Mechanical properties of Ferro-Piezoceramics

Springer Series in Materials Science

Volumn 140, Issue 1, 2011, Pages 469-542

  Lupascu, Doru C ^a   Schröder, Jörg ^a   Lynch, Christopher S ^b   Kreher, Wolfgang ^c   Westram, Ilona ^d  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

^d DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84866462045     PISSN: 0933033X     EISSN: None     Source Type: Book Series    
DOI: 10.1007/978-90-481-2875-4_10     Document Type: Article

References (230)

1. Curie P, Curie J (1881) Contractions et dilatations produites par des tensions électriques dans les cristaux hémièdres à faces inclinées. Comptes rendus de l'Acad. Sci., séance du 26 décembre 1881, XCIII, p. 1137
2. Valasek J (1921) Piezoelectric Activity of Rochelle Salt under Various Conditions. Phys Rev. 17: 422-423
3. Jaffe B, Cook Jr. WR, Jaffe H (1971) Piezoelectric Ceramics. Academic Press, Marietta OH
4. Zhang S, Lee S-M, Kim D-H, Lee H-Y, Shrout TR (2007) Electromechanical Properties of PMN-PZT Piezoelectric Single Crystals Near Morphotropic Phase Boundary Compositions. J. Am. Ceram. Soc. 90: 3859-3862
5. 3. I. Structure and room temperature properties. J. Appl. Phys. 103: 034107
6. Lupascu DC, Rödel J (2005) Fatigue in Bulk Lead Zirconate Titante Actuator Materials, Adv. Eng. Mater. 7: 882-897
7. Morozov M, Lupascu DC (2009) Ferroelectric Properties, in Ceramics Science and Technology. Vol. 2, Chen I-W, Riedel R, Eds, Wiley VCH, Weinheim
8. Muralt P (2008) Recent Progress in Materials Issues for Piezoelectric MEMS, J. Am. Ceram. Soc. 91: 1385-1396
9. Scott JF (2007) Applications of modern ferroelectrics, Science 315: 954-959
10. Nan C-W, Bichurin MI, Dong S, Viehland D, Srinivasan G (2008) Multiferroic magnetoelectric composites: Historical perspective, status, and future directions, J. Appl. Phys. 103: 031101
11. Eerenstein W, Mathur ND, Scott JF (2006) Multiferroic and magnetoelectric materials, Nature 442: 759-765
12. Fiebig M (2005) Revival of the magnetoelectric effect. J. Phys. D: Appl. Phys. 38: R123-R152
13. Damjanovic D (2005) Hysteresis in piezoelectric and ferroelectric materials. Chapter 4 in Vol. III of "Science of hysteresis" ed. G. Bertotti and I. Mayergoyz, Eds., Elsevier, Amsterdam: 337-465
14. Schneider G (2007) Influence of Electric Field and Mechanical Stresses on the Fracture of Ferroelectrics, Annu. Rev. Mater. Res. 37: 491-538
15. 3 Ceramics. Adv. Ceram. Mater. 1: 61-63
16. Strukov BA, Levanyuk AP (1998) Ferroelectric Phenomena in Crystals, Springer, Berlin
17. Devonshire AF (1954) Theory of Ferroelectrics, Adv. Phys. 3: 85-129
18. Strukov BA, Levanyuk AP (1998) Ferroelectric Phenomena in Crystals, Springer, Berlin
19. Bertotti G, Mayergoyz I (2005) Science of hysteresis, Elsevier, Amsterdam
20. 3 crystals. Phys. Rev. B 50: 5941-5949
21. Jackson JD (1975) Classical Electrodynamics. John Wiley & Sons, New York
22. 3 Single Crystals. Phys. Rev. 95: 690-698
23. 3 single crystals. Phys. Rev. 98: 409-413
24. Berlincourt D, Jaffe H (1958)"Elastic and piezoelectric coefficients of single-crystal barium titanate." Phys. Rev. 111: 143-148
25. 3 single crystals. J. Appl. Phys. 32: 1685-1687
26. Merz WJ (1964) Polarization processes in barium titanate, Ueber Polarisationsvor-gaenge in BaTiO3. Nachrichtentechnische Fachberichte 29: 37-40
27. 3 system. Ferroelectrics 37: 579-582
28. 3 single crystals. Jpn. J. Appl. Phys., Part 1: 21: 1298-1302
29. Kato K, Suzuki K, Uchino K (1990) Observation of the domain motion in ferroelectric single crystals with a diffuse phase transition. Nippon Seramikkusu Kyokai Gakujutsu Ronbunshi/J. Ceram. Soc. Jpn. 98: 840-845
30. Waser R, Baiatu T, Härdtl K-H (1990) DC electrical degradation of perovskite-type titanates. II. Single crystals. J. Am. Ceram. Soc. 73: 1654-1662
31. Mulvihill ML, Cross LE, Uchino K (1995) Low-temperature observation of relaxor ferroelectric domains in lead zinc niobate. J. Am. Ceram. Soc. 78: 3345-3351
32. Mulvihill ML, Cross LE, Uchino K (1996) Dynamic motion of the domain configuration in relaxor ferroelectric single crystals as a function of temperature and electric field. Ferroelectrics 186: 325-328
33. Mulvihill ML, Park SE, Risch G, Li Z, Uchino K, Shrout TR (1996) Role of processing variables in the flux growth of lead zinc niobate-lead titanate relaxor ferroelectric single crystals. Jpn. J. Appl. Phys., Part 1: 35: 3984-3990
34. 3 single crystals. J. Crystal Growth 167: 628-637
35. Mulvihill ML, Cross LE, Cao W, Uchino K (1997) Domain-related phase transition like behaviour in lead zinc niobate relaxor ferroelectric single crystals. J. Am. Ceram. Soc. 80: 1462-1468
36. Park SE, Shrout TR (1997) Characteristics of relaxor-based piezoelectric single crystals for ultrasonic transducers. IEEE Trans. Ultrason., Ferroelectrics Freq. Control 44: 1140-1147
37. Park SE, Shrout TR (1997) Ultrahigh strain and piezoelectric behaviour in relaxor based ferroelectric single crystals. J. Appl. Phys. 82: 1804-1811.
