
 (MPa) 13.2 50.8 158.1 188.4 Fig. 5. The crack path in 55 m thick alumina layer of Y±ZrO2/Al2O3 composite (inverted image). Fig. 6. The crack path in alumina layer of Y±ZrO2/Al2O3 composite as a function of layer thickness: (a) 19.5m and (b) 8.2 m (inverted image). 258 H. Tomaszewski et al

The role of residual stresses in layered composites of y-ZrO2 and A120 16522 (a) Position across the layer, um Fig 9. Frequency shift of the RI line and compressive stresses 508 in 25 um thick alumina layer of Y-ZrO2/Al2O3 composite as a function of position across the layer. stress minimum in the center of thicker alumina layers can be the result of internal relaxation of stresses The compressive stress gradient( the difference of 16524 stress between the layer boundary and the center of SA 35/ the layer) listed in Table 2 can be correlated with e85° the angles of crack deflection. Good correspon dence indicates that the gradient can be regarded an important factor responsible for the degree of crack deflection and further contribution of crack Fig. 7. The crack path in alumina layer of Y-ZrO2/Al2o deflection mechanism in enhancing the toughness composite at the crack front ( inverted image) observed in layered composites(see Table 3) To the stress distribution shown at Fig. 3 one new stress component should be added however. Finite element calculations 2, 3 show that in layered materials not only biaxial stresses exist at the surface and far from the surface. but a stress perpendicular to the layer plane existing near the free surface that is highly localized, decreasin rapidly face to becom dligible distance approximately on the order of the layer 1o thickness, also. This stress has a sign opposite to Position acros that of the biaxial stresses deep within the layer Thus, when the biaxial stresses are compressive 250 there is a tensile stress perpendicular to the layer at and near the surface. This reversal of stresses was also observed by Cox 4 during his analysis of inclusions located either within a body or at the surface. Thus. a tensile stress field. localized near the surface, will be present in layers when the stress o far from the surface is biaxial compressive. These tensile stresses can cause the extension of preexist- Fig8. Frequency shift of the Ri line and compressive stresses ing cracks. Such a cracks along the center of the in 10 um thick alumina layer of Y-ZrO2/Al2O3 composite as a two phase Al2O3/3Y-ZrO2 layer(300 um) bonded function of position acro by two much thicker (3000 um)3Y-ZrO2 layers

stress minimum in the center of thicker alumina layers can be the result of internal relaxation of stresses. The compressive stress gradient (the di€erence of stress between the layer boundary and the center of the layer) listed in Table 2 can be correlated with the angles of crack de¯ection. Good correspon￾dence indicates that the gradient can be regarded as an important factor responsible for the degree of crack de¯ection and further contribution of crack de¯ection mechanism in enhancing the toughness observed in layered composites (see Table 3). To the stress distribution shown at Fig. 3 one new stress component should be added however. Finite element calculations12,13 show that in layered materials not only biaxial stresses exist at the surface and far from the surface, but a stress perpendicular to the layer plane existing near the free surface that is highly localized, decreasing rapidly from the surface to become negligible at a distance approximately on the order of the layer thickness, also. This stress has a sign opposite to that of the biaxial stresses deep within the layer. Thus, when the biaxial stresses are compressive, there is a tensile stress perpendicular to the layer at and near the surface. This reversal of stresses was also observed by Cox14 during his analysis of inclusions located either within a body or at the surface. Thus, a tensile stress ®eld, localized near the surface, will be present in layers when the stress far from the surface is biaxial compressive. These tensile stresses can cause the extension of preexist￾ing cracks. Such a cracks along the center of the two phase Al2O3/3Y±ZrO2 layer (300m) bonded by two much thicker (3000m) 3Y±ZrO2 layers Fig. 7. The crack path in alumina layer of Y±ZrO2/Al2O3 composite at the crack front (inverted image). Fig. 8. Frequency shift of the R1 line and compressive stresses in 10 m thick alumina layer of Y±ZrO2/Al2O3 composite as a function of position across the layer. Fig. 9. Frequency shift of the R1 line and compressive stresses in 25m thick alumina layer of Y±ZrO2/Al2O3 composite as a function of position across the layer. The role of residual stresses in layered composites of Y±ZrO2 and Al2O3 259

