Abstract
Reliability and life time of smart materials are crucial features for the development and design of actuator and sensor devices. Being widely used and exhibiting brittle failure characteristics, ceramic ferroelectrics are of particular interest in this field. Due to manifold interactions of the complex nonlinear constitutive behavior on the one hand and the damage evolution in terms of microcrack growth on the other, modeling and simulation are inevitable to investigate influence parameters on strength, reliability and life time. Two approaches are presented, both based on the same constitutive law and damage model. The one is going along with a discretisation scheme exploiting the finite element method (FEM). The so-called condensed approach, on the other hand, considers just one characteristic point in the material, nonetheless accounting for polycrystalline grain interactions. The focus of the simulations is two-fold. Life-time predictions in terms of high cycle fatigue under electromechanical loading conditions are presented based on the condensed approach. Second, the formation of macroscopic cracks at electrode tips in a stack actuator is investigated applying the FEM.
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References
Chen X, Fang DN, Hwang KC (1997) Micromechanics simulation of ferroelectric polarization switching. Acta Mater 45:3181–3189
Cocks ACT, McMeeking RM (1999) A phenomenological constitutive law for the behavior of ferroelectric ceramics. Ferroelectrics 228:219–228
Dittmer R, Webber KG, Aulbach E, Jo W, Tan X, Rödel J (2013) Electric-field-induced polarization and strain in 0.94(Ba1/2Na1/2)TiO3-0.06BaTiO3 under uniaxial stress. Acta Mater 61:1350–1358
Dittmer R, Webber KG, Aulbach E, Jo W, Tan X, Rödel J (2013) Optimal working regime of lead-zirconate-titanate for actuation applications. Sensor Actuat A-Phys 189:187–194
Enderlein M (2007) Finite elemente Verfahren zur bruchmechanischen Analyse von Rissen in piezoelektrischen Strukturen bei transienter elektromechanischer Belastung. PhD thesis, Freiberg
Fan J, Stoll WA, Lynch CS (1999) Nonlinear constitutive behavior of soft and hard pzt: experiments and modeling. Acta Mater 47:4415–4425
Foerderreuther A (2003) Mechanische Eigenschaften von BaTiO3-Keramiken unter mechanischer und elektrischer Belastung. PhD thesis, Stuttgart
Gellmann R, Ricoeur A (2012) Extended semi-analytical investigations of crack growth resistance behavior in ferroelectric materials. Acta Mech 223:2357–2368
Gellmann R, Ricoeur A (2012) Some new aspects of boundary conditions at cracks in piezoelectrics. Arch Appl Mech 82:841–852
Gellmann R, Ricoeur A (2014) Numerical analysis of domain switching and damage evolution in ferroelectric devices. Proc Mech Multi Mat 2:29–32
Gellmann R, Ricoeur A, Merkel E, Wang Z (2013) Generalized boundary conditions and effective properties in cracked piezoelectric solids. Proc Appl Math Mech 13:225–226
Gross D, Seelig T (2011) Fracture mechanics: with an introduction to Micromechanics. Springer, Berlin
Huber JE, Fleck NA (2001) Multi-axial electrical switching of a ferroelectric: theory versus experiment. J Mech Phys Solids 49:785–811
Huber JE, Fleck NA, Landis CM, McMeeking RM (1999) A constitutive model for ferroelectric polycrystals. J Mech Phys Solids 47:1663–1697
Huo Y, Jiang Q (1997) Modeling of domain switching in polycrystalline ferroelectric cermanics. Smart Mater Struct 6:441–447
Hwang SC, Lynch CS, McMeeking RM (1995) Ferroelectric/ferroelastic interactions and a polarization switching model. Acta Metall Mater 43:2073–2084
Jaffe B, Cook WR, Jaffe H (1971) Piezoelectric ceramics. Academic Press, London
Kachanov M (1992) Effective elastic properties of cracked solids: critical review of some basic concepts. Appl Mech Rev 45:304–335
Kamlah M (2001) Ferroelectric and ferroeleastic piezoceramics—modeling of electromechanical hysteresis phenomena. Continuum Mech Thermodyn 13:219–268
