Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Curved and Layered Structures

Editor-in-Chief: Tornabene, Francesco

CiteScore 2018: 1.60

SCImago Journal Rank (SJR) 2018: 0.546
Source Normalized Impact per Paper (SNIP) 2018: .496

Open Access
See all formats and pricing
More options …

Probabilistic fracture investigation of symmetric angle ply laminated composite plates using displacement correlation method

Achchhe Lal / P. Palekar Shailesh
Published Online: 2016-01-28 | DOI: https://doi.org/10.1515/cls-2016-0004


The second order statistics of mixed mode stress intensity factors (MSIF) of single edge V-notched angle ply laminated composite plate subjected to uniaxial tensile load with uncertinity in the system properties using displacement correlation method (DCM) is evaluated. The random system properties such as material properties, crack opening and crack length are modelled as combined uncorrelated and correlated random system variables. A C0 finite element method (FEM) based on higher order shear deformation plate theory (HSDT) is used for basic formulation. The Taylor series based first order perturbation technique (FOPT), second order perturbation technique (SOPT) are used and direct Monte Carlo simulation (MCS) is performed to evaluate the statistics (mean and coefficient of variance) of the mixed mode SIFs. The present work signifies the accurate analysis of frature behaviour by influence of different random variables and fibre orientations on the fracture behaviour in angle ply laminates.

Keywords: Stress intensity factor; V-notched laminated composite plate; finite element method; displacement correlation method; perturbation technique; Monte Carlo simulation


  • [1] Bergmann H. W., Eggers H., Awerbuch J., Fracture mechanics aspects of composite materials, Acta Astronautica, 1987, 15(3), 149-155.CrossrefGoogle Scholar

  • [2] Chandra R., Guruprasad K., Numerical Estimation of Stress Intensity Factors in Patched Cracked Plates. Engineering Fracture Mechanics, 1987, 21(5), 559-569.CrossrefGoogle Scholar

  • [3] Bahei-El-Din Y. A., Dvorak G. J., Wu J.F., Fracture of fibrous metal matrix composites-II. modeling and numerical analysis, Engineering Fracture Mechanics, 1989, 34 (1), 105-123.CrossrefGoogle Scholar

  • [4] Andersons J., Tarasovs S., Sparnin E. S., Finite fracture mechanics analysis of crack onset at a stress concentration in a UD glass/epoxy composite in off-axis tension, Composites Science and Technology, 2010, 70, 1380–1385.CrossrefWeb of ScienceGoogle Scholar

  • [5] S.H. Ju, Finite element calculation of stress intensity factors for interface notches. Computer Methods in Applied Mechanics and Engineering, 2010, 199, 2273–2280.Web of ScienceGoogle Scholar

  • [6] Ju S.H., Chiu C.Y., Jhao B.J., Determination of V-notch SIFs in multi-material anisotropic wedges by digital correlation experiments, International Journal of Solids and Structures, 2010, 47, 894–900.Google Scholar

  • [7] Patricio M., Mattheij R.M.M., Crack paths in composite materials, Engineering Fracture Mechanics, 2010, 77, 2251–2262.CrossrefWeb of ScienceGoogle Scholar

  • [8] Kaman M. O., Effect of fibre orientation on fracture toughness of laminated composite plates [0/Θ]s, Engineering Fracture Mechanics, 2011, 78, 2521–2534.Google Scholar

  • [9] Treifi M., Oyadiji S. O., Derek K. L.T., Computations of modes I and II stress intensity factors of sharp notched plates under in-plane shear and bending loading by the fractal-like finite element method, International Journal of Solids and Structures, 2008, 45, 6468–6484.Google Scholar

  • [10] Treifi M., Oyadiji S. O., Derek K. L.T., Computations of the stress intensity factors of double-edge and centre V-notched plates under tension and anti-plane shear by the fractal-like finite element method, Engineering Fracture Mechanics, 2009, 76, 2091–2108.CrossrefWeb of ScienceGoogle Scholar

  • [11] Treifi M., Oyadiji S. O., Bi-material V-notch stress intensity factors by the fractal-like finite element method, Engineering Fracture Mechanics, 2013, 105, 221–237.CrossrefWeb of ScienceGoogle Scholar

  • [12] Rudraraju S. S., Salvi A., Garikipati K., Waas A. M., In-plane fracture of laminated fiber reinforced composites with varying fracture resistance: Experimental observations and numerical crack propagation simulations, International Journal of Solids and Structures, 2010, 47, 901–911.Google Scholar

