Am. Ceran.So.8s151222-28202) journal Factors Affecting Threshold Strength in Laminar Ceramics Containing n Compressive Layers Masa p, rao and Fred F, Lange Materials Department, University of California, Santa Barbara, California 93106 Compressive layers placed within a laminate can arrest cracks. component). Although Eq. (1) describes a new toughening phe With increasing applied stress, the arrested crack can propa- nomenon. it was shown that after its rearrangement, a mor gate through the compressive layer These phenomena produce profound statement could be made concerning the strength statis a material with threshold strength, i. e, failure cannot occur tics of a brittle material. Namely, it was shown that failure would below a critical applied stress. A previously reported stress only occur at an applied stress that would cause the crack to fully intensity function describes different variables, e.go, magnitude extend across the compressive layer. Using this statement by of compressive stress, thickness of compressive layer, and setting 2a=t,+ 21, and K=Ke the critical stress intensity factor distance between compressive layers, which govern threshold for the compressive layer material, Eq (1)could be rearranged to strength. Laminar composites composed of thicker Al2 O, produce an expression for threshold strength, i.e., a stress beloy layers separated by thinner Al,O,mullite layers were fabri- which failure could not occur. cated to test the different variables that are predicted to govern threshold strength. The data agreed well with the K predicted values only when the magnitude of compressive stress and/or the thickness of the compressive layer were low For these conditions, the crack extended straight through the compressive layers, as assumed by the model used to predict threshold strength On the other hand, when the compressive 2r stress and/or layer thickness were large, threshold strength was larger than the predicted value. In addition, for these conditions, the crack bifurcated through the compressive laver. The angle between the bifurcated cracks increased with The purpose of the current work was to determine experimen- increasing compressive stress. tally the effect of the different independent variables in Eq. (3) This was accomplished by fabricating and testing an extensive series of different laminate architectures to determine the effect of Introduction three variables: the magnitude of residual compression. the thick ness of the compressive layers, and the thickness of the thicker T HAS been demonstrated that uniformly spaced compressive tensile layers. As shown below, the model correctly predicts layers can stop the otherwise catastrophic propagation of cracks, threshold strength only when the compressive stress and/or thick truncating the statistical strength distribution of brittle materials to ness of the compressive layer is small. For these cases, the crack stress intensity function was introduced to describe how the increasing applied stress, as assumed by the model used to develop arrested crack within the tensile layer is shielded from the applied Eq. (3). On the other hand. when the compressive stress and/or stress as the crack propagates through the bounding layers co hickness of the compressive layer is large, the crack bifurcates taining biaxial compressive stresses. within the compressive layer and produces a threshold strength ger than predicted by Eq.(3) K=0(m0+(0(+)m(2) IL. Experimental Procedure tensile stress, a the half-crack length, and Specimen Preparation of the compressive and tensile layers. To independently determine the effect of each of the three respectively nitude of the biaxial residual stress within variables, multilayered laminar composites of widely varying e thinner compressive layers, U, can be described by rchitecture and compressive layer compositions were fabricated via a sequential slip casting technique described elsewhere -E,[1+ ) Laminate architectures for each of the three studies were chosen that two of the three parameters were held nearly constant Specifics of the laminate architectures (i.e, compressive and Er is the residual differential thermal strain, E-E/(I-v ensile layer thickness and compressive layer compositions) used Youngs modulus, and v the Poissons ratio(i represents the for each study are detailed in Section Il All laminate specimens contained thicker tensile layers com- sm ed of 0.95 volume fraction Al, O,(ds= 0.6 um; AKP-15 mitomo Chemicals, Tokyo, Japan) and 0.05 volume fraction M. D. Thouless-contributing editor Zr(3Yo 0.4 um: TZ-3Ys, Tosoh. Tokyo, Japan): ZrO was included for control of grain growth. Compressive layers were fabricated from different mixtures of mullite (dsn = 0.7 um MULSM, Baikowski, France)and Al,O, The fraction of mullite 187812 Received March 29, 2001: approved November 19, 2001 was one factor that determined the magnitude of compressive can Ceramic Society tress. For the thicker tensile layers containing Al, O,(with 0.05