38. 2/3)O3using the bond valence approach. J. Am. Ceram. Soc. 80: 3217-3220
39. 3 single crystals under electric field along [111] direction. Proc. IEEE Ultrasonics Symp. 1: 625-628
40. 3 single crystals produced by solution Bridgman method. J. Am. Ceram. Soc. 81: 2785-2788
41. Kobayashi T, Saitoh S, Harada K, Shimanuki S, Yamashita Y, (1998) Growth of large and homogeneous PZN-PT single crystals for medical ultrasonic array transducers. ISAF 98. Proc. 11th IEEE Int. Symp. Appl. Ferroel.: 235-238
42. 3 crystals. Ferroelectrics 207: 519-526
43. 3 single crystals. Ferroelectrics, Lett. Sect. 26: 107-116
44. 3 single crystals. Ferroelectrics 221: 67-71
45. Dammak H, Lebon A, Calvarin G (1999) Kinetic study of PZN single crystal polarization under a static electric field. Ferroelectrics 235: 151-158
46. 3 - 8% PbTiO3. Appl. Phys. Lett. 74: 2848-2850
47. 3 single crystal produced by solution Bridgman method. Jpn. J. Appl. Phys., Part 1: 38(9B): 5512-5515
48. 3 thin films and their electromechanical properties. Integr. Ferroelectrics 25: 125-133
49. 3 single crystals. J. Appl. Phys. 85: 2810-2814
50. Luo H, Xu G, Wang P, Yin Z (1999) Growth and characterization of relaxor ferroelectric PMNT single crystals. Ferroelectrics 231: 97-102
51. Paik DS, Park SE, Shrout TR, Hackenberger W (1999) Dielectric and piezoelectric properties of perovskite materials at cryogenic temperatures. J. Mater. Sci. 34: 469-473
52. Yanagisawa K, Rendon-Angeles JC, Kanai H, Yamashita Y (1999) Stability and single crystal growth of dielectric materials containing lead under hydrothermal conditions. J. Eur. Ceram. Soc. 19: 1033-1036
53. 3 single crystals. Ferroelectrics 229: 223-232
54. 3 single crystals. J.Appl. Phys. 86: 5733-5738
55. Cross LE (1994) Relaxor ferroelectrics: An overview. Ferroelectrics 151: 305-320
56. Uchino K, Furuta A (1992) Destruction mechanism of multilayer ceramic actuators. Proc. 8th IEEE Int. Symp. Appl. Ferroel.195-198
57. Furuta A, Uchino K (1994) Destruction mechanism of multilayer ceramic actuators: case of antiferroelectrics. Ferroelectrics 160: 277-285
58. Chen W, Lynch CS (1998) Model for simulating polarization switching and AF-F phase changes in ferroelectric ceramics. J. Intell. Mater. Syst. Struct. 9: 427-431
59. Liu T, Lynch CS (2003) Ferroelectric properties of [110], [001] and [111] poled relaxor single crystals: measurements and modelling. Acta mater. 51: 407-416
60. McLaughlin EA, Liu T, Lynch CS (2005) Relaxor ferroelectric PMN-32%PT crystals under stress and electric field loading: II-33-mode measurements. Acta mater. 53: 4001-4008
61. Liu T, Oates WS, Wan S, Lynch CS (2005) Crack initiation at electrode edges in PZN-4.5%PT single crystals. J. Intell. Mater. Syst. Struct. 16: 373-379
62. Liu T, Lynch CS (2006) Orientation dependence of nonlinearity and hysteresis in PZN-4.5%PT single crystals I: Unipolar response. J. Intell. Mater. Syst. Struct. 17: 953-957
63. Liu T, Lynch CS (2006) Orientation dependence of nonlinearity and hysteresis in PZN-4.5%PT single crystals II: Bipolar electromechanical response. J. Intell. Mater. Syst. Struct. 17: 931-937
64. McLaughlin EA, Liu T, Lynch CS (2004) Relaxor ferroelectric PMN-32%PT crystals under stress and electric field loading: I-32 mode measurements. Acta mater. 52: 3849-3857
65. Liu T (2004) Electromechanical Behaviour of Relaxor Ferroelectric Crystals. PhD Thesis, The Georgia Institute of Technology, Atlanta, GA, USA
66. Lines ME, Glass AM (1977) Principles and Applications of Ferroelectrics and related Materials. Clarendon Press, Oxford
67. Fett T, Thun G (1998) Determination of room-temperature tensile creep of PZT. J. Mater. Sci. Lett. 17: 1929-1932
68. Lupascu DC, Fedosov S, Verdier C, von Seggern H, Rödel J (2004) Stretched Exponential Relaxation in Fatigued Lead-Zirconate-Titanate. J. Appl. Phys. 95: 1386-1390
69. 3 thin films. J. Appl. Phys. 89: 2332-2336
