April 2008 Nondestructive Measurement of the Residual Stress Profile the fine details concerning its repartition between the constituent phases. More variables need to be taken into account in the M. Lewis, "Apparent Fracture Toughness of Si3N4-Based Laminates with Resid micromechanical models describing the stress in a composite al Compressive or Tensile Stresses in Surface Layers, Acta Mater. 53. 289-96 created in nonequilibrium conditions. This further confirms the importance of a direct, experimental measurement of the High Reliability Alumina-Mullite Ceramic Laminates, "J. Am. Ceram Soc. 88 through-the-thickness stresses, which can be properly obtained by synchrotron radiation X-ray diffraction WHy. t Mavo and M. Bertoldi. "Design and Production of Ceramic Laminates with High Mechanical Resistance and Reliability. Acta Mater, 54. 4929-37 16A. Costabile and V. M. Sglavo, "Influence of the Architecture on the Me- The residual stress in a set of millimeter-thick symmetric ceramic chanical performances of Alumina-Zirconit-Mu aminates made of a blend of alumina zirconia and mullite was ci. Technol,45.,11038(2006. analyzed by using synchrotron radiation white-beam diffrac- Bertoldi, "High Reliability Ceramic Laminates by Design, Ph D. Thesis, tion. Using a narrow beam and energy-dispersive mode allowed University of Trento. 2004. Q. Ma and D. R. Clarke, ""Stress Measurement in Single Crystal and Poly a true through-thickness scanning of the specimen with gauge ystalline Ceramics Using Their Optical Fluorescence, J. Am. Ceram Soc. 76[6] plume and shape kept constant from point to point. Average stress results are in good agreement with the design Sergo, D. M. Lipkin, G. de Portu, and David R. Clarke, "Edge Stresses in data. Traditional models for the description of composites are not able to fully describe the partitioning of stresses over the various p V. Hauk. Structural and Residual Stress Analysis by Non-Destructive Methods the percolation limit for zirconia in alumina is overcome The approach proposed here can be used to validate theoret 503 in Diffraction Analysis of the ical residual stress profiles in more general multilayer systems. 38 Microstructure of Materials, Edited by E.J. Mittemeier and P Scardi. Springer 2U. Welzel, P. Lamparter, M. Leoni, and E. J. Mittemeijer, "The Determina ses in Thin Films: Modelling Elastic Grain Interaction philos. 3[36]4045-5702003) The au is, U.K(CCLRC) and the EU ens: On the Concepts of Diffraction Elastic rovision of beamtime at the Daresbury Laboratory SRs. Dr. M. Golsha R. V Martins, and A. Kvick, "A High Energy support. The assoc ope for Local Strain Measurements within Bulk Materials, Mater. Sci. knowledged for the thorough check of the manuscript and the useful discussions M. Turski, P J. Withers and T. Buslap "High- amples Using Full-Profile Analysis of Ener -Dispersive Synchrotron Diffraction Data, "J. Appl. Cryst, 37, 883-9 R Lawn, Fracture of Brittle Solids, 2nd edition, Cambridge University Press, stress and Microstress Using X-Rays, Synchrotron and Neutrons, "JpN. Soc. 四g.Mn.J.A,473252-63(20 UK.1993 nsistent Estimates for Elastic constants vis, A. Kristoffersson. E Carlstrom, and w.J. Clegg, "Fabrication and of Random Polycrystals with Hexagonal, Trigonal, and Tetragonal Symmetries. tion in Ceramic Laminates with Porous Interlayers, " J. An. Ceram. 2369-74(2000) d. Macc. PTho, molson, T. atwood.E.M. Gullikson. M. R Howells. B Bw. J. Clegg. K Kendall, and MeN. Alford, " A Simple Way to Make Tough Ceramics, "Nature(London ), 347, 455-57(1990). W. M. Kriven and D.-H. Kuo. High-Strength Flaw- Tolerant Oxide Ceramic Oxide Ceramic J.H. Scofield A, L. Robinson and). H. Underwood :x-Ray mission Energies Composite U.S. Pat. No lughan. Lawrence Berkeley National Laboratory, Berkeley, CA, 2001 sow Kreher and W Pompe, Internal Stresses in Heterogeneous Solids.Akademie- Growth Inhibitor in Surface and Promoter in Interior U.S. Pat. No. 3. 