Skip to main content
SpringerLink
Log in

Electrostatic tractions at crack faces and their influence on the fracture mechanics of piezoelectrics

  • Original Paper
  • Published:
International Journal of Fracture Aims and scope Submit manuscript

Abstract

The influence of electrostatic tractions acting upon crack faces on the fracture mechanical quantities in piezoelectric materials under electromechanical loading is investigated. The physical background are the mechanical and dielectric equilibria at an interface between two dielectric domains and related mechanical stresses. The model is applied to a crack problem, where a dielectric interface exists between the solid material and the insulating crack medium. The analytical solution for a crack in an infinite piezoelectric body accounting for intrinsic charges and electrostatic stresses on the crack faces gives insight into the influence of crack boundary conditions on the field intensity factors. Varying loading conditions and the dielectric permittivity of the flaw yields a parameter range in which induced crack surface tractions are relevant. Then, the calculation of the J-integral for thermodynamically consistent crack boundary conditions is discussed. The line integral along the crack faces is replaced by a simple jump term. This approach comes out to be exact only for a simplified model of the electrostatic tractions.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Barenblatt GI (1962) The mathematical theory of equilibrium cracks in brittle fracture. Academic Press (Adv Appl Mech) 7: 55–129

    MathSciNet  Google Scholar 

  • Cherepanov G (1967) Rasprostranenie trechin v sploshnoi srede (About crack advance in the continuum). Prikladnaja Matematika i Mekhanica 31: 478–488

    Google Scholar 

  • Dugdale D (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8: 100–104

    Article  ADS  Google Scholar 

  • Eshelby JD (1951) The force on an elastic singularity. Phil Trans R Soc Lond A 244: 87–112

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • Eshelby JD (1975) The elastic energy-momentum tensor. J Elast 5: 321–335

    Article  MATH  MathSciNet  Google Scholar 

  • Hao TH, Shen ZY (1994) A new electric boundary condition of electric fracture mechanics and its applications. Eng Fract Mech 47: 793–802

    Article  Google Scholar 

  • Kemmer G, Balke H (1999) Kraftwirkung auf die Flanken nichtleitender Risse in Piezoelektrika. In: GAMM 98 (short communications in mathematics and mechanics, ZAMM), 79, pp 509–510

  • Landis CM (2004) Energetically consistent boundary conditions for electromechanical fracture. Int J Solids Struct 41: 6291–6315

    Article  MATH  Google Scholar 

  • Landis CM, McMeeking RM (2000) Modeling of fracture in ferroelectric ceramics. In: Proceedings of SPIE, 3992, pp 176–184

  • Lenk A (1974) Elektromechanische Systeme, Band 2 (Systeme mit verteilten Parametern). VEB Verlag Technik, Berlin

    Google Scholar 

  • Maugin GA, Epstein M (1991) The electroelastic energy-momentum tensor. Proc R Soc Lond A 433: 299–312

    Article  MATH  ADS  MathSciNet  Google Scholar 

  • McMeeking RM (1989) Electrostrictive stresses near crack-like flaws. J Appl Math Phys (ZAMP) 40: 615–627

    Article  MATH  Google Scholar 

  • McMeeking RM (1999) Crack tip energy release rate for a piezoelectric compact tension specimen. Eng Fract Mech 64: 217–244

    Article  Google Scholar 

  • McMeeking RM (2004) The energy release rate for a Griffith crack in a piezoelectric material. Eng Fract Mech 71: 1169–1183

    Google Scholar 

  • Pak YE (1990) Crack extension force in a piezoelectric material. J Appl Mech 57: 647–653

    Article  MATH  Google Scholar 

  • Pak YE (1992) Linear electro-elastic fracture mechanics of piezoelectric materials. Int J Fract 54: 79–100

    Article  CAS  Google Scholar 

  • Pak YE, Herrmann G (1986) Conservation laws and the material momentum tensor for the elastic dielectric. Int J Eng Sci 24: 1365–1374

    Article  MATH  MathSciNet  Google Scholar 

  • Parton VZ (1976) Fracture mechanics of piezoelectric materials. Acta Astronaut 3: 671–683

    Article  MATH  Google Scholar 

  • Rice JR (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. J Appl Mech 35: 379–386

    Google Scholar 

  • Ricoeur A, Kuna M (2003) Influence of electric fields on the fracture of ferroelectric ceramics. J Eur Ceram Soc 23: 1313–1328

    Article  CAS  Google Scholar 

  • Ricoeur A, Kuna M, (2008) Electrostatic tractions at dielectric interfaces and their implication for crack boundary conditions. Mech Res Commun. doi:10.1016/j.mechrescom.2008.09.009

  • Ricoeur A, Enderlein M, Kuna M (2005) Calculation of the J-integral for limited permeable cracks in piezoelectrics. Arch Appl Mech 74: 536–549

    Article  MATH  Google Scholar 

  • 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: 2235–2241

    Article  CAS  Google Scholar 

  • 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

    Article  CAS  Google Scholar 

  • Wippler K, Ricoeur A, Kuna M (2004) Towards the computation of electrically permeable cracks in piezoelectrics. Eng Fract Mech 71: 2567–2587

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. TU Bergakademie Freiberg, Institute of Mechanics and Fluid Dynamics, Lampadiusstraße 4, 09596, Freiberg, Germany

    A. Ricoeur & M. Kuna

Authors
  1. A. Ricoeur
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Kuna
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Ricoeur.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ricoeur, A., Kuna, M. Electrostatic tractions at crack faces and their influence on the fracture mechanics of piezoelectrics. Int J Fract 157, 3–12 (2009). https://doi.org/10.1007/s10704-009-9321-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10704-009-9321-z

Keywords

Search

Navigation