such as a crack bridging or transformation toughening tionally gradient ceramics for engineering application can be more effective at preventing small cracks from EMPA was funded in this project by BBw, the Swiss growing unstably Federal office for Education and Science. under con- tract number 99.0785 7. Conclusions References The apparent fracture toughness as a function of the crack length parameter a= Y(a)a"has been calculated [U Chan M.Ann Rev Mater Sci 1997:27:249 for the Si3 N4/Si3N4-30 wt% TiN laminates with residual [2 Clegg WJ, Kendall K, Alford NMcN, Button TW, Birchall JD. compressive or tensile stresses in the top layers. The Nature I'990:347:455 toughness increases in the layers with a compressive stress 3] Lakshminarayanan R, Shetty DK, Cutler RA. J Am Ceram Soc as the crack length increases, and it decreases in the layers (4) Lugovy M, Orlovskaya N, slyunyayev with a tensile stress as the crack continues to grow The Sanchez-Herencia AJ. Comp Sci Techi experimentally measured Kapp values for the laminates [5] Marshall DB, Ratto JJ, La F.J Am Ceram Soc show an excellent fit with the calculated values it was 1991;74(12):2979 found that a threshold stress exists for cracks of a certain [6 Finot M, Suresh S, Giannakopoulos AE. Proc Int Symp Struct length. Stable crack growth occurs for the majority of Func Grad Mater 1995: 3: 223. [7 Yoo J, Cho K, Bae ws, Cima M, Suresh S. J Am Ceram Soc cracks with a threshold stress as indicated by the Kapp-a 9881(1)21 graph. The cracks with a small length will propagate [8]Thompson SC, Pandit A, Padture NP, Suresh S. J Am Ceram Soc unstably because the applied stress intensity factor is al- 200285(8):2059 ways higher than a fracture resistance of the laminate 9 Lugovy M, Orlovskaya N, Berroth K, Kuebler J. Comp Sci stress is small enough. the situation can occur where no stable crack growth exists (10 Blattner AJ, Lakshminarayanan R, Shetty DK. Eng Fract Mech for cracks with tips located within the first compressive [Il]Evans AG. J Am Ceram Soc 1990: 73(2): 187 layer. Therefore, it is important to introduce high resid DJ. J Am Ceram Soc ual compressive stresses that will provide a steep slope of 2001;84(8):1827 the apparent fracture toughness curve to include cracks 13 Moon RJ, Hoffman M, Hilden J, Bowman K, Trumble K, Roedel J J Am Ceram Soc 2002: 85(6: 1505. Obtaining a high residual compressive stress in the first [15] Kuebler J. Ceram Eng Sci Proc 1997: 18: 155-62 layer is an effective way of providing high toughness at [16] Kuebler J ASTM STP 1409,J.A Salem. In: Jenkins MG, Quinn small crack lengths, thereby ensuring the improved flaw tolerance and surface damage resistance 0-8031-2880-0:2002.p.93. [18 Lugovy M, Slyunyayev V, Subbotin V, Orlovskaya N, Gogotsi G. Acknowledgement [19 Rawley JE. Int J Fract 1976: 12: 475 [0 Sajgalik P, Lences Z, Dusza J. Factors influencing the residual The work was supported by the European Co tresses in layered silicon nitride based composites. In: Engineer ing Ceramics96: Higher reliability through processing, NATO on. It is a part of the Project 1CA2-CT-2000-10020 ASI series. 3. High Technology, vol. 25. Dordrecht: Kluwer Copernicus-2"Silicon nitride based laminar and func- Academic Publishers: 1997. p 301such as a crack bridging or transformation toughening can be more effective at preventing small cracks from growing unstably. 