Kamlah M, Tsakmakis C (1999) Phenomenological modeling of non-linear electromechanical coupling in ferroelectrics. Int J Solids Struct 36:669–695
Kessler H, Balke H (2001) On the local and average energy release in polarization switching phenomena. J Mech Phys Solids 49:953–978
Lange S, Ricoeur A (2015) A condensed microelectromechanical approach for modeling tetragonal ferroelectrics. Int J Solids Struct 54:100–110
Li F (2014) Ultrahigh superelastic and actuation strains in ferroelectric crystals by reversible electromechanical domain switching. In: 5th international congress on ceramics, Beijing p 250
Li Q, Ricoeur A, Enderlein M, Kuna M (2010) Evaluation of electromechanical coupling effect by microstructural modeling of domain switching in ferroelectrics. Mech Res Commun 37:332–336
Lu W, Fang DN, Li CQ, Hwang KC (1997) Nonlinear electric-mechanical behavior and micromechanics modelling of ferroelectric domain evolution. Acta Mater 47:3181–3189
Lynch CS (1996) The effect of uniaxial stress on the electro-mechanical response of 8/65/35 plzt. Acta Mater 44:4137–4148
Michelitsch T, Kreher WS (1998) A simple model for the nonlinear material behavior of ferroelectrics. Acta Mater 46:5085–5094
Pak Y (1992) Linear electro-elastic fracture mechanics of piezoelectric materials. Int J Fract 54:79–100
Paris P, Erdogan F (1963) A critical analysis of crack propagation laws. J Basic Eng 85:528–534
Parton VZ, Kudryavtsev BA (1988) Electromagnetoelasticity. Gordon and Breach Science Publishers, New York
Ricoeur A, Kuna M (2003) Influence of electric fields on the fracture of ferroelectric ceramics. J Eur Ceram Soc 23:1313–1328
Ricoeur A, Gellmann R, Wang Z (2014) Influence of inclined electric fields on the effective fracture toughness of piezoelectric ceramics. Acta Mech. doi:10.1007/s00707-014-1190-5
Salz CRJ, Hoffman M, Westram I, Rödel J (2005) Cyclic fatigue crack growth in pzt under mechanical loading. J Am Ceram Soc 88:1331–1333
Sosa H (1990) On the fracture mechanics of piezoelectric solids. Int J Solids Struct 29:1–15
Stephan P, Schaber K, Stephan K, Mayinger F (2010) Thermodynamik—band 2: Mehrstoffsysteme und chemische Reaktionen. Springer, Berlin
Suo Z (1993) Models for breakdown-resistant dielectric and ferroelectric ceramics. J Mech Phys Solids 41:1155–1176
Wang B, Han J (2007) An accumulation damage model for fatigue fracture of ferroelectric ceramics. Eng Fract Mech 74:1456–1467
Wang X, Jiang L (2003) The effective electroelastic property of piezoelectric media with parallel dielectric cracks. Int J Solids Struct 40:5287–5303
Westram I, Oates WS, Lupascu DC, Roedel J, Lynch C (2007) Mechanism of electric fatigue crack growth in lead zirconate titanate. Acta Mater 55:301–312
Westram I, Ricoeur A, Emmerich A, Roedel J, Kuna M (2007) Fatigue crack growth law for ferroelectrics under cyclic electrical and combined electromechanical loading. J Eur Ceram Soc 27:2485–2494
Yang X, Chen C, Hu Y (2003) A static damage constitutive model for piezoelectric materials. In: Mechanics of electromagnetic solids, Kluwer Academic Publishers, pp 259–272
Zheng M, Su Y, Zhou G (1999) Damage model for flexural strength variation of ferroelectric materials induced by electric field. Theoret Appl Fract Mech 32:137–145
Zhou D, Kamlah M (2005) Dielectric and piezoelectric performance of soft PZT piezoceramics under simultaneous alternating electromechanical loading. J Eur Ceram Soc 25:2415–2420
Zhu T, Yang W (1999) Fatigue crack growth in ferroelectrics driven by cyclic electric loading. J Mech Phys Solids 47:81–97
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Ricoeur, A., Lange, S., Gellmann, R. (2016). Modeling Approaches to Predict Damage Evolution and Life Time of Brittle Ferroelectrics. In: Hütter, G., Zybell, L. (eds) Recent Trends in Fracture and Damage Mechanics. Springer, Cham. https://doi.org/10.1007/978-3-319-21467-2_11
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DOI: https://doi.org/10.1007/978-3-319-21467-2_11
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