×

zbMATH — the first resource for mathematics

Singularity analysis of planar cracks in three-dimensional piezoelectric semiconductors via extended displacement discontinuity boundary integral equation method. (English) Zbl 1403.74266
Summary: The displacement discontinuity boundary integral equation method is extended to analyze the singularity of near-border fields of the planar crack of arbitrary shape in the isotropic plane of a three-dimensional transversely isotropic piezoelectric semiconductor. The hyper-singular boundary integral equations are derived in terms of the displacement, electric potential and carrier density discontinuities across the crack faces, in which body integrals for the carrier density are introduced. Based on the finite-part integrals, singularity exponents and asymptotic expressions of the crack border fields are obtained. The stress, electric displacement and electric current intensity factors are given in terms of the displacement, electric potential and carrier density discontinuities. Finite element results for penny-shaped and line cracks based on the piezoelectric-conductor iterative method are used to verify the derivations of the intensity factors.

MSC:
74S15 Boundary element methods applied to problems in solid mechanics
65N38 Boundary element methods for boundary value problems involving PDEs
74F15 Electromagnetic effects in solid mechanics
74R10 Brittle fracture
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Hutson, A. R., Piezoelectricity and conductivity in zno and cds, Phys Rev Lett, 4, 505-507, (1960)
[2] White, D. L., Amplification of ultrasonic waves in piezoelectric semiconductors, J Appl Phys, 33, 2547-2554, (1962) · Zbl 0105.22802
[3] Hutson, A. R.; White, D. L., Elastic wave propagation in piezoelectric semiconductors, J Appl Phys, 33, 40-47, (1962)
[4] Yang, J. S.; Zhou, H. G., Amplification of acoustic waves in piezoelectric semiconductor plates, Int J Solids Struct, 42, 3171-3183, (2005) · Zbl 1123.74031
[5] Dahiya, R. S.; Metta, G.; Valle, M.; Adami, A., Piezoelectric oxide semiconductor field effect transistor touch sensing devices, Appl Phys Lett, 95, 034105, (2009)
[6] Rees, G. J., Strained layer piezoelectric semiconductor devices, Microelectron J, 28, 957-967, (1997)
[7] Withers, R. S., Electron devices on piezoelectric semiconductors: a device model, IEEE Trans Son Ultrason, 31, 117-123, (1984)
[8] Wu, W. Z.; Wang, L.; Li, Y. L.; Zhang, F.; Lin, L.; Niu, S.; Chenet, D.; Zhang, X.; Hao, Y. F.; Heinz, T. F.; Hone, J.; Wang, Z. L., Piezoelectricity of single-atomic-layer mos2 for energy conversion and piezotronics, Nature, 514, 470-474, (2014)
[9] Hickernell, F. S., The piezoelectric semiconductor and acoustoelectronic device development in the sixties, IEEE Trans Ultrason Ferroelectr Freq Control, 5, 737-745, (2005)
[10] Wang, X. D.; Zhou, J.; Song, J. H.; Liu, J.; Xu, N. S.; Wang, Z. L., Piezoelectric field effect transistor and nanoforce sensor based on a single zno nanowire, Nano Lett, 6, 2768-2772, (2006)
[11] Liu, Y.; Zhang, Y.; Yang, Q.; Niu, S. M.; Wang, Z. L., Fundamental theories of piezotronics and piezo-phototronics, Nano Energy, 14, 257-275, (2015)
[12] Wen, X. N.; Wu, W. Z.; Pan, C. F.; Hu, Y. F.; Yang, Q.; Wang, Z. L., Development and progress in piezotronics, Nano Energy, 14, 276-295, (2015)
[13] del Alamo, J. A.; Joh, J., Gan HEMT reliability, Microelectron Reliab, 49, 1200-1206, (2009)
[14] Yang, J. S., An anti-plane crack in a piezoelectric semiconductor, Int J Fract, 136, L27-L32, (2005) · Zbl 1197.74145
