Journal of Mechanical Science and Technology

, Volume 32, Issue 12, pp 5823–5829 | Cite as

The influence of material shear nonlinearity on multidirectional laminates in terms of failure envelopes

  • Hongli Jia
  • Hyun-Ik YangEmail author
  • Tae-won Kang


Influence of material shear nonlinearity on multidirectional laminates in terms of failure envelopes was investigated. In applying classic laminate theory, elastic constants were employed in transverse and longitudinal directions, while initial shear modulus was substituted by the secant shear modulus, which was achieved by means of Ramberg-Osgood model. The fracture curves were generated from maximum stress, Tsai-Wu and Puck criteria. The similarities and differences between nonlinear and linear shear models can be expressed in terms of symmetric balanced laminates [±θ°]2s and asymmetric laminates [0°2/±θ°], which are both arranged by material E-glass/MY750 oriented at different directions. All σ1 - σ2 failure envelopes due to material nonlinearity extend outward in tensile and compressive directions, but the phenomenon is not obvious with increasing ply angles. Similarly, the differences of all σ1 - τ12 failure envelopes between nonlinear shear analysis and linear shear analysis are decreasing with increased ply angles. Ply orientations and loading directions are involved in the effect of nonlinear shear properties on failure envelopes. According to the failure modes obtained from maximum stress criterion, it is reasonably derived that the influence of material shear nonlinearity will lead whether the failure envelopes from the other two failure criteria are more conservative or not.


Failure envelopes GFRP Nonlinear shear property Ramberg-Osgood model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    P. D. Soden, M. J. Hinton and A. S. Kaddour, Lamina properties, lay–up configurations and loading conditions for a range of fibre reinforced composite laminates, Composite Science and Technology, 58 (7) (1998) 1011–1022.CrossRefGoogle Scholar
  2. [2]
    J. Andersons, J. Modniks and E. Sparnins, Modeling the nonlinear deformation of flax–fiber–reinforced polymer matrix laminates in active loading, J. of Reinforced Plastics and Composites, 34 (3) (2015) 248–256.CrossRefGoogle Scholar
  3. [3]
    S. Ogihara, S. Kobayashi and K. L. Reifnider, Characterization of nonlinear behavior of carbon/epoxy unidirectional and angle–ply laminates, Advanced Composite Materials, 11 (3) (2003) 239–254.CrossRefGoogle Scholar
  4. [4]
    T. Yokozeki, T. Ogasawara and T. Ishikawa, Nonlinear behavior and compressive strength of unidirectional and multidirectional carbon fiber composite laminates, Composites Part A: Applied Science and Manufacturing, 37 (11) (2006) 2069–2079.CrossRefGoogle Scholar
  5. [5]
    T. Kroupa, V. Laš and R. Zemčík, Improved nonlinear stress–strain relation for carbon–epoxy composites and identification of material parameters, J. of Composite Materials, 45 (9) (2011) 1045–1057.CrossRefGoogle Scholar
  6. [6]
    T. Yokozeki, T. Ogasawara and T. Ishikawa, Effects of the fiber nonlinear properties on the compressive strength prediction of unidirectional carbon–fiber composites, Composite Science and Technology, 65 (14) (2005) 2140–2147.CrossRefGoogle Scholar
  7. [7]
    Zand Behrad, Modelling of composite laminates subjected to multiaxial, Doctoral Dissertation, Ohio State University (2007) Retrieved from Scholar
  8. [8]
    W. P. Lin and H. T. Hu, Nonlinear analysis of fiberreinforced composite laminates subjected to uniaxial tensile load, J. of Composite Materials, 36 (12) (2002) 1429–1450.CrossRefGoogle Scholar
  9. [9]
    F. Hassani, M. M. Shokrieh and L. B. Lessard, A fully nonlinear 3D constitutive relationship for the stress analysis of a pin–loaded composite laminate, Composite Science and Technology, 62 (3) (2002) 429–439.CrossRefGoogle Scholar
  10. [10]
    C. T. Sun and J. L. Chen, A micromechanical model for plastic behavior of fibrous composites, Composite Science and Technology, 40 (2) (1991) 115–129.MathSciNetCrossRefGoogle Scholar
  11. [11]
    R. Haj–Ali and H. Kilic, Nonlinear constitutive models for pultruded FRP composites, Mechanics of Materials, 35 (8) (2003) 791–801.CrossRefGoogle Scholar
  12. [12]
    A. Puck and H. Schürmann, Failure analysis of FRP laminates by means of physically based phenomenological models. Composite Science and Technology, 58 (7) (1998) 1045–1068.CrossRefGoogle Scholar
  13. [13]
    A. Puck, J. Kopp and M. Knops, Guidelines for the determination of the parameters in Puck’s action plane strength criterion, Composite Science and Technology, 62 (3) (2002) 371–378.CrossRefGoogle Scholar

Copyright information

© The Korean Society of Mechanical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringHanyang UniversityAnsanKorea
  2. 2.Department of Mechanical DesignHanyang UniversityAnsanKorea

Personalised recommendations