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Finite Fracture Mechanics: A Useful Tool to Analyze Cracking Mechanisms in Composite Materials

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The Structural Integrity of Carbon Fiber Composites

Abstract

The coupled criterion is a finite fracture mechanics approach which couples an energy condition and a stress condition to predict crack initiation at stress concentration points. It is here used to study various cracking mechanisms in composite materials at different scales. The paper focuses on edge delamination at the mesoscale and also considers crack nucleation in the vicinity of a matrix crack at the microscale.

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References

  1. P.W.R. Beaumont, in Structural Integrity and the Implementation of Engineering Composite Materials, Chapter 15, ed. by P.W.R. Beaumont, C. Soutis, A. Hodzic. Structural Integrity and Durability of Advanced Composites: Innovative Modelling Methods and Intelligent Design (Woodhead Publishing Limited, 2015), pp. 353–396, ISBN 9780081001370

    Google Scholar 

  2. M. Kashtalyan, C. Soutis, Analysis of composite laminates with intra- and interlaminar damage. Prog. Aerosp. Sci. 41, 152–173 (2005). doi:10.1016/j.paerosci.2005.03.004

    Article  Google Scholar 

  3. J.A. Nairn, Matrix microcracking in composites. Polymer matrix composites 2, 403–432. Polymer Matrix Composites, Chapter 13, ed. by R. Talreja, J.-A. Manson, Volume 2 of Comprehensive Composite Materials, A. Kelly and C. Zweben, eds., (Elsevier Science, 2000)

    Google Scholar 

  4. A. Parvizi, K.W. Garrett, J.E. Bailey, Constrained cracking in glass fibre-reinforced epoxy cross-ply laminates. J. Mater. Sci. 13, 195–201 (1978)

    Article  Google Scholar 

  5. D.T.G. Katerelos, J. Varna, C. Galiotis, Energy criterion for modeling damage evolution in cross-ply composite laminates. Compos. Sci. Technol. 68, 2318–2324 (2008). doi:10.1016/j.compscitech.2007.09.014

    Article  Google Scholar 

  6. L.N. McCartney, Physically based damage models for laminated composites. Proc. Inst. Mech. Eng. Part L J. Mater. Des. Appl. 217, 163–199 (2003). doi:10.1177/146442070321700301

    Google Scholar 

  7. Z. Hashin, Finite thermoelastic fracture criterion with application to laminate cracking analysis. J. Mech. Phys. Solids 44, 1129–1145 (1996)

    Article  Google Scholar 

  8. E. Martin, D. Leguillon, Energetic conditions for interfacial failure in the vicinity of a matrix crack in brittle matrix composites. Int. J. Solids Struct. 41, 6937–6948 (2004). doi:10.1016/j.ijsolstr.2004.05.044

    Article  Google Scholar 

  9. D. Taylor, P. Cornetti, N. Pugno, The fracture mechanics of finite crack extension. Eng. Fract. Mech. 72, 1021–1038 (2005). doi:10.1016/j.engfracmech.2004.07.001

    Article  Google Scholar 

  10. D. Leguillon, Strength or toughness? A criterion for crack onset at a notch. Eur. J. Mech. A/Solids 21, 61–72 (2002)

    Article  Google Scholar 

  11. P. Cornetti, N. Pugno, A. Carpinteri, D. Taylor, Finite fracture mechanics: a coupled stress and energy failure criterion. Eng. Fract. Mech. 73, 2021–2033 (2006). doi:10.1016/j.engfracmech.2006.03.010

    Article  Google Scholar 

  12. D. Leguillon, Z. Yosibash, Crack onset at a notch. Influence of the notch tip radius. Int. J. Fract. 122, 1–21 (2003)

    Article  Google Scholar 

  13. A. Sapora, P. Cornetti, A. Carpinteri, A finite fracture mechanics approach to V-notched elements subjected to mixed-mode loading. Eng. Fract. Mech. 97, 216–226 (2013). doi:10.1016/j.engfracmech.2012.11.006

    Article  Google Scholar 

  14. J. Andersons, S. Tarasovs, E. Spārniņš, Finite fracture mechanics analysis of crack onset at a stress concentration in a UD glass/epoxy composite in off-axis tension. Compos. Sci. Technol. 70, 1380–1385 (2010). doi:10.1016/j.compscitech.2010.04.017

    Article  Google Scholar 

  15. P.P. Camanho, G.H. Erçin, G. Catalanotti, S. Mahdi, P. Linde, A finite fracture mechanics model for the prediction of the open-hole strength of composite laminates. Compos. Part A Appl. Sci. Manuf. 43, 1219–1225 (2012). doi:10.1016/j.compositesa.2012.03.004

