Influence of poling angle on a mode-III non-centric semi-permeable crack in the piezoelectric strip under linearly varying load over developed zones

References

• B.L. Wang and Y.W. Mai, On the electrical boundary conditions on the crack surfaces in piezoelectric ceramics, Int. J. Eng. Sci., vol. 41, no. 6, pp. 633–652, 2003. DOI: 10.1016/S0020-7225(02)00149-0.
   Web of Science ®Google Scholar
• Y.D. Li and K.Y. Lee, The shielding effect of the imperfect interface on a mode III permeable crack in a layered piezoelectric sensor, Eng. Fract. Mech., vol. 76, no. 7, pp. 876–883, 2009. DOI: 10.1016/j.engfracmech.2008.12.011.
   Web of Science ®Google Scholar
• R.R. Bhargava and P.R. Verma, Strip-electro-mechanical yield model for transversely situated two semi-permeable collinear cracks in piezoelectric strip, Theor. App. Fract. Mech., vol. 81, pp. 32–49, 2016. DOI: 10.1016/j.tafmec.2015.10.009.
   Web of Science ®Google Scholar
• R.R. Bhargava and P.R. Verma, A study of crack-face boundary conditions for piezoelectric strip cut along two equal collinear cracks, Adv. Appl. Math. Mech., vol. 8, no. 4, pp. 573–587, 2016. DOI: 10.4208/aamm.2014.m866.
   Web of Science ®Google Scholar
• X. Zhong, Y. Wu, and K. Zhang, An extended dielectric crack model for fracture analysis of a thermopiezoelectric strip, Acta Mech. Solida Sin., vol. 33, no. 4, pp. 521–545, 2020. DOI: 10.1007/s10338-019-00149-9.
   Web of Science ®Google Scholar
• F. Narita and Y. Shindo, Anti-plane shear crack growth rate of piezo-electric ceramic body with finite width, Theor. App. Fract. Mech., vol. 30, no. 2, pp. 127–132, 1998. DOI: 10.1016/S0167-8442(98)00049-4.
   Web of Science ®Google Scholar
• F. Narita and Y. Shindo, Fatigue crack propagation in a piezoelectric ceramic strip subjected to mode-III loading, Acta Mech., vol. 137, no. 1-2, pp. 55–63, 1999. DOI: 10.1007/BF01313144.
   Web of Science ®Google Scholar
• C.Q. Ru, Effect of electrical polarization saturation on stress intensity factors in a piezoelectric ceramic, Int. J. Solids Struct., vol. 36, no. 6, pp. 869–883, 1999. DOI: 10.1016/S0020-7683(97)00331-4.
   Web of Science ®Google Scholar
• V. Loboda, Y. Lapusta, and A. Sheveleva, Analysis of pre-fracture zones for an electrically permeable crack in an interlayer piezoelectric materials, Int. J. Fract., vol. 142, no. 3-4, pp. 307–313, 2007. DOI: 10.1007/s10704-006-9034-5.
   Web of Science ®Google Scholar
• X.C. Zhong and K.S. Zhang, Electroelastic analysis of an electrically dielectric Griffith crack in piezoelectric layer, Int. J. Eng. Sci., vol. 48, no. 6, pp. 612–623, 2010. DOI: 10.1016/j.ijengsci.2010.02.002.
   Web of Science ®Google Scholar
• D.K. Yi, Z.M. Xiao, J. Zhuang, and I. Sridhar, On the plastic zone size and crack tip opening displacement of a sub-interface crack in an infinite bi-material plate, Philos. Mag., vol. 91, no. 26, pp. 3456–3472, 2011. DOI: 10.1080/14786435.2011.586374.
   Web of Science ®Google Scholar
• C.Y. Fan, Y.F. Zhao, M.H. Zhao, and E. Pan, Analytical solution of a semi-permeable crack in a 2D piezoelectric medium based on the PS model, Mech. Res. Commun., vol. 40, pp. 34–40, 2012. DOI: 10.1016/j.mechrescom.2012.01.001.
   Web of Science ®Google Scholar
• Y. Lapusta, O. Viun, and V. Loboda, Modeling of pre-fracture zones for limited permeable crack in piezoelectric materials, Arch. Appl. Mech., vol. 84, no. 8, pp. 1205–1220, 2014. DOI: 10.1007/s00419-014-0879-1.