  • [13] Filippi S., Lazzarin P., Tovo R., Developments of some explicit formulas useful to describe elastic stress fields ahead of notches in plates, International Journal of Solids and Structures, 2002, 39, 4543–4565.Google Scholar

  • [14] Lazzarin P., Filippi S., A generalized stress intensity factor to be applied to rounded V-shaped notches. International Journal of Solids and Structures, 2006, 43, 2461–2478.Google Scholar

  • [15] Lazzarin P., Campagnolo A., Berto F., A comparison among some recent energy-and stress-based criteria for the fracture assessment of sharp V-notched components under Mode I loading, Theoretical and Applied Fracture Mechanics, 2014, 71, 21–30.Web of ScienceCrossrefGoogle Scholar

  • [16] Yao X.F., Yeh H.Y., Xu W., Fracture investigation at V-notch tip using coherent gradient sensing (CGS). International Journal of Solids and Structures, 2006, 43, 1189–1200.Google Scholar

  • [17] Wu Z., Liu Y., Analytical solution for the singular stress distribution due to V-notch in an orthotropic plate material, Engineering Fracture Mechanics, 2008, 75, 2367–2384.Web of ScienceCrossrefGoogle Scholar

  • [18] Niu Z., Cheng C., Ye J., Recho N., A new boundary element approach of modeling singular stress fields of plane V-notch problems, International Journal of Solids and Structures, 2009, 46, 2999–3008.Google Scholar

  • [19] Ayatollahi M.R., Torabi A. R., Brittle fracture in rounded-tip V-shaped notches, Materials and Design, 2010, 31, 60–67.Google Scholar

  • [20] Garcia I.G., Leguillon D., Mixed-mode crack initiation at a v-notch in presence of an adhesive joint, International Journal of Solids and Structures, 2012, 49, 2138–2149.Google Scholar

  • [21] Vratnica M., Pluvinage G., Jodin P., Cvijovic Z., Rakin M., Burzic Z., Geric K., Notch fracture toughness of high-strength Al alloys, Materials and Design, 2013, 44, 303–310.Google Scholar

  • [22] Lei J., Sun P., Bui T. Q., Determination of fracture parameters for interface cracks in transverse isotropic magnetoelectroelastic composites, Curved and Layered Structures, 2015, 2, 271–278.Google Scholar

  • [23] Viola E., Tornabene F., Ferretti E., Fantuzzi N., GDQFEM numerical simulations of continuous media with cracks and discontinuities. CMES-Comp. Model. Eng., 2013, 94(4), 331-369.Google Scholar

  • [24] Liu H., Zhou Z., S. Pan, Non-local theory solution for a 3D rectangular permeable crack in piezoelectric composite materials, Composite Structures, 2015, 119, 513-527.Google Scholar

  • [25] Zhao Y., Zhao M., Pan E., Displacement discontinuity analysis of a nonlinear interfacial crack in three-dimensional transversely isotropic magneto-electro-elastic bi-materials, Engineering Analysis with Boundary Elements, 2015, 61, 254–264.Google Scholar

  • [26] Li Y., Viola E., Size effect investigation of a central interface crack between two bonded dissimilar materials, Composite Structures, 2013, 105, 90-107.CrossrefWeb of ScienceGoogle Scholar

  • [27] Chopra P.S., Wang P.Y., Hartz B. J., Probabilistic prediction of multiple fracture under service conditions, Nuclear Engineering and Design, 1974, 28, 446-458.CrossrefGoogle Scholar

  • [28] Rahman S., Probabilistic fracture mechanics: J-estimation and finite element methods, Engineering Fracture Mechanics, 2001, 68, 107-125.CrossrefGoogle Scholar

  • [29] Alkhateb H., Ostaz A. A., Alzebdeh K. I., Developing a stochastic model to predict the strength and crack path of random composites, Composites Part B, 2009, 40, 7–16.Google Scholar

  • [30] Gayathri P., Umesh K., Ganguli R., Effect of matrix cracking and material uncertainty on composite plates, Reliability Engineering and System Safety, 2010, 95, 716–728.Google Scholar

  • [31] Chowdhury S. M., Song C., Gao W., Probabilistic fracture mechanics by using Monte Carlo simulation and the scaled boundary finite element method, Engineering Fracture Mechanics, 2011, 78, 2369–2389.Web of ScienceCrossrefGoogle Scholar

