Abstract
Several types of bonds may exist at the juncture between adjacent phases in contact. On the microscale of many composite materials, most desired is a perfect bond along a sharp spatial boundary S of vanishing thickness. It guarantees that both traction and displacement vectors remain continuous on S. Contact between phase surfaces may also involve presence of one or more interphases, thin bonded layers of additional homogeneous phases introduced, for example, as coatings on particles or fibers, or as products of an interfacial chemical reaction. During composites manufacture and/or loading, an interface is expected to transmit certain tractions between adjacent constituents. When the resolved tensile and/or shear stress reaches a high magnitude, the interface may become imperfect by allowing partial or complete decohesion, a displacement jump, possibly accompanied by a distribution of ‘adhesive’ tractions. In an opposite situation, a high compressive stress may cause radial cracking in one of the phases in contact, or in the surrounding matrix. While magnitudes of interface tractions determine material propensity to distributed damage, the work required by either decohesion or radial cracking must be provided by release of potential energy, which is proportional to phase volume Chap. 5. Therefore, small inhomogeneities are less likely sources of damage than large ones.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Additional References for Chapter 9
Benveniste, Y. (2006). A general interface model for a three-dimensional curved thin anisotropic interphase between two anisotropic media. Journal of the Mechanics and Physics of Solids, 54, 708–734.
Benveniste, Y., & Berdichevsky, O. (2010). On two models of arbitrarily curved three-dimensional thin interphases in elasticity. International Journal of Solids and Structures, 47, 1899–1915.
Benveniste, Y., & Miloh, T. (2001). Imperfect soft and stiff interfaces in two-dimensional elasticity. Mechanics of Materials, 33, 309–323.
Cammarata, R. C., Trimble, T. M., & Srolovitz, D. J. (2000). Surface stress model for instrinsic stresses in thin films. Journal of Materials Research, 15, 2468–2474.
Chen, T., & Dvorak, G. J. (2006). Fibrous nanocomposites with interface stress: Hill’s and Levin’s connections for effective moduli. Applied Physics Letters, 88, 211912. 1–3.
Chen, T., Chiu, M. S., & Weng, C. N. (2006). Derivation of the generalized Young-Laplace equation of curved interfaces in nano-scaled solids. Journal of Applied Physics, 100, 1–5.
Chen, T., Dvorak, G. J., & Yu, C. C. (2007a). Solids containing spherical nano- inclusions with interface stresses: Effective properties and thermal-mechanical connections. International Journal of Solids and Structures, 44, 941–955.
Chen, T., Dvorak, G. J., & Yu, C. C. (2007b). Size-dependent elastic properties of unidirectional nano-composites with interface stresses. Acta Mechanica, 188, 39–54.
Dionne, P. J., Ozisik, R., & Picu, R. C. (2005). Structure and dynamics of polyethylene nanocomposites. Macromolecules, 38, 9351–9358.
Dionne, P. J., Picu, R. C., & Ozisik, R. (2006). Adsorption and desorption dynamics of linear polymer chains to spherical nanoparticles: A Monte Carlo investigation. Macromolecules, 39, 3089–3092.
Duan, H. L., Wang, J., Huang, Z. P., & Karihaloo, B. L. (2005a). Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress. Journal of the Mechanics and Physics of Solids, 53, 1574–1596.
Duan, H. L., Wang, J., Huang, Z. P., & Karihaloo, B. L. (2005b). Eshelby formalism for nano-inhomogeneities. Proceedings of the Royal Society of London, A 461, 3335–3353.
Gibbs, J. W. (1928). The collected works of J.W. Gibbs (Vol. 1, p. 315). Longmans: New York.
Gurtin, M. E., & Murdoch, A. I. (1975). A continuum theory of elastic material surfaces. Archive for Rational Mechanics and Analysis, 57, 291–323, and 59, 389–390.
Gurtin, M. E., Weissmuller, J., & Larche, F. (1998). A general theory of curved deformable interfaces in solids at equilibrium. Philosophical Magazine A, 78, 1093–1109.
Hatami-Marbini, H., & Picu, R. C. (2009). Heterogeneous long-range correlated deformation of semiflexible random fiber networks. Physical Review E, 80, 046703-1-11.