May 2002 Factors Affecting Threshold Strength in Laminar Ceramics Containing Thin Compressive Layers 223 olume fraction Zr(3Y )O2), dispersed aqueous slurries containing (2) Residual Compressive Stress Determination 0.30 volume fraction solids were formulated at pH Il using Biaxial, residual, compressive stresses produced by the differ tetramethyl ammonium hydroxide(TMA-OH) Dispersed aqueous ential thermal contraction of the laminates during cooling from the slurries containing 0. 15 volume fraction of the mullite/Al o densification temperature were determined using Eq. (2), and the mixture used to form the compressive layers were formulated at property data are listed in Table I. In these calculations, it wa the same pH. Both slurries were homogenized by attrition milling assumed that all differential strain was dissipated via creep until (3 mm Zr(3Y)O, milling media; Model Szegvari Attritor. Union the materials were cooled to 1200 C4 Process, Akron, OH) and then allowed to equilibrate for 12 h The elastic modulus of the multiphase compressive layers wa before casting. The magnitude of residual compression, oe, within estimated using the lower bound estimate of Ravichandran the compressive layers was varied by changing the volume fraction of mullite within the compressive layers from 0. 10 to 0.70(balanc 、(CEE2+E)1+c)2-E+EE2 (cE1+E2)(1+c) (4) Al,O,). Although different laminar architectures were fabricated to investigate the effect of architecture on threshold strength, architectures were fabricated with similar layer thickness ratios in of the two constituent phases, the an attempt to keep the compressive stress nearly identical for the phase. The coefficient of thermal different architectures produced with the same material combina = was estimated using the analysis of Turner" iom e plates(-70 mm X 60 mm x 4 mm before firing) K,V,+a,k,V were cast, dried at room tem perature for several days, and fired K,VI+kv2 1550C/2 h in air (5 C/min heating and cooling rate). The minates were composed of an alternating stacking sequence of where a, is the coefficient of thermal expansion of either constit- five thick tensile layers and four thin compressive layers. How ever, while each of the four compressive layers was of the same Poisson's ratio, however, was estimated using a simple rule of ickness. the laminates were intentionally designed to have much ixtures, as suggested by Ravichandran. The rule of mixtures thicker outermost tensile layers(-700-1500 um) than the three was also used to determine the properties of the multiphase tensile inner tensile layers (200-550 um), as shown in Fig. 1. This layers as well, because of the small volume fraction of the second particular design was chosen to facilitate casting of the thin hase within the tensile layers compressive layers. The residual compressive stresses within the thin compressive layers of some representative architectures were measured using a from the plates, and one of the lateral surfaces of each specimen phezospectroscopic met od that determined stress by measuring was polished to a 6 um finish with a diamond abrasive. With a Vickers indenter and loads between 2 and 5 kg, cracks of varying impurities within the AL,O,. Following a procedure described size(-100-300 um) were introduced into the center of the central free edges--on the polished surface of compressive layers in the inset of Fig. I. The indenter cracks ensured that stable crack laminates that had been ground down at a shallow angle (-1) relative to the laminar plane to form a wedge. By examining only extension would occur through the bounding compressive layers the thickest part of the compressive layer, the contribution of the with increasing applied stress, which would enable the measure- underlying tensile Al,O, laver's fluorescence yin the compres ctra was mini ment of threshold strength mized, ensuring accurate stress measurement Monolithic control specimens(without compressive layers) of sive layer. the tensile layer composition were also fabricated by the same procedure outlined above. Identical indenter cracks were intro- (3) Mechanical Testing duced into these control specimens. In addition, a set of control All specimens were tested in the transverse four-point flexure specimens was produced that did not have indenter cracks configuration (1. e, loading direction parallel to the laminate plane) using a screw-driven mechanical testing machine operating in displacement control (crosshead speed =0.01 mm/min, spans of and 30 mm Outer Tensile Layers Inner Tensile Layers that the indented face of the specimen was put in tension, as shown 200-550um thick in the inset of Fig. 1. The tensile stress applied to the crack on 0.95 volume fraction Al,O3/ the surface of the specimen, Ua, was calculated by substituting the 0.05 volume fraction Zr(3Y)O 0.05 volume fraction Zr(3Y)O applied load and specimen dimensions into the bending beam formula for four-point flexural loading 3P(s-s) (6) Pa is the appli nd s, the outer espectively, b the specimen width; and h the spe Observations of the crack on the tensile surface of the lar Table I. Material Property Data for Laminate Constituents Compressive Layers Property 0. 10-0, 70 volume fraction mullite Material (x10C)(GPa) Poissons ratio Transverse 4-pt Flexure showin shows 5.30 From Ref. 17.From Ref 2
