Buckling Delamination of a Rectangular Viscoelastic Sandwich Plate Containing Interface Inner Cracks
Publication: Journal of Engineering Mechanics
Volume 140, Issue 1
Abstract
In this paper, buckling delamination around interface inner cracks contained within the simply supported elastic and viscoelastic rectangular sandwich plate under biaxial loading is studied. It is assumed that the materials of the face layers are viscoelastic and the material of the core layer is pure elastic. Moreover, it is assumed that the material of the core layer is stiffer than the materials of the face layers. Within these assumptions it is supposed that between the face and core layers there are rectangular inner cracks, the locations of which are symmetric with respect to the plate geometry. The edge surfaces of the cracks have insignificant initial imperfections before the loading. The evolution of these initial imperfections with the flow of time is investigated within the scope of the three-dimensional (3D) geometrically nonlinear field equations of the theory of viscoelasticity. For determination of the values of the critical parameters (buckling force, time, and buckling mode), the initial imperfection criterion (i.e., the case where the size of the initial imperfection starts to increase and grows indefinitely) is used. Mathematical modeling of the corresponding boundary value problem is formulated within the framework of the piecewise homogeneous body model. To solve the corresponding boundary-value problems, boundary form perturbation techniques, the Laplace transform, 3D FEM modeling and the Schapery method are used. The numerical results related to the influence of the materials or geometrical parameters of the plate on the critical parameters and critical time are presented and analyzed.
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References
Adolfsson, K., Enelund, M., and Olsson, P. (2005). “On the fractional order model of viscoelasticity.” Mech. Time-Depend. Mater., 9(1), 15–34.
Akbarov, S. D. (1998). “On the three dimensional stability loss problems of elements of constructions fabricated from the viscoelastic composite materials.” Mech. Compos. Mater., 34(6), 537–544.
Akbarov, S. D. (2013). Stability loss and buckling delamination: Three-dimensional approach for elastic and viscoelastic composites, Springer, Heidelberg, Germany.
Akbarov, S. D., and Karakaya, S. (2011). “3D analyses of the stability loss of the circular solid cylinder made from viscoelastic composite material.” Comput., Mater., Continua, 22(1), 1–38.
Akbarov, S. D., and Rzayev, O. G. (2002a). “Delamination of unidirectional viscoelastic composite materials.” Mech. Compos. Mater., 38(1), 17–24.
Akbarov, S. D., and Rzayev, O. G. (2002b). “On the buckling of the elastic and viscoelastic composite circular thick plate with a penny-shaped crack.” Eur. J. Mech. A/Solids, 21(2), 269–279.
Akbarov, S. D., and Rzayev, O. G. (2003). “On the delamination of a viscoelastic composite circular plate.” Int. Appl. Mech., 39(3), 368–374.
Akbarov, S. D., Sisman, T., and Yahnioglu, N. (1997). “On the fracture of the unidirectional composites in compression.” Int. J. Eng. Sci., 35(12–13),1115–1136.
Akbarov, S. D., and Tekercioglu, R. (2007). “Surface undulation instability of the viscoelastic half-space covered with the stack of layers in bi-axial compression.” Int. J. Mech. Sci., 49(6), 778–789.
Akbarov, S. D., and Yahnioglu, N. (2001). “The method for investigation of the general theory of stability problems of structural elements fabricated from the viscoelastic composite materials.” Composites Part B: Eng., 32(5), 475–482.
Akbarov, S. D., and Yahnioglu, N. (2010). “Delamination buckling of a rectangular orthotropic composite plate containing a band crack.” Mech. Compos. Mater., 46(5), 493–504.
Akbarov, S. D., Yahnioglu, N., and Karatas, E. E. (2010a). “Buckling delamination of a rectangular plate containing a rectangular crack and made from elastic and viscoelastic composite materials.” Int. J. Solids Struct., 47(25–26), 3426–3434.
Akbarov, S. D., Yahnioglu, N., and Rzayev, O. G. (2007). “On the influence of singular-type finite elements on the critical force in studying the buckling of a circular plate with a crack.” Int. Appl. Mech., 43(9), 1048–1056.
Akbarov, S. D., Yahnioglu, N., and Tekin, A. (2010b). “3D FEM analyses of the buckling delamination of a rectangular sandwich plate containing interface rectangular cracks and made from elastic and viscoelastic materials.” Comput. Model. Eng. Sci., 64(2), 147–185.
Arman, Y., Zor, M., and Aksoy, S. (2006). “Determination of critical delamination diameter of laminated composite plates under buckling loads.” Compos. Sci. Technol., 66(15), 2945–2953.
Aviles, F., and Carlsson, L. A. (2006). “Three-dimensional finite element buckling analysis of debonded sandwich panels.” J. Compos. Mater., 40(11), 993–1008.
Bažant, Z. P. (1974). “Three-dimensional harmonic functions near termination or intersection of gradient singularity lines: A general numerical methods.” Int. J. Eng. Sci., 12(3), 221–243.
Bogdanov, V. L., Guz, A. N., and Nazarenko, V. M. (2009). “Fracture of a body with a periodic set of coaxial cracks under forces directed along them: An axisymmetric problem.” Int. Appl. Mech., 45(2), 111–124.
Bolotin, V. V. (1996). “Delaminations in composite structures: Its origin, buckling, growth and stability.” Composites, Part B: Eng., 27(2), 129–145.
Borodachev, N. M. (1976). “Contact problem for a stamp with a rectangular base.” J. Appl. Math. Mech., 40(3), 505–512.
Chai, H., Babcock, C. D., and Knauss, W. G. (1981). “One dimensional modeling of failure in laminated plates by delamination buckling.” Int. J. Solids Struct., 17(11), 1069–1083.
