3558 Journal of the American Ceramic Society--Kaur et al VoL 90. No lI VI. Conclusions D. B. Marshall and M. V Swain, Crack Resistance Curves in Magnesia- Partially-Stabilized Zirconia, J. Am. Ceram. Soc. 71. 399-404(1988). 1. The interaction between crack-driving force and crack ce Curves of surface growth resistance can be depicted on a crack-stability map that plots normalized transition crack lengths for stable and unstable CR田 handran.ly chao anddk s8C or and flaw crack growths for a toughened ceramic as a function of the ratio (1993) ensitivity of Ce-TZP/Al O3 Composite, J. Am. Ceran. Soc., 76. 961-9 of the crack-initiation toughness and the plateau tough eR M. MeMeeking and A. G. Evans, "Mechanisms of Transformation Tough- 2. For the R curve described by the empirical exponential ening in Brittle Materials. " J. Am. Ceran. Soc., 65, 242-6(1982) function, stable crack growth is encountered when Ko/ko< 0.197 R-Curve) Behavior of Toughened Alumina and Silicon Nitride, " J. Am. Ceram. of crack lengths for toughened ceramics that satisfy the condi tion Ko/K <0. 197 when they exhibit the exponential R-curve 41 Small Elliptical Surface Cracks in Finite-Thickness Plates, Eng. Fract. Mech., 11, behavior 4. All ceramics with an R-curve behavior exhibit an in- IL. S. Raju and J. C. Newman Jr,"An Empirical Stress-Intensity Factor creased Weibull modulus as compared with ceramics with flat qmi K aw thar S and M. Kur an. "Fatigue crack rowth (ri a surface A truly flaw-insensitive strength can be expected only for (1978) Flaw, " Adv. Res. Strength Fract. Mater, Int. Conf. Fract, 4th, 1977. 2. 1361-72 those ceramics that exhibit stable crack growth due to rising J. Alcala and M. Anglada, "Indentation Precracking of Y-TZP: Implications ack-growth resistance to r-Curves and su Mat.Sc.Eg,A245,267-76 Kendall, N. MeN. Alford. S. R. Tan, and J D Toughness on Weibull Modulus of Ceramic Bend Stren 中 R. F. Cook and D. R. Clarke. "Fracture Stability. R-Curves and Strength D. Munz. "What Can We Learn from R-Curve Measurements. J. Am. Ceram. Variability. "Acta Metall. 36, 555-62(1988). ID. K Shetty and J S. Wang,""Crack Stability and Strength Distribution of -D. B. Marshall. ""Strength Characteristics of Transformation-Toughened Ceramics That Exhibit Rising Crack-Growth-Resistance (R-Curve) Behavior Zirconia, J. Am. Ceran. Soc., 69, 173-80(1986 J.Am.Cera.Soc,72.11s862(1989)VI. Conclusions 1. The interaction between crack-driving force and crack￾growth resistance can be depicted on a crack-stability map that plots normalized transition crack lengths for stable and unstable crack growths for a toughened ceramic as a function of the ratio of the crack-initiation toughness and the plateau toughness. 2. For the R curve described by the empirical exponential function, stable crack growth is encountered when K0/KNo 0.197. 3. A flaw-insensitive fracture stress is expected over a range of crack lengths for toughened ceramics that satisfy the condi￾tion K0/KNo0.197 when they exhibit the exponential R-curve behavior. 4. All ceramics with an R-curve behavior exhibit an in￾creased Weibull modulus as compared with ceramics with flat crack-growth resistance. 5. A truly flaw-insensitive strength can be expected only for those ceramics that exhibit stable crack growth due to rising crack-growth resistance. References 1 D. Munz, ‘‘What Can We Learn from R-Curve Measurements,’’ J. Am. Ceram. Soc., 90, 1–15 (2007). 2 D. B. Marshall, ‘‘Strength Characteristics of Transformation-Toughened Zirconia,’’ J. Am. Ceram. Soc., 69, 173–80 (1986). 3 D. B. Marshall and M. V. Swain, ‘‘Crack Resistance Curves in Magnesia– Partially-Stabilized Zirconia,’’ J. Am. Ceram. Soc., 71, 399–404 (1988). 4 R. W. Steinbrech and O. Schmenkel, ‘‘Crack-Resistance Curves of Surface Cracks in Alumina,’’ J. Am. Ceram. Soc., 71, C-271–3 (1988). 5 N. Ramachandran, L. Y. Chao, and D. K. Shetty, ‘‘R-Curve Behavior and Flaw Insensitivity of Ce-TZP/Al2O3 Composite,’’ J. Am. Ceram. Soc., 76, 961–9 (1993). 6 R. M. McMeeking and A. G. Evans, ‘‘Mechanisms of Transformation Tough￾ening in Brittle Materials,’’ J. Am. Ceram. Soc., 65, 242–6 (1982). 7 A. G. Evans and R. M. McMeeking, ‘‘On the Toughening of Ceramics by Strong Reinforcements,’’ Acta Metall., 34, 2435–41 (1986). 8 N. Ramachandran and D. K. Shetty, ‘‘Rising Crack-Growth-Resistance (R-Curve) Behavior of Toughened Alumina and Silicon Nitride,’’ J. Am. Ceram. Soc., 74, 2634–41 (1991). 9 I. S. Raju and J. C. Newman Jr., ‘‘Stress-Intensity Factors for a Wide Range of Small Elliptical Surface Cracks in Finite-Thickness Plates,’’ Eng. Fract. Mech., 11, 817–29 (1979). 10I. S. Raju and J. C. Newman Jr., ‘‘An Empirical Stress-Intensity Factor Equation for the Surface Crack,’’ Eng. Fract. Mech., 15, 185–92 (1981). 11M. Kawahara and M. Kurihara, ‘‘Fatigue Crack Growth from a Surface Flaw,’’ Adv. Res. Strength Fract. Mater., Int. Conf. Fract., 4th, 1977, 2, 1361–72 (1978). 12J. Alcala and M. Anglada, ‘‘Indentation Precracking of Y-TZP: Implications to R-Curves and Strength,’’ Mat. Sci. Eng., A245, 267–76 (1998). 13K. Kendall, N. McN. Alford, S. R. Tan, and J. D. Birchall, ‘‘Influence of Toughness on Weibull Modulus of Ceramic Bend Strength,’’ J. Mater. Res., 1, 120–3 (1986). 14R. F. Cook and D. R. Clarke, ‘‘Fracture Stability, R-Curves and Strength Variability,’’ Acta. Metall., 36, 555–62 (1988). 15D. K. Shetty and J. S. Wang, ‘‘Crack Stability and Strength Distribution of Ceramics That Exhibit Rising Crack-Growth-Resistance (R-Curve) Behavior,’’ J. Am. Ceram. Soc., 72, 1158–62 (1989). & 3558 Journal of the American Ceramic Society—Kaur et al. Vol. 90, No. 11