652.378 ch28,1972. erlag, Berlin, Germany, 1989 G Q. Ma, w Pompe, J. D. French, and D. R. Clarke, "Residual Stresses in Microstructural Engineering with Duplex and Laminar Ceramic Composites, Mater, 42[45] 1673-81( 1994). L M. Chan and G. A. Miller, Design of Lam- 3Z. Hashin and S. Shtrikman, "A Variational Approach to Theory of the Elastic Behavior of Multifaced Materials. " J. Mech. Solids, 11. 127-35 inated Ceramic Composite for Improved Strength and Toughness, "J. Am. Ceram 3H. Toraya, "Effect of YO,s Dopant on Unit Cell Parameters of ZrO, at Low BR. Latkshminarayanan, D K. Shetty, and R.A. Cutler, "Toughening of Lay- Ceram. Soc., 72 [4]662-4 M.P. Rao. A.J. Sanchez-Herencia G.E. Beltz R. M. McMeeking, andF.F and R. Torrecillas, "Percolative M, ec, Moya, S. Deville, J. Chevalier, G. Fantoz Lange, "" Laminar Ceramics That Exhibit a Threshold strengt 3H. Ledbetter, S. Kim, and D. Balzar, "Elastic Properties of Mullite, "J.Am. amn.So,8I10258(199 Orlovskaya, M. Lugovy, V o.J. Adams M. Chheda. J. Shih. J. San nd S. Yarmolenko, ""Robust Design and Man- H. Schneider. K. Okada. and J. A. Pask, Mullite and Mullite Ceramics. ufacturing of Ceramic Laminates with Controlled Thermal Residual Stresses for D J. Green, An Introduction to the Mechanical Properties of Ceramics. Cam IN. Orlovskaya, J Kuebler, V. Subbotin, and M. Lugovy, "Design of Si,Ne- e比比 C de Jonghe and C.S. Lee, "Modeling of Thermal Stresses Based Ceramic Laminates by the Residual Stresses. "J.Mater. Sci- 40, 5443-50the fine details concerning its repartition between the constituent phases. More variables need to be taken into account in the micromechanical models describing the stress in a composite created in nonequilibrium conditions. This further confirms the importance of a direct, experimental measurement of the through-the-thickness stresses, which can be properly obtained by synchrotron radiation X-ray diffraction. IV. Conclusions The residual stress in a set of millimeter-thick symmetric ceramic laminates made of a blend of alumina, zirconia, and mullite was analyzed by using synchrotron radiation white-beam diffrac￾tion. Using a narrow beam and energy-dispersive mode allowed a true through-thickness scanning of the specimen with gauge volume and shape kept constant from point to point. Average stress results are in good agreement with the design data. Traditional models for the description of composites are not able to fully describe the partitioning of stresses over the various phases in each lamina. Large deviations appear when the percolation limit for zirconia in alumina is overcome. The approach proposed here can be used to validate theoret￾ical residual stress profiles in more general multilayer systems.38 Acknowledgments The authors wish to acknowledge the Council for the Central Laboratory of the Research Councils, U.K. (CCLRC) and the EU under the TMS project for provision of beamtime at the Daresbury Laboratory SRS. Dr. M. Golshan (CCLRC Daresbury Laboratory) is also acknowledged for useful discussion and experimental support. The associate editor and unknown referees are also ac￾knowledged for the thorough check of the manuscript and the useful discussions that followed. References 1 B. R. Lawn, Fracture of Brittle Solids, 2nd edition, Cambridge University Press, Cambridge, U.K., 1993. 2 J. B. Davis, A. Kristoffersson, E. Carlstrom, and W. J. Clegg, ‘‘Fabrication and Crack Deflection in Ceramic Laminates with Porous Interlayers,’’ J. Am. Ceram. Soc., 83 [10] 2369–74 (2000). 3 W. J. Clegg, K. Kendall, and McN. 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