    Article  Google Scholar 

  16. E. Martin, D. Leguillon, N. Carrère, A coupled strength and toughness criterion for the prediction of the open hole tensile strength of a composite plate. Int. J. Solids Struct. 49, 3915–3922 (2012). doi:10.1016/j.ijsolstr.2012.08.020

    Article  Google Scholar 

  17. N. Carrère, E. Martin, D. Leguillon, Comparison between models based on a coupled criterion for the prediction of the failure of adhesively bonded joints. Eng. Fract. Mech. 138, 185–201 (2015). doi:10.1016/j.engfracmech.2015.03.004

    Article  Google Scholar 

  18. S. Hell, P. Weißgraeber, J. Felger, W. Becker, A coupled stress and energy criterion for the assessment of crack initiation in single lap joints: a numerical approach. Eng. Fract. Mech. 117, 112–126 (2014). doi:10.1016/j.engfracmech.2014.01.012

    Article  Google Scholar 

  19. A. Moradi, N. Carrère, D. Leguillon, E. Martin, J.-Y. Cognard, Strength prediction of bonded assemblies using a coupled criterion under elastic assumptions: effect of material and geometrical parameters. Int. J. Adh. Adhes. 47, 73–82 (2013). doi:10.1016/j.ijadhadh.2013.09.044

    Article  Google Scholar 

  20. P. Weißgraeber, W. Becker, Finite Fracture Mechanics model for mixed mode fracture in adhesive joints. Int. J. Solids Struct. 50, 2383–2394 (2013). doi:10.1016/j.ijsolstr.2013.03.012

    Article  Google Scholar 

  21. P. Weißgraeber, D. Leguillon, W. Becker, A review of finite fracture mechanics: crack initiation at singular and non-singular stress raisers. Arch. Appl. Mech. (2015). doi:10.1007/s00419-015-1091-7

    Google Scholar 

  22. V. Mantič, Prediction of initiation and growth of cracks in composites. Coupled stress and energy criterion of the finite fracture mechanics. ECCM-16th European Conference on Composite Materials, Seville, Spain, 22–26 June 2014

    Google Scholar 

  23. A. Carpinteri, Notch sensitivity in fracture testing of aggregative materials. Eng. Fract. Mech. 16, 467–481 (1982)

    Article  Google Scholar 

  24. P. Weißgraeber, S. Hell, W. Becker, Crack nucleation in negative geometries. Eng. Fract. Mech. (2016). doi:10.1016/j.engfracmech.2016.02.045

    Google Scholar 

  25. D. Leguillon, E. Sanchez-Palencia, Computation of Singular Solutions in Elliptic Problems and Elasticity (Wiley, 1987)

    Google Scholar 

  26. D. Leguillon, E. Sanchez-Palencia, in Fracture in Heterogeneous Materials, Weak and Strong Singularities. ed. by P. Ladevèze, O. Zienkiewicz. Proceedings of the European Conference on New Advances in Computational Structural Mechanics (Elsevier, Amsterdam, 1992), pp. 229–236

    Google Scholar 

  27. Z. Yosibash, A. Bussiba, I. Gilad, Failure criteria for brittle elastic materials. Int. J. Fract. 125, 307–333 (2004)

    Article  Google Scholar 

  28. Z. Yosibash, E. Priel, D. Leguillon, A failure criterion for brittle elastic materials under mixed-mode loading. Int. J. Fract. 141, 291–312 (2006). doi:10.1007/s10704-006-0083-6

    Article  Google Scholar 

  29. J. Hebel, R. Dieringer, W. Becker, Modelling brittle crack formation at geometrical and material discontinuities using a finite fracture mechanics approach. Eng. Fract. Mech. 77, 3558–3572 (2010). doi:10.1016/j.engfracmech.2010.07.005

    Article  Google Scholar 

  30. C. Mittelstedt, W. Becker, Interlaminar stress concentrations in layered structures - part I: a selective literature survey on the free-edge effect since 1967. J. Compos. Mater. 38, 1037–1062 (2004)

    Article  Google Scholar 

  31. N.J. Pagano, G.A. Schoeppner, in Delamination of Polymer Matrix Composites, Problems and Assessment. ed. by A. Kelly, C. Zweben. Comprehensive Composite Materials, vol 2 (Elsevier, 2000), pp. 423–434

    Google Scholar 

  32. J.M. Whitney, R.J. Nuismer, Stress fracture criteria for laminated composites containing stress concentrations. J. Compos. Mater. 8, 253–265 (1974). doi:10.1177/002199837400800303

    Article  Google Scholar 

  33. A.S.D. Wang, in Fracture Analysis of Interlaminar Cracking. ed. by N.J. Pagano. Interlaminar Response of Composite Materials (Elsevier, 1989), pp. 69–109.