260 H. Tomaszewski et al Table 3. Toughness of Y-ZrO2/Al2O3 composite as a function of barrier layer thickness and composition Composition of alumine Mixture of barrier layer alumina barrier layer (um) K1e,(MPam2)720±842±999±10.06±71± 0-150-550·760.33 0-41 Position across the layer, Hm layer as was shown by FEM calculations and rne d by Ho et al. seems to be helpful ele- ment in explana stress gradient in the crack deflection process observed in reported layered composites. The crack deflection in alumina barrier layers is a result of Position across the layer, um interaction of residual compressive stress acting in the plane parallel to the layers, and perpendicular Fig. 10. Frequency shift of the RI line and compressive stres- to the layer and notch plane, tensile stress, both ses in 40 um thick alumina layer of Y-Zroz/Al2O3 composite present in laminate after cooling from fabrication as a function of position across the layer temperature and the third one, tensile applied stress in bending of notched beam. For a maximum of compressive stress gradient(the minimum of compressive stress) observed in the case of 60 m thick alumina layer the tensile perpendicular stress begins to dominate and in a result the crack deflects in the center of the layer and propagates along the layer and then deflects back to the per pendicular direction when the compressive stress increases from the minimum in the center of the layer to the maximal value at the interface, as can be seen from Fig. 5. In the case of the thinnest alumina layer where the compressive stress across the layer becomes almost unchangable (the gra dient is in minimum) the crack propagates through the layer without deflection The results obtained for composites with barrier layers made of an oxide mixture instead of a pure 30 50 60 Al_03 prepared to minimize the larger shrinkage of Position across the lay Y-ZrO2(see Table 1)are good confirmation of the thesis on the role of compressive stress gradient in Fig. 11. Frequency shift of the Ri line and compressive stres- observed crack deflection. Residual stresses in ses in 60 um thick alumina layer of Y-ZrO /AlO3 composite these layers should be present also, but their dis- as a function of position across the layer tribution seems to be different. It is expected they have rather local character--alumina grains in a mixture are stressed by zirconia grains and vice were observed after cooling from fabrication tem versa. Although perpendicular stress exists in perature by Ho et al. >and it was found that for a this type of layers also, such a distribution of given residual stress, crack extension without any compressive stress should result in a lack of crack external stress will take place only when the layer deflection. As it shown at Fig 12, crack propagates hickness is greater than a critical value through the barrier layer without deflection inde In our case matrix and barrier layer thickness pendently on layer thickness. The magnitude of was equal (10 to 60 um) and cracks parallel to the frequency shift of the RI line and compressive layers were not found. But the presence of tensile stress in this case are slightly higher than in layers stress perpendicular to the alumina layer plane made of a pure alumina, but independent on posi with the maximum localized in the center of this tion across the layer(Fig 13)

were observed after cooling from fabrication tem￾perature by Ho et al. 15 and it was found that for a given residual stress, crack extension without any external stress will take place only when the layer thickness is greater than a critical value. In our case matrix and barrier layer thickness was equal (10 to 60m) and cracks parallel to the layers were not found. But the presence of tensile stress perpendicular to the alumina layer plane with the maximum localized in the center of this layer as was shown by FEM calculations12,13 and con®rmed by Ho et al. 15 seems to be helpful ele￾ment in explanation of the role of compressive stress gradient in the crack de¯ection process observed in reported layered composites. The crack de¯ection in alumina barrier layers is a result of interaction of residual compressive stress acting in the plane parallel to the layers, and perpendicular to the layer and notch plane, tensile stress, both present in laminate after cooling from fabrication temperature and the third one, tensile applied stress in bending of notched beam. For a maximum of compressive stress gradient (the minimum of compressive stress) observed in the case of 60m thick alumina layer the tensile perpendicular stress begins to dominate and in a result the crack de¯ects in the center of the layer and propagates along the layer and then de¯ects back to the per￾pendicular direction when the compressive stress increases from the minimum in the center of the layer to the maximal value at the interface, as can be seen from Fig. 5. In the case of the thinnest alumina layer where the compressive stress across the layer becomes almost unchangable (the gra￾dient is in minimum) the crack propagates through the layer without de¯ection. The results obtained for composites with barrier layers made of an oxide mixture instead of a pure Al2O3 prepared to minimize the larger shrinkage of Y±ZrO2 (see Table 1) are good con®rmation of the thesis on the role of compressive stress gradient in observed crack de¯ection. Residual stresses in these layers should be present also, but their dis￾tribution seems to be di€erent. It is expected they have rather local characterÐalumina grains in a mixture are stressed by zirconia grains and vice versa. Although perpendicular stress exists in this type of layers also, such a distribution of compressive stress should result in a lack of crack de¯ection. As it shown at Fig. 12, crack propagates through the barrier layer without de¯ection inde￾pendently on layer thickness. The magnitude of frequency shift of the R1 line and compressive stress in this case are slightly higher than in layers made of a pure alumina, but independent on posi￾tion across the layer (Fig. 13). Fig. 11. Frequency shift of the R1 line and compressive stres￾ses in 60 m thick alumina layer of Y±ZrO2/Al2O3 composite as a function of position across the layer. Fig. 10. Frequency shift of the R1 line and compressive stres￾ses in 40 m thick alumina layer of Y±ZrO2/Al2O3 composite as a function of position across the layer. Table 3. Toughness of Y±ZrO2/Al2O3 composite as a function of barrier layer thickness and composition Composition of barrier layer Alumina Mixture of alumina and zirconia Thickness of barrier layer (m) 10 25 40 60 45 KIc, (MPa m1/2) 7.20‹ 0.15 8.42‹ 0.55 9.99‹ 0.76 10.06‹ 0.33 7.11‹ 0.41 260 H. Tomaszewski et al

