A simplified evaluation of the mechanical energy release rate of kinked cracks in piezoelectric materials using the boundary element method

Published on Jul 14, 2017in Engineering Fracture Mechanics4.406
路 DOI :10.1016/J.ENGFRACMECH.2017.07.008
Jun Lei11
Estimated H-index: 11
(Beijing University of Technology),
Chuanzeng Zhang35
Estimated H-index: 35
(University of Siegen)
Sources
Abstract
Abstract Based on the concept of the hoop field intensity factors of an initial crack prior to any kink, an apparent hoop mechanical (strain) energy release rate (MERR) is defined to approximate the MERR of a piezoelectric crack with an infinitesimal kink at any arbitrary angle. The validity and the efficiency of the simplified approximation are examined by numerical examples using the boundary element method (BEM). The generalized crack-opening-displacements or displacement jumps are computed by the traction boundary integral equations (BIEs). By using the displacement extrapolation method, the crack-tip field intensity factors of any arbitrarily kinked crack in linear piezoelectric materials are obtained and the BEM results are validated by comparing them with the available reference analytical results. Then, the differences between the conventional field intensity factors and MERR of an infinitesimally kinked crack and the hoop field intensity factors and hoop MERR of the main crack prior to any kink are numerically analyzed. Finally, the crack propagation in an infinite linear piezoelectric material is numerically simulated. The paths of the crack growth are predicted by adopting four different fracture criteria, namely, the maximum hoop stress intensity factor (SIF) and MERR fracture criteria for the main crack-tip before the next propagation, and the maximum KI and MERR fracture criteria for the kinked tip of the main crack with an infinitesimal branch at an arbitrary kinking angle evaluated by using a trial crack extension technique. The comparisons among these results show that the present simplified approximation can efficiently provide a sufficient accuracy for numerical simulation of crack growth in linear piezoelectric materials.
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Abstract To evaluate the crack-tip field intensity factors of a piezoelectric crack with any inclined angle, the current widely-used interaction integral method (I-integral) is here extended to the boundary element applications under some coordinate transformations. As well, a new modified crack closure integral method (MCCI) is proposed by considering the discontinuous quarter-point singular elements for the crack-face discretization arising from the dual boundary element method (BEM). This dua...
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From the viewpoint of fracture mechanics, of importance is the near-tip field which can be characterized as field intensity factors. In this paper, the crack-tip field intensity factors of the stress and electric displacement in two dimensional piezoelectric solids are evaluated by using four approaches including the displacement extrapolation, the stress method, the J-integral and the modified crack closure integral method (MCCI) based on a boundary element method (BEM). The strongly singular d...
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#1S X Xu (Cornell University)H-Index: 1
#2R. K. N. D. Rajapakse (UBC: University of British Columbia)H-Index: 44
Applicability of energy release rate criteria to piezoelectric materials is examined in this paper. The angular distribution of strain and total energy release rates at a crack tip in a plane piezoelectric medium is first formulated by using a branched crack model. By relaxing the commonly held assumption of self-similar crack propagation and incorporating in the fracture toughness anisotropy, the criteria of modified strain energy release rate and modified total energy release rate are applied ...
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Abstract Any attempt made to separate energy into electrical and mechanical parts may lead to inconsistencies as they do not necessarily decouple. This is illustrated by application of the energy density function in the linear theory of piezoelasticity. By assuming that a critical energy density function prevails at the onset of crack initiation, it is possible to establish the relative size of an inner and outer damage zone around the crack tip; they correspond to the ligaments at failure cause...
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#1X.-L. Xu (UM: University of Manitoba)H-Index: 2
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Abstract The plane problem of a brittle piezoceramic with an arbitrarily oriented branched crack is theoretically investigated in this study. Lekhnitskii鈥檚 complex potentials and a distributed dislocation model are employed to formulate the problem. The crack closure is taken into consideration. The branched crack problem is reduced to solving three singular integral equations. The accuracy of the present scheme is confirmed by comparison with the existing results in the literature. The results ...
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Abstract The intrinsic coupling between the mechanical and the electric fields assigns a uniquefeature for the fracture in a piezoelectric solid. We model the kink of a crack by continuousdistribution of edge dislocations and electric dipoles. The problem admits an approach based onthe Stroh formalism. A set of coupled singular integral equations are derived for the dislocationand electric dipole density functions associated with a kinked crack. Numerical results indicatethat the crack tends to ...
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