70. Zhou D, Kamlah M (2005) Determination of room-temperature creep of soft lead zirconate titanate piezoceramics under static electric fields. J. Appl. Phys. 98: 104107
71. Lupascu DC (2004) Fatigue in ferroelectric ceramics and related issues. Springer, Heidelberg
72. Zhou D, Kamlah M, Munz D (2005) Effects of Bias Electric Fields on the Non-linear Ferroelastic Behaviour of Soft Lead Zirconate Titanate Piezoceramics. J. Am. Ceram. Soc. 88: 867-874
73. 3 ceramics: PhD thesis, École Polytechnique Fédérale de Lausanne, Switzerland
74. Arlt G, Neumann H (1988) Internal Bias in Ferroelectric Ceramics: Origin and Time Dependence. Ferroelectrics 87: 109-120
75. Rosen CZ, Hiremath BV, Newnham R (1992) Key Papers in Physics, Piezoelectricity, Am. Inst. Phys., New York
76. Uchino K (1997) Piezoelectric Actuators and Ultrasonic Motors, Kluwer, Boston
77. Setter N, Ed. (2002) Piezoelectric Materials in Devices, Ceramics Laboratory, Lausanne
78. offmann MJ, Hammer M, Endriss A, Lupascu DC (2001) Correlation between microstructure, strain behaviour, and acoustic emission of soft PZT ceramics. Acta Mater. 49: 1301-1310
79. Jones JL (2007) The use of diffraction in the characterization of piezoelectric materials. J. Electroceram. 19: 67-79
80. 3 at its morphotropic phase boundary: Investigations from local to average structure. Phys. Rev. B75: 184117
81. Fett T, Munz D, Thun G (1999) Tensile and Bending Strength of Piezoelectric Ceramics. J. Mater. Sci. Lett. 18: 1899-1902
82. Munz D, Fett T (1999) Ceramics: Mechanical Properties, Failure Behaviour, Materials Selection. Springer, Heidelberg
83. Fett T, Munz D, Thun D (1998) Nonsymmetric deformation behaviour of PZT determined in bending tests. J. Am. Ceram. Soc. 81: 269-272
84. Balke N, Lupascu DC, Granzow T, Rödel J (2007) Fatigue of Lead Zirconate Titanate Ceramics II: Sesquipolar Loading. J. Am. Ceram. Soc. 90: 1088-1093
85. Chen W, Lynch CS (2001) Multiaxial constitutive behaviour of ferroelectric materials. J. Engin. Mater. Techn., Transa. ASME 123: 169-175
86. Shieh J, Huber JE, Fleck NA (2003) An evaluation of switching criteria for ferroelectrics under stress and electric field. Acta mater. 51: 6123-6137
87. Kounga-Njiwa AB, Lupascu DC, Rödel J (2004) Crack tip switching zone in ferroelectric ferroelastic materials. Acta Mater. 52: 4919-4927
88. Kounga-Njiwa AB, Aulbach E, Granzow T, Rödel J (2007) Influence of radial stress on the poling behaviour of lead zirconate titanate ceramics. Acta Mater. 55:675-680
89. Kounga AB, Granzow T, Aulbach E, Hinterstein M, Rödel J (2008) High-temperature poling of ferroelectrics. J. Appl. Phys. 104: 024116
90. Hall DA (2001) Review: Nonlinearity in piezoelectric ceramics. J. Mater. Sci. 36: 4575-4601
91. Bhattacharya K, Ravichandran G (2003) Ferroelectric perovskites for electromechanical actuation. Acta mater. 51: 5941-5960
92. Huber JE (2005) Micromechanical modelling of ferroelectrics. Curr. Opinion Solid State Mater. Sci. 9: 100-106
93. Landis CM (2004) Non-linear constitutive modelling of ferroelectrics. Curr. Opinion Solid State Mater. Sci. 8: 59-69
94. Robert G, Damjanovic D, Setter N, Turik AV (2001) Preisach modelling of piezoelectric nonlinearity in ferroelectric ceramics. J. Appl. Phys. 89: 5067-5074
95. Zhou X, Chattopadhyay A (2001) Hysteresis Behaviour and Modelling of Piezoceramic Actuators. Trans. ASME, J. Appl. Mech. 68: 270-277
96. Kamlah M, Tsakmakis C (1999) Phenomenological modelling of the non-linear electromechanical coupling in ferroelectrics. Int. J. Solids Struct. 36: 669-695
97. Huber JE, Fleck NA (2001) Multiaxial electrical switching of a ferroelectric: theory versus experiment. J. Mech. Phys. Solids 49: 785-811
98. McMeeking RM, Landis CM (2002) A phenomenological multiaxial constitutive law for switching in polycrystalline ferroelectric ceramics. Int. J. Engng. Sci. 40: 1553-1577
