Acta Mechanica Solida Sinica

, Volume 23, Issue 3, pp 240–247 | Cite as

Predictive Approach to Failure of Composite Laminates with Equivalent Constraint Model

Article

Abstract

This work established a new analytical model based upon the equivalent constraint model (ECM) to constitute an available predictive approach for analyzing the ultimate strength and simulating the stress/strain response of general symmetric laminates subjected to combined loading, by taking into account the effect of matrix cracking. The ECM was adopted to mainly predict the in-plane stiffness reduction of the damaged laminate. Basic consideration that progressive matrix cracking provokes a re-distribution of the stress fields on each lamina within laminates, which greatly deteriorates the stress distributed in the primary load-bearing lamina and leads to the final failure of the laminates, is introduced for the construction of the failure criterion. The effects of lamina properties, lay-up configurations and loading conditions on the behaviors of the laminates were examined in this paper. A comparison of numerical results obtained from the established model and other existed models and published experimental data was presented for different material systems. The theory predictions demonstrated great match with the experimental observations investigated in this study.

Key words

composite laminates equivalent constraint model primary load-bearing lamina progressive matrix cracking strength 

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References

  1. [1]
    Hinton, M.J. and Soden, P.D., Predicting failure in composite laminates: The background to the exercise. Composite Science and Technology, 1998, 58(7): 1001–1010.CrossRefGoogle Scholar
  2. [2]
    Hinton, M.J., Kaddour, A.S. and Soden, P.D., Evaluation of failure prediction in composite laminates: Background to ‘part B’ of the exercise. Composite Science and Technology, 2002, 62(12–13): 1481–1488.CrossRefGoogle Scholar
  3. [3]
    Zhang, J., Fan, J. and Hermann, K.P., Delaminations induced by constrained transverse cracking in symmetric composite laminates. International Journal of Solids and Structures, 1999, 36(6): 813–846.CrossRefGoogle Scholar
  4. [4]
    Okabe, T., Nishikawa, M. and Takeda, N., Numerical modeling of progressive damage in fiber reinforced plastic cross-ply laminates. Composite Science and Technology, 2008, 68(10–11): 2282–2289.CrossRefGoogle Scholar
  5. [5]
    Reifsnider, K.L. and Stinchcomb, W.W., A critical-element model of the residual strength and life of fatigue-loaded composite coupons. In: Composite Materials: Fatigue and Fracture, Hahn, H.T. (ed.), ASTM STP 907, Philadephia PA, 1986, 298–313.CrossRefGoogle Scholar
  6. [6]
    Zheng, S.F., Denda, M. and Weng, G.J., Interfacial partial debonding and its influence on the elasticity of a two-phase composite. Mechanics of Materials, 2000, 32(12): 695–709.CrossRefGoogle Scholar
  7. [7]
    Maimi, P., Camanho, P.P., Mayugo, J.A. and Davila, C.G., A continuum damage model for composite laminates — Part I: Constitutive model. Mechanics of Materials, 2007, 39(10): 897–908.CrossRefGoogle Scholar
  8. [8]
    Highsmith, A.L. and Reifsnider, K.L., Stiffness reduction mechanisms in composite laminates. In: Damage Composite Materials, Reifsnider, K.L. (ed.), ASTM STP 775, Philadephia PA, 1982, 103–117.Google Scholar
  9. [9]
    Nuismer, R.J. and Tan, S.C., Constitutive relations of a cracked composite lamina. Journal of Composite Materials, 1988, 22(4): 306–321.CrossRefGoogle Scholar
  10. [10]
    Hashin, Z., Analysis of cracked laminates: A variational approach. Mechanics of Materials, 1985, 4(2): 121–136.CrossRefGoogle Scholar
  11. [11]
    Armanios, E.A., Sriram, P. and Badir, A.M., Fracture analysis of transverse crack-tip and free-edge delamination in laminated composites. In: Composite Materials: Fatigue Fracture, ASTM STP 1110, Philadephia PA, 1991: 269–286.Google Scholar
  12. [12]
    Abdelrahman, W.G. and Nayfeh, A.H., Stress transfer and stiffness reduction in orthogonally cracked laminates. Mechanics of Materials, 1999, 31(5): 303–316.CrossRefGoogle Scholar
  13. [13]
    Leblond, P., Mahi, A.E. and Berthelot, J.M., 2D and 3D numerical models of transverse cracking in cross-ply laminates. Composite Science and Technology, 1996, 56(7): 793–796.CrossRefGoogle Scholar
  14. [14]
    Toledo, M.W.E., Nallim, L.G. and Luccioni, B.M., A micro-macromechanical approach for composite laminates. Mechanics of Materials, 2008, 40(11): 885–906.CrossRefGoogle Scholar
