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Strip-coalesced interior zone model for two unequal collinear cracks weakening piezoelectric media

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Abstract

In this paper, a mathematical strip-saturation model is proposed for a poled transversely isotropic piezoelectric plate weakened by two impermeable unequal-collinear hairline straight cracks. Remotely applied in-plane unidirectional electromechanical loads open the cracks in mode-I such that the saturation zone developed at the interior tips of cracks gets coalesced. The developed saturation zones are arrested by distributing over their rims in-plane normal cohesive electrical displacement. The problem is solved using the Stroh formalism and the complex variable technique. The expressions are derived for the stress intensity factors (SIFs), the lengths of the saturation zones developed, the crack opening displacement (COD), and the energy release rate. An illustrative numerical case study is presented for the poled PZT-5H ceramic to investigate the effect of prescribed electromechanical loads on parameters affecting crack arrest. Also, the effect of different lengths of cracks on the SIFs and the local energy release rate (LERR) has been studied. The results obtained are graphically presented and analyzed.

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Authors and Affiliations

  1. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, 247667, India

    R. R. Bhargava & K. Jangid

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  1. R. R. Bhargava
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  2. K. Jangid
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Correspondence to K. Jangid.

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Bhargava, R.R., Jangid, K. Strip-coalesced interior zone model for two unequal collinear cracks weakening piezoelectric media. Appl. Math. Mech.-Engl. Ed. 35, 1249–1260 (2014). https://doi.org/10.1007/s10483-014-1890-9

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  • DOI: https://doi.org/10.1007/s10483-014-1890-9

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