Skip to main content
SpringerLink
Log in

Evaluations on VCCT and CZM methods of delamination propagation simulation for composite specimens

  • Original Paper
  • Published:
Aerospace Systems Aims and scope Submit manuscript

Abstract

Fiber-reinforced composite laminates are widely used in aerospace and other fields. Delamination damage is the main damage form of laminates, which has always been one of the focus problems of composite mechanics. Virtual crack closure technique (VCCT) and cohesive zone modeling (CZM) are two well-known numerical methods frequently used for crack propagation modeling. In this study, to better understand the advantages and limitations of these two methods, as well as the process of practical application, the evaluations on them are conducted. A double cantilever beam (DCB) specimen, an end notched flexure (ENF) specimen, and a mixed-mode bending (MMB) specimen as benchmark examples are modeled in ABAQUS. The mode I, mode II, and mixed-mode (I + II) delamination initiation and propagation behaviors of unidirectional specimens are simulated using two above methods. Finite element (FE) results are compared with experimental results available in the literature to verify the validity of the FE models. Finally, the accuracy, convergence speed, run-time, mesh dependency, and influence of modeling parameters of each method are discussed based on the simulation of DCB test.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16

Similar content being viewed by others

Data availability

Not applicable.

References

  1. Gliszczynski A, Samborski S, Wiacek N, Rzeczkowski J (2019) Mode I interlaminar fracture of glass/epoxy unidirectional laminates. Part II: numerical analysis. Materials (Basel) 12:1604. https://doi.org/10.3390/ma12101604

    Article  Google Scholar 

  2. Anderson TL (2005) Fracture mechanics: Fundamentals and applications. CRC Press, Boca Raton

    Book  MATH  Google Scholar 

  3. Babaevsky PG, Kulik SG (1991) Crack resistance of cured polymer compositions. Khimiya Publ, Moscow, p 336

    Google Scholar 

  4. Babayevsky PG, Saliyenko NV, Novikov GV (2019) Used of experimentally determined parameters of the cohesive zone in the numerical evaluation of the resistance to delamination of polymer composites materials. Perspektivny’e material’ 3:74–81. https://doi.org/10.30791/1028-978X-2019-3-74-81

    Article  Google Scholar 

  5. Yakovlev NO, Gulyaev AI, Lashov OA (2016) Fracture toughness of laminated polymer composites (review). Trudy’ VIAM 4:12. https://doi.org/10.18577/2307-6046-2016-0-4-12-12

    Article  Google Scholar 

  6. Yakovlev NO, Gulyaev AI, Krylov VD, Shurtakov SV (2016) Microstructure and properties of the structural composite material at static interlaminar fracture toughness test. Novosti materialovedeniya Nauka i texnika 1:9

    Google Scholar 

  7. Irwin GR (1957) Analysis of stresses and strains near the end of a crack traversing a plate. J Appl Mech 24:361–364. https://doi.org/10.1115/1.4011547

    Article  Google Scholar 

  8. Robinson P, Javidrad F, Hitchings D (1995) Finite element modelling of delamination growth in the DCB and edge delaminated DCB specimens. Compos Struct 32:275–285. https://doi.org/10.1016/0263-8223(95)00047-X

    Article  Google Scholar 

  9. Fawaz SA (1998) Application of the virtual crack closure technique to calculate stress intensity factors for through cracks with an elliptical crack front. Eng Fract Mech 59:327–342. https://doi.org/10.1016/s0013-7944(97)00126-4

    Article  Google Scholar 

  10. Krueger R (2004) Virtual crack closure technique: history, approach, and applications. Appl Mech Rev 57:109–143. https://doi.org/10.1115/1.1595677

    Article  Google Scholar 

  11. Shokrieh MM, Heidari-Rarani M, Rahimi S (2012) Influence of curved delamination front on toughness of multidirectional DCB specimens. Compos Struct 94:1359–1365. https://doi.org/10.1016/j.compstruct.2011.11.035

