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Relation Between Elastic Properties and Stress Intensity Factors for Composites with Rigid-Line Reinforcements

  • Letters in Fracture and Micromechanics
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Abstract

Stiffness and failure resistance are two properties of a composite material that are known to be difficult (if not impossible) to improve simultaneously. They are of a competing nature: while stiffness is an effective property of a homogenized microstructure, failure resistance is highly sensitive to local microstructural details. In the present work we establish a direct link between these two properties on the example of a composite material reinforced with rigid lines. More specifically, we relate rigid lines’ contribution into effective compliance to stress intensity factors at their tips. Such a link provides useful insights into the source of competition between stiffness and failure resistance and suggests a way to overcome this persistent trend.

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References

  • Atkinson C.: Some ribbon-like inclusion problems. International Journal of Engineering Science 11, 243–266 (1973)

    Article  MATH  Google Scholar 

  • Ballarini R. (1987). An integral equation approach for rigid-line inhomogeneity problems, Int. J. Fracture 33, R23–R26.

    Google Scholar 

  • Brussat T.R., Westmann R.A.: A Westergaard-type stress function for line inclusion problems. International Journal of Solids and Structures 11, 665–677 (1975)

    Article  MATH  Google Scholar 

  • Dundurs J., Markenscoff X.: A Green’s function formulation of anticracks and their interaction with load-induced singularities. ASME J. Appl. Mech. 56, 550–555 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  • Fornes T.D., Paul D.R.: Modeling properties of nylon 6/clay nanocomposites using composite theories. Polymer 44, 4993–5013 (2003)

    Article  CAS  Google Scholar 

  • Gorbatikh, L. (2004). On elastic compliances of interfacial cracks. International Journal of Fracture 127/2, L141–L148.

    Google Scholar 

  • Gorbatikh, L. and Pingle, P. (2007). On incompressibility of a matrix in naturally occurring composites. Applied Physics Letters 91/24, 241–913.

    Google Scholar 

  • Gorbatikh L., Kachanov M.: A simple technique for constructing the full stress and displacement fields in elastic plates with multiple cracks. Engineering Fracture Mechanics 66, 51–63 (2000)

    Article  Google Scholar 

  • Hurtado J.A., Dundurs J., Mura T.: Lamellar inhomogeneities in a uniform stress field. J Mech Phys Solids 44(1), 1–21 (1996)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  • Kachanov M.: Elastic solids with many cracks: a simple method of analysis. International Journal of Solids and Structures 23, 23–43 (1987)

    Article  MATH  Google Scholar 

  • Miyagawa H., Drzal L.T.: Intercalation and Exfoliation of Clay Nanoplatelets in Epoxy-Based Nanocomposites: TEM and XRD Observations. Polymer Engineering and Science 46, 452–463 (2006)

    Article  CAS  Google Scholar 

  • Ni L., Nemat-Nasser N.S.: A general duality principle in elasticity. Mechanics of Materials 24, 87–123 (1996)

    Article  Google Scholar 

  • Osman M., Rupp J.E.P., Suter U.W.: Tensile properties of polyethylene-layered silicate nanocomposites. Polymer 46, 1653–1660 (2005)

    Article  CAS  Google Scholar 

  • Pingle P., Sherwood J., Gorbatikh L.: Properties of rigid-line inclusions as building blocks of naturally occurring composites. Composites Science and Technology 68, 2267–2272 (2008)

    Article  CAS  Google Scholar 

  • Rice, J.R. (1975). Continuum mechanics and thermodynamics of plasticity in relation to microscale deformation mechanics. In: Constitutive equations in plasticity (Argon, A. ed), MIT Press Cambridge, pp. 22–73.

  • Sevostianov I., Kachanov M.: Elastic compliance of an annular crack. International Journal of Fracture 110, L51–L54 (2001)

    Article  Google Scholar 

  • Tsukrov I. (2000). Elastic moduli of composites with rigid elliptical inclusions. Int J Fract. 101, L29–34

    Google Scholar 

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Correspondence to Larissa Gorbatikh.

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Gorbatikh, L., Lomov, S.V. & Verpoest, I. Relation Between Elastic Properties and Stress Intensity Factors for Composites with Rigid-Line Reinforcements. Int J Fract 161, 205–212 (2010). https://doi.org/10.1007/s10704-009-9433-5

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  • DOI: https://doi.org/10.1007/s10704-009-9433-5

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