Landau, L. D., & Lifshitz, E. M. (1987). Fluid mechanics (2nd ed.). Oxford: Pergamon Press.
Miller, R. E., & Shenoy, V. B. (2000). Size-dependent elastic properties of nanosized structural elements. Nanotechnology, 11, 139–147.
Nix, W. D., & Gao, H. (1998). An atomistic interpretation of interface stress. Scripta Materialia, 39, 1653–1661.
Ozmusul, M. S., & Picu, R. C. (2002). Elastic moduli for particulate composites with graded filler-matrix interfaces. Polymer Composites, 23, 110–119.
Ozmusul, M. S., & Picu, R. C. (2003). Structure of linear polymeric chains confined between spherical impenetrable walls. The Journal of Chemical Physics, 118, 11239–11248.
Ozmusul, M. S., Picu, R. C., Sternstein, S. S., & Kumar, S. (2005). Lattice Monte Carlo simulations of chain conformations in polymer nanocomposites. Macromolecules, 38, 4495–4500.
Picu, R. C. (2009). Multiscale approach to predicting the mechanical behavior of polymeric melts. In B. Farahmand (Ed.), Virtual testing and predictive modeling: Fatigue and fracture allowances. Dordrecht: Springer.
Picu, R. C., Sarvestani, A., & Ozmusul, M. S. (2004). Elastic moduli of polymer nanocomposites derived from their molecular structure. In V. M. Harik (Ed.), Trends in nanoscale mechanics: Analysis of nanostructured materials and multiscale modeling (pp. 61–88). Dordrecht: Kluwer Academic Press.
Povstenko, Y. Z. (1993). Theoretical investigation of phenomena caused by heterogeneous surface tension in solids. Journal of the Mechanics and Physics of Solids, 41, 1499–1514.
Ramanathan, T., Liu, H., & Brinson, L. C. (2005). Functionalized SWNT polymer nanocomposites for dramatic property improvement. Journal of Polymer Science: Polymer Physics, 43, 2269–2279.
Ramanathan, T., Abdala, A. A., Stankovich, S., et al. (2008). Functionalized graphene sheets for polymer nanocomposites. Nature Nanotechnology, 3(6), 327–331.
Sarvestani, A. S., & Picu, R. C. (2005). A frictional molecular model for the viscoelasticity of entangled polymer nanocomposites. Rheologica Acta, 45, 132–141.
Sharma, P., & Ganti, S. (2004). Size-dependent Eshelby’s tensor for embedded nano-inclusions incorporating surface/interface energies. ASME Journal of Applied Mechanics, 71, 663–671.
Sharma, P., Ganti, S., & Bhate, N. (2003). Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities. Applied Physics Letters, 82, 535–537.
Spaepen, F. (2000). Interfaces and stresses in thin films. Acta Materialia, 48, 31–42.
Tvergaard, V. (2003). Debonding of short fibers among particulates in metal matrix composites. International Journal of Solids and Structures, 40, 6957–6967.
Watcharotone, S., Wood, C. D., Friedrich, R., Chen, X., Qiao, R., Putz, K. W., & Brinson, L. C. (2011). Revealing the effects of interphase, interface and substrate on mechanical properties of polymers using coupled experiments and modeling of nanoindentation. Advanced Engineering Materials, 13, 400–404.
Yang, F. Q. (2004). Size-dependent effective modulus of elastic composite materials: Spherical nanocavities at dilute concentrations. Journal of Applied Physics, 95, 3516–3520.
Chen, T. (1993a). Green’s functions and the non-uniform transformation problem in a piezoelectric medium. Mechanics Research Communications, 20, 271–278.
Ferrante, J., Smith, J. R., & Rose, J. H. (1982). Universal binding energy relations in metallic adhesion. In J. M. Georges (Ed.), Microscopic aspects of adhesion and lubrication (pp. 19–30). Amsterdam: Elsevier.
Laws, N. (1975). On interfacial discontinuities in elastic composites. Journal of Elasticity, 5, 227–235.
Chen, T. (1993b). The rotation of a rigid ellipsoidal inclusion embedded in an anisotropic piezoelectric medium. International Journal of Solids and Structures, 30, 1983–1995.