99. Landis CM (2002) Fully coupled, multiaxial, symmetric constitutive laws for polycrystalline ferroelectric ceramics. J. Mech. Phys. Solids 50: 127-152
100. Schröder J, Romanowski H (2005) A thermodynamically consistent mesoscopic model for transversely isotropic ferroelectric ceramics in a coordinate-invariant setting. Arch. Appl. Mech. 74: 863-877
101. Klinkel S (2006) A phenomenological constitutive model for ferroelastic and ferroelectric hysteresis effects in ferroelectric ceramics. Int. J. Solids Struct. 43: 7197-7222
102. Mehling V, Tsakmakis C, Gross D (2007) Phenomenological model for the macroscopical material behaviour of ferroelectric ceramics. J. Mech. Phys. Solids 55: 2106-2141
103. Hwang SC, Lynch CS, McMeeking RM (1995) Ferroelectric/ferroelastic interactions and a polarization switching model. Acta metall. mater. 43: 2073-2084
104. Delibas B, Arockiarajan A, Seemann W (2006) Rate dependent properties of perovskite type tetragonal piezoelectric materials using micromechanical model. Int. J. Solids Struct. 43: 697-712
105. Smith RC, Seelecke S, Dapino M, Ounaies Z (2006) A unified framework for modelling hysteresis in ferroic materials. J. Mech. Phys. Solids 54: 46-85
106. Menzel A, Arockiarajan A, Sivakumar SM (2008) Rate dependent properties of perovskite type tetragonal piezoelectric materials using micromechanical model. Smart Mater. Struct. 17: 15026
107. Zhang ZK, Fang DN, Soh AK (2006) A new criterion for domain-switching in ferroelectric materials. Mech. Mater. 38: 25-32
108. Shaikh MG, Phanish S, Sivakumar SM (2006) Domain switching criteria for ferroelectrics. Comp. Mater. Sci. 37: 178-186
109. Li FX, Fang DN, Soh AK (2004) An analytical axisymmetric model for the polinghistory dependent behaviour of ferroelectric ceramics. Smart Mater. Struct. 13: 668-675
110. Li FX, Rajapakse RKND (2007) A constrained domain-switching model for polycrys-talline ferroelectric ceramics. Part I: Model formulation and application to tetragonal materials. Acta mater. 55: 6472-6480
111. Ricinschi D, Okuyama M (2005) A nucleation-growth model for ferroelectric hysteresis loops with complete and partial switching. J. Eur. Ceram. Soc. 81: 2357-2361
112. Lo VC, Chung WY, Chow SC (2007) Simulation of electromechanical responses of ferroelectric ceramics driven by combined alternating electrical and mechanical loadings. J. Appl. Phys. 101: 114111
113. Wang J, Shi S-Q, Chen LQ, Li Y, Zhang T-Y (2004) Phase field simulations of ferroelectric/ferroelastic polarization switching. Acta mater. 52: 749-764
114. Soh AK, Song YC, Niz Y (2006) Phase Field Simulations of Hysteresis and Butterfly Loops in Ferroelectrics Subjected to Electro-Mechanical Coupled Loading. J. Am. Ceram. Soc. 89: 652-661
115. Arlt G (1990) Twinning in ferroelectric and ferroelastic ceramics: stress relief. J. Mater. Sci. 25: 2655-2666
116. Rödel J, Kreher WS (2000) Self-consistent modelling of non-linear effective properties of polycrystalline ferroelectric ceramics. Comp. Mater. Sci. 19: 123-132
117. Kreher WS, Rödel J (2002) Dissipative domain wall motion and macroscopic response of ferroelectric ceramics. Ferroelectrics 269: 51-56
118. Su Y, Weng GJ (2006) A polycrystal model for the anisotropic behaviour of a fully poled ferroelectric ceramic. J. Appl. Phys. 100: 114110-1-8
119. Rödel J, Kreher WS (2003) Modelling linear and nonlinear behaviour of polycrystalline ferroelectric ceramics. J. Eur. Ceram. Soc. 23: 2297-2306
120. Huber JE, Fleck NA, Landis CM, McMeeking RM (1999) A constitutive model for ferroelectrics. J. Mech. Phys. Solids 47: 1663-1697
121. Huber JE, Fleck NA (2004) Ferroelectric switching: a micromechanics model versus measured behaviour. Eur. J. Mech. A/Solids 23: 203-217
122. Zhou D, Kamlah M, Laskewitz B (2006). Multiaxial non-proportional polarization rotation tests of soft PZT piezoceramics under electric field loading. Proc. SPIE Vol. 6170, 617009, San Diego, CA, United States, Armstrong WD, Ed.