    Article  Google Scholar 

  12. Orifici AC, Krueger R (2012) Benchmark assessment of automated delamination propagation capabilities in finite element codes for static loading. Finite Elem Anal Des 54:28–36. https://doi.org/10.1016/j.finel.2012.01.006

    Article  Google Scholar 

  13. Shokrieh MM, Rajabpour-Shirazi H, Heidari-Rarani M, Haghpanahi M (2012) Simulation of mode i delamination propagation in multidirectional composites with R-curve effects using VCCT method. Comput Mater Sci 65:66–73. https://doi.org/10.1016/j.commatsci.2012.06.025

    Article  Google Scholar 

  14. Valvo PS (2014) A physically consistent virtual crack closure technique for I/II/III mixed-mode fracture problems. Proc Mater Sci 3:1983–1987. https://doi.org/10.1016/j.mspro.2014.06.319

    Article  Google Scholar 

  15. Samborski S (2016) Numerical analysis of the DCB test configuration applicability to mechanically coupled Fiber Reinforced Laminated Composite beams. Compos Struct 152:477–487. https://doi.org/10.1016/j.compstruct.2016.05.060

    Article  Google Scholar 

  16. Xu XP, Needleman A (1993) Void nucleation by inclusion debonding in a crystal matrix. Model Simul Mater Sci Eng 1:111–132. https://doi.org/10.1088/0965-0393/1/2/001

    Article  Google Scholar 

  17. Camanho PP, Dávila CG, De Moura MF (2003) Numerical simulation of mixed-mode progressive delamination in composite materials. J Compos Mater 37:1415–1438. https://doi.org/10.1177/0021998303034505

    Article  Google Scholar 

  18. Fan C, Jar PYB, Cheng JJR (2008) Cohesive zone with continuum damage properties for simulation of delamination development in fibre composites and failure of adhesive joints. Eng Fract Mech 75:3866–3880. https://doi.org/10.1016/j.engfracmech.2008.02.010

    Article  Google Scholar 

  19. Lu X, Ridha M, Chen BY, Tan VBC, Tay TE (2019) On cohesive element parameters and delamination modelling. Eng Fract Mech 206:278–296. https://doi.org/10.1016/j.engfracmech.2018.12.009

    Article  Google Scholar 

  20. Nguyen N, Waas AM (2016) A novel mixed-mode cohesive formulation for crack growth analysis. Compos Struct 156:253–262. https://doi.org/10.1016/j.compstruct.2015.11.015

    Article  Google Scholar 

  21. Ji QH, Zhu P, Lu JH (2017) Numerical simulation and parameter identification of delamination failure for laminate. J Zhejiang Univ 51:954–960. https://doi.org/10.3785/j.issn.1008-973X.2017.05.015

    Article  Google Scholar 

  22. Barrett JD, Foschi RO (1977) Mode II stress-intensity factors for cracked wood beams. Eng Fract Mech 9:371–378. https://doi.org/10.1016/0013-7944(77)90029-7

    Article  Google Scholar 

  23. Russell AJ, Street KN (1982) Factors affecting the interlaminar fracture energy of graphite/epoxy laminates[C]//progress in science and engineering of composites. In: Proceedings of the 4th International Conference on Composite Materials, Tokyo: Japan Soc for Composite Materials, pp 279–286

  24. Carlsson LA, Gillespie JW, Pipes RB (1986) On the analysis and design of the End Notched Flexure (ENF) specimen for mode II testing. J Compos Mater 20:594–604. https://doi.org/10.1177/002199838602000606

    Article  Google Scholar 

  25. Gillespie JW, Carlsson LA, Pipes RB (1986) Finite element analysis of the end notched flexure specimen for measuring mode II fracture toughness. Compos Sci Technol 27:177–197. https://doi.org/10.1016/0266-3538(86)90031-X

    Article  Google Scholar 

  26. Akhavan-Safar A, Salamat-talab M, Ajdani A, Ayatollahi MR, da Silva LFM (2020) Mode II fracture energy characterization of brittle adhesives using compliance calibration method. Fatigue Fract Eng Mater Struct 43:1928–1937. https://doi.org/10.1111/ffe.13244