Chakrabarti, A., Topdar, P., and Sheikh, A. H. (2006). “Vibration and buckling of laminated sandwich plates having interfacial imperfections.” Eur. J. Mech. A/Solids, 25(6), 981–995.
Cheung, Y. K., Tham, L. G., and Chong, K. P. (1982). “Buckling of sandwich plate by finite layer method.” Comput. Struct., 15(2), 131–134.
Ferry, J. D. (1970). Viscoelastic properties of polymers, 2nd Ed., Wiley, New York.
François, D., Pineau, A., and Zaoui, A. (2013). Mechanical behaviour of materials: Fracture mechanics and damage, Vol. 2, Springer, Dordrecht, Netherlands.
FTN77 (Compaq Visual Fortran Professional Edition 6.1.0) [Computer software]. Summerville, SC, Compaq.
Gioia, G., and Ortiz, M. (1997). “Delamination of compressed thin films.” Adv. Appl. Mech., 33, 119–192.
Groover, M. P. (2010). Fundamentals of modern manufacturing: Materials, process, and systems, 4th Ed., Wiley, Denver.
Guz, A. N. (1999). Fundamentals of the three-dimensional theory of stability of deformable bodies, Springer, Berlin.
Guz, A. N., Dyshel, M. N., and Nazarenko, V. M. (2004). “Fracture and stability of materials with cracks: Approaches and results.” Int. Appl. Mech., 40(12), 1323–1359.
Guz, A. N., and Nazarenko, V. M. (1985a). “Symmetric failure of the half-space with penny-shaped crack in compression.” Theor. Appl. Fract. Mech., 3(3), 233–245.
Guz, A. N., and Nazarenko, V. M. (1985b). “Theory of near-surface delamination of composite materials under compression along the macro-crack.” Mech. Compos. Mater., 21(5), 826–833.
Guz, A. N., and Nazarenko, V. M. (1989a). “Fracture mechanics of materials in compression along a crack, constructional materials.” Int. Appl. Mech., 25(10), 3–18.
Guz, A. N., and Nazarenko, V. M. (1989b). “Fracture mechanics of materials in compression along a crack, highly elastic materials.” Int. Appl. Mech., 25(9), 3–32.
Henshell, R. D., and Shaw, K. G. (1975). “Crack tip finite elements are unnecessary.” Int. J. Numer. Methods Eng., 9(3), 495–507.
Hutchinson, J. W., He, M. Y., and Evans, A. G. (2000). “The influence of imperfections on the nucleation and propagation of buckling driven delaminations.” J. Mech. Phys. Solids, 48(4), 709–734.
Hutchinson, J. W., and Suo, Z. (1992). “Mixed mode cracking in layered materials.” Adv. Appl. Mech., 29, 63–191.
Hwang, S. F., and Mao, C. P. (1999). “The delamination buckling of single-fibre system and interply hybrid composites.” Compos. Struct., 46(3), 279–287.
Kachanov, L. M. (1976). “Fracture of composite materials by means a delamination.” Mekh. Polim., 5, 918–922.
Moon, M. W., Lee, K. R., Oh, K. H., and Hutchinson, J. W. (2004). “Buckle delamination on patterned substrates.” Acta Mater., 52(10), 3151–3159.
Nilsson, K. F., and Giannakopoulos, A. E. (1995). “A finite element analysis of configurational stability and finite growth of buckling driven delamination.” J. Mech. Phys. Solids, 43(12), 1983–2021.
Rabotnov, Yu. N. (1980). Elements of hereditary solid mechanics, Mir, Moscow.
Rzayev, O. G. (2002). “Local buckling around an interfacial crack in a viscoelastic sandwich plate.” Mech. Compos. Mater., 38(3), 233–242.
Rzayev, O. G., and Akbarov, S. D. (2002). “Local buckling of the elastic and viscoelastic coating around the penny-shaped interface crack.” Int. J. Eng. Sci., 40(13), 1435–1451.
Rvachev, V. L. (1959). “The pressure on an elastic half-space of a stamp with wedge-shaped platform.” J. Appl. Math. Mech., 23(1), 229–233.
Schapery, R. A. (1962). “Approximate methods of transform inversion for viscoelastic stress analysis.” Proc., 4th U.S. National Congress of Applied Mechanics, ASME, New York, 1075–1085.
Shariyat, M. (2010). “A generalized high-order global-local plate theory for nonlinear bending and buckling analyses of imperfect sandwich plates subjected to thermo-mechanical loads.” Compos. Struct., 92(1), 130–143.
Short, G. J., Guild, F. J., and Pavier, M. J. (2001). “The effect of delamination geometry on the compressive failure of composite laminates.” Compos. Sci. Technol., 61(14), 2075–2086.
Somers, M., Weller, T., and Abramovich, H. (1992). “Buckling and postbuckling behavior of delaminated sandwich beams.” Compos. Struct., 21(4), 211–232.
Thouless, M. D., Jensen, H. M., and Liniger, E. G. (1994). “Delamination from edge flaws.” Proc. R. Soc. London, Ser. A, 447(1930), 271–279.
Wang, J. S., and Evans, A. G. (1998). “Measurement and analysis of buckling and buckle propagation in compressed oxide layers on super ally substrates.” Acta Mater., 46(14), 4993–5005.
Zienkiewicz, O. C., and Taylor, R. L. (1989). The finite element methods: Basic formulation and linear problems, Vol. 1, 4th Ed., McGraw Hill, Oxford, U.K.
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Published In
Journal of Engineering Mechanics
Volume 140 • Issue 1 • January 2014
Pages: 134 - 148
Copyright
© 2014 American Society of Civil Engineers.
History
Received: Sep 28, 2012
Accepted: Apr 26, 2013
Published online: Apr 30, 2013
Published in print: Jan 1, 2014
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