  15. [15]
    Soden, P.D., Hinton, M.J. and Kaddour, A.S., Biaxial test results for strength and deformation of a range of E-glass and carbon fiber reinforced composite laminates: Failure exercise benchmark data. Composite Science and Technology, 2002, 62(12–13): 1489–1514.CrossRefGoogle Scholar
  16. [16]
    Rotem, A., Prediction of laminate failure with the rotem failure criterion. Composite Science and Technology, 1998, 58(7): 1083–1094.CrossRefGoogle Scholar
  17. [17]
    Puck, A. and Schürmann, H., Failure analysis of FRP laminates by means of physically based phenomeno-logical models. Composite Science and Technology, 1998, 58(7): 1045–1067.CrossRefGoogle Scholar
  18. [18]
    Edge, E.C., Stress-based grant-sanders method for predicting failure of composite laminates. Composite Science and Technology, 1998, 58(7): 1033–1041.CrossRefGoogle Scholar
  19. [19]
    Butalia, T.S. and Wolfe, W.E., A strain-energy-based non-linear failure criterion: comparison of numerical predictions and experimental observations for symmetric composite laminates. Composite Science and Technology, 2002, 62(12–13): 1697–1710.CrossRefGoogle Scholar
  20. [20]
    Zhang, J., Fan, J. and Soutis, C., Analysis of multiple cracking in [±θm/90n]s composite laminates — Part I: In-plane stiffness properties. Composites, 1992, 23(5): 291–298.CrossRefGoogle Scholar
  21. [21]
    Zhang, J., Fan, J. and Soutis, C., Analysis of multiple cracking in [±θm/90n]s composite laminates — Part II: Development of transverse ply crack. Composites, 1992, 23(5): 299–304.CrossRefGoogle Scholar
  22. [22]
    Zhang, J. and Herrmann, K.P., Stiffness degradation induced by multiplayer intralaminar cracking in composite laminates. Composites Part A, 1999, 30(5): 683–706.CrossRefGoogle Scholar
  23. [23]
    Zhang, J., Herrmann, K.P. and Fan, J., A theoretical model of matrix cracking in composite laminates under thermomechanical loading. Acta Mechanica Solida Sinica, 2001, 14(4): 299–305.Google Scholar
  24. [24]
    Liu, K.S. and Tsai, S.W., A progressive quadratic failure criterion for a laminate. Composite Science and Technology, 1998, 58(7): 1023–1032.CrossRefGoogle Scholar
  25. [25]
    Soden, P.D., Hinton, M.J. and Kaddour, A.S., Lamina properties, lay-up configurations and loading conditions for a range of fiber-reinforced composite laminates. Composite Science and Technology, 1998, 58(7): 1011–1022.CrossRefGoogle Scholar
  26. [26]
    Peters, P.W.M., The strength of 0/90 graphite-epoxy laminates with crack 90°-layers. Poster paper presented at Conf: Testing Evaluation and Quality Control of Composites, University of Surrey, Guildford, UK, step -14. 1983.Google Scholar
  27. [27]
    Bailey, J.E., Curtis, P.T. and Parvizi, A., On the transverse cracking and longitudinal splitting behaviour of glass and carbon fiber reinforced epoxy cross ply laminates and the effect of poisson and thermally generated strain. Proceedings of the Royal Society London A, 1979, 366: 599–623.CrossRefGoogle Scholar
  28. [28]
    Zeng, Q.D., Ma, R. and Fan, F.Q., Micro-statistical analysis of ultimate tensile strength of cross-ply laminates. Acta Mechanica Sinica, 1994, 26(4): 451–461 (in Chinese).Google Scholar
  29. [29]
    Hinton,M.J., Personal Communication with Organizers of Failure Exercise, 1997.Google Scholar
  30. [30]
    Wolfe, W.E. and Butalia, T.S., A strain-based failure criterion for non-linear analysis of composite laminates subjected to biaxial loading. Composite Science and Technology, 1998, 58(7): 1107–1124.CrossRefGoogle Scholar
  31. [31]
    Zinoviev, P.A., Lebedeva, O.V. and Tairova, L.P., A coupled analysis of experimental and theoretical results on the deformation and failure of composite laminates under a state of plane stress. Composite Science and Technology, 2002, 62(12–13): 1711–1723.CrossRefGoogle Scholar
  32. [32]
    Karihaloo, B.L. and Stang, H., Buckling-driven delamination growth in composite laminates: Guidelines for assessing the threat posed by interlaminar matrix delamination. Composites Part B, 2008, 39(2): 386–395.CrossRefGoogle Scholar

Copyright information

© The Chinese Society of Theoretical and Applied Mechanics and Technology 2010

Authors and Affiliations

  1. 1.School of Materials Science and EngineeringSouthwest UniversityChongqingChina
  2. 2.School of Architecture and EnvironmentSichuan UniversityChengduChina
  3. 3.Department of Mechanics and Shanghai Institute of Applied Mathematics and MechanicsShanghai UniversityShanghaiChina

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