J. L Jones et al. I Acta Materialia 55(2007)5538-5548 5. Conclusions 6 Lupascu DC, Santos e Lucato SL, Rodel J, Kreuzer M, Lynch CS. Appl Phys Lett 2001: 78: 2554. For a soft tetragonal PZT ceramic, in-plane ferroelastic o) Hackemann S, Pfeifer w I Eur ceram Soc 200323: 41 domain orientations and lattice strains near a crack tip are measured in situ using high-energy synchrotron X-rays in [9] Meschke F, Raddatz O, Kolleck A, Schneider GA. J Am Ceram Soc transmission geometry with a two-dimensional detector. 2000:83:353 Preferred domain orientations are spatially asymmetri [0 Yang w, Zhu T J Mech Phys Solids 1998: 46: 291 about the crack tip for a single angle, n, from the crack face I]Bowman KJ. Mechanical Behavior of Materials. New York: John and correlate with the spatial distribution of projected [12] Behnken H. Some basic relations to the stress analysis using deviatoric stress from a finite element model. The process diffraction methods. In: Hauk V. editor. Structural and Residual zone sizes are comparable to those measured in prior works Stress Analysis by Nondestructive Methods. Amsterdam: Elsevier but are found to be directionally dependent around the Science: 1997. p 39 crack tip. The III lattice strains are also directionally (14) Fett T, Munz D, Thun G ]Am Ceram Soc 2003: 6: 1427 dependent around the crack tip and correlate with the pro- 15]Chen W, Lynch CS. J Eng Mater Technol 2001: 123: 169 jected deviatoric strains in the finite element model. A large [16] Liss K-D. Bartels A, Schreyer A, Clemens H. Textures Microstruct degree of domain switching irreversibility is observed near 2003:35:219 the crack face and reversible domain switching is observed [7] Vullum PE, Mastin J, Wright J, Einarsrud M-A, Holmestad R at larger distances from the crack face Grande T. Acta Mater 2006: 54- 2615. [18] Miller MP, Bernier JV, Park JS, Kazimirov A. Rev Sci Instr 2005;76:13903 Acknowledgement [19] Daniels JD, Jones JL, Finlayson TR. J Phys D: Appl Phys 2006:39:5294 This research was supported by the US National Science [20] Jones JL, Pramanick A, Nino JC, Motahari SM, Ustundag E Daymond MR, et al. Appl Phys Lett 2007: 90: 172909 Foundation,award number OISE-0402066, the University (21 Jones JL, Hoffman M j Am Ceram Soc 2006: 89: 3721 of Florida, and the US Department of Energy via the Ames (22) ASTM standard E 399.90 Annual Book of ASTM Standards. Laboratory. Use of the Advanced Photon Source was sup- [23] ASTM standard E 561-98 Annual Book of ASTM Standards ported by the US Department of Energy, Office of Science, [24] Hammersley AP ESRF Internal Report, ESRF9SHAOIT, FIT2D Office of Basic Energy Sciences, under Contract No. DE v9.129 Reference Manual V3. 1(1998). AC02-06CH11357. The authors also acknowledge the tech- [25] Hammersley AP, Svensson So, Hanfiand M, Fitch AN, Hausermann nical assistance and helpful suggestions of G. Tutuncu 26) Jones JL, Slamovich EB, Bowman KJ. J Appl Phys 2005: 97: 034113 (ISU), S.Y. Lee(ISU), and J. Almer(APS) [27] Kounga-Njiwa AB, Fett T, Lupascu DC, Rodel J. Eng Fract Mech [28] Hall DA, Steuwer A, Cherdhirunkorn B, Mori T, Withers PJ. J Appl References Phys200496:4245 29] Hall DA, Steuwer A, Cherdhirunkorn B, Withers PJ, Mori TJ Mech [] dos Santos e Lucato SL, Lupascu DC, Rodel J J Am Ceram Phys Solids 2005: 53: 249. 2000:83:424 30]SM. Motahari, Study of Constitutive Behavior of Ferroelectrics via [2]Kounga Njiwa AB, Lupascu DC, Rodel J. Acta Mater 2004: 52: 4919. Self-Consistent Modeling and Neutron Diffraction. Ph. D. Thesis [3] Salz CRJ, Hoffman M, Westram I, Rodel J. J Am Ceram Soc California Institute of Technology, 2007, pp. 87-92. 2005:88:1331. 31] Evans AG, Cannon RM. Acta Metall 1986: 34: 761 4 Landis CM. J Mech Phys Solids 2003: 51: 1347. 