Abstract
Interfacial weak bonding affects piezothermoelastic responses of piezoelectric composite laminates. To simplify the complicated piezothermoelastic constitutive laws at a weak interface, three assumptions on interfacial bonding conditions are made. They are (i) the relations between the interfacial displacement jumps and the interfacial transverse stresses; (ii) the relation (electrically semi-permeable assumption) between the interfacial potential jump and the interfacial normal electric displacement; (iii) the relation between the interfacial temperature jump and the interfacial normal opening. These assumptions form a set of systematic descriptions of three-fields-coupling at a weak interface and result in a linear mathematical formulation. The piezothermoelastic solutions of cross-ply piezoelectric laminates with weak interfaces in cylindrical bending are deduced. Some benchmark numerical results are obtained, and the effects of interfacial weak bonding on the piezothermoelastic responses are discussed.
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Lu X., Liu D.: Interlayer shear slip theory for cross-ply laminates with nonrigid interfaces. AIAA J. 30, 1063–1073 (1992)
Liu D., Xu L., Lu X.: Stress analysis of imperfect composite laminates with an interlaminar bonding theory. Int. J. Numer. Meth. Eng. 37, 2819–2839 (1994)
Schmidt, R., Librescu, L.: A refined theory of anisotropic laminated composite plates featuring nonrigidly bonded interfaces. In: Proceedings of the 15th Canadian Congr. Appl. Mech., University of Victoria, pp. 234–235 (1995)
Cheng Z.-Q., Jemah A.K., Williams F.W.: Theory for multilayered anisotropic plates with weakened interfaces. J. Eng. Mech. 63, 1019–1026 (1996)
Williams T.O., Addessio F.L.: A general theory for laminated plates with delaminations. Int. J. Solids Struct. 34, 2003–2024 (1997)
Shu X., Soldatos K.P.: An accurate stress analysis model for angle-ply laminates with weak bonded layers. Acta Mech. 150, 161–178 (2001)
Shu X., Soldatos K.P.: An accurate de-lamination model for weakly bonded laminates subjected to different sets of edge boundary conditions. Int. J. Mech. Sci. 43, 935–959 (2001)
Soldatos K.P., Shu X.: Modelling of perfectly and weakly bonded laminated plates and shallow shells. Compos. Sci. Tech. 61, 247–260 (2001)
Shu X.: Vibration and bending of antisymmetrically angly-ply laminated plates with perfectly and weakly bonded layers. Compos. Struct. 53, 245–255 (2001)
Seeley C.E., Chattopadhyay A.: Experimental investigation of composite beams with piezoelectric actuation and debonding. Smart Mater. Struct. 7, 502–511 (1998)
Seeley C.E., Chattopadhyay A.: Modeling of adaptive composites including debonding. Int. J. Solids Struct. 36, 1823–1843 (1999)
Icardi U., Di Sciuva M., Librescu L.: Dynamic response of adaptive cross-ply cantilevers featuring interlaminar bonding imperfections. AIAA J. 38, 499–506 (2000)
Sun D., Tong L., Atluri S.N.: Effects of piezoelectric sensor/actuator debonding on vibration control of smart beams. Int. J. Solids Struct. 38, 9033–9051 (2001)
Sun D., Tong L.: Control stability analysis of smart beams with debonded piezoelectric actuator layer. AIAA J. 40, 1852–1859 (2002)
Chen W.Q., Lee K.Y.: Exact solution of angle-ply piezoelectric laminates in cylindrical bending with interfacial imperfections. Compos. Struct. 65, 329–337 (2004)
Chen W.Q., Lee K.Y.: Benchmark solution of angle-ply piezoelectric-laminated cylindrical panels in cylindrical bending with weak interfaces. Arch. Appl. Mech. 74, 466–476 (2005)
Shu X.: Modelling of cross-ply piezoelectric composite laminates in cylindrical bending with interfacial shear slip. Int. J. Mech. Sci. 47, 1673–1692 (2005)
Shu X.: Thermoelastic delamination of composite laminates with weak interfaces. Compos. Struct. 84, 310–318 (2008)
Kapuria S., Dube G.P., Dumir P.C., Sengupta S.: Levy-type piezothermoelastic solution for hybrid plate using first order shear deformation theory. Compos. Part B 28, 535–546 (1997)
Sharma J.N., Pal M., Chand D.: Three-dimensional vibration analysis of piezothermoelastic cylindrical panel. Int. J. Eng. Sci. 42, 1655–1673 (2004)
Kapuria S., Achary G.G.S.: Benchmark 3D solution and assessment of a zigzag theory for free vibration of hybrid plates under initial electrothermomechanical stresses. Compos. Sci. Tech. 68, 297–311 (2008)
Needleman A.: A continuum model for void nucleation by inclusion debonding. J. Appl. Mech. 54, 525–531 (1987)
Needleman A.: An analysis of decohesion along an imperfect interface. Int. J. Fract. 42, 21–40 (1990)
Corigliano A.: Formulation, identification, and use of interface models in the numerical analysis of composite delamination. Int. J. Solids Struct. 30, 2779–2811 (1993)
Zhang H., Gu Y., Zhong W.: Finite element analysis of the coupling effects of heat conduction and contact (in Chinese). Acta Solids Sinica 20, 217–224 (2000)
Benveniste Y.: On the decay of end effects in conduction phenomena: a sandwich strip with imperfect interfaces of low or high conductivity. J. Appl. Phys. 86, 1273–1279 (1999)
Hashin Z.: Thin interphase/imperfect interface in conduction. J. Appl. Phys. 89, 2261–2267 (2001)
Partonm V.Z.: Fracture mechanics of piezoelectric materials. Acta Astro. 3, 671–683 (1976)
Deeg, W.F.: The analysis of dislocation crack and inclusion problems in piezoelectric solid. (Ph.D. thesis) Stanford, Stanford University (1980)
Pak Y.E.: Crack extension force in a piezoelectric material. J. Appl. Mech. 57, 647–653 (1990)
Hao T.H., Shen Z.Y.: A new electric boundary condition of electric fracture mechanics and its applications. Eng. Fract. Mech. 47, 793–802 (1994)
Fan H., Sze K.Y.: A micro-mechanics model for imperfect interface in dielectric materials. Mech. Mater. 33, 363–373 (2001)
Gem W.K., Kang Y.L.: Influence of weak interfaces on buckling of orthotropic piezoelectric rectangular laminates. Compos. Struct. 82, 290–294 (2008)
Heyliger P.R., Brooks S.: Exact solutions for laminated piezoelectric plates in cylindrical bending. J. Appl. Mech. 63, 903–910 (1996)
Pagano N.J.: Exact solution for rectangular bidirectional composites and sandwich plates. J. Compos. Mater. 4, 20–34 (1970)
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An erratum to this article can be found at http://dx.doi.org/10.1007/s00707-010-0325-6
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Shu, X. Piezothermoelastic responses of piezoelectric composite laminates with weak interfaces. Acta Mech 214, 327–340 (2010). https://doi.org/10.1007/s00707-010-0296-7
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DOI: https://doi.org/10.1007/s00707-010-0296-7