Free-Edge and Ply Cracking Effect in Angle-Ply Laminated Composites Subjected to In-Plane Loads
Publication: Journal of Engineering Mechanics
Volume 133, Issue 12
Abstract
This paper presents a semianalytical method for the prediction of interlaminar stresses and displacements near the free edges and ply cracks in general angle-ply laminates subjected to biaxial extensions and/or in plane shear deformation. The method is based on a state space representation of the three-dimensional equations of elasticity. Numerical solutions are obtained by using layer refinement in the through thickness direction and Fourier series expansion in the other directions. By this approach, an angle-ply laminate may be composed of an arbitrary number of monoclinic layers and each layer may have different material property and thickness. This method guarantees continuous fields of all interlaminar stresses across interfaces between material layers. Numerical results are compared with those obtained from other methods. It is found that the theory provides a satisfactory approximation to the stress singularities near the free edges and ply cracks. Numerical solutions for antisymmetric laminates under extension and general laminates under shearing are new in the literature and can be used as benchmarks for validating new models.
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Acknowledgments
Financial support of this work from the ORS Awards and the University of Leeds is gratefully acknowledged.
References
Altus, E., Rotem, A., and Shmueli, M. (1980). “Free-edge effect in angle-ply laminates-A new three-dimensional finite difference solution.” J. Compos. Mater., 14(1), 21–30.
Becker, W. (1993). “Closed-form solution for the free-edge effect in cross-ply laminates.” Compos. Struct., 26(1–2), 39–45.
Berthelot, J. (1999). Composite materials: Mechanical behaviour and structural analysis, Springer, New York.
Bhaskar, K., Varadan, T. K., and Jacob, C. (2000). “Free-edge stresses in laminated cylindrical shells due to axisymmetric transverse loads.” J. Aeronaut. Soc. India, 52(1), 26–38.
Cho, M., and Yoon, J. (1999). “Free-edge interlaminar stress analysis in composite laminates by the extended Kantorovich method.” AIAA J., 37(5), 656–660.
Davet, J. L., and Destuynder, P. (1986). “Free-edge stress concentration in composite laminates: A boundary layer approach.” Comput. Methods Appl. Mech. Eng., 59(2), 129–140.
Dong, S. B., and Goetshel, D. B. (1982). “Edge effects in laminated composite plates.” J. Appl. Mech., 49(1), 129–135.
Dong, S. B., Pister, K. S., and Taylor, R. L. (1962). “On the theory of laminated anisotropic shells and plates.” J. Aerosp. Sci., 29(8), 969–975.
Gaudenzi, P., Mannini, A., and Carbonaro, R. (1998). “Multilayer higher-order finite elements for the analysis of free-edge stresses in composite laminates.” Int. J. Numer. Methods Eng., 41(5), 851–873.
Herakovich, C. T. (1989). “Free edge effects in laminated composites.” Handbook of composites, Vol. 2, Structure and design, C. T. Herakovich, and Y. M. Tarnopol’skii, eds., Elsevier Science, Amsterdam, The Netherlands, 187–230.
Hsu, P. W., and Herakovich, C. T. (1977). “Edge effects in angle-ply composite laminates.” J. Compos. Mater., 11(4), 422–428.
Icardi, U., and Bertetto, A. M. (1995). “An evaluation of the influence of geometry and material properties at free-edges and at corners of composite laminates.” Comput. Struct., 57(4), 555–571.
Kant, T., and Swaminathan, K. (2000). “Estimation of transverse interlaminar stresses in laminated composites—A selective review and survey of current developments.” Compos. Struct., 49(1), 65–75.
Kassapoglou, C., and Lagace, P. A. (1986). “An efficient method for the calculation of interlaminar stresses in composite materials.” J. Appl. Mech., 53(4), 744–750.
Kassapoglou, C., and Lagace, P. A. (1987). “Closed-form solutions for the interlaminar stress field in angle-ply and cross-ply laminates.” J. Compos. Mater., 21(4), 292–308.
Kim, J. Y., and Hong, C. S. (1991). “Three-dimensional finite element analysis of interlaminar stresses in thick composite laminates.” Comput. Struct., 40(6), 1395–1404.
Kim, T., and Atluri, S. N. (1994). “Interlaminar stresses in composite laminates under out-of-plane shear/bending.” AIAA J., 32(8), 1700–1708.
Ko, C. C., and Lin, C. C. (1992). “Method for calculating interlaminar stresses in symmetric laminates containing a circular hole.” AIAA J., 30(1), 197–204.
Lessard, L. B., Schmidt, A. S., and Shokrieh, M. M. (1996). “Three-dimensional stress analysis of free-edge effects in a simple composite cross-ply laminate.” Int. J. Solids Struct., 33(15), 2243–2259.
Lindemann, J., and Becker, W. (2002). “The tendency for free-edge delamination in laminates and its minimization.” Compos. Sci. Technol., 62(2), 233–242.
