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An enhanced beam-theory model of the mixed-mode bending (MMB) test—Part II: Applications and results

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An Erratum to this article was published on 17 January 2013

Abstract

The paper presents an enhanced beam-theory (EBT) model of the mixed-mode bending (MMB) test, whereby the specimen is considered as an assemblage of two sublaminates partly connected by an elastic–brittle interface. Analytical expressions for the compliance, energy release rate, and mode mixity are deduced. A compliance calibration strategy enabling numerical or experimental evaluation of the interface elastic constants is also presented. Furthermore, analytical expressions for the crack length correction parameters—analogous to those given by the corrected beam-theory (CBT) model for unidirectional laminated specimens—are furnished for multidirectional laminated specimens, as well. Lastly, an example application to experimental data reduction is presented.

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References

  1. Crews JH Jr, Reeder JR (1988) A mixed-mode bending apparatus for delamination testing. NASA TM-100662. http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19890001574_1989001574.pdf

  2. Reeder JR, Crews JH Jr (1990) Mixed-mode bending method for delamination testing. AIAA J 28(7):1270–1276. doi:10.2514/3.25204

    Article  ADS  Google Scholar 

  3. Reeder JR, Crews JH Jr (1992) Redesign of mixed-mode bending delamination test to reduce nonlinear effects. J Compos Technol Res 14(1):12–19. doi:10.1520/CTR10078J

    Article  Google Scholar 

  4. Reeder JR (2003) Refinements to the mixed-mode bending test for delamination toughness. J Compos Technol Res 25(4):191–195. doi:10.1520/CTR10961J

    Google Scholar 

  5. ASTM (2006) Standard test method for mixed mode I-mode II interlaminar fracture toughness of unidirectional fiber reinforced polymer matrix composites, D6671/D6671M-06. Am Soc Testing Mat, West Conshohocken. doi:10.1520/D6671_D6671M-06

    Google Scholar 

  6. Adams DF, Carlsson LA, Pipes RB (2003) Experimental characterization of advanced composite materials, 3rd edn. CRC Press, Boca Raton

    MATH  Google Scholar 

  7. Bennati S, Fisicaro P, Valvo PS (2013) An enhanced beam-theory model of the mixed-mode bending (MMB) test—Part I: Literature review and mechanical model. Meccanica. doi:10.1007/s11012-012-9686-3

  8. Kinloch AJ, Wang Y, Williams JG, Yayla P (1993) The mixed-mode delamination of fibre composite materials. Compos Sci Technol 47(3):225–237. doi:10.1016/0266-3538(93)90031-B

    Article  ADS  Google Scholar 

  9. Williams JG (1989) End corrections for orthotropic DCB specimens. Compos Sci Technol 35(4):367–376. doi:10.1016/0266-3538(89)90058-4

    Article  Google Scholar 

  10. Kanninen MF (1973) An augmented double cantilever beam model for studying crack propagation and arrest. Int J Fract 9(1):83–92. doi:10.1007/BF00035958

    Google Scholar 

  11. Wang Y, Williams JG (1992) Corrections for mode II fracture toughness specimens of composites materials. Compos Sci Technol 43(3):251–256. doi:10.1016/0266-3538(92)90096-L

    Article  Google Scholar 

  12. Bhashyan S, Davidson BD (1997) Evaluation of data reduction methods for the mixed mode bending test. AIAA J 35(3):546–552. doi:10.2514/2.129

    Article  ADS  Google Scholar 

  13. Wang JL, Qiao PZ (2004) Novel beam analysis of end notched flexure specimen for mode-II fracture. Eng Fract Mech 71(2):219–231. doi:10.1016/S0013-7944(03)00096-1

    Article  MathSciNet  Google Scholar 

  14. de Morais AB (2011) Novel cohesive beam model for the End-Notched Flexure (ENF) specimen. Eng Fract Mech 78(17):3017–3029. doi:10.1016/j.engfracmech.2011.08.019

    Article  Google Scholar 

  15. Jumel J, Budzik MK, Ben Salem N, Shanahan MER (2013) Instrumented end notched flexure—crack propagation and process zone monitoring. Part I: Modelling and analysis. Int J Solids Struct 50(2):297–309. doi:10.1016/j.ijsolstr.2012.08.028

    Article  Google Scholar 

  16. de Morais AB, Pereira AB (2006) Mixed mode I + II interlaminar fracture of glass/epoxy multidirectional laminates—Part 1: Analysis. Compos Sci Technol 66(13):1889–1895. doi:10.1016/j.compscitech.2006.04.006