Journal of the American Ceramic Sociery-Rao and Lange = showed that, in all ion and estimated by Eq (2), and the values measured for selected 550/ arrest of the occurred before failure, indicating that specimens using piezospectroscow a data points shown in Fig.2: th was the threshold strength Five specimens were tested for all data points but one had standard deviations $%. The one exception was for the 0.70 volume fraction mullite 200/25 lami- (4 Crack Path Observations nate, where only one specimen out of fifteen failed from the As reported below, observations of the fracture surfaces indi indenter crack. Lack of failure from the indentation cracks was due compressive layer or bifurcate as it entered the compressive layer. um compressive layers that sandwiched the 200 um AlO, layers Using procedures detailed elsewhere, crack extension on the was, in turn, sandwiched between much thicker layers (-150 external tensile surface of select specimens was observed during um) of monolithic Al,O, that composed the outer surfaces of the loading with cellulose acetate replicas. As shown below, bifurca specimens, as discussed previously in Section IL. Because the tion could only be revealed by observing the crack path beneath threshold strength of this specific architecture approached that of the surface. To view the crack path beneath the surface, select the average strength of the Al,O, itself, failure in all but one specimens were loaded to a stress just below their failure strength specimen initiated from defects within the thick outer Al,O and then unloaded. The material on the tensile surface was then layers. Fractography of the specimens that did not fail at the indent removed to a depth of -50 um from the original surface, and the revealed that the indenter cracks had only partially propagated specimen was repolished and observed under an optical micro ope(Model Eclipse ME6O0, Nikon, Japan). Fracture surfaces through their bounding compressive layers before the catastrophic also detailed the path of bifurcating cracks when observed using thick outer layers scanning electron microscopy(Model 6300, JEOL USA, Inc. Peabody, MA) As can be seen in Fig. 2. the experimental data closely followed those predicted by Eq (3)for the laminates in which the magnitude of residual compression was low(0. 10 and 0.25 volume fraction mullite). In addition, the fracture surfaces of these laminates were I. Results observed to be relatively flat, indicating that the crack propagated (1) Effect of Magnitude of Residual Compression straight across the compressive layer, as predicted by the model e Two different laminate architectures, one composed of 200 um Conversely, Fig. 2 also reflects the inability of the model to sile layers and 25 um compressive layers(hereafter designated accurately describe threshold strength when the level of residual as 200/25), and the other composed of 550 um tensile layers and compression was large(. 40, 0.55, and 0.70 volume fraction produced for this study. It was hoped that the use of this dual than that predicted by Eq(3), the crack stepped from one layer to architecture strategy would allow probing of the critical thickness another. which, as detailed below, was indicative of crack bifur condition for one or more of the residual stress states chosen, i.e. cation. In the laminates that displayed a steplike fracture surface, for a given compressive layer composition, bifurcation would the magnitude of the deviation of measured threshold strengths occur in the thicker compressive layers of the 550/55 laminate, but from those predicted by Eq (3)increased with increased residual not in the thinner 200/25 one compression within the compressive layers The threshold strengths measured for the 550/55 and 200/25 s are reported in Fig. 2 and Table Il, along with the hs predicted by Eq.(3), assuming a value of K = 2.7 2 for the mullite/AL, O, materials. Figure 2 also reports (2) Effect of Compressive Layer Thicknesses the strengths the monolithic specimens, with and The effect of compressive layer thickness, I,, on threshold indenter cracks. Table Il reports the values of residual compression strength was investigated by fabricating compressive layers with thicknesses ranging from -20 to -70 um for two different sets of laminate architectures, where tensile layer thickness was fixed at Volume Fraction Mullite in Compressive Layer of compressive layers formed of 0. 25 volume fraction mullite balance Al,O,) and the other composed of compressive layers indented Monolith Strength formed of 0. 