123. Pathak A, McMeeking RM (2008) Three-dimensional finite element simulations of ferroelectric polycrystals under electrical and mechanical loading. J. Mech. Phys. Solids 56: 663-683
124. Huo Y, Jiang Q (1997) Modelling of domain switching in polycrystalline ferroelectric ceramics. Smart Mater. Struct. 6: 441-447
125. Kamlah M, Jiang Q (1999) A constitutive model for ferroelectric PZT ceramics under uniaxial loading. Smart Mater. Struct. 8: 441-459
126. Lu W, Fang DN, Li CQ, Hwang KC (1999) Nonlinear electric-mechanical behaviour and micromechanical modelling of ferroelectric domain evolution. Acta mater. 47: 2913-2926
127. Li WF, Weng GJ (2002) A theory of ferroelectric hysteresis with a superimposed stress. J. Appl. Phys. 91: 3806-3815
128. Liu F, Li HJ, Wang TC (2008) Energy principle and nonlinear electric-mechanical behaviour of ferroelectric ceramics. Acta Mechanica 198: 147-170
129. Zhou D, Kamlah M (2006) Room-temperature creep of soft PZT under static electrical and compressive stress loading. Acta mater. 54: 1389-1396
130. Liu QD, Huber JE (2006) Creep in ferroelectrics due to unipolar electrical loading. J. Eur. Ceram. Soc. 26: 2799-2806
131. Kim S-J, Jiang Q (2002) A finite element model for rate-dependent behaviour of ferroelectric ceramics. Int. J. Solids Struct. 39: 1015-1030
132. Belov AY, Kreher WS (2007) Micromechanics of ferroelectrics: From domain walls to piezoceramic devices. Ferroelectrics 351: 79-87
133. Chong KB, Guiu F, Reece MJ (2008) Thermal activation of ferroelectric switching. J. Appl. Phys. 103: 14101
134. Belov AY, Kreher WS (2005) Viscoplastic behaviour of perovskite type ferroelectrics. Mater. Sci. Eng. B 118: 7-11
135. Belov AY, Kreher WS (2005) Viscoplastic models for ferroelectric ceramics. J. Europ. Ceram. Soc. 25: 2567-2571
136. Maugin GA, Pouget J, Drouot R, Collet B (1992) Nonlinear electromechanical couplings. Wiley, New York
137. Chen P, Peercy P (1979) One dimensional dynamic electromechanical constitutive relations of ferroelectric materials. Acta Mech. 31: 231-241
138. Chen PJ, Tucker TJ (1981) One dimensional polar mechanical and dielectric responses of the ferroelectric ceramic PZT 65/35 due to domain switching. Int. J. Eng. Sci. 19: 147-158
139. Bassiouny E, Ghaleb AF, Maugin GA (1988) Thermodynamical formulation for coupled electromechanical hysteresis effects-I. Basic equations. Int. J. Eng. Sci. 26: 1279-1295
140. Bassiouny E, Ghaleb AF, Maugin GA (1988) Thermodynamical formulation for coupled electromechanical hysteresis effects-II. Poling of ceramics. Int. J. Eng. Sci. 26: 1297-1306
141. Bassiouny E, Maugin GA (1989) Thermodynamical formulation for coupled electrome-chanical hysteresis effects-III. Parameter identification. Int. J. Eng. Sci. 27: 975-987
142. Landis CM, McMeeking RM (2001) A self-consistent constitutive model for switching in polycrystalline barium titanate. Ferroelectrics 255: 13-34
143. Hashin Z, Shtrikman S (1962) On some variational principles in anisotropic and non-homogeneous elasticity. J. Mech. Phys. Sol. 10: 335-342
144. Walpole LJ (1966) On bounds for the overall elastic moduli of inhomogeneous system. J. Mech. Phys. Sol. 14: 151-162
145. Kröner E (1977) Bounds for effective elastic moduli of disordered materials. J. Mech. Phys. Sol. 25: 137-155
146. Willis JR (1966) Bounds and self-consistent estimates for the overall properties of anisotropic composites. J. Mech. Phys. Sol., 25:185-202
147. Francfort GA, Murat F (1986) Homogenization and optimal bounds in linear elasticity. Arch. Rat. Mech. Anal. 94: 307-334
148. Nemat-Nasser S, Hori M (1993) Micromechanics: Overall Properties of Heterogeneous Materials. North-Holland, London
149. Chen T (1994) Micromechanical estimates of the overall thermoelectroelastic moduli of multiphase fibrous composites. Int. J. Sol. Struct. 31: 3099-3111
150. Chen T (1993) Piezoelectric properties of multiphase fibrous composites: Some theoretical results. J. Mech. Phys. Sol. 41: 1781-1794
151. Dunn ML, Taya M (1993) Micromechanics predictions of the effective electroelastic moduli of piezoelectric composites. Int. J. Sol. Struct. 30: 161-175
152. Dunn ML,Taya M (1993) An analysis of piezoelectric composite materials containing ellipsoidal inhomogeneities. Proc. R. Soc. A 443(1918): 265-287
