Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic

Gao, Hangshan; Zhang, Tong‐Yi; Tong, Penger

doi:10.1016/s0022-5096(96)00108-1

Cited by 456 publications

(217 citation statements)

References 27 publications

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“…The results in Fig. 9 show that the approximate field solution of [5] could predict the correct crack growth behavior for Case I if the energy density criterion is used instead of that based on the energy release rate. The objection of a negative energy release rate can thus be removed.…”

Section: Normalized Crack Growth Segmentsmentioning

confidence: 96%

“…An assessment of this phenomenon was made in [12,13] by solving the exact piezoelastic field equations and applying the energy density criterion. When the results of failure analysis [4,5] disagrees with those found by tests, there exists the possibilities that the field solution or the failure criterion is at fault. It is also possible that both the field solution and failure criterion are incorrect.…”

Section: Criterion For Crack Initiation and Growthmentioning

confidence: 96%

“…It is also possible that both the field solution and failure criterion are incorrect. To be shown is that the simplified version of the field solution [5] can explain crack growth enhancement and retardation if the energy release rate criterion is replaced by the energy density criterion that has the capability to treat multiscale crack extension behavior.…”

Section: Criterion For Crack Initiation and Growthmentioning

confidence: 99%

“…The challenge is to test the same criterion for different field solutions under different conditions. One of the objectives of this work is to demonstrate that the phenomenon of crack growth enhancement and retardation can be explained by combining a field solution with the appropriate fracture criterion while the oversimplified criterion may lead to disagreement with test data [4,5] and results that contradict physics [1,6] such as negative energy release rate.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A field model interpretation of crack initiation and growth behavior in ferroelectric ceramics: change of poling direction and boundary condition

Sih

2002

Theoretical and Applied Fracture Mechanics

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Strain energy density expressions are obtained from a field model that can qualitatively exhibit how the electrical and mechanical disturbances would affect the crack growth behavior in ferroelectric ceramics. Simplification is achieved by considering only three material constants to account for elastic, piezoelectric and dielectric effects. Cross interaction of electric field (or displacement) with mechanical stress (or strain) is identified with the piezoelectric effect; it occurs only when the pole is aligned normal to the crack. Switching of the pole axis by 90°and 180°is examined for possible connection with domain switching. Opposing crack growth behavior can be obtained when the specification of mechanical stress r 1 and electric field E 1 or ðr 1 ; E 1 Þ is replaced by strain 1 and electric displacement D 1 or ð 1 ; D 1 Þ. Mixed conditions ðr 1 ; D 1 Þ and ð 1 ; E 1 Þ are also considered. In general, crack growth is found to be larger when compared to that without the application of electric disturbances. This includes both the electric field and displacement. For the eight possible boundary conditions, crack growth retardation is identified only with ðE 1 y ; r 1 y Þ for negative E 1 y and ðD 1 y ; 1 y Þ for positive D 1 y while the mechanical conditions r 1 y or 1 y are not changed. Suitable combinations of the elastic, piezoelectric and dielectric material constants could also be made to suppress crack growth.

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Section: Normalized Crack Growth Segmentsmentioning

confidence: 96%

Section: Criterion For Crack Initiation and Growthmentioning

confidence: 96%

Section: Criterion For Crack Initiation and Growthmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A field model interpretation of crack initiation and growth behavior in ferroelectric ceramics: change of poling direction and boundary condition

Sih

2002

Theoretical and Applied Fracture Mechanics

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“…It is even less remotely concerned with brittle and ductile fracture [38]. Unsuccessful attempts made to explain the enhancement and retardation of crack growth due to electric ®eld reversal [31,32] are indicative of the limitation of the energy release rate concept.…”

Section: Stable and Non-stable Growthmentioning

confidence: 99%

Mesofracture mechanics: a necessary link

Sih

Liu

2001

Theoretical and Applied Fracture Mechanics

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Classical fracture mechanics is based on the premise that small scale features could be averaged to give a larger scale property such that the assumption of material homogeneity would hold. Involvement of the material microstructure, however, necessitates di erent characteristic lengths for describing di erent geometric features. Macroscopic parameters could not be freely exchanged with those at the microscopic scale level. Such a practice could cause misinterpretation of test data. Ambiguities arising from the lack of a more precise range of limitations for the de®nitions of physical parameters are discussed in connection with material length scales. Physical events overlooked between the macroscopic and microscopic scale could be the link that is needed to bridge the gap. The classical models for the creation of free surface for a liquid and solid are oversimpli®ed. They consider only the translational motion of individual atoms. Movements of groups or clusters of molecules deserve attention. Multiscale cracking behavior also requires the distinction of material damage involving at least two di erent scales in a single simulation. In this connection, special attention should be given to the use of asymptotic solution in contrast to the full ®eld solution when applying fracture criteria. The former may leave out detail features that would have otherwise been included by the latter. Illustrations are provided for predicting the crack initiation sites of piezoceramics. No de®nite conclusions can be drawn from the atomistic simulation models such as those used in molecular dynamics until the non-equilibrium boundary conditions can be better understood. The speci®cation of strain rates and temperatures should be synchronized as the specimen size is reduced to microns. Many of the results obtained at the atomic scale should be ®rst identi®ed with those at the mesoscale before they are assumed to be connected with macroscopic observations. Hopefully,``mesofracture mechanics'' could serve as the link to bring macrofracture mechanics closer to microfracture mechanics. Ó

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A partition of unity‐based multiscale approach for modelling fracture in piezoelectric ceramics

Verhoosel

Remmers

Gutiérrez

2009

Numerical Meth Engineering

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SUMMARYThe development of models for a priori assessment of the reliability of micro electromechanical systems is of crucial importance for the further development of such devices. In this contribution a partition of unity-based cohesive zone finite element model is employed to mimic crack nucleation and propagation in a piezoelectric continuum. A multiscale framework to appropriately represent the influence of the microstructure on the response of a miniaturized component is proposed. It is illustrated that using the proposed multiscale method a representative volume element exists. Numerical simulations are performed to demonstrate the constitutive homogenization framework.

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Local and global energy release rates for an electrically yielded crack in a piezoelectric ceramic

Cited by 456 publications

References 27 publications

A field model interpretation of crack initiation and growth behavior in ferroelectric ceramics: change of poling direction and boundary condition

A field model interpretation of crack initiation and growth behavior in ferroelectric ceramics: change of poling direction and boundary condition

Mesofracture mechanics: a necessary link

A partition of unity‐based multiscale approach for modelling fracture in piezoelectric ceramics

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