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Journal of Failure Analysis and Prevention

, Volume 17, Issue 5, pp 1011–1018 | Cite as

Delamination Modeling of Double Cantilever Beam of Unidirectional Composite Laminates

Technical Article---Peer-Reviewed

Abstract

Delamination crack growth in a double cantilever beam laminated composites is modeled by using simple stress analysis beam theory combined with simple linear elastic fracture mechanics and consideration of the theory of elastic failure in mechanics of material. Furthermore, advanced finite element (FE) model is built up. The FE approach employs surface cohesive zone model that is used to simulate the debonding and crack propagation. The analytical modeling, moreover, cracks growth and strain measurements, which are obtained from FE models, are compared with the available published experimental work. The predicted results give good agreement with interlaminar fracture toughness and maximum load which correspond to crack initiation point. The FE models results agree well with the available experimental data for both crack initiation and propagation.

Keywords

Fracture toughness Delamination DCB Cohesive surface Crack propagation 

List of symbols

\(\sigma_{\text{co}}\)

Cohesive stress

GIC

Mode I surface release energy or fracture toughness

F

The load at the end of arm

E

The Young’s modulus

I

The second moment of area

b

Beam width

h

Beam thickness

v

Total vertical displacement

u

Half displacement

C

Compliance

\(\partial A\)

Crack extension area

\(\sigma_{\text{b}}\)

Bending stress

Y

Distance from point load at crack tip

UE

Stored elastic energy

M(x)

Bending moment in x axis plane

G

Surface release energy

\(\sigma_{\text{u}}\)

Un-notch tensile strength

Xt

Transverse tensile strength

Eeff

Effective Young’s modulus

Keff

Effective stiffness

\(\delta_{\text{o}}\)

Critical initiation traction–separation displacement

\(\delta_{\text{f}}\)