  • [32] Rahman S., Chakraborty A., Stochastic multiscale fracture analysis of three-dimensional functionally graded composites, Engineering Fracture Mechanics, 2011, 78, 27–46.Web of ScienceCrossrefGoogle Scholar

  • [33] Sobey A. J., Blake J. I. R., Shenoi R. A., Monte Carlo reliability analysis of tophat stiffened composite plate structures under out of plane loading, Reliability Engineering and System Safety, 2013, 110, 41–49.Google Scholar

  • [34] Lal A., Kapania R.K., Stochastic Critical Stress Intensity Factor Response of Single Edge Notched Laminated Composite Plate, 54th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference, Boston, Massachusetts (USA), 2013, DOI: 10.2514/6.2013-1615.CrossrefGoogle Scholar

  • [35] Kim J. H., Paulino G. H., Mixed-mode fracture of orthotropic functionally graded materials using finite elements and the modified crack closure method, Engineering Fracture Mechanics, 2002, 69, 1557–1586.CrossrefGoogle Scholar

  • [36] Mahmoud M.K., Fracture toughness of single-edge notched fibre reinforced composite, Polymer-Plastics Technology and Engineering, 2003, 42, 659–76.Google Scholar

  • [37] Kumagai S., Yasuhide S., Experimental and analytical evaluation of the notched tensile fracture of CFRP woven laminates at low temperatures, Journal of Composite Materials, 2004, 38, 1151-1164.CrossrefGoogle Scholar

  • [38] Lee B., Sankar B.V., Lay-up independent fracture criterion for notched laminated composites, Science Technology, 2006, 66, 2491–2499.Google Scholar

  • [39] Mikhaluk D.S., Truong T. C., Borovkov A. I., Lomov S.V., Verpoest I., Experimental observations and finite element modeling of damage initiation and evolution in carbon/epoxy non-crimp fabric composites, Engineering Fracture Mechanics, 2008, 75, 2751–66.CrossrefGoogle Scholar

  • [40] Banks-Sills L., Update application of the finite element method to linear elastic fracture mechanics, Applied Mechanics Reviews, 2010, 63, 1-17.Web of ScienceGoogle Scholar

  • [41] Lal A., Choksi P., Singh B.N., Stochastic nonlinear free vibration analysis of piezo laminated composite conical shell panel subjected to thermoelectromechanical loading with random material properties, TRANSE ASME Journal of Applied Mechanics, 2012, 79(6), Doi:10.1115/1.4006765.CrossrefGoogle Scholar

  • [42] Lal A., Patel D., Singh B.N., Stochastic nonlinear failure analysis of laminated composite plates under compressive transverse loading, Composite Structures, 2012, 94, 1211-1223.CrossrefWeb of ScienceGoogle Scholar

  • [43] Shankara C.A., Iyenger N. G. R., A C0 Element for the free vibration analysis of laminated composite plates, Journal of Sound and Vibration, 1996, 191 (5), 721–738.Google Scholar

  • [44] Lin Y.K., Yang J.N., On statistical moments of fatigue crack propagation, Engineering Fracture Mechanics, 1983, 18, 243–256.CrossrefGoogle Scholar

  • [45] Besterfield G. H., Liu W. K., Lawrence M.A., Belytschko T., Fatigue crack growth reliability by probabilistic finite elements, Computational Methods in Applied Mechanical Engineering, 1991, 86, 297-320.Google Scholar

  • [46] Kleiber M., Hien T.D., The stochastic finite element method, John Wiley & Sons, 1992.Google Scholar

  • [47] Nigam N.C., Narayanan S., Applications of random vibrations, Narosa New Delhi, 1994.Google Scholar

  • [48] Mulani S.B., Uncertainty quantification of dynamic problem with large uncertainties, Ph.D. thesis, Virginia Polytechnic Institute and State University, 2006.Google Scholar

  • [49] Haldar A., Mahadevan S., Reliability assessment using stochastic finite element analysis, John Wiley & Sons, 2000.Google Scholar

  • [50] Lindgren G., Rootźen H., Sandsten M., Stationary stochastic processes, Chapman & Hall CRC, 2013.Google Scholar

About the article

Received: 2015-11-01

Accepted: 2015-12-15

Published Online: 2016-01-28

Published in Print: 2016-01-01

Citation Information: Curved and Layered Structures, Volume 3, Issue 1, ISSN (Online) 2353-7396, DOI: https://doi.org/10.1515/cls-2016-0004.

Export Citation

© 2016 Achchhe Lal et al., published by De Gruyter Open. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in