153. Benveniste Y (1993) Universal relations in piezoelectric composites with eigenstress and polarization fields, part I: Binary media: Local fields and effective behaviour. J. Appl. Mech. 60: 265-269
154. Benveniste Y (1993) Universal relations in piezoelectric composites with eigenstress and polarization fields, part II: Multiphase media-effective behaviour. J. Appl. Mech. 60: 270-275
155. Benveniste Y (1993) Exact results in the micromechanics of fibrous piezoelectric composites exhibiting pyroelectricity. Proc. R. Soc. A 441(1911): 59-81
156. Benveniste Y (1997) Piezoelectric inhomogeneity problems in anti-plane shear and in plane electric fields how to obtain the coupled fields from the uncoupled dielectric solution. Mech. Mater. 25: 59-65
157. Hori M, Nemat-Nasser S (1998) Universal bounds for effective piezoelectric moduli. Mech. Mat. 30: 1-19
158. Silva ECN, Fonseca JSO, Kikuchi N (1998) Optimal design of periodic piezocomposites. Comp. Meth. Appl. Mech. Eng. 159: 49-77
159. Silva ECN, Nishiwaki S, Fonseca JSO, Kikuchi N (1999) Optimization methods applied to material and flextensional actuator design using the homogenization method. Comp. Meth. Appl. Mech. Eng. 172: 241-271
160. Li Z, Wang C, Chen C (2003) Effective electromechanical properties of transversely isotropic piezoelectric ceramics with microvoids. Comp. Mat. Sci. 27: 381-392
161. Uetsuji Y, Nakamura Y, Ueda S, Nakamachi E (2004) Numerical investigation on ferroelectric properties of piezoelectric materials using a crystallographic homogenization method. Model. Sim. Mat. Sci. Eng. 12: S303-S317
162. Sanchez-Palencia E (1980) Non-Homogeneous Media and Vibration Theory (Lecture Notes in Physics vol. 172). Springer, Berlin
163. Hill R (1972) On constitutive macro-variables for heterogeneous solids at finite strain. Proc. R. Soc. A 326(1565): 131-147
164. Hill R (1985) On the micro-to-macro transition in constitutive analyses of elastoplastic response at finite strain. Proc. Cam. Phil. Soc. 98: 579-590
165. Suquet PM (1986) Homogenization Techniques for Composite Materials, Lecture Notes in Physics 272, chapter Elements of homogenization for inelastic solid mechanics, pp. 193-278. Springer-Verlag
166. Krawietz A (1986) Materialtheorie: Mathematische Beschreibung des phnomenolo-gischen thermomechanischen Verhaltens. Springer-Verlag, Berlin
167. Miehe C, Schröder J, Schotte J (1999) Computational homogenization analysis in finite plasticity simulation of texture development in polycrystalline materials. Comp. Meth. Appl. Mech. Eng. 171: 387-418
168. Schröder (2000) Homogenisierungsmethoden der nichtlinearen Kontinuumsmechanik unter Beachtung von Instabilitäten. Bericht aus der Forschungsreihe des Instituts für Mechanik (Bauwesen), Lehrstuhl I, Universität Stuttgart
169. Schröder J, Keip M-A (2010) A framework for the two-scale homogenization of electromechanically coupled boundary value problems. In M Kuczma and K Wilmanski, editors, Computer Methods in Mechanics, 311-329, Springer
170. Schröder J, Keip M-A (2009) Multiscale Modeling of Electro-Mechanically Coupled Materials: Homogenization Procedure and Computation of Overall Moduli. In M Kuna and A Ricoeur, editors, IUTAM Symposium on Multiscale Modelling of Fatigue, De-mage and Fracture in Smart Materials Systems, in press
171. Romanowski H, Schröder J (2005) Coordinate invariant modelling of the ferroelectric hysteresis within a thermodynamically consistent framework. A mesoscopic approach. In Y. Wang and K. Hutter, eds., Trends in Applications of Mathematics and Mechanics, pp. 419-428. Shaker Verlag, Aachen
172. Romanowski H (2006) Kontinuumsmechanische Modellierung ferroelektrischer Materi-alien im Rahmen der Invariantentheorie. PhD thesis, Institut für Mechanik, Fakultät Ingenieurwissenschaften, Abteilung Bauwissenschaften, Universität Duisburg-Essen.
173. Schröder J, Gross D (2004) Invariant formulation of the electromechanical enthalpy function of transversely isotropic piezoelectric materials. Arch. Appl. Mech. 73: 533-552
174. Schröder J, Romanowski H (2005) A thermodynamically consistent mesoscopic model for transversely isotropic ceramics in a coordinate-invariant setting. Archive of Applied Mechanics 74, 863-877.