32] Hannink RH, Kelly PM, Muddle BC. J Am Ceram So [] Glazounov E, Kungl H, Reszat J-T,Hoffmann M, Kolleck A, Schneider GA. et al. J Am Ceram Soc 2001: 84: 2921 33] Bowman K, Chen IW.J Am Ceram Soc 1993: 76: 113.5. Conclusions For a soft tetragonal PZT ceramic, in-plane ferroelastic domain orientations and lattice strains near a crack tip are measured in situ using high-energy synchrotron X-rays in transmission geometry with a two-dimensional detector. Preferred domain orientations are spatially asymmetric about the crack tip for a single angle, g, from the crack face and correlate with the spatial distribution of projected deviatoric stress from a finite element model. The process zone sizes are comparable to those measured in prior works but are found to be directionally dependent around the crack tip. The 1 1 1 lattice strains are also directionally dependent around the crack tip and correlate with the pro￾jected deviatoric strains in the finite element model. A large degree of domain switching irreversibility is observed near the crack face and reversible domain switching is observed at larger distances from the crack face. Acknowledgement This research was supported by the US National Science Foundation, award number OISE-0402066, the University of Florida, and the US Department of Energy via the Ames Laboratory. Use of the Advanced Photon Source was sup￾ported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under Contract No. DE￾AC02-06CH11357. The authors also acknowledge the tech￾nical assistance and helpful suggestions of G. Tutuncu (ISU), S.Y. Lee (ISU), and J. Almer (APS). References [1] dos Santos e Lucato SL, Lupascu DC, Ro¨del J. J Am Ceram Soc 2000;83:424. [2] Kounga Njiwa AB, Lupascu DC, Ro¨del J. Acta Mater 2004;52:4919. [3] Salz CRJ, Hoffman M, Westram I, Ro¨del J. J Am Ceram Soc 2005;88:1331. [4] Landis CM. J Mech Phys Solids 2003;51:1347. [5] Glazounov E, Kungl H, Reszat J-T, Hoffmann M, Kolleck A, Schneider GA, et al. J Am Ceram Soc 2001;84:2921. [6] Lupascu DC, dos Santos e Lucato SL, Ro¨del J, Kreuzer M, Lynch CS. Appl Phys Lett 2001;78:2554. [7] Hackemann S, Pfeiffer W. J Eur Ceram Soc 2003;23:141. [8] Fo¨rderreuther A, Thurn G, Zimmermann A, Aldinger F. J Eur Ceram Soc 2002;22:2023. [9] Meschke F, Raddatz O, Kolleck A, Schneider GA. J Am Ceram Soc 2000;83:353. [10] Yang W, Zhu T. J Mech Phys Solids 1998;46:291. [11] Bowman KJ. Mechanical Behavior of Materials. New York: John Wiley and Sons; 2004. [12] Behnken H. Some basic relations to the stress analysis using diffraction methods. In: Hauk V, editor. Structural and Residual Stress Analysis by Nondestructive Methods. Amsterdam: Elsevier Science; 1997. p. 39. [13] Cao H, Evans AG. J Am Ceram Soc 1993;76:890. [14] Fett T, Munz D, Thun G. J Am Ceram Soc 2003;86:1427. [15] Chen W, Lynch CS. J Eng Mater Technol 2001;123:169. [16] Liss K-D, Bartels A, Schreyer A, Clemens H. Textures Microstruct 2003;35:219. [17] Vullum PE, Mastin J, Wright J, Einarsrud M-A, Holmestad R, Grande T. Acta Mater 2006;54:2615. [18] Miller MP, Bernier JV, Park JS, Kazimirov A. Rev Sci Instr 2005;76:113903. [19] Daniels JD, Jones JL, Finlayson TR. J Phys D: Appl Phys 2006;39:5294. [20] Jones JL, Pramanick A, Nino JC, Motahari SM, U¨ stu¨ndag E, Daymond MR, et al. Appl Phys Lett 2007;90:172909. [21] Jones JL, Hoffman M. J Am Ceram Soc 2006;89:3721. [22] ASTM standard E 399-90. Annual Book of ASTM Standards. [23] ASTM standard E 561-98. Annual Book of ASTM Standards. [24] Hammersley AP. ESRF Internal Report, ESRF98HA01T, FIT2D V9.129 Reference Manual V3.1 (1998). [25] Hammersley AP, Svensson SO, Hanfland M, Fitch AN, Ha¨usermann D. High Pressure Res 1996;14:235. [26] Jones JL, Slamovich EB, Bowman KJ. J Appl Phys 2005;97:034113. [27] Kounga-Njiwa AB, Fett T, Lupascu DC, Ro¨del J. Eng Fract Mech 2006;73:309. [28] Hall DA, Steuwer A, Cherdhirunkorn B, Mori T, Withers PJ. J Appl Phys 2004;96:4245. [29] Hall DA, Steuwer A, Cherdhirunkorn B, Withers PJ, Mori T. J Mech Phys Solids 2005;53:249. [30] S.M. Motahari, Study of Constitutive Behavior of Ferroelectrics via Self-Consistent Modeling and Neutron Diffraction, Ph.D. Thesis, California Institute of Technology, 2007, pp. 87–92. [31] Evans AG, Cannon RM. Acta Metall 1986;34:761. [32] Hannink RH, Kelly PM, Muddle BC. J Am Ceram Soc 2000;83: 461. [33] Bowman KJ, Chen IW. J Am Ceram Soc 1993;76:113. 5548 J.L. Jones et al. / Acta Materialia 55 (2007) 5538–5548