Hashin, Z. (2002). Thin interphase/imperfect interface in elasticity with application to coated fiber composites. Journal of the Mechanics and Physics of Solids, 50, 2509–2537.
Hill, R. (1972). An invariant treatment of interfacial discontinuities in elastic composites. In L. I. Sedov (Ed.), Continuum mechanics and related problems of analysis, N. I. Muskhelishvili 80th anniversary volume (pp. 597–604). Moscow: Acad. Sciences.
Hill, R. (1983). Interfacial operators in the mechanics of composite media. Journal of the Mechanics and Physics of Solids, 31, 247–357.
Laws, N. (1977). The determination of stress and strain concentrations in an ellipsoidal inclusion in an anisotropic material. Journal of Elasticity, 7, 91–97.
Hill, R. (1961). Discontinuity relations in mechanics of solids. In I. N. Sneddon & R. Hill (Eds.), Progress in solid mechanics (Vol. II, pp. 245–276). Amsterdam: North Holland Publications.
Hashin, Z. (1991). The spherical inclusion with imperfect interface. Journal of Applied Mechanics, 58, 444–449.
Kunin, I. A., & Sosnina, E. G. (1973). Stress concentration on an ellipsoidal inhomogeneity in an anisotropic elastic medium. Prikl. Mat. Mekh., 37, 306–315.
Hashin, Z. (1990). Thermoelastic properties of fiber composites with imperfect interface. Mechanics of Materials, 8, 333–348.
Eshelby, J. D. (1957). The determination of the elastic field of an ellipsoidal inclusion, and related problems. Proceedings of the Royal Society London A, 241, 376–396.
Walpole, L. J. (1981). Elastic behavior of composite materials: Theoretical foundations. In Advances in applied mechanics (Vol. 21, pp. 169–242). New York: Academic.
Herakovich, C. T. (1998). Mechanics of fibrous composites. New York: Wiley.
Achenbach, J. D., & Zhu, H. (1989). Effect of interfacial zone on mechanical behavior and failure of fiber-reinforced composites. Journal of the Mechanics and Physics of Solids, 37, 381–393.
Jefferson, G., Haritos, G. K and McMeeking, R. M. (2002)The elastic response of a cohesive aggregate – a discrete element model with coupled particle interactions. J. Mech. Phys. Solids, 50, 2539–2575.
Benveniste, Y., & Miloh, T. (2001). Imperfect soft and stiff interfaces in two-dimensional elasticity. Mechanics of Materials, 33, 309–323.
Jasiuk, I., Mura, T., & Tsuchida, E. (1988). Thermal stresses and thermal expansion coefficient of short fiber composites with sliding interfaces. Journal of Engineering Materials and Technology, 110, 96–110.
Jasiuk, I., & Kouider, M. W. (1993). The effect of an inhomogeneous interphase on elastic constants of transversely isotropic composites.
Qu, J. (1993). The effect of slightly weakened interface on the overall elastic properties of composite materials. Mechanics of Materials, 14, 269–281
Zhou, L. G., & Huang, H. (2004), Are Surfaces Elastically Softer or Stiffer? Applied Physics Letters, 84, 1940–1942.
Shim, H. W., Zhou, L. G., Huang, H., & Cale, T. S. (2005). Nanoplate elasticity under surface reconstruction. Applied Physics Letters 86, 151912-1-3.
Liang, H. Y., Upmanyu, M., & Huang, H. (2005). Size dependent elasticity of nanowires: Non-linear effects. Physical Review B 71, 241403R-1-4.
Park, H. S., Klein, P. A., & Wagner, G. J. (2006). A surface Cauchy-Born model for nanoscale materials. International Journal for Numerical Methods in Engineering, 68, 1072–1095.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media B.V.
About this chapter
Cite this chapter
Dvorak, G.J. (2013). Interfaces and Interphases. In: Micromechanics of Composite Materials. Solid Mechanics and Its Applications, vol 186. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-4101-0_9
Download citation
DOI: https://doi.org/10.1007/978-94-007-4101-0_9
Published:
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-4100-3
Online ISBN: 978-94-007-4101-0
eBook Packages: EngineeringEngineering (R0)