    Article  Google Scholar 

  27. Reeder JR, Crews JH (1992) Redesign of the mixed-mode bending delamination test to reduce nonlinear effects. J Compos Technol Res 14:12–19. https://doi.org/10.1520/ctr10078j

    Article  Google Scholar 

  28. Wu H, Settgast RR, Fu P, Morris JP (2021) An enhanced virtual crack closure technique for stress intensity factor calculation along arbitrary crack fronts and the application in hydraulic fracturing simulation. Rock Mech Rock Eng 54:2943–2957. https://doi.org/10.1007/s00603-021-02428-9

    Article  Google Scholar 

  29. Settgast RR, Fu P, Walsh SDC, White JA, Annavarapu C, Ryerson FJ (2017) A fully coupled method for massively parallel simulation of hydraulically driven fractures in 3-dimensions. Int J Numer Anal Methods Geomech 41:627–653. https://doi.org/10.1002/nag.2557

    Article  Google Scholar 

  30. Benzeggagh ML, Kenane M (1996) Measurement of mixed-mode delamination fracture toughness of unidirectional glass/epoxy composites with mixed-mode bending apparatus. Compos Sci Technol 56:439–449. https://doi.org/10.1016/0266-3538(96)00005-X

    Article  Google Scholar 

  31. Reeder JR (2013) 3-D mixed mode delamination fracture criteria—An experimentalist’s perspective. Destech Publications, Lancaster

    Google Scholar 

  32. Heidari-Rarani M, Sayedain M (2019) Finite element modeling strategies for 2D and 3D delamination propagation in composite DCB specimens using VCCT, CZM and XFEM approaches. Theor Appl Fract Mech 103:102246. https://doi.org/10.1016/j.tafmec.2019.102246

    Article  Google Scholar 

  33. Turon A, Davila CG, Camanho PP et al (2007) An engineering solution for mesh size effects in the simulation of de-lamination using cohesive zone models. Eng Fract Mech 74:1665–1682. https://doi.org/10.1016/j.engfracmech.2006.08.025

    Article  Google Scholar 

  34. Gliszczynski A, Wiącek N (2021) Experimental and numerical benchmark study of mode II interlaminar fracture toughness of unidirectional GFRP laminates under shear loading using the end-notched flexure (ENF) test. Compos Struct 258:113190. https://doi.org/10.1016/j.compstruct.2020.113190

    Article  Google Scholar 

  35. Deng J, Lu TJ, Yin QZ (2021) Analysis on I- II mixed interlaminar crack propagation of composite MMB specimens. Acta Aeronaut Astronaut Sin 42:224241. https://doi.org/10.7527/S1000-68932.020.24241

    Article  Google Scholar 

Download references

Funding

This work was supported by the Natural Science Foundation of China [grant number 12072199].

Author information

Authors and Affiliations

  1. Shanghai Jiao Tong University, Shanghai, China

    Rui Liu & Zhefeng Yu

  2. Moscow Aviation Institute, Moscow, Russian Federation

    Fedor Nasonov

Authors
  1. Rui Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhefeng Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fedor Nasonov
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

RL was primarily responsible for the modeling and writing of the article, including designing and implementing the research methodology, conducting data analysis, and drafting the manuscript. ZY contributed to the conceptualization of the project, providing valuable insights and expertise in the field of study, and assisting in the development of the research design. FN participated in the writing and conceptualization of the project, providing critical feedback and suggestions during the manuscript preparation process. All authors read and approved the final version of the article, ensuring the accuracy and integrity of the research findings presented.

Corresponding author

Correspondence to Zhefeng Yu.

Ethics declarations

Conflict of interest

There is no conflict of interest.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, R., Yu, Z. & Nasonov, F. Evaluations on VCCT and CZM methods of delamination propagation simulation for composite specimens. AS 6, 621–632 (2023). https://doi.org/10.1007/s42401-023-00231-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42401-023-00231-8

Keywords

Search

Navigation