The role of residual stresses in layered composites of y-ZrO2 and A120 261 4 Conclu The aim of this work was to determine the residual stress effect on character of crack ation 5e ya layered ceramic composites prepared by sequential centrifuging of powder suspensions During tests of controlled crack growth a distinct crack deflection in alumina layers was observed. As it occured the value of crack deflection angle was proportional to the layer thickness. In the case of layer thicknesses 16973 below 10 um the crack was found to be undeflected In barrier layers made of an oxide mixture crack deflection did not happen independently on layer thickness. This observations have been explained by measurements of residual stress distribution in bar. rier layers. The magnitude of compressive stress in alumina layer on the layer boundary was indepen dent on layer thickness. However the layer thickness 1898 affected the gradient of stresses. The compressive stresses were found to decrease from the boundary of layer to the centre of alumina layer and here reached the minimum. The correlation between the value of crack deflection angle and the magnitude of stress gradient was observed. In the case of layer with thicknesses less than 10 um, where crack did not deflect, the compressive stress gradient reached 16981 very small value. In the barrier layers made of an oxide mixture, higher compressive stresses were found. however the distribution and local character of these stresses resulted in the lack of crack deflec- (b) tion independently on layer thickness Elongation of crack way caused by crack deflec 12. The crack path during fracture of Y-ZrO,/Al, O, tion in alumina layer seemed to be responsible for posite with barrier layers made of alumina and zirconia observed enhancement in toughness of composites studied in a function of layer thickness Acknowledgements This work was supported by Polish Committee for Scientific Research under grant No. 7S202 04607 References 1. Clarke, F.J. P, Residual strain and fracture stress-grain size relationships in brittle solids. Acta Metall, 1964 Position across the layer, um 2. Evans, A. G, Microfracture from thermal expansion ani- sotropy. Acta Metall., 1978, 26( 3. Clarke. D. R. Microfracture from anisotropic shape changes etal.,1980,28(3) 4. Tvegaard. v. and Hutchinson, J. w. Microcraking in ceramics induced by thermal expansion or elastic aniso- tropy. J. Amer. Ceram Soc., 1988, 71(3), 157-16 5. Ortiz. M. and Molinari, A. Microstructural residua the layer, um tresses in ceramic materials. J. Mech. Phvs. Solids, 1988 4) Fig. 13. Frequency shift of the Ri line and compressive stres 6. Cook, R. F. Fairbanks. C. J. Lawn in 45 um thick barrier layer made of an oxide mixture of Y.-W, Crack resistance by interfacial bi Y-ZrO2/Al,O3 composite as a function of position across the etermining strength characteristics. J. lay 2(3)

4 Conclusions The aim of this work was to determine the residual stress e€ect on character of crack propagation in layered ceramic composites prepared by sequential centrifuging of powder suspensions. During tests of controlled crack growth a distinct crack de¯ection in alumina layers was observed. As it occured the value of crack de¯ection angle was proportional to the layer thickness. In the case of layer thicknesses below 10m the crack was found to be unde¯ected. In barrier layers made of an oxide mixture crack de¯ection did not happen independently on layer thickness. This observations have been explained by measurements of residual stress distribution in bar￾rier layers. The magnitude of compressive stress in alumina layer on the layer boundary was indepen￾dent on layer thickness. However the layer thickness a€ected the gradient of stresses. The compressive stresses were found to decrease from the boundary of layer to the centre of alumina layer and here reached the minimum. The correlation between the value of crack de¯ection angle and the magnitude of stress gradient was observed. In the case of layer with thicknesses less than 10m, where crack did not de¯ect, the compressive stress gradient reached very small value. In the barrier layers made of an oxide mixture, higher compressive stresses were found. However the distribution and local character of these stresses resulted in the lack of crack de¯ec￾tion independently on layer thickness. Elongation of crack way caused by crack de¯ec￾tion in alumina layer seemed to be responsible for observed enhancement in toughness of composites studied in a function of layer thickness. Acknowledgements This work was supported by Polish Committee for Scienti®c Research under grant No. 7S202 04607. References 1. Clarke, F. J. P., Residual strain and fracture stress±grain size relationships in brittle solids. Acta Metall., 1964, 12(2), 139±143. 2. Evans, A. G., Microfracture from thermal expansion ani￾sotropy. Acta Metall., 1978, 26(5), 1845±1853. 3. Clarke, D. R., Microfracture in brittle solids resulting from anisotropic shape changes. Acta Metall., 1980, 28(3), 913±924. 4. Tvegaard, V. and Hutchinson, J. W., Microcraking in ceramics induced by thermal expansion or elastic aniso￾tropy. J. Amer. Ceram. Soc., 1988, 71(3), 157±166. 5. Ortiz, M. and Molinari, A., Microstructural residual stresses in ceramic materials. J. Mech. Phys. Solids, 1988, 36(4), 385±400. 6. Cook, R. F., Fairbanks, C. J., Lawn, B. R. and Mai, Y.-W., Crack resistance by interfacial bridging: its role in determining strength characteristics. J. Mater. Res., 1987, 2(3), 345±356. Fig. 13. Frequency shift of the R1 line and compressive stres￾ses in 45m thick barrier layer made of an oxide mixture of Y±ZrO2/Al2O3 composite as a function of position across the layer. Fig. 12. The crack path during fracture of Y±ZrO2/Al2O3 composite with barrier layers made of alumina and zirconia mixture. The role of residual stresses in layered composites of Y±ZrO2 and Al2O3 261

