Calculation of the J-integral for limited permeable cracks in piezoelectrics

Ricoeur, Andreas; Enderlein, M.; Kuna, Meinhard

doi:10.1007/s00419-004-0370-5

Cited by 20 publications

(19 citation statements)

References 25 publications

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“…Moreover, Gauss' integral theorem has been applied to introduce the domain V enclosed by the line S and the limit sign has been omitted on the right hand side. For a limited permeable crack it was shown by Ricoeur et al (2005) that the line integral Eq. 19 with t C 2 = 0 can be replaced by the expression…”

Section: Calculation Of the J-integral For Limited Permeable Cracksmentioning

confidence: 98%

“…On the outer boundary S a it is defined as q = 0, on the inner crack tip contour S it is q = 1. Based on the closed contour S = S a ∪ S + ∪ (−S ) ∪ S − excluding the crack tip singularity, the first component of the J -integral is given by (Ricoeur et al 2005;Ricoeur and Kuna 2003)…”

Section: Calculation Of the J-integral For Limited Permeable Cracksmentioning

confidence: 99%

“…The final section deals with the calculation of the J -integral for arbitrary crack configurations accounting for dielectrically and thermodynamically consistent boundary conditions. A generalization of the procedure outlined by Ricoeur et al (2005) leads to an integral-free term for mechanical and electrical crack face loads which is exact, if simplifying assumptions are made.…”

Section: Introductionmentioning

confidence: 99%

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

Ricoeur

Kuna

2009

Int J Fract

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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.

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Section: Calculation Of the J-integral For Limited Permeable Cracksmentioning

confidence: 98%

Section: Calculation Of the J-integral For Limited Permeable Cracksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Ricoeur

Kuna

2009

Int J Fract

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“…This semiconsistent way of modeling a crack in a dielectric or piezoelectric body is today well estabilished. The efficient calculation of the J -integral including intrinsic crack surface charges has then been investigated by Ricoeur et al [9]. Electrostatic tractions induced on the crack faces have first been included into the considerations by Kemmer and Balke [10].…”

Section: Introductionmentioning

confidence: 99%

Some new aspects of boundary conditions at cracks in piezoelectrics

Gellmann

Ricoeur

2011

Arch Appl Mech

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Fracture mechanical investigations of piezoelectric materials as components of smart structures have become popular in the last 30 years. In the early years of research, boundary conditions at crack faces have been adopted from pure mechanical systems under the assumption that boundaries were traction free. From the electrostatic point of view, cracks have been assumed to be either free of charge or fully permeable. Later, limitedly permeable crack boundary conditions have become popular among the community, nevertheless still assuming traction-free crack faces. Recently, the theoretical framework has been extended to include electrostatically induced mechanical tractions in crack models yielding a significant crack closure effect. However, these models are still simple, neglecting, e.g., the piezoelectric field coupling. In this work, we present an extended model for crack surface tractions yielding some interesting effects. In particular, the orientation of the electrical field with respect to the poling axis becomes important. Furthermore, applying a collinear stress parallel to the crack faces influences the Mode-I stress intensity factor and a Mode-II shear loading couples to the Mode-I SIF.

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“…(1) requires an iterative scheme yielding a distribution of the intrinsic charge density along the crack surfaces. Indeed, Riceour et al [40] considered a dielectric crack surrounded by a piezoelectric solid with intrinsic crack surface charges, whereas Haug and McMeeking [39] considered a crack with extrinsic surface charge, i.e., free charge accumulation. In the present investigation, our attention is focused on the Coulombic traction and its influence on the SIF and ERR without a detailed treatment to clarify the intrinsic crack surface charge [43] or the free charge accumulation [39].…”

Section: Basic Solutions Of Piezoelectric Materials With the Non-zero mentioning

confidence: 99%

Why traction-free? Piezoelectric crack and Coulombic traction

Chen

2007

Arch Appl Mech

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The non-zero traction condition is introduced in piezoelectric crack problems with the unknown Coulombic traction acting on the crack surfaces. An analytical solution under this condition is obtained by means of the generalized Stroh formalism and by accounting for the permittivity of medium inside the crack gap. As the crack in such materials can be thought of as a low-capacitance medium carrying a potential drop, the Coulombic traction always pulls the two opposite surfaces of the crack together. It is proved that under relatively larger mechanical loading and relatively smaller electrical field, the Coulombic traction may be negligible and the previous investigations under the traction-free crack condition may be accepted in a tolerant way, otherwise the Coulombic traction may lead to some erroneous results with over 10% relative errors. It is also shown that, unlike the traction-free crack condition, the applied electric field does change the Mode I stress intensity factor (SIF) for a central crack in an infinite plane piezoelectric material, and in this way may significantly influence piezoelectric fracture. It is also concluded that the variable tendencies of the normalized SIF and the ERR against the applied electric field depend on the mechanical loading levels. This load-dependence feature may lead to a transformation of the normalized SIF and the ERR from an even functional dependence to an odd functional dependence on the applied electric field.

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Calculation of the J-integral for limited permeable cracks in piezoelectrics

Cited by 20 publications

References 25 publications

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

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

Some new aspects of boundary conditions at cracks in piezoelectrics

Why traction-free? Piezoelectric crack and Coulombic traction

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