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Arc-shaped interfacial crack in a non-homogeneous electro-elastic hollow cylinder with orthotropic dielectric layer. (English) Zbl 1293.74383

Summary: The purpose of this present work is to study the arc-shaped interfacial cracking problem in a hollow cylinder that consists of an inner orthotropic dielectric layer and an outer functionally graded piezoelectric layer. Based on the method of variable separation, the problem is reduced to a Cauchy singular integral equation, which is solved by the Lobatto-Chebyshev quadrature technique. Numerical results of the stress intensity factor are obtained and the effects of geometrical and physical quantities on the fracture parameter are surveyed in details.

MSC:

74R10 Brittle fracture
74F15 Electromagnetic effects in solid mechanics
74G70 Stress concentrations, singularities in solid mechanics
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[1] Dai HL, Dai T, Zheng HY (2012) Stresses distributions in a rotating functionally graded piezoelectric hollow cylinder. Meccanica 47:423–436 · Zbl 1293.74096 · doi:10.1007/s11012-011-9447-8
[2] Abd-Alla AM, Abo-Dahab SM, Mahmoud SR (2011) Wave propagation modeling in cylindrical human long wet bones with cavity. Meccanica 46:1413–1428 · Zbl 1271.74312 · doi:10.1007/s11012-010-9398-5
[3] Li YD, Lee KY, Feng FX (2011) Interface edge crack in a multiferroic semicylinder. Meccanica 46:1393–1399 · Zbl 1271.74392 · doi:10.1007/s11012-010-9399-4
[4] Shariyat M (2012) A general nonlinear global-local theory for bending and buckling analyses of imperfect cylindrical laminated and sandwich shells under thermomechanical loads. Meccanica 47:301–319 · Zbl 1293.74299 · doi:10.1007/s11012-011-9438-9
[5] Lin CP (2012) A piezoelectric screw dislocation interacting with a half-plane trimaterial composite. Meccanica. doi: 10.1007/s11012-012-9564-z · Zbl 1293.74105
[6] Yas MH et al. (2012) Three-dimensional free vibration analysis of functionally graded piezoelectric annular plates on elastic foundations. Meccanica 47:1401–1423 · Zbl 1293.74215 · doi:10.1007/s11012-011-9525-y
[7] Gu B, Yu SW, Feng XQ (2002) Transient response of an interface crack between dissimilar piezoelectric layers under mechanical impacts. Int J Solids Struct 39:1743–1756 · Zbl 1040.74042 · doi:10.1016/S0020-7683(02)00013-6
[8] Li XF (2003) Electroelastic analysis of an internal interface crack in a half-Plane consisting of two bonded dissimilar piezoelectric quarter-planes. Meccanica 38:309–323 · Zbl 1032.74551 · doi:10.1023/A:1023329710354
[9] Zhou ZG, Liang J, Wang B (2003) Two collinear permeable cracks in a piezoelectric layer bonded to two half spaces. Meccanica 38:467–475 · Zbl 1062.74600 · doi:10.1023/A:1024672419875
[10] Ueda S (2008) A cracked functionally graded piezoelectric material strip under transient thermal loading. Acta Mech 199:53–70 · Zbl 1148.74023 · doi:10.1007/s00707-007-0561-6
[11] Zhou ZG, Hui JF, Wu LZ (2008) Basic solution of a mode-I limited-permeable crack in functionally graded piezoelectric materials. Meccanica 43:21–35 · Zbl 1163.74546 · doi:10.1007/s11012-007-9091-5
[12] Chue CH, Hsu WH (2008) Antiplane internal crack normal to the edge of a functionally graded piezoelectric/piezomagnetic half plane. Meccanica 43:307–325 · Zbl 1163.74542 · doi:10.1007/s11012-007-9096-0
[13] Li YD, Lee KY (2009) Fracture analysis on the arc-shaped interface in a layered cylindrical piezoelectric sensor polarized along its axis. Eng Fract Mech 76:2065–2073 · doi:10.1016/j.engfracmech.2009.05.017
[14] Li YD, Lee KY (2009) Crack tip shielding and anti-shielding effects of the imperfect interface in a layered piezoelectric sensor. Int J Solids Struct 46:1736–1742 · Zbl 1217.74103 · doi:10.1016/j.ijsolstr.2008.12.023
[15] Hsu WH, Chue CH (2009) Mode III fracture problem of an arbitrarily oriented crack in an FGPM strip bonded to a homogeneous piezoelectric half plane. Meccanica 44:519–534 · Zbl 1258.74187 · doi:10.1007/s11012-008-9188-5
[16] Erasmo V, Claudia B, Giuseppe V (2009) A non-conventional approach for crack problems in piezoelectric media under electromechanical loading. Int J Fract 157:75–192 · Zbl 1308.74053
[17] Li YS, Feng J, Xu ZH (2009) A penny-shaped interface crack between a functionally graded piezoelectric layer and a homogeneous piezoelectric layer. Meccanica 44:377–387 · Zbl 1241.74033 · doi:10.1007/s11012-008-9177-8
[18] Sei U, Toru I (2010) Two parallel penny-shaped or annular cracks in a functionally graded piezoelectric strip under electric loading. Acta Mech 210:57–70 · Zbl 1397.74175 · doi:10.1007/s00707-009-0184-1
[19] Li YD, Lee KY (2010) Anti-plane shear fracture of the interface in a cylindrical smart structure with functionally graded magneto-electro-elastic properties. Acta Mech 212:139–149 · Zbl 1351.74027 · doi:10.1007/s00707-009-0251-7
[20] Feng FX, Lee KY, Li YD (2011) Multiple cracks on the arc-shaped interface in a semi-cylindrical magneto-electro-elastic composite with an orthotropic substrate. Eng Fract Mech 78:2029–2041 · doi:10.1016/j.engfracmech.2011.03.016
[21] Muskhelishvili NI (1953) Some basic problems of the mathematical theory of elasticity. Cambridge University Press, Cambridge · Zbl 0052.41402
[22] Li X (2008) Integral equation. Science Press, Beijing · Zbl 1152.45307
[23] Wei HX, Li YD, Lee KY (2010) Interfacial fracture analysis of a semicircular cylindrical guide rail. Mech Based Des Struct Mach 38:190–203 · doi:10.1080/15397731003648341
[24] Ding SH, Li X (2008) Anti-plane problem of periodic interface cracks in a functionally graded coating-substrate structure. Int J Fract 153:53–62 · Zbl 1273.74438 · doi:10.1007/s10704-008-9302-7
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