   Web of Science ®Google Scholar
• R.R. Bhargava and P.R. Verma, Mathematical model of electrical and mechanical yielding for piezoelectric strip weakened by a non-centric semi-permeable crack, App. Math. Model., vol. 39, no. 2, pp. 531–547, 2015. DOI: 10.1016/j.apm.2014.06.007.
   Web of Science ®Google Scholar
• Z.M. Khelifia, H. Ferdjanib, and A.B. Chaouchec, The mode III problem of a Dugdale-Barenblatt interfacial crack in a FGM strip bonded to a homogeneous strip by the integral method, Eng. Fract. Mech., vol. 223, pp. 1077–1081, 2020.
   Web of Science ®Google Scholar
• L.P. Harrop, Application of a modified Dugdale model to the K vs COD relation, Eng. Fract. Mech., vol. 10, no. 4, pp. 807–816, 1978. DOI: 10.1016/0013-7944(78)90035-8.
   Web of Science ®Google Scholar
• D.S. Dugdale, Yielding of steel sheets containing slits, J. Mech. Phys. Solids, vol. 8, no. 2, pp. 100–104, 1960. DOI: 10.1016/0022-5096(60)90013-2.
   Web of Science ®Google Scholar
• R.R. Bhargava and S. Kumar, Generalised strip yield crack arrest model for a piezoelectric strip with transverse crack, Asian J. Exp. Sci., vol. 22, pp. 67–78, 2008.
   Google Scholar
• R.R. Bhargava and A. Setia, A strip yield model solution for an internally cracked piezoelectric strip, Mech. Compos. Mater., vol. 44, no. 5, pp. 451–464, 2008. DOI: 10.1007/s11029-008-9038-5.
   Web of Science ®Google Scholar
• T.C. Wang, Analysis of strip electric saturation model of crack problem in piezoelectric materials, Int. J. Solids Struct., vol. 37, no. 42, pp. 6031–6049, 2000. DOI: 10.1016/S0020-7683(99)00255-3.
   Web of Science ®Google Scholar
• R.R. Bhargava and N. Saxena, Solution for a cracked piezoelectric plate subjected to variable load on plastic zones under mode-I deformation, J. Mat. Proc. Tech., vol. 164-165, pp. 1495–1499, 2005. DOI: 10.1016/j.jmatprotec.2005.02.087.
   Web of Science ®Google Scholar
• K. Jangid and R.R. Bhargava, Influence of polarization on two unequal semi-permeable cracks in a piezoelectric media, SFC, vol. 10, no. 3-4, pp. 129–144, 2018. DOI: 10.3233/SFC-170205.
   Google Scholar
• S. Singh, K. Sharma, and T.Q. Bui, New analytical solutions for modified polarization saturation models in piezoelectric materials, Meccanica, vol. 54, no. 15, pp. 2443–2459, 2019. DOI: 10.1007/s11012-019-01084-2.
   Web of Science ®Google Scholar
• P.R. Verma and R.R. Verma, Poling angle effect on two mode-III semi-permeable collinear cracks in a piezoelectric strip: Strip-saturation model, Appl. Math. Model., vol. 88, pp. 573–588, 2020. DOI: 10.1016/j.apm.2020.06.063.
   Web of Science ®Google Scholar
• S.M. Kwon, Electrical nonlinear anti-plane shear crack in a functionally graded piezoelectric strip, Int. J. Solids Struct., vol. 40, no. 21, pp. 5649–5667, 2003. DOI: 10.1016/S0020-7683(03)00316-0.
   Web of Science ®Google Scholar
• W.F. Deeg, The Analysis of Dislocation, Crack and Inclusion Problems in Piezoelectric Solids, Stanford University, 1980. PhD thesis,
   Google Scholar
• V.Z. Parton, Fracture mechanics of piezoelectric materials, Acta Astron., vol. 3, no. 9–10, pp. 671–683, 1976. DOI: 10.1016/0094-5765(76)90105-3.
   Google Scholar
• T.H. Hao and Z.Y. Shen, A new electric boundary condition of electric fracture mechanics and its applications, Eng. Fract. Mech., vol. 47, pp. 793–802, 1994.
   Web of Science ®Google Scholar
• I.M. Ryzhik and I.S. Gradshteyn, Table of Integrals, Series and Products, Academic Press, New York, 1965.
   Google Scholar
• S. Shen, T. Nishioka, Z.B. Kuang, and Z. Liu, Nonlinear electromechanical interfacial fracture for piezoelectric materials, Mech. Mater., vol. 32, no. 1, pp. 57–64, 2000. DOI: 10.1016/S0167-6636(99)00036-8.
   Web of Science ®Google Scholar