7. Conclusions The apparent fracture toughness as a function of the crack length parameter a˜ = Y(a)a1/2 has been calculated for the Si3N4/Si3N4–30 wt% TiN laminates with residual compressive or tensile stresses in the top layers. The toughness increases in the layers with a compressive stress as the crack length increases, and it decreases in the layers with a tensile stress as the crack continues to grow. The experimentally measured Kapp values for the laminates show an excellent fit with the calculated values. It was found that a threshold stress exists for cracks of a certain length. Stable crack growth occurs for the majority of cracks with a threshold stress as indicated by the Kapp–a˜ graph. The cracks with a small length will propagate unstably because the applied stress intensity factor is al￾ways higher than a fracture resistance of the laminate. If the residual compressive stress is small enough, the situation can occur where no stable crack growth exists for cracks with tips located within the first compressive layer. Therefore, it is important to introduce high resid￾ual compressive stresses that will provide a steep slope of the apparent fracture toughness curve to include cracks of a short length in the region of stable crack growth. Obtaining a high residual compressive stress in the first layer is an effective way of providing high toughness at small crack lengths, thereby ensuring the improved flaw tolerance and surface damage resistance. Acknowledgement The work was supported by the European Commis￾sion. It is a part of the Project 1CA2-CT-2000-10020 Copernicus-2 ‘‘Silicon nitride based laminar and func￾tionally gradient ceramics for engineering application’’. EMPA was funded in this project by BBW, the Swiss Federal Office for Education and Science, under con￾tract number 99.0785. References [1] Chan M. Ann Rev Mater Sci 1997;27:249. [2] Clegg WJ, Kendall K, Alford NMcN, Button TW, Birchall JD. Nature 1990;347:455. [3] Lakshminarayanan R, Shetty DK, Cutler RA. J Am Ceram Soc 1996;79(1):79. [4] Lugovy M, Orlovskaya N, Slyunyayev V, Gogotsi G, Kuebler J, Sanchez-Herencia AJ. Comp Sci Technol 2002;62:819. [5] Marshall DB, Ratto JJ, Lange FF. J Am Ceram Soc 1991;74(12):2979. [6] Finot M, Suresh S, Giannakopoulos AE. Proc Int Symp Struct Func Grad Mater 1995;3:223. [7] Yoo J, Cho K, Bae WS, Cima M, Suresh S. J Am Ceram Soc 1998;81(1):21. [8] Thompson SC, Pandit A, Padture NP, Suresh S. J Am Ceram Soc 2002;85(8):2059. [9] Lugovy M, Orlovskaya N, Berroth K, Kuebler J. Comp Sci Technol 1999;59:1429. [10] Blattner AJ, Lakshminarayanan R, Shetty DK. Eng Fract Mech 2001;68:1. [11] Evans AG. J Am Ceram Soc 1990;73(2):187. [12] Sglavo VM, Larentis L, Green DJ. J Am Ceram Soc 2001;84(8):1827. [13] Moon RJ, Hoffman M, Hilden J, Bowman K, Trumble K, Roedel J. J Am Ceram Soc 2002;85(6):1505. [14] Hbaieb K, McMeeking RM. Mech Mater 2002;34:755. [15] Kuebler J. Ceram Eng Sci Proc 1997;18:155–62. [16] Kuebler J. ASTM STP 1409, J.A. Salem. In: Jenkins MG, Quinn GD, editors. ASTM, West Conshohocken, PA, USA, ISBN 0-8031-2880-0; 2002. p. 93. [17] Fett T, Munz D. J Mater Sci Lett 1990;9:1403. [18] Lugovy M, Slyunyayev V, Subbotin V, Orlovskaya N, Gogotsi G. Comp Sci Technol 2004;64:1947. [19] Srawley JE. Int J Fract 1976;12:475. [20] Sajgalik P, Lences Z, Dusza J. Factors influencing the residual stresses in layered silicon nitride based composites. In: Engineer￾ing Ceramics
96: Higher reliability through processing, NATO ASI series. 3. High Technology, vol. 25. Dordrecht: Kluwer Academic Publishers; 1997. p. 301. 296 M. Lugovy et al. / Acta Materialia 53 (2005) 289–296