40 volume fraction mullite(balance Al, O,),were chosen in the hope that they would illustrate the critical residual k Bifurcation compression dependence of bifurcation for any and/or all the given compressive layer thicknesses. The chosen laminate architectures also ensured that the residual compression within the compressive 200 um Al O,/ 25 am xx v% Mullite layers of laminates of the same compressive layer composition varied by no more than 10% from one another Table Ill and Fig. 3 report the threshold strength for these 55乒xX minates, along with the strengths estimated by the application of Monolith Strength, 2a.-350 um Eq (3). The strengths of the indented monoliths are also reported in Fig. 3 for comparison. Five specimens are tested for all data points in Fig 3, and the standard deviation of each point is =%. Figure 3 shows. once again, that the model accurately describes Estimated Residual Compression, o(MPa) the behavior of the laminates only when either the level of residual compression was low (all 0.25 volume fraction laminates)or Fig.2. Plot of measured threshold strength versus magnitude of residual compressive layer thickness was small (0.40 volume fraction enote results for 550/55 um xx volume fraction mullite and 200/25 um xx fracture surfaces of the laminates that fell within predictions were volume fraction mullite specimens, respectively. (-)indicates theory (E flat, whereas those that deviated from the predictions were compression(---)indicates strength of monolithie specimens of tensile stepped. Also, in the laminates that displayed this stepping, the (3)) predictions based on laminate architecture and magnitude of residu. er col at are either unindented or indented with 5 kg Vickers magnitude of the deviation of the measured and predicted indent, Standard deviation for all data points, except 220/250.70 volume threshold strengths increased with increased compressive layer raction point, is <5%
May 2002 Factors Affecting Threshold Strength in Laminar Ceramics Containing Thin Compressive Layers Table IL. Estimated and Measured Values of Residual Compression and Threshold Strength for Laminates Used for Residual Compression Effect Study 20X)25 laminate 550/55 laminate Compressive layer Residual compression, o Threshold strength, u,he Residual compression. U. Threshold strength, a.he ( volume fraction Eq.(3 Measured mullite (MPa (MPa) 0 202±3191±3 94±0 151 256±5 352±2363±2 44±1 210±4 491+2 378±10 646±5 349±5 531±11 657±2 736±4 283±2 617 799±1 859±1 334±2 535±20 Table Ill. Estimated and Measured Values of Threshold Strength and Estimated Values of Residual Compression for s Used in Compressive Layer Thickness Effect Study 500/xx Hm 0.25 Volume fraction mullite 500xx im 0.40 Volume fraction mullite Threshold strength. (h Compress Threshold strength, o Measured 19±1 171±2 165±1 23±1 527±1 2l1±1 35±0 359±0 516± 294±13 54±4 352±2 191±2 210±4 54±1 237± 378±10 74±1 338±0 204±1 234+6 + 488±2 257±2 421±9 FUnindented Monolith Strength =62921I8MPa 500 um in two different sets of laminate architectures with a impressive layer thickness fixed at 25 um. Table IV and Fig. 4 report these measurements along with the estimates of residual k Bifurcation stress and threshold strength determined by application of Eqs. (2) 350 two different indentation loads(2 and 5 kg) were presented in Fig xx gm 40v% Mullite 4 for comparison. Two different indenter loads were required in this part of the study to ensure that the precrack was large enough to cause cracking to initiate at a stress below the threshold strength. xx um 25 v%b Mullite but not so large that it affected the residual stress distribution Monolith Strength, Za.-350 within the compressive layers. Five specimens were tested for all data points in Fig. 4. and the standard deviation of each point was Figure 4 shows, as did Figs. 2 and 3 earlier, that the predicted 60 e Layer Thickness, t, (am) 0.25 volume fraction mullite laminates. However, the agreement was not as good for the 0. 40 volume fraction laminates. Fracture Fig. 3. Plot of thickness. Square and circular symbols denote results for 500/xx um 0. 25 whereas those of the 0. 40 volume fraction laminates exhibited specimens, respectively.() indicates theory(Eq (3) predictions based compressive layer (s20 um lateral deflection not related to are indented with 5 kg Vickers indent Standard deviation for all data points (4) Observations of Crack Paths in Bifurcating Laminates As reported elsewhere, crack replication experiments for lami- (3) Effect of Tensile Layer Thicknesses nates where the compressive stress and thickness of the compres sive layer were small showed that the crack extended straight The effect of tensile layer thickness, I2, on threshold strength across the compressive layer. Concurrent K determinations for was investigated by varying tensile layer thickness from -200 to these specimens showed that Eq (I)was in good agreement with Table IV. Estimated and Measured Values of Threshold Strength and Estimated Values of Residual Compression for Laminates used in Tensile Laver Thickness Effect Study xxx/25 Hm 0.25 Volume fraction mullite xxx/25 um 0.40 Volume fraction mullite Tensile Threshold strength, w e Threshold strength, ,nt Eq1(3) 210±0 344±2 248± 09±2 90±11 222 266±5 511±1 324±10 362±1 202±1 213±2 361±2 520±2 239±2 296±6 502±4 369±1 171±2 165±1 508±4 527±1 211±2 237±7