    Google Scholar 

  34. R.Y. Kim, S.R. Soni, Experimental and analytical studies on the onset of delamination in laminated composites. J. Compos. Mater. 18, 70–80 (1984). doi:10.1177/002199838401800106

    Article  Google Scholar 

  35. E. Martin, D. Leguillon, N. Carrère, A twofold strength and toughness criterion for the onset of free-edge shear delamination in angle-ply laminates. Int. J. Solids Struct. 47, 1297–1305 (2010). doi:10.1016/j.ijsolstr.2010.01.018

    Article  Google Scholar 

  36. B.R. Pipes, N.J. Pagano, Interlaminar stresses in composite laminates under uniform axial extension. J. Compos. Mater. 4, 538–548 (1970)

    Google Scholar 

  37. L. Lagunegrand, T. Lorriot, R. Harry, H. Wargnier, J. Quenisset, Initiation of free-edge delamination in composite laminates. Compos. Sci. Technol. 66, 1315–1327 (2006). doi:10.1016/j.compscitech.2005.10.010

    Article  Google Scholar 

  38. D. Leguillon, A method based on singularity theory to predict edge delamination of laminates. Int. J. Fract. 100, 538–548 (1999)

    Article  Google Scholar 

  39. I.G. García, V. Mantič, A. Blázquez, F. París, Transverse crack onset and growth in cross-ply laminates under tension. Application of a coupled stress and energy criterion. Int. J. Solids Struct. 51, 3844–3856 (2014). doi:10.1016/j.ijsolstr.2014.06.015

    Article  Google Scholar 

  40. B.S. Majumdar, D.B. Gundel, R.E. Dutton, S.G. Warrier, N.J. Pagano, Evaluation of the tensile interface strength in brittle matrix composite systems. J. Am. Ceram. Soc. 81, 1600–1610 (1998)

    Article  Google Scholar 

  41. N.J. Pagano, On the micromechanical failure modes in a class of ideal brittle matrix composites, Part 1. Coated-fiber composites. Compos. Part B 29B, 93–119 (1998)

    Article  Google Scholar 

  42. J.A. Bennett, R.J. Young, Micromechanical aspects of fibre/crack interactions in an aramid/epoxy composite. Compos. Sci. Technol. 57, 945–956 (1997)

    Article  Google Scholar 

  43. Y. Kagawa, K. Goto, Direct observation and modelling of the crack fibre interaction process in continuous fibre-reinforced ceramics: model experiments. Mater. Sci. Eng. A250, 285–290 (1998)

    Article  Google Scholar 

  44. L.R. Xu, Y.Y. Huang, A.J. Rosakis, Dynamic crack deflection and penetration at interfaces in homogeneous materials: experimental studies and model predictions. J. Mech. Phys. Solids 51, 461–486 (2003)

    Article  Google Scholar 

  45. J. Cook, J.E. Gordon, A mechanism for the control of crack propagation in all-brittle systems. Proc. R. Soc. 282A, 508–520 (1964)

    Article  Google Scholar 

  46. E. Martin, B. Poitou, D. Leguillon, J.M. Gatt, Competition between deflection and penetration at an interface in the vicinity of a main crack. Int. J. Fract. 151, 247–268 (2008). doi:10.1007/s10704-008-9228-0

    Article  Google Scholar 

  47. D. Leguillon, E. Martin, in Crack Nucleation at Stress Concentration Points in Composite Materials – Application to the Crack Deflection by an Interface, Chapter 10, ed. by V. Mantic. Mathematical Methods and Models in Composites, Décembre 2013, vol 5, Computational and Experimental Methods in Structures (Imperial College Press, 2012), pp. 401–424, e ISBN: 978-1-84816-784-1

    Google Scholar 

  48. C. Lacroix, D. Leguillon, E. Martin, The influence of an interphase on the deflection of a matrix crack in a ceramic matrix. Compos. Sci. Technol. 62, 519–523 (2002)

    Article  Google Scholar 

  49. D. Leguillon, E Martin, The strengthening effect caused by an elastic contrast—part I: the bimaterial case. Int. J. Fract. 179, 157–167 (2012). doi:10.1007/s10704-012-9787-y

    Google Scholar 

  50. D. Leguillon, E. Martin, The strengthening effect caused by an elastic contrast—part II: stratification by a thin stiff layer. Int. J. Fract. 179, 169–178 (2012). doi:10.1007/s10704-012-9785-0

    Google Scholar 

  51. D. Leguillon, E. Martin, O. Ševeček, R. Bermejo, Application of the coupled stress-energy criterion to predict the fracture behaviour of layered ceramics designed with internal compressive stresses. Eur. J. Mech. A/Solids 54, 94–104 (2015). doi:10.1016/j.euromechsol.2015.06.008

