What Do We Know About Surface Charges on Cracks in Ferroelectric Ceramics?

  • Andrea R. Engert
  • Frank Felten
  • Hans Jelitto
  • Gerold A. SchneiderEmail author
Conference paper
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 24)


The present work investigates the static and time dependent electric potential distribution around cracks in a poled ferroelectric ceramic by Kelvin Probe Force Microscopy (KFM). In a first step a Vickers indentation crack in poled lead zirconate titanate (PZT) was subjected to static electric fields of up to 500V/mm in poling direction, and the potential distribution around the crack was measured. In a second step, the polarity of the applied voltage was reversed against the poling direction during the measurement of the potential. Using a simple model, an effective dielectric constant of the crack, as well as the surface charge density on the crack face were calculated as a function of the distance from the crack tip, the applied field and the time. The results are discussed with reference to free charges on the crack surface, electrically induced domain switching at the crack tip and crack bridging.


Crack Surface Applied Electric Field Crack Opening Displacement Crack Path Surface Charge Density 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We thank Rodrigo Pacher Fernandez and Claudia Neusel for the measurement of the electrical conductivity of PZT and the DFG (German Science Foundation) for supporting this project under the grant number SCHN 372/12-2.


  1. 1.
    Balke H, Kemmer G, Drescher J (1997) Some remarks on the fracture mechanics of piezoelectric solids. MicroMaterials Conference “MicroMat 1997”, pp 398–401Google Scholar
  2. 2.
    Hao TH, Shen ZY (1994) A new electric boundary-condition of electric fracture-mechanics and its applications. Eng Fract Mech 47(6):793–802CrossRefGoogle Scholar
  3. 3.
    McMeeking RM (2004) The energy release rate for a Griffith crack in a piezoelectric material. Eng Fract Mech 71(7–8):1149–1163CrossRefGoogle Scholar
  4. 4.
    Landis CM (2004) Energetically consistent boundary conditions for electromechanical fracture. Int J Solids Struct 41(22–23):6291–6315zbMATHCrossRefGoogle Scholar
  5. 5.
    Landis CM (2005) Energetically consistent boundary conditions for electromechanical fracture (Erratum, vol 41, pg 6291, 2004). Int J Solids Struct 42(8):2461–2463zbMATHCrossRefGoogle Scholar
  6. 6.
    Li WY, McMeeking RM, Landis CM (2008) On the crack face boundary conditions in electromechanical fracture and an experimental protocol for determining energy release rates. Eur J Mech A-Solids 27(3):285–301zbMATHCrossRefGoogle Scholar
  7. 7.
    Jelitto H, Felten F, Swain MV, Balke H, Schneider GA (2007) Measurement of the total energy release rate for cracks in PZT under combined mechanical and electrical loading. J Appl Mech-Trans ASME 74(6):1197–1211CrossRefGoogle Scholar
  8. 8.
    Jelitto H, Felten F, Hausler C, Kessler H, Balke H, Schneider GA (2005) Measurement of energy release rates for cracks in PZT under electromechanical loads. J Eur Ceram Soc 25(12):2817–2820CrossRefGoogle Scholar
  9. 9.
    Jelitto H, Kessler H, Schneider GA, Balke H (2005) Fracture behavior of poled piezoelectric PZT under mechanical and electrical loads. J Eur Ceram Soc 25(5):749–757CrossRefGoogle Scholar
  10. 10.
    Häusler C, Jelitto H, Neumeister P, Balke H, Schneider GA (2009) Interfacial fracture of piezoelectric multilayer actuators under mechanical and electrical loading. Int J Fract 160(1):43–54CrossRefGoogle Scholar
  11. 11.
    Haug A, McMeeking RM (2006) Cracks with surface charge in poled ferroelectrics. Eur J Mech A-Solids 25(1):24–41zbMATHCrossRefGoogle Scholar
  12. 12.
    Schneider GA, Felten F, McMeeking RM (2003) The electrical potential difference across cracks in PZT measured by Kelvin Probe Microscopy and the implications for fracture. Acta Mater 51(8):2235–2241CrossRefGoogle Scholar
  13. 13.
    Felten F (2006) PhD thesis: Anwendung der Rastersondenmikroskopie zur Bestimmung bruchmechanischer Parameter und lokaler piezoelektrischer Eigenschaften von Ferroelektrika. Book series: Berichte aus der Materialwissenschaft, Shaker Verlag,AachenGoogle Scholar
  14. 14.
    Kalinin SV, Bonnell DA (2001) Local potential and polarization screening on ferroelectric surfaces. Phys Rev B 63(12):125411CrossRefGoogle Scholar
  15. 15.
    Jacobs HO, Leuchtmann P, Homan OJ, Stemmer A (1998) Resolution and contrast in Kelvin probe force microscopy. J Appl Phys 84(3):1168–1173CrossRefGoogle Scholar
  16. 16.
    Johnson Matthey (2009) Piezoceramic Masses. Online available from: or
  17. 17.
    Lawn BR (1993) Fracture of brittle solids. book series: Cambridge solid state science series, 2 edn. Cambridge University Press, CambridgeGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2011

Authors and Affiliations

  • Andrea R. Engert
    • 1
  • Frank Felten
    • 2
  • Hans Jelitto
    • 1
  • Gerold A. Schneider
    • 1
    Email author
  1. 1.Institut für keramische HochleistungswerkstoffeTechnische Universität Hamburg-HarburgHamburgGermany
  2. 2.Robert Bosch GmbH, Corporate Sector Research and Advance EngineeringStuttgartGermany

Personalised recommendations