175. Schrder J, Romanowski H, Kurzhöfer I (2007) A computational meso-macro transition procedure for electro-mechanical coupled ceramics. In Schröder J, Lupascu D, Balzani D, eds., First Seminar on the Mechanics of Multifunctional Materials, Bad Honnef, Germany, May 7th - 10th 2007. Institut für Mechanik, Fakultät Ingenieurwissenschaften, Abteilung Bauwissenschaften, Universität Duisburg-Essen
176. Kurzhöfer I (2007) Mehrskalen-Modellierung polycrystalliner Ferroelektrika basierend auf diskreten Orientierungsverteilungsfunktionen. PhD thesis, Institut für Mechanik, Fakultät Ingenieurwissenschaften, Abteilung Bauwissenschaften, Universität DuisburgEssen
177. Hill R (1963) Elastic properties of reinforced solids: Some theoretical principles. J. Mech. Phys. Sol. 11: 357-372
178. Boehler JP (1987) Introduction to the invariant formulation of anisotropic constitutive equations. In Applications of Tensor Functions in Solid Mechanics, Boehler JP, editor, pp. 3-65. Springer, Wien
179. Kamlah M, Böhle U (2001) Finite element analysis of piezoceramic components taking into account ferroelectric hysteresis behaviour. Int. J. Solids Struct. 38: 605-633
180. Pohanka RC, Freiman SW, Okazaki K, Tashiro S (1983) Fracture of piezoelectric materials. In Fracture Mechanics of Ceramics, ed. RC Bradt, AG Evans, DPH Hasselman, FF Lange, 5:353-64. New York: Plenum Press
181. Freiman SW, Pohanka RC (1989) Review of Mechanically Related Failures of Ceramic Capacitors and Capacitor Materials. J. Am. Ceram. Soc. 72: 2258-2263
182. Winzer SR, Shankar N, Ritter AP (1989) Designing cofired multilayer electrostrictive actuators for reliability. J. Am. Ceram. Soc. 72: 2246-2257
183. Cao HC, De Graef M, Evans AG (1993) Structure and properties at the ferroelectric/electrode interface between lead zirconate titanate and copper. J. Am. Ceram. Soc. 76(12): 3019-3023
184. Furuta A, Uchino K (1993) Dynamic observation of crack propagation in piezoelectric multilayer actuators. J. Am. Ceram. Soc. 76: 1615-1617
185. Aburatani, H., S. Harada, Uchino K, Furuta A, Fuda Y (1994). Destruction mechanisms in ceramic multilayer actuators. Jpn. J. Appl. Phys., Part 1, 33(5B): 3091-3094
186. Hao TH, Gong X, Suo Z (1996) Fracture mechanics for the design of ceramic multilayer actuators. J. Mech. Phys. Solids 44: 23-48
187. Fan J, Niu H, Lynch CS (1998) An experimental and theoretical study of electric field effects on cracked ceramics. J. Mater. Sci. Lett. 17: 189-192
188. Lynch CS (1998) Fracture of ferroelectric and relaxor electro-ceramics: influence of electric field. Acta mater. 46: 599-608
189. Ru CQ, Mao X, Epstein M (1998) Electric-field induced interfacial cracking in multilayer electrostrictive actuators. J. Mech. Phys. Solids 46: 1301-1318
190. Dos Santos e Lucato SL, Lupascu DC, Kamlah M, Rödel J, Lynch CS (2001) Constraint-induced crack initiation at electrode edges in piezoelectric ceramics. Acta mater. 49: 2751-2759
191. Dos Santos e Lucato SL, Bahr HA, Pham V-B, Lupascu DC, Balke H, Rödel J, Bahr U (2002) Electrically driven cracks in piezoelectric ceramics: Experiments and fracture mechanics analysis. J. Mech. Phys. Solids 50: 2333-2353
192. Maeng S-Y, Lee D-K, Choi J-W, Kim H-J, Kang C-Y, Sahn-Nahm, Yoon S-J (2005) Design and fabrication of multilayer actuator using floating electrode. Mater. Chem. Phys. 90: 405-410
193. Kusukawa K, Shiozaki Y (2007) Electric loading - Induced cracking behaviour at electrode edges in PZT ceramics. Key Engin. Mater. 352: 267-270
194. Westram I, Ricoeur A, Emrich A, Rödel J, Kuna M (2007) Fatigue crack growth law for ferroelectrics under cyclic electrical and combined electromechanical loading. J. Eur. Ceram. Soc. 27: 2485-2494
195. Megherhi MH, Dayton GO, Shrout TR, Mecholsky JJ (1990) Indentation fracture of lead magnesium niobate-based multilayer composite structures. J. Mater. Res. 5: 515-523
196. Davis JB, Cao HC, Bao G, Evans AG (1991). Fracture energy of interfaces. An elastic indentation technique. Acta metall. mater. 39: 1019-1024
197. Lynch CS, Yang W, Collier L, Suo Z, McMeeking RM (1995) Electric-field-induced cracking in ferroelectric ceramics. Ferroelectrics 166: 11-30
198. 3 crystal. Acta mater. 49: 2993-2999
199. Fang F, Yang W (2002) Indentation-induced cracking and 90 degrees domain switching pattern in barium titanate ferroelectric single crystals under different poling. Mater. Lett. 57: 198-202
200. Fang F, Li YH, Yang W (2005) Effect of poling directions on the electric-field-induced fatigue crack growth in barium titanate ferroelectric single crystals. Ferroelectrics 322: 11-21
