International Journal of Fracture

, Volume 142, Issue 3–4, pp 277–287 | Cite as

Generic Overlapping Cracks in Polymers: Modeling of Interaction

  • Ramaswamy Sankar
  • Alan J. Lesser
Original Paper


This paper deals with modeling of the interaction in overlapping cracks that the authors have earlier identified to be generic to a wide range of polymeric systems (Ramasamy and Lesser, J Polym Sci B Phys, 2003). A complex stress function method is used for evaluating stress intensity factors for interacting cracks. The interaction between two parallel overlapping cracks is considered first. It is shown for this case that the stress intensity factor can fall below the threshold value when there is sufficient overlap, leading to arrest of crack growth at the overlapping tip. Then the interaction in a doubly periodic infinite array of cracks is considered. The interaction in the array is found to be non-linear. However, at a given stress level, the highest density of stable cracks is related to the threshold value for crack propagation Kth though a simple set of equations. It is also shown that in an infinite array of cracks, the energy release rate criterion for crack growth is different from the stress intensity factor criterion due to a reduced stiffness of the material.


Crack interaction Shielding Modeling Rubber modified polymers 


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  1. Anderson TL (2004) Fracture mechanics; Fundamentals and applications. Int CRC, NYGoogle Scholar
  2. Chudnovsky A, Kachanov M (1983) Interaction of a crack with a field of microcracks. J Eng Sci 21(8):1009–1018CrossRefGoogle Scholar
  3. Chen YZ (1984) General case of multiple crack problems in an infinite plate. Eng Fract Mech 20(4):591–597CrossRefGoogle Scholar
  4. Datsyshin A, Savruk MP (1973) A system of arbitrarily oriented cracks in elastic solids. J Appl Math Mech 37(2):326–332CrossRefGoogle Scholar
  5. Donald AM, Kramer EJ (1982) Internal structure of rubber particles and craze break-down in high-impact polystyrene (HIPS). J Mater Sci 17(8):2351–2358CrossRefGoogle Scholar
  6. Horrii H, Nemat-Nasser S (1985) Elastic fields of interacting in homogeneities. Int J Solids Struct 21:731–745CrossRefGoogle Scholar
  7. Kachanov M (1993) Elastic solids with many cracks and related problems. In: Hutchinson J, Wu T (eds) Advances in applied mechanics. Academic, New York, p 259Google Scholar
  8. Karihaloo BL, Wang J, Grzybowski M (1996) Doubly periodic arrays of bridged cracks and short-fibre reinforced cementitious materials. J Mech Phys Solids 44(10):1565–1586CrossRefGoogle Scholar
  9. Ramaswamy S, Lesser AJ (2003) Genetic crack patterns in rubber-modified polymers under biaxial stress states. J Polym Sci Part B Phys 41(19): 2248–2256CrossRefGoogle Scholar
  10. Raman A, Farris RJ, Lesser AJ (2003) What is RSS? J Appl Polym Sci 88(2):550–564CrossRefGoogle Scholar
  11. Wilfong DL, Hiltner A, Baer E (1986) Advances in chemistry series. In: Paul DR, Sperling LH (eds) American Chemical SocietyGoogle Scholar
  12. Wang GS, Feng XT (2001) The interaction of multiple rows of periodical cracks. Intl J Fracture 110(1):73–100CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.University of MassachusettsAmherstUSA

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