[15] Hu, Y. T.; Zeng, Y.; Yang, J. S., A mode III crack in a piezoelectric semiconductor of crystals with 6 mm symmetry, Int J Solids Struct, 44, 3928-3938, (2007) · Zbl 1124.74043
[16] Sladek, J.; Sladek, V.; Pan, E.; Young, D. L., Dynamic anti-plane crack analysis in functional graded piezoelectric semiconductor crystals, CMES-Comput Model Eng Sci, 99, 273-296, (2014) · Zbl 1356.74188
[17] Sladek, J.; Sladek, V.; Pan, E.; Wünsche, M., Fracture analysis in piezoelectric semiconductors under a thermal load, Eng Fract Mech, 126, 27-39, (2014)
[18] Sladek, J.; Sladek, V.; Bishay, P. L.; Garcia-Sanche, F., Influence of electric conductivity on intensity factors for cracks in functionally graded piezoelectric semiconductors, Int J Solids Struct, 59, 79-89, (2015)
[19] Fan, C. Y.; Yan, Y.; Xu, G. T.; Zhao, M. H., Piezoelectric-conductor iterative method for fracture analysis of piezoelectric semiconductors via the finite element method, Eng Fract Mech, (2016), (to be published)
[20] Snyder, M. D.; Cruse, T. A., Boundary-integral equation analysis of cracked anisotropic plates, Int J Fract, 11, 315-327, (1975)
[21] Blandford, G. E.; Ingraffea, A. R.; Liggett, J. A., Two-dimensional stress intensity factor computations using the boundary element method, Int J Numer Meth Eng, 17, 387-404, (1981) · Zbl 0463.73082
[22] Hong, H. K.; Chen, J. T., Derivations of integral equations of elasticity, J Eng Mech, 114, 1028-1044, (1988)
[23] Crouch, S. L., Solution of plane elasticity problems by the displacement discontinuity method. I. infinite body solution, Int J Numer Meth Eng, 10, 301-343, (1976) · Zbl 0322.73016
[24] Zhao, M. H.; Cheng, C. J.; Liu, Y. J., Boundary integral equations and boundary element method for three-dimensional fracture mechanics, Eng Anal Bound Elem, 13, 333-338, (1994)
[25] Sladek, V.; Sladek, J., Three dimensional crack analysis for an anisotropic body, Appl Math Model, 6, 374-380, (1982) · Zbl 0492.73102
[26] Sladek, V.; Sladek, J., Three-dimensional curved crack in an elastic body, Int J Solids Struct, 19, 425-436, (1983) · Zbl 0512.73086
[27] Zhao, M. H.; Shen, Y. P.; Liu, Y. J.; Liu, G. N., Isolated crack in three-dimensional piezcelectric solid: part II - stress intensity factors for circular crack, Theor Appl Fract Mech, 26, 141-149, (1997)
[28] Zhao, M. H.; Fan, C. Y.; Yang, F.; Liu, T., Analysis method of planar cracks of arbitrary shape in the isotropic plane of a three-dimensional transverselyisotropic magnetoelectroelastic medium, Int J Solids Struct, 44, 4505-4523, (2007) · Zbl 1175.74077
[29] Hong, H. K.; Chen, J. T., Generality and special cases of dual integral equations of elasticity, J Chin Soc Mech Eng, 9, 1-9, (1988)
[30] Liu, Y. J.; Li, Y. X., Revisit of the equivalence of the displacement discontinuity method and boundary element method for solving crack problems, Eng Anal Bound Elem, 47, 64-67, (2014) · Zbl 1297.74106
[31] Sadao, A., Properties of group-IV, III-V and II-VI semiconductors, (2005), John Wiley & Sons England
[32] Navon, D. H., Semiconductor Microdevices and Materials, (1986), CBS College New York
[33] Ding, H. J.; Chen, W. Q.; Jiang, A. M., Green׳s functions and boundary element method for transversely isotropic piezoelectric materials, Eng Anal Bound Elem, 28, 975-987, (2004) · Zbl 1112.74550
[34] Wang, X. M.; Shen, Y. P., Theorem of work reciprocity for pyroelectricelastic media with application, Acta Mech Sin, 28, 244-250, (1996), [in Chinese]
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.