1226 Journal of the American Ceramic Sociery-Rao and Lange Vol. 85. No. 5 Other bifurcation leg Unindented Monolith Strength 629 118 MPa 400 25 um 40 v% Mullite 25 um 25 vS Mullite eolith Strength, 2aoc-350 Km 150250350450 Tensile Layer Thickness, t, (am) 4. Plot of measured threshold strength versus tensile layer thickness. Fig. 6 electron micrograph of fracture surface indicates theory (Eq (3) predictions based on laminate architecture and of one of raction mullite specimens in region near magnitude of residual compression. (--- indicates strength of monolithic rea on left of picture) showing transition between cracking observed on tensile surface(see Fig. 5) and bifurcation that occurred within bulk, beneath penetration depth of edge crack (see Fig 7) experimental results. In the current study, specimens that exhibited greater than the depth of the edge crack, Fig. 6 shows that the crack Tm山 produced flat tracture surace O Eq, propagated across the comp画可 that cracks that enter the compressive layer do so by bifurcation, a Specimens that exhibited crack bifurcation also contained second method for observing the crack path, which requires edge crack that ran along the center of the compressive layer. shown in Fig. 5. As detailed elsewhere, these edge cracks were polishing. best details the bifurcation phenomena. Figure 7 clearly aused by tensile stresses that arose at and close to the surface shows that the crack bifurcates as it enters the compressive layer they were only produced when the combination of the compressive artifact, because it only propagates deeper into the compressive he thickness of the compressive layer. As shown in Fig. 5. the the observation of fracture surfaces and by the observation shown crack that was observed by replication on the free surface( tensile in Fig. 7 itself. The edge crack does not exist between the two layer until it stopped at the edge crack. Catastror branches of the bifurcated crack, confirming that the bifurcated ic failure did not crack exists before the edge crack propagates deeper into the occur when the crack stopped at the edge crack, but rather at a compressive layer during material removal higher stress, without any apparent further extension of the crack on the free surface. As shown in Fig. 6. ol bservations of the fracture the bisector (from Fig. 7)are 57.5, 61.0, and 67.5 for the 0.40 surface showed that the straight extension of the crack onl occurred near the free surface(within -30 um for the architecture 0.55, and 0.70 volume fraction mullite specimens, respectively Therefore, given the otherwise similar architectures of these three shown in Fig. 6). For distances from the free surface that were specimens, the observations indicate that the bifurcation deflection angle increases with residual compression within the compressive IV. Discussion It is immediately apparent from Figs. 2-4 that the experimental data for laminates with thin compressive layers and/or low level of residual compression agreed well with those predicted by Eq (c) (3). For laminates where agreement was good, crack extension -10 um occurred straight across the compressive layer, which was the crack path used to develop Eq. (3). In addition, previous stress Fig. 5. Optical micrographs, taken using intensity factor determinations showed excellent agreement for of 550/550.55 volume fraction mullite specimens taken during loading at inability of Eq. (3) to describe threshold strength when the applied stresses of a) 100, b) 151, c) 201, d)251, and e)301 MPa. compressive layer thickness and/or level of residual compression Specimen withstood further loading to 389 MPa without any further is large; viz., threshold strength is larger than that predicted. In opagation of crack observed, after which catastropl each of these cases, the crack bifurcated as it propagated through Note: Cracking observed along midplane of aused by applied loading. This cracking was the compressive layer. of specimen revealed by grinding and polishing during preparation of i While quantitative explanation of the cause of bifurcation and any loading. It was merely an edge crack th ied on the free surface contribution to threshold strength are beyond the scope of the current work, a plot of residual compression versus compressive into compressive layer to depth roughly equal to that of compressive layer layer thickness for the laminates in the current study, reported in thickness Fig. 8, yields a qualitative description of the conditions observed