Critical crack opening

tn

Normal contact stress

ts

Shear contact stress

tt

Traction contact stress

GIC, GIIC, and GIIIC

Mode I, II, and III surface release energy

References

  1. 1.
    P.P. Camanho, C. Davila, M. De Moura, Numerical Simulation of Mixed-Mode Progressive Delamination in Composite Materials. J. Compos. Mater. 37(16), 1415–1438 (2003)CrossRefGoogle Scholar
  2. 2.
    V. La Saponara, H. Muliana, R. Haj-Ali, G.A. Kardomateas, Experimental and Numerical Analysis of Delamination Growth in Double Cantilever Laminated Beams. Eng. Fract. Mech. 69(6), 687–699 (2002)CrossRefGoogle Scholar
  3. 3.
    A.C. Garg, Delamination—A Damage Mode in Composite Structures. Eng. Fract. Mech. 29(5), 557–584 (1988)CrossRefGoogle Scholar
  4. 4.
    V.V. Bolotin, Delaminations in Composite Structures: Its Origin, Buckling, Growth and Stability. Compos. Part B Eng. 27(2), 129–145 (1996)CrossRefGoogle Scholar
  5. 5.
    S.T. Pinho, Modelling Failure of Laminated Composites Using Physically-Based Failure Models (Imperial College London (University of London), London, 2005)Google Scholar
  6. 6.
    S. Pinho, L. Iannucci, P. Robinson, Formulation and Implementation of Decohesion Elements in an Explicit Finite Element Code. Compos. Part A Appl. Sci. Manuf. 37(5), 778–789 (2006)CrossRefGoogle Scholar
  7. 7.
    J.C. Sosa, N. Karapurath, Delamination Modelling of GLARE Using the Extended Finite Element Method. Compos. Sci. Technol. 72(7), 788–791 (2012)CrossRefGoogle Scholar
  8. 8.
    Y. Mohammed, M.K. Hassan, A. Hashem, Analytical Model to Predict Multiaxial Laminate Fracture Toughness from 0 ply Fracture Toughness. Polym. Eng. Sci. 54(1), 234–238 (2014)CrossRefGoogle Scholar
  9. 9.
    Y. Mohammed, K. Mohamed, A. Hashem, Finite Element Computational Approach of Fracture Toughness in Composite Compact-Tension Specimens. Int. J. Mech. Mechatron. Eng. 12(4), 57–61 (2010)Google Scholar
  10. 10.
    F. Greco, P. Lonetti, R. Zinno, An Analytical Delamination Model for Laminated Plates Including Bridging Effects. Int. J. Solids Struct. 39(9), 2435–2463 (2002)CrossRefGoogle Scholar
  11. 11.
    P. Liu, Z. Gu, Finite Element Analysis of Single-Leg Bending Delamination of Composite Laminates Using a Nonlinear Cohesive Model. J. Fail. Anal. Prev. 15(6), 846–852 (2015)CrossRefGoogle Scholar
  12. 12.
    O. Allix, A. Corigliano, Geometrical and Interfacial Non-linearities in the Analysis of Delamination in Composites. Int. J. Solids Struct. 36(15), 2189–2216 (1999)CrossRefGoogle Scholar
  13. 13.
    P. Camanho, F. Matthews, Delamination Onset Prediction in Mechanically Fastened Joints in Composite Laminates. J. Compos. Mater. 33(10), 906–927 (1999)CrossRefGoogle Scholar
  14. 14.
    C.G. Davila, E.R. Johnson, Analysis of Delamination Initiation in Postbuckled Dropped-ply Laminates. AIAA J. 31(4), 721–727 (1993)CrossRefGoogle Scholar
  15. 15.
    M. De Moura, J. Gonçalves, A. Marques, P. De Castro, Prediction of Compressive Strength of Carbon–Epoxy Laminates Containing Delamination by Using a Mixed-Mode Damage Model. Compos. Struct. 50(2), 151–157 (2000)CrossRefGoogle Scholar
  16. 16.
    R. Kim, S. Soni, Experimental and Analytical Studies on the Onset of Delamination in Laminated Composites. J. Compos. Mater. 18(1), 70–80 (1984)CrossRefGoogle Scholar
  17. 17.
    E. Reedy, F. Mello, T. Guess, Modeling the Initiation and Growth of Delaminations in Composite Structures. J. Compos. Mater. 31(8), 812–831 (1997)CrossRefGoogle Scholar
  18. 18.
    P. Yayla, Fracture Surface Morphology of Delamination Failure of Polymer Fiber Composites Under Different Failure Modes. J. Fail. Anal. Prev. 16(2), 264–270 (2016)CrossRefGoogle Scholar
  19. 19.
    X.K. Li, P.F. Liu, Delamination Analysis of Carbon Fiber Composites Under Dynamic Loads Using Acoustic Emission. J. Fail. Anal. Prev. 16(1), 142–153 (2016)CrossRefGoogle Scholar
  20. 20.
    C.H. Wang, Introduction to Fracture Mechanics (DSTO Aeronautical and Maritime Research Laboratory, Melbourne, 1996)Google Scholar
  21. 21.
    E. Hearn, Mechanics of Materials, Vols. 1–2 (Pergamon Press, Oxford, 1985)Google Scholar
  22. 22.
    B.J. Goodno, J.M. Gere, Mechanics of Materials (Cengage Learning, Boston, 2016)Google Scholar
  23. 23.
    D.S. Dugdale, Yielding of Steel Sheets Containing Slits. J. Mech. Phys. Solids 8(2), 100–104 (1960)CrossRefGoogle Scholar
  24. 24.
    G.I. Barenblatt, The Mathematical Theory of Equilibrium Cracks in Brittle Fracture. Adv. Appl. Mech. 7, 55–129 (1962)CrossRefGoogle Scholar
  25. 25.
    M.K. Hassan, Y. Mohammed, T. Salem, A. Hashem, Prediction of Nominal Strength of Composite Structure Open Hole Specimen Through Cohesive Laws. Int. J. Mech. Mech. Eng. IJMME-IJENS 12, 1–9 (2012)Google Scholar
  26. 26.
    Y. Mohammed, M.K. Hassan, H. Abu El-Ainin, A. Hashem, Size Effect Analysis in Laminated Composite Structure Using General Bilinear Fit. Int. J. Nonlinear Sci. Numer. Simul. 14(3–4), 217–224 (2013)Google Scholar
  27. 27.
    Y. Mohammed, M.K. Hassan, H.A. El-Ainin, A. Hashem, Size Effect Analysis of Open-Hole Glass Fiber Composite Laminate Using Two-Parameter Cohesive Laws. Acta Mech. 226(4), 1027–1044 (2015)CrossRefGoogle Scholar
  28. 28.
    A. Standard, D5528-94a, Standard Test Method for Mode I Interlaminar Fracture Toughness of Unidirectional Continuous Fiber Reinforced Polymer Matrix Composites, Philadelphia, PA, USA (1994)Google Scholar
  29. 29.
    M. Ramamurthi, J.-S. Lee, S.-H. Yang, Y.-S. Kim, Delamination Characterization of Bonded Interface in polymer Coated Steel Using Surface Based Cohesive Model. Int. J. Precis. Eng. Manuf. 14(10), 1755–1765 (2013)CrossRefGoogle Scholar
  30. 30.
    A. Version, 6.9. 1, User Documentation (2009)Google Scholar
  31. 31.
    J. Planas, Z. Bažant, M. Jirásek, Reinterpretation of Karihaloo’s Size Effect Analysis for Notched Quasibrittle Structures. Int. J. Fract. 111(1), 17–28 (2001)CrossRefGoogle Scholar
  32. 32.
    C. Soutis, N. Fleck, P. Smith, Failure Prediction Technique for Compression Loaded Carbon Fibre-Epoxy Laminate with Open Holes. J. Compos. Mater. 25(11), 1476–1498 (1991)CrossRefGoogle Scholar
  33. 33.
    J. Bieniaś, H. Dębski, B. Surowska, T. Sadowski, Analysis of Microstructure Damage in Carbon/Epoxy Composites Using FEM. Comput. Mater. Sci. 64, 168–172 (2012)CrossRefGoogle Scholar
  34. 34.
    A. Turon, C.G. Davila, P.P. Camanho, J. Costa, An Engineering Solution for Mesh Size Effects in the Simulation of Delamination Using Cohesive Zone Models. Eng. Fract. Mech. 74(10), 1665–1682 (2007)CrossRefGoogle Scholar
  35. 35.
    T.L. Anderson, T. Anderson, Fracture Mechanics: Fundamentals and Applications (CRC Press, Boca Raton, 2005)Google Scholar
  36. 36.
    P.P. Camanho, P. Maimí, C. Dávila, Prediction of Size Effects in Notched Laminates Using Continuum Damage Mechanics. Compos. Sci. Technol. 67(13), 2715–2727 (2007)CrossRefGoogle Scholar
  37. 37.
    P. Maimí, P.P. Camanho, J. Mayugo, C. Dávila, A Continuum Damage Model for Composite Laminates: Part II—Computational Implementation and Validation. Mech. Mater. 39(10), 909–919 (2007)CrossRefGoogle Scholar
  38. 38.
    M.Y. Abdellah, M.K. Hassan, Numerical Analysis of Open Hole Specimen Glass Fiber Reinforced Polymer. Nonlinear Eng. 3(3), 141–147 (2014)CrossRefGoogle Scholar

Copyright information

© ASM International 2017

Authors and Affiliations

  1. 1.Mechanical Engineering Department, Faculty of EngineeringSouth Valley UniversityQenaEgypt

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