    Article  Google Scholar 

  52. V. Mantič, Interface crack onset at a circular cylindrical inclusion under a remote transverse tension. Application of a coupled stress and energy criterion. Int. J. Solids Struct. 46, 1287–1304 (2009). doi:10.1016/j.ijsolstr.2008.10.036

    Article  Google Scholar 

  53. M.Y. He, J.W. Hutchinson, Crack deflection at an interface between dissimilar elastic materials. Int. J. Solids Struct. 25, 1053–1067 (1989)

    Article  Google Scholar 

  54. D. Martinez, V. Gupta, Energy criterion for crack deflection at an interface between two orthotropic media. J. Mech. Phys. Solids 42, 1247–1271 (1994)

    Article  Google Scholar 

  55. E. Martin, D. Leguillon, C. Lacroix, A revisited criterion for crack deflection at an interface in a brittle bimaterial. Compos. Sci. Technol. 61, 1671–1679 (2001)

    Article  Google Scholar 

  56. J. Parmigiani, M. Thouless, The roles of toughness and cohesive strength on crack deflection at interfaces. J. Mech. Phys. Solids 54, 266–287 (2006). doi:10.1016/j.jmps.2005.09.002

    Article  Google Scholar 

  57. I.G. García, V. Mantič, E. Graciani, Debonding at the fibre–matrix interface under remote transverse tension. One debond or two symmetric debonds? Eur. J. Mech. A/Solids 53, 75–88 (2015). doi:10.1016/j.euromechsol.2015.02.007

    Article  Google Scholar 

  58. I.G. García, D. Leguillon, Mixed-mode crack initiation at a v-notch in presence of an adhesive joint. Int. J. Solids Struct. 49, 2138–2149 (2012). doi:10.1016/j.ijsolstr.2012.04.018

    Article  Google Scholar 

  59. L. Banks-Sills, Interface fracture mechanics: theory and experiment. Int. J. Fract. 191, 131–146 (2015). doi:10.1007/s10704-015-9997-1

    Article  Google Scholar 

  60. E. Martin, D. Leguillon, A strain energy density criterion for the initiation of edge debonding. Theor. Appl. Fract. Mech. 79, 58–61 (2015). doi:10.1016/j.tafmec.2015.06.011

    Article  Google Scholar 

  61. E. Martin, T. Vandellos, D. Leguillon, N. Carrère, Initiation of edge debonding: coupled criterion versus cohesive zone model. Int. J. Fract. (2016). doi:10.1007/s10704-016-0101-2

    Google Scholar 

  62. F. Berto, P. Lazzarin, A review of the volume-based strain energy density approach applied to V-notches and welded structures. Theor. Appl. Fract. Mech. 52, 183–194 (2009). doi:10.1016/j.tafmec.2009.10.001

    Article  Google Scholar 

  63. C. Henninger, D. Leguillon, E. Martin, Crack initiation at a V-notch—comparison between a brittle fracture criterion and the Dugdale cohesive model. ComptesRendusMécanique 335, 388–393 (2007). doi:10.1016/j.crme.2007.05.018

    Google Scholar 

  64. S. Murer, D. Leguillon, Static and fatigue failure of quasi-brittle materials at a V-notch using a Dugdale model. Eur. J. Mech. A/Solids 29, 109–118 (2010). doi:10.1016/j.euromechsol.2009.10.005

    Article  Google Scholar 

  65. D. Leguillon, M.C. Lafarie-Frenot, Y. Pannier, E. Martin, Prediction of the surface cracking pattern of an oxidized polymer induced by residual and bending stresses. Int. J. Solids Struct. 91, 89–101 (2016)

    Google Scholar 

  66. D. Leguillon, An attempt to extend the 2D coupled criterion for crack nucleation in brittle materials to the 3D case. Theor. Appl. Fract. Mech. 74, 7–17 (2014). doi:10.1016/j.tafmec.2014.05.004

    Article  Google Scholar 

  67. M.L. Dunn, W. Suwito, S. Cunningham, Fracture initiation at sharp notches: correlation using critical stress intensities. Int. J. Solids Struct. 34, 3873–3883 (1997)

    Article  Google Scholar 

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Martin, E., Leguillon, D., Carrère, N. (2017). Finite Fracture Mechanics: A Useful Tool to Analyze Cracking Mechanisms in Composite Materials. In: Beaumont, P., Soutis, C., Hodzic, A. (eds) The Structural Integrity of Carbon Fiber Composites. Springer, Cham. https://doi.org/10.1007/978-3-319-46120-5_19

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