Estimation of Composite Laminate Design Allowables Using the Statistical Characteristics of Lamina Level Test Data

  • Nam, Kyungmin (Department of Aerospace Engineering, Seoul National University) ;
  • Park, Kook Jin (Department of Aerospace Engineering, Seoul National University) ;
  • Shin, SangJoon (Department of Aerospace Engineering, Seoul National University) ;
  • Kim, Seung Jo (Department of Aerospace Engineering, Seoul National University) ;
  • Choi, Ik-Hyeon (Korea Aerospace Research Institute)
  • Received : 2015.05.22
  • Accepted : 2015.06.26
  • Published : 2015.09.30


A methodology for determining the design allowables of composite laminates by using lamina level test data and finite element analysis (FEA) is proposed and verified in this paper. An existing method that yields the laminate design allowables by using the complete test results for laminates was improved to reduce the expensive and time-consuming tests. Input property samples for FEA were generated after considering the statistical distribution characteristics of lamina level test data., and design allowables were derived from several FEA analyses of laminates. To apply and verify the proposed method, Hexcel 8552 IM7 test data were used. For both un-notched and open-hole laminate configurations, it was found that the design allowables obtained from the analysis correctly predicted the laminate test data within the confidence interval. The potential of the present simulation to substitute the laminate tests was demonstrated well.



  1. CMH-17, Composite Materials Handbook, Federal Aviation Administration, 2012.
  2. DOT/FAA/AR-03/19, Material Qualification and Equivalency for Polymer Matrix Composite Material Systems: Updated Procedure, Federal Aviation Administration, 2003.
  3. J. Astill, C. Nosseir, and M. Shinozuka, "Impact Loading on Structures with Random Properties", J. Structural Mechanics, Vol. 1, No. 1, 1972, pp. 63-77.
  4. K. P. Oh, "A Monte Carlo Study of the Strength of Unidirectional Fiber-Reinforced Composites", J. Composite Materials, Vol. 13, 1979, pp. 311-328.
  5. H. Fukuda, and T. W. Chou, "Monte Carlo Simulation of the Strength of Hybrid Composites", J. Composite Materials, Vol. 16, 1982, pp. 371-385.
  6. K. Goda, and S. L. Pheonix, "Reliability Approach to the Tensile Strength of Unidirectional CFRP Composites by Monte Carlo Simulation in a Shear-Lag Model", Composite Science and Technology, Vol. 50, 1994, pp. 457-468.
  7. J. Yuan, Y. Xia, and B. Yang, "A Note on the Monte Carlo Simulation of the Tensile Deformation and Failure Process of Unidirectional Composites", Composite Science and Technology, Vol. 52, 1994, pp. 197-204.
  8. Y. Zhou, H. Mahfuz, and S. Jeelani, "Numerical Simulation for High Strain Rate Failure Process of Unidirectional Sicf-Al Composites", Int. J. Damage Mechanics, Vol. 14, No. 4, 2005, pp. 321-341.
  9. G. Vinckenroy, and W. Wilde, "The Use of Monte Carlo Techniques in Statistical Finite Element Methods for the Determination of the Structural Behaviour of Composite Materials Structural Components", Composite Structures, Vol. 32, 1995, pp. 247-253.
  10. S. J. Lee, I. G. Kim, and M. H. Jang, "Reliability Analysis for Composite Plate with the Various Design Requirements", J. The Korean Society for Composite Materials, Vol. 20, No. 4, 2007, pp. 25-30.
  11. P. Marek, M. Gustar, and T. Anagnos, Simulation-Based Reliability Assessment, CRC Press, 1995.
  12. J. H. Kim, and S. J. Kim, "A Multifrontal Solver Combined with Graph Partitioners", AIAA Journal, Vol. 38, No. 8, Aug. 1999, pp. 964-970.
  13. S. J. Kim, C. S. Lee, and J. H. Kim, "Large-Scale Structural Analysis by Parallel Multifrontal Solver through Internet Based Pcs", AIAA Journal, Vol. 40, No. 2, 2002, pp. 359-367.
  14. J. H. Kim, C. S. Lee, and S. J. Kim, "High-Performance Domain-Wise Parallel Direct Solver for Large-Scale Structural Analysis", AIAA Journal, Vol. 43, No. 3, 2005, pp. 662-67034.
  15. J. W. Park, S. H. Park, and S. J. Kim, "Optimization with High-Cost Objective Function Evaluations in a Computing Grid and an Application to Simulation-Based Design", Int. J. High Performance Computing Applications, Vol. 23, No. 1, 2009, pp. 62-83.
  16. K. J. Park, H. Kang et al., "Strength Prediction on Composite Laminates Including Material Nonlinearity and Continuum Damage Mechanics", Korean J. of Aerospace Engineering, Vol. 42, No. 11, 2014, pp. 927-936.
  17. K. Marlett, et al., Hexcel 8552 IM7 Unidirectional Prepreg 190 gsm & 35%RC Qualification Material Property Data Report, CAM-RP-2009-015 Rev. A, NIAR, Wichita State University, 2011.
  18. T. W. Anderson, and D. A. Darling, "Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes", The Annals of Mathematical Statistics, Vol. 23, No. 2, 1952, pp. 193-212.
  19. M. D. McKay, R. J. Beckman, and W. J. Conover, "A Comparison of Three Methods for Selection Values of Input Variables in the Analysis of Output from a Computer Code", Technometrics, Vol. 21, No. 2, 1979, pp. 239-245.
  20. R. L. Iman, and W. J. Conover, "A Distribution-Free Approach to Inducing Rank Correlation among Input Variables", Communications in Statistics-Simulation and Computation, Vol. 11, 1982, pp. 311-334.
  21. D. Vose, Risk Analysis: A Quantitative Guide, John Wiley & Sons, New York, 2000
  22. S. Marino, et al., "A Methodology for Performing Global Uncertainty and Sensitivity Analysis in Systems Biology", J. Theoretical Biology, Vol. 254, No. 1, 2008, pp. 178-196.
  23. Frank J. Massey Jr., "The Kolmogorov-Smirnov Test for Goodness of Fit", J. the American Statistical Association, Vol. 46, No. 253, 1951, pp. 68-78.
  24. M. L. Shooman, Probabilistic Reliability: An Engineering Approach, McGraw-Hill, 1968.
  25. A. Haldar, and S. Mahadevan, Reliability Assessment Using Stochastic Finite Element Analysis, John Wiley and Sons, 2000.
  26. R. Billinton, and W. Li, Reliability Assessment of Electric Power Systems Using Monte Carlo Methods, Plenum Press, 1994.