201. Kolleck A, Schneider GA, Meschke FA (2000) R-curve behaviour of BaTiO3-and PZT ceramics under the influence of an electric field applied parallel to the crack front. Acta Mater. 48: 4099-4113
202. Dos Santos e Lucato SL (2003) Crack-growth-velocity-dependent R-curve behaviour in lead zirconate titanate. J. Am. Ceram. Soc. 86: 1037-1039
203. Felten F, Schneider GA, Knoblauch V (2005) In situ investigation of subcritical crack growth in lead zirconate titanate ceramics using atomic force microscopy. Acta mater. 53: 4051-4056
204. Kounga-Njiwa AB, Fett T, Lupascu DC, Rödel J (2006). Effect of geometry and electrical boundary conditions on R-curves for lead zirconate titanate ceramics. Engin. Fract. Mech. 73(3): 309-317
205. Oates WS, Lynch CS, Lupascu DC, Kounga-Njiva AB, Aulbach E, Rödel J (2004) Subcritical crack growth in lead zirconate titanate. J. Am. Ceram. Soc. 87: 1362-1364
206. Dos Santos e Lucato SL, Lupascu DC, Rödel J (2000) Effect of Poling Direction on R-Curve Behaviour in Lead Zirconate Titanate. J. Am. Ceram. Soc. 83: 424-426
207. Oates WS, Lynch CS, Kounga-Njiwa AB, Lupascu DC (2005) Anisotropic fracture behaviour in ferroelectric relaxor PZN-4.5%PT single crystals. J. Am. Ceram. Soc. 88: 1838-1844
208. Lupascu DC, Kreuzer M, Lucato SLS, Rödel J, Lynch CS (2001) A liquid crystal display of stress fields in ferroelectrics. Appl. Phys. Lett. 78: 2554-2556
209. Liu ZW, Fang DN, Xie HM, Lee JJ (2007) Study of effect of 90 degrees domain switching on ferroelectric ceramics fracture using the moire interferometry. Acta mater. 55: 3911-3922
210. ASTM E-399: Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness KIc of Metallic Materials
211. Waser R, Ed. (2005) Nanoelectronics and information technology, Wiley-VCH, Weinheim
212. Cao H, Evans AG (1994) Electric-field-induced fatigue crack growth in piezoelectrics. J. Am. Ceram. Soc. 77: 1783-1786
213. Weitzing H, Schneider GA, Steffens J, Hammer M, Hoffmann MJ (1999) Cyclic fatigue due to electric loading in ferroelectric ceramics. J. Eur. Ceram. Soc. 19: 1333-1337
214. Zhu T, Fang F, Yang W (1999) Fatigue crack growth in ferroelectric ceramics below the coercive field. J. Mat. Sci. Let. 18: 1025-1027
215. Zhu T, Yang W (1999) Fatigue crack growth in ferroelectrics driven by cyclic electric loading. Mech. Phys. Sol. 47: 81-9
216. Jiang LZ, Sun CT (1999) Crack growth behaviour in piezoceramics under cyclic loads. Ferroelectrics 233: 211-233
217. Shang JK, Tan X (2001) A maximum strain criterion for electric-field-induced fatigue crack propagation in ferroelectric ceramics. Mat. Sci. Eng. A301: 131-139
218. Liu B, Fang DN, Hwang KC (2002) Electric-field induced crack growth in ferroelectric ceramics. Mat. Lett. 54: 442-446
219. Shieh J, Huber JE, Fleck NA (2006) Fatigue crack growth in ferroelectrics under electrical loading. J. Eur. Ceram. Soc. 26: 95-109
220. Westram I, Laskewitz B, Lupascu DC, Kamlah M, Rödel J (2007) Electric-field induced crack initiation from a notch in a ferroelectric ceramic. J. Am. Ceram. Soc. 90: 2849-2854
221. Westram I, Oates WS, Lupascu DC, Rödel J, Lynch CS (2006) Mechanism of electric fatigue crack growth in lead zirconate titanate. Acta mater. 55: 301-312
222. Westram I, Kungl H, Hoffmann MJ, Rödel J (2008) Influence of crystal structure on crack propagation under cyclic electric loading in lead-zirconate-titanate. J. Eur. Ceram. Soc. 29: 425-430
223. 3 under Cyclic Electric Loading. Ph. D. Thesis, Darmstadt University of Technology, Darmstadt, Germany
224. Salz RJ, Hoffman M, Westram I, del J (2005) Cyclic Fatigue Crack Growth in PZT Under Mechanical Loading. J. Am. Ceram. Soc. 88: 1331-1333
225. Suo Z (1993) Models for breakdown-resistant dielectric and ferroelectric ceramics. J. Mech. Phys. Solids 41: 1155-1176
226. Yang W, Suo Z (1994) Cracking in ceramic actuators caused by electrostriction. J. Mech. Phys. Solids 42: 649-664
227. McMeeking RM, Hwang SC (1997) On the potential energy of a piezoelectric inclusion and the criterion for ferroelectric switching. Ferroelectrics 200: 151-173
228. Yang, W (2002) Mechatronic reliability: electric failures, mechanical electrical coupling, domain switching, mass flow instabilities. Springer, Berlin
229. Mao GZ, Fang DN (2004) Fatigue crack growth induced by domain switching under electromechanical load in ferroelectrics. Theoret. Appl. Fract. Mech. 41: 115-123
230. Zheng J, Takahashi S, Yoshikawa S, Uchino K, de Vries JWC (1996) Heat generation in Multilayer Piezoelectric Actuators. J. Am. Ceram. Soc. 79: 3193-3198