H. Tomaszewski et al 7. Svain, M. V, R-curve behaviour in a polycrystalline alu- 12. Harrison, N. L. and Harrison. W. J. The stresses in an mina material. Mater. Sci. Lett. 1986. 5. 1393-1395 dhesive laver. Adhes 1972.3. 195-21 8. Faber, K. T. and Evans, A. G, Crack deflection pro- 13. Kirchner, H, Convay, J. and Segall, A. E, Effect of cesses-I. Theory. Acta Metall., 1983, 31(4), 565-576 joint thickness and residual stresses on the properties 9. Faber, K. T. and Evans, A. G, Crack deflection pro- of ceramic adhesive joints: I. Finite element analysi 10. Hsses-1L. Experiment. Acta Metall, 1983, 31(4), 577-584 of stresses in joints. J. Amer. Ceram. Soc., 1987, 70(2). 104-109 spectroscopic coefficients for chromium-doped sapphire 14. Cox, B N, Surface displacements and stress generated by J.Amer. Ceran.Soe.1995,78(5),1347-1354 11. Evans, A. G. Fracture mechanics determination. In 564-570 Fracture Mechanics of Ceramics, Vol. 1, ed. R. C. Bradt, 15. Ho, s, Hillman, C, Lange, F. F and Suo, Z, Surface D. P. H. Hasselman and F. F. Lange. Plenum Press cracking in layers under biaxial, residual compressive ew York,1974,pp.17-48 stress. J. Amer. Ceram. Soc., 1995, 78(9), 2353-2355

7. Svain, M. V., R-curve behaviour in a polycrystalline alu￾mina material. J. Mater. Sci. Lett., 1986, 5, 1393±1395. 8. Faber, K. T. and Evans, A. G., Crack de¯ection pro￾cessesÐI. Theory. Acta Metall., 1983, 31(4), 565±576. 9. Faber, K. T. and Evans, A. G., Crack de¯ection pro￾cessesÐII. Experiment. Acta Metall., 1983, 31(4), 577±584. 10. He, J. and Clarke, D. R., Determination of the piezo￾spectroscopic coecients for chromium-doped sapphire. J. Amer. Ceram. Soc., 1995, 78(5), 1347±1354. 11. Evans, A. G., Fracture mechanics determination, In Fracture Mechanics of Ceramics, Vol. 1, ed. R. C. Bradt, D. P. H. Hasselman and F. F. Lange. Plenum Press, New York, 1974, pp. 17±48. 12. Harrison, N. L. and Harrison, W. J., The stresses in an adhesive layer. J. Adhes., 1972, 3, 195±212. 13. Kirchner, H., Convay, J. and Segall, A. E., E€ect of joint thickness and residual stresses on the properties of ceramic adhesive joints: I. Finite element analysis of stresses in joints. J. Amer. Ceram. Soc., 1987, 70(2), 104±109. 14. Cox, B. N., Surface displacements and stress generated by a semi-elipsoidal surface inclusion. J. Appl. Mech., 1989, 56, 564±570. 15. Ho, S., Hillman, C., Lange, F. F. and Suo, Z., Surface cracking in layers under biaxial, residual compressive stress. J. Amer. Ceram. Soc., 1995, 78(9), 2353±2359. 262 H. Tomaszewski et al