May 2002 Factors Affecting Threshold Strength in Laminar Ceramics Containing Thin Compressive Layers The critical thickness necessary for bifurcation appears to follow a relationship similar to the one developed for edge cracking. 2 GE 0.34(1-v2) (7) where Ge, E. and v are the critical strain energy release rate. Youngs modulus, and Poisson's ratio of the compressive layer material, respectively: o the magnitude of residual compression within the compressive layer; and 0.34 a dimensionless parameter Agreement is further improved when the dimensionless param- eter is reduced from 0.34 to 0. 17. The physical significance of this factor-of-two reduction is not fully understood, but most likely lies in the differences in the crack geometries of the two systems While a link between edge cracking and bifurcation has been established elsewhere. further studies of the bifurcation phenom na are expected to produce greater understanding It is interesting to note that while bifurcation is clearly evident in the laminates with thick compressive layers and/ large levels of residual compression, this bifurcation does ne share the same characteristic "mountainlike fracture surface 、、 ies, the bifurcated crack was observed to propagate down to and (c) then along the midplane of the compressive layer. However, as can be seen in Fig. 7, this type of behavior was not seen in the current study. This discrepancy was likely due to the differ- Fig. 7. Optical micrographs of bifurcation of crack beneath tensile ences in loading configuration used for each study. Despite the surfaces of 550/55 laminates with compressive layer compositions of a) fact that four-point flexure was used in each of these studies, in 0. 40. b)0.55, and c)0.70 volume fraction mullite. Angles each branch of previous studies, the loading axis was normal to the laminar bifurcated crack make with their bisector measured from micrographs are 7.5, 61.0, and 67.5.. Note: Observed edge crack is artifact that refor plane, while in the current study, it was parallel. The stress on new free surface exposed by grinding, as evidenced by its absence gradient developed within specimens tested with the between branches of bifurcated crack where tensile surface stresses are axis normal to the laminar plane could provide the driving force relieved. Although micrographs above seem to imply that bifurcated crack for the propagation of cracking along the laminar plane. No propagates along midplane. this is an artifact as well. As can be seen on such driving force exists when the loading axis is parallel to the laminar plane, perhaps explaining why the crack does not trajectory through compressive layers until it reaches next tensile layer proceed parallel to the tensile axis 80 V. Conclusions The previously reported model describing threshold strengths Edge Cracking Bifurcation in laminar composites is valid only when the crack propagates straight through the compressive layer, as assumed by the model. This occurs only when the compressive stress and/or 50 thickness of the compressive layer is small. At larger compres sive stresses and/or compressive layer thicknesses, the crack bifurcates as it propagates through the compressive layer and produces a threshold strength much larger than predicted by the 20 E 10 No Edge Cracking nor Bifurcatio Acknowledgments 0 I00 1200 The authors thank Vladimir Tolpygo for his assistance in making the piezospec. Magnitude of Residual Compression, o(MPa) troscopic measurements used to verify the calculated value of residual stress within Fig layer thickness versus magnitude of estimated residual compression, indicating conditions observed for bifurcation in References current study, Closed symbols represent specimens in which neither edge M. P Rao, A. J. Sanchez- Herencia. G. E, Beltz, R. M. McMeeking, and F. F. racking nor bifurcation is observed, while open symbols represen specimens in which both edge cracking and bifurcation are observed. Lange. "Laminar Ceramics That Exhibit a Threshold Strength. "Science (WashingtoN, (---) indicates predicted critical layer thickness for edge cracking for DC).286,102-105199) C. Hillman, Z. Suo, and F, F. Lange. ""Cracking of Laminates Subjected to Biaxial values of dimensionless parameters of a)0.34 and b)0. 17. Note: Furthest ensile Stresses. "J. Am. Ceram. Soc., 79 (81 2127-33(1996) Te most datum point to right represents data from similar Al,O,/mulli Alumina and Alumina/ Zirconia laminates tested in Ref. I. Standard deviation for all data points is <5%. Multilayer Composites by Slip Casting, "J. Am. Cerain. Soc., 72[8] 1511-13(1989) V. Sergo, x. Wang. D, R. Clarke, and P. F. Becher, "Residual Stresses Alumina/Cerit-Stabilized Zirconia Composites. "J. Ant, Ceram, Soc.. 78[8]2213-14 K. Ravichandran."Elastic Properties of Two Phase Composites, J, Amm. Ceram for bifurcation, As can be seen only occurs when the Soc. 77 15) 1178-84(1994) hickness of the compressive lay magnitude of residual mal-Expansion Stresses in Reinforced Plastics, "/, Res, Bur. pression Is ases, edge cracks are Q Ma and D R. Clarke, "Piezospectroscopic Determination of Residual Stresses observed on the surfaces of the compressive layers before testing in Polycrystalline Alumina. "J, Am. Ceram. Soc., 77[21 298-302(1994)
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