A Mode-III strip saturation model for two collinear semi-permeable cracks in a piezoelectric media

R.R.Bhargava; Kamlesh Jangid; Pavitra Tripathi; R.R.Bhargava; Kamlesh Jangid; Pavitra Tripathi

doi:10.3934/matersci.2016.4.1507

AIMS Materials Science

2016, Volume 3, Issue 4: 1507-1519. doi: 10.3934/matersci.2016.4.1507

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A Mode-III strip saturation model for two collinear semi-permeable cracks in a piezoelectric media

1.
Department of Mathematics, Indian Institute of Technology, Roorkee-247667, India
2.
Department of Humanities English & Applied Sciences, Rajasthan Technical University, Kota-324010, India

Received: 25 August 2016 Accepted: 31 October 2016 Published: 10 November 2016

In this paper, a mode-III strip-saturation model is proposed for a piezoelectric ceramic plate weakened by two equal collinear, semi-permeable hairline cracks. A mathematical model is obtained using Stroh’s formalism and solved using matrix Hilbert problem. Analytic closed form expressions are derived for various fracture parameters such as crack sliding displacement, crack opening potential drop, field intensity factor and energy release rate. An illustrative numerical case study is presented for impermeable, semi-permeable and permeable crack face boundary conditions for different piezoceramics. The results obtained are presented graphically, discussed and concluded. It is observed that the model proposed is capable of crack arrest under small-scale electric saturation.
- crack sliding displacement,
- energy release rate,
- piezoelectric ceramics,
- saturation zone,
- semi-permeable cracks
Citation: R.R.Bhargava, Kamlesh Jangid, Pavitra Tripathi. A Mode-III strip saturation model for two collinear semi-permeable cracks in a piezoelectric media[J]. AIMS Materials Science, 2016, 3(4): 1507-1519. doi: 10.3934/matersci.2016.4.1507

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Abstract

In this paper, a mode-III strip-saturation model is proposed for a piezoelectric ceramic plate weakened by two equal collinear, semi-permeable hairline cracks. A mathematical model is obtained using Stroh’s formalism and solved using matrix Hilbert problem. Analytic closed form expressions are derived for various fracture parameters such as crack sliding displacement, crack opening potential drop, field intensity factor and energy release rate. An illustrative numerical case study is presented for impermeable, semi-permeable and permeable crack face boundary conditions for different piezoceramics. The results obtained are presented graphically, discussed and concluded. It is observed that the model proposed is capable of crack arrest under small-scale electric saturation.

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