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Meinhard Kuna: Physics and Engineering at the Crack Tip—A Retrospective Read chapter Read first chapter

2016 | OriginalPaper | Chapter

Interaction of Cracks and Domain Structures in Thin Ferroelectric Films

Authors : D. Schrade, R. Müller, D. Gross

Published in: Recent Trends in Fracture and Damage Mechanics

Publisher: Springer International Publishing

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Abstract

The fracture behavior of ferroelectric materials is a complex problem that has been addressed in numerous experimental and theoretical studies. Several factors have been identified to play an important role, such as the applied electric field, the medium inside the crack, the electrical conditions on the crack faces, and polarization switching at or near the crack tip. In this investigation, a phase field model for ferroelectric domain evolution is used to calculate crack tip driving forces for mode-I cracks in barium titanate thin films. The driving forces are obtained by employing the theory of configurational forces, which is equivalent to considering the J-integral. Simulations are done for permeable, impermeable, semi-permeable, and energetically consistent crack face conditions with both air and water as crack medium. The finite element calculations are performed for films with thicknesses varying from 5 to 30 nm. The results show that the impermeable, semi-permeable and energetically consistent conditions lead to similar crack tip driving forces if air is used as crack medium. In the absence of mechanical loading, strong electric fields result in a closing crack tip driving force, while the use of water as crack medium leads to opposite driving forces. It can be confirmed that polarization switching at the crack tip has a significant effect on the driving force.