    Article  Google Scholar 

  17. Pereira AB, de Morais AB (2006) Mixed mode I + II interlaminar fracture of glass/epoxy multidirectional laminates—Part 2: Experiments. Compos Sci Technol 66(13):1896–1902. doi:10.1016/j.compscitech.2006.04.008

    Article  Google Scholar 

  18. de Morais AB, Pereira AB (2007) Interlaminar fracture of multidirectional glass/epoxy laminates under mixed-mode I + II loading. Mech Compos Mater 43(3):233–244. doi:10.1007/s11029-007-0023-1

    Article  Google Scholar 

  19. Pereira AB, de Morais AB (2008) Mixed mode I + II interlaminar fracture of carbon/epoxy laminates. Composites. Part A 39(2):322–333. doi:10.1016/j.compositesa.2007.10.013

    Article  Google Scholar 

  20. Bennati S, Colleluori M, Corigliano D, Valvo PS (2009) An enhanced beam-theory model of the asymmetric double cantilever beam (ADCB) test for composite laminates. Compos Sci Technol 69(11–12):1735–1745. doi:10.1016/j.compscitech.2009.01.019

    Article  Google Scholar 

  21. Jones RM (1999) Mechanics of composite materials, 2nd edn. Taylor & Francis, Philadelphia

    Google Scholar 

  22. Vannucci P, Verchery G (2001) A special class of uncoupled and quasi-homogeneous laminates. Compos Sci Technol 61(10):1465–1473. doi:10.1016/S0266-3538(01)00039-2

    Article  Google Scholar 

  23. Ozdil F, Carlsson LA (1999) Beam analysis of angle-ply laminate mixed-mode bending specimens. Compos Sci Technol 59(6):937–945. doi:10.1016/S0266-3538(98)00128-6

    Article  Google Scholar 

  24. Timoshenko SP (1984) Strength of materials: elementary theory and problems, vol 1. Krieger, Melbourne

    Google Scholar 

  25. Strand7 (2005) Theoretical manual: theoretical background to the Strand7 finite element analysis system, 1st edn. G+D Computing, Sidney

    Google Scholar 

  26. Hutchinson JW, Suo Z (1991) Mixed mode cracking in layered materials. Adv Appl Mech 29(C):63–191. doi:10.1016/S0065-2156(08)70164-9

    Article  Google Scholar 

  27. 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(6):594–604. doi:10.1177/002199838602000606

    Article  Google Scholar 

  28. Fan C, Ben Jar P-Y, Cheng J-JR (2006) Revisit the analysis of end-notched-flexure (ENF) specimen. Compos Sci Technol 66(10):1497–1498. doi:10.1016/j.compscitech.2006.01.016

    Article  Google Scholar 

  29. Valvo PS (2008) Does shear deformability influence the mode II delamination of laminated beams?. In: ECF17—17th European conference on fracture, 2–5 September 2008, Brno, Czech Republic

  30. Corigliano A (1993) Formulation, identification and use of interface models in the numerical analysis of composite delamination. Int J Solids Struct 30(20):2779–2811. doi:10.1016/0020-7683(93)90154-Y

    Article  MATH  Google Scholar 

  31. Budzik MK, Jumel J, Ben Salem N, Shanahan MER (2013) Instrumented end notched flexure—crack propagation and process zone monitoring. Part II: Data reduction and experimental. Int J Solids Struct 50(2):310–319. doi:10.1016/j.ijsolstr.2012.08.030

    Article  Google Scholar 

  32. Ducept F, Davies P, Gamby D (1997) An experimental study to validate tests used to determine mixed mode failure criteria of glass/epoxy composites. Composites. Part A 28(8):719–729. doi:10.1016/S1359-835X(97)00012-2

    Article  Google Scholar 

  33. Pereira AB (2006) Fractura interlaminar de compósitos de matriz polimérica. PhD thesis, University of Aveiro. http://ria.ua.pt/bitstream/10773/2549/1/2007001048.pdf

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Acknowledgements

The financial support of the Italian Ministry of Education, University and Research (MIUR) under programme PRIN 2008 “Light structures based on multiscale material in civil engineering: stiffness and strength, assembly and industrial repeatability” (Prot. N. 20089RJKYN_002) is gratefully acknowledged.

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Correspondence to Paolo S. Valvo.

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Bennati, S., Fisicaro, P. & Valvo, P.S. An enhanced beam-theory model of the mixed-mode bending (MMB) test—Part II: Applications and results. Meccanica 48, 465–484 (2013). https://doi.org/10.1007/s11012-012-9682-7

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  • DOI: https://doi.org/10.1007/s11012-012-9682-7

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