Pagano, N. J. (1974). “On the calculation of interlaminar normal stress in composite laminate.” J. Compos. Mater., 8(1), 65–81.
Pipes, R. B., and Pagano, N. J. (1970). “Interlaminar stresses in composite laminates under uniform axial extension.” J. Compos. Mater., 4(4), 538–548.
Pipes, R. B., and Pagano, N. J. (1974). “Interlaminar stresses in composite laminates—An approximate elastic solution.” J. Appl. Mech., 41(3), 668–672.
Puppo, A. H., and Evensen, H. A. (1970). “Interlaminar shear in laminated composite under generalized plane stress.” J. Compos. Mater., 4(2), 204–220.
Reddy, J. N. (1987). “A generalization of two-dimensional theories of laminated composite plates.” Commun. Appl. Numer. Methods, 3(3), 173–180.
Reissner, E., and Stavsky, Y. (1961). “Bending and stretching of certain types of heterogeneous aelotropic elastic plates.” J. Appl. Mech., 28(3), 402–408.
Salamon, N. J. (1978). “Interlaminar stresses in a layered composite laminate in bending.” Fibre Sci. Technol., 11(4), 305–317.
Sheng, H. Y., and Ye, J. Q. (2003). “A three-dimensional state space finite element solution for laminated composite cylindrical shells.” Comput. Methods Appl. Mech. Eng., 192(19), 2441–2459.
Tahani, M., and Nosier, A. (2000). “Edge effects of uniformly loaded cross-ply composite laminates.” Mater. Des., 24(8), 647–658.
Tahani, M., and Nosier, A. (2003a). “Free edge analysis of general cross-ply composite laminates under extension and thermal loading.” Compos. Struct., 60(1), 91–103.
Tahani, M., and Nosier, A. (2003b). “Three-dimensional interlaminar stress analysis at free edges of general cross-ply composite laminates.” Mater. Des., 24(2), 121–130.
Tang, S. (1975). “A boundary layer theory. 1: Laminated composites in plane stress.” J. Compos. Mater., 9(1), 33–41.
Wang, A. S. D., and Crossman, F. W. (1977). “Some new results on free edge effects in symmetric composite laminates.” J. Compos. Mater., 11(1), 92–106.
Wang, S. S., and Choi, I. (1982a). “Boundary-layer effects in composite laminates. 1: Free-edge stress singularities.” J. Appl. Mech., 49(3), 541–548.
Wang, S. S., and Choi, I. (1982b). “Boundary-layer effects in composite laminates. 2: Edge stress solutions and basic characteristics.” J. Appl. Mech., 49(3), 549–560.
Webber, J. P. H., and Mortan, S. K. (1993). “An analytical solution for the thermal stresses at the free-edges of laminated plates.” Compos. Sci. Technol., 46(2), 175–185.
Ye, J. Q. (2003). Laminated composite plates and shells: 3D modeling, Springer, London.
Ye, J. Q., and Sheng, H. Y. (2003). “Free-edge effect in cross-ply laminated hollow cylinders subjected axisymmetric transverse loads.” Int. J. Mech. Sci., 45(18), 1309–1329.
Ye, J. Q., Sheng, H. Y., and Qin, Q. H. (2004). “A state space finite element for laminated composites with free edges and subjected to transverse and in-plane loads.” Comput. Struct., 82(15–16), 1131–1141.
Ye, J. Q., and Soldatos, K. P. (1994a). “Three-dimensional stress analysis of orthotropic and cross-ply laminated hollow cylinders and cylindrical panels.” Comput. Methods Appl. Mech. Eng., 117(3–4), 331–351.
Ye, J. Q., and Soldatos, K. P. (1994b). “Three dimensional vibration of laminated cylinders and cylindrical panels with a symmetric or an antisymmetric cross-ply lay-up.” Composites Eng., 4(4), 429–458.
Ye, J. Q., and Soldatos, K. P. (1995). “Three-dimensional buckling analysis of laminated composite hollow cylinders and cylindrical panels.” Int. J. Solids Struct., 32(13), 1949–1962.
Yi, S., and Hilton, H. H. (1997). “Finite element analysis of free edge stresses in nonlinear viscoelastic composites under uniaxial extension, bending and twisting loadings.” Int. J. Numer. Methods Eng., 40(22), 4225–4237.
Yuan, F. G., and Selek, M. C. (1993). “Transverse cracking and stiffness reduction in composite laminates.” J. Reinf. Plast. Compos., 12(9), 987–1015.
Zhang, D., Ye, J. Q., and Sheng, H. Y. (2006). “Free-edge and ply cracking effect in cross-ply laminated composites under uniform extension and thermal loading.” Compos. Struct., 76(4), 314–325.
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Information
Published In
Journal of Engineering Mechanics
Volume 133 • Issue 12 • December 2007
Pages: 1268 - 1277
Copyright
© 2007 ASCE.
History
Received: Mar 7, 2006
Accepted: Jun 7, 2007
Published online: Dec 1, 2007
Published in print: Dec 2007
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