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previous chapter Transition from Flat to Slant Fracture in Ductile Materials
next chapter Modeling Approaches to Predict Damage Evolution and Life Time of Brittle Ferroelectrics
Literature
1.
Abdollahi A, Arias I (2012) Phase-field modeling of crack propagation in piezoelectric and ferroelectric materials with different electromechanical crack conditions. J Mech Phys Solids 60(12):2100–2126MathSciNetCrossRef
2.
Arlt G, Sasko P (1980) Domain configuration and equilibrium size of domains in BaTiO3 ceramics. J Appl Phys 51(9):4956–4960
3.
Beom HG, Atluri SN (2003) Effect of electric fields on fracture behavior of ferroelectric ceramics. J Mech Phys Solids 51(6):1107–1125CrossRefMATH
4.
Chen YH, Hasebe N (2005) Current understanding on fracture behaviors of ferroelectric/piezoelectric materials. J Intell Mater Syst Struct 16:673–687CrossRef
5.
Deeg WF (1980) The analysis of dislocation, cracks, and inclusion problems in piezoelectric solids. Ph.D. thesis, Stanford University, Stanford
6.
Fang D, Jiang Y, Li S, Sun CT (2007) Interactions between domain switching and crack propagation in poled BaTiO3 single crystal under mechanical loading. Acta Mater 55(17):5758–5767CrossRef
7.
Gurtin ME (1996) Generalized Ginzburg-Landau and Cahn-Hilliard equations based on a microforce balance. Physica D 92(3–4):178–192MathSciNetCrossRefMATH
8.
Hao TH, Shen ZY (1994) A new electric boundary condition of electric fracture mechanics and its applications. Eng Fract Mech 47:793–802CrossRef
9.
Jiang LZ, Sun CT (2001) Analysis of indentation cracking in piezoceramics. Int J Solids Struct 38(10–13):1903–1918CrossRefMATH
10.
Keip MA, Schrade D, Thai HNM, Schröder J, Svendsen B, Müller R, Gross D (2015) Coordinate-invariant phase field modeling of ferroelectrics, part II: application to composites and polycrystals. GAMM-Mitteilungen 38(1):115–131
11.
12.
Landis CM (2004) Energetically consistent boundary conditions for electromechanical fracture. Int J Solids Struct 41:6291–6315CrossRefMATH
13.
Li Q, Kuna M (2012) Evaluation of electromechanical fracture behavior by configurational forces in cracked ferroelectric polycrystals. Comput Mater Sci 57:94–101CrossRef
14.
Li W, Landis CM (2011) Nucleation and growth of domains near crack tips in single crystal ferroelectrics. Eng Fract Mech 78(7):1505–1513CrossRef
15.
Li Y, Sun Y, Li F (2013) Domain texture dependent fracture behavior in mechanically poled/depoled ferroelectric ceramics. Ceram Int 39(8):8605–8614CrossRef
16.
17.
McMeeking RM (2004) The energy release rate for a griffith crack in a piezoelectric material. Eng Fract Mech 71:1149–1163CrossRef
18.
Meschke F, Kolleck A, Schneider GA (1997) R-curve behavior of BaTiO3 due to stress-induced ferroelastic domain switching. J Eur Ceram Soc 17:1143–1149CrossRef
19.
20.
Mueller R, Kolling S, Gross D (2002) On configurational forces in the context of the finite element method. Int J Numer Meth Eng 53(7):1557–1574MathSciNetCrossRefMATH
21.
Park S, Sun CT (1995) Fracture criteria for piezoelectric ceramics. J Eur Ceramics Soc 78(6):1475–1480CrossRef
22.
23.
Qiao H, Wang J, Chen W (2012) Phase field simulation of domain switching in ferroelctric single crystal with electrically permeable and impermeable cracks. Acta Mech Sol Sinica 25(1):1–8CrossRef
24.
Ricoeur A, Kuna M (2003) Influence of electric fields on the fracture of ferroelectric ceramics. J Eur Ceram Soc 23(8):1313–1328CrossRef
25.
Schmitt LA, Schönau KA, Theissmann R, Fuess H, Kungl H, Hoffmann M (2007) Composition dependence of the domain configuration and size in Pb(Zr1−x Ti x )O3 ceramics. J Appl Phys 101(7):074107
26.
Schrade D, Mueller R, Xu BX, Gross D (2007) Domain evolution in ferroelectric materials: a continuum phase field model and finite element implementation. Comput Meth Appl Mech Eng 196(41–44):4365–4374CrossRefMATH
27.
Schrade D, Müller R, Gross D (2013) On the physical interpretation of material parameters in phase field models for ferroelectrics. Arch Appl Mech 83:1393–1413CrossRefMATH
28.
Schrade D, Müller R, Gross D, Keip MA, Thai H, Schröder J (2014) An invariant formulation for phase field models in ferroelectrics. Int J Solids Struct 51:2144–2156CrossRef
29.
Schrade D, Keip MA, Thai HNM, Schröder J, Svendsen B, Müller R, Gross D (2015a) Coordinate-invariant phase field modeling of ferroelectrics, part I: model formulation and single-crystal simulations. GAMM-Mitteilungen 38(1):102–114
30.
Schrade D, Müller R, Gross D, Steinmann P (2015) Phase field simulations of the poling behavior of BaTiO3 nano-scale thin films with SrRuO3 and Au electrodes. Eur J Mech A/Solids 49:455–466CrossRef
31.
Song YC, Soh AK, Ni Y (2007) Phase field simulation of crack tip domain switching in ferroelectrics. J Phys D Appl Phys 40(4):1175–1182CrossRef
32.
Su Y, Landis CM (2007) Continuum thermodynamics of ferroelectric domain evolution: theory, finite element implementation, and application to domain wall pinning. J Mech Phys Solids 55(2):280–305MathSciNetCrossRefMATH
33.
Su Y, Chen H, Li JJ, Soh AK, Weng GJ (2011) Effects of surface tension on the size-dependent ferroelectric characteristics of free-standing BaTiO3 nano-thin films. J Appl Phys 110(084108):1–6
34.
35.
36.
Tenne DA, Turner P, Schmidt JD, Biegalski M, Li YL, Chen LQ, Soukiassian A, Trolier-McKinstry S, Schlom DG, Xi XX, Fong DD, Fuoss PH, Eastman JA, Stephenson GB, Thompson C, Streiffer SK (2009) Ferroelectricity in ultrathin BaTiO3 films: probing the size effect by ultraviolet Raman spectroscopy. Phys Rev Lett 103(177601):1–4
37.
Wang J, Landis CM (2004) On the fracture toughness of ferroelectric ceramics with electric field applied parallel to the crack front. Acta Mater 52(12):3435–3446CrossRef
38.
Wang J, Zhang TY (2007) Phase field simulations of polarization switching-induced toughening in ferroelectric ceramics. Acta Mater 55(7):2465–2477CrossRef
39.
Xu BX, Schrade D, Gross D, Mueller R (2010) Phase field simulation of domain structures in cracked ferroelectrics. Int J Fract 165:163–173CrossRefMATH
40.
Zhang TY, Gao CF (2004) Fracture behaviors of piezoelectric materials. Theor Appl Fract Mech 41(1–3):339–379CrossRef
Metadata
Title
Interaction of Cracks and Domain Structures in Thin Ferroelectric Films
Authors
D. Schrade
R. Müller
D. Gross
Copyright Year
2016
Book
Recent Trends in Fracture and Damage Mechanics

Print ISBN: 978-3-319-21466-5

Electronic ISBN: 978-3-319-21467-2

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-21467-2_10

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