The Role of First Order Surface Effects in Linear Elastic Fracture Mechanics

• Author / Creator

  KIM, CHUN IL

• Structures at relatively small scales (e.g. nano/micro scale) behave
  differently in comparison to those examined at the macro scale. This is
  mainly because a high surface area to volume ratio is present at this scale
  making physical factors such as surface stress/energy and electromagnetic
  forces much more significant. In particular, ‘surface effects’ induced by a
  local environmental change of the region near the surface of solids, greatly
  influence the general behavior of the corresponding bulk material especially
  when the scale of materials become compatible with the nano/micro scale.
  This in turn, suggest that a more accurate and comprehensive description
  of the general behavior of an elastic solid with one or more surfaces can be
  achieved by incorporating a description of the separate surface mechanics
  near each surface of the solid.
  In the dissertation, we examine the effects of first-order surface elasticity in
  linear elastic fracture mechanics. A complete analysis has been performed
  for both plane and anti-plane deformations and for cases in which cracks
  are present in a homogeneous material and subsequently in the interface
  between two dissimilar elastic materials. It is shown that the introduction
  of the effects of first-order surface elasticity results in, in most cases, the
  reduction of the stress singularity at the crack tip from the classical strong
  square root singularity to a weaker logarithmic singularity. In particular,
  the refined model (with first-order surface effects integrated) predicts a
  more realistic description of size-dependent stress distributions commonly
  existing at the small scale structures. In the case of an interface crack
  arising in the interfacial region between two dissimilar materials, the
  refined model removes the classical oscillatory behaviors of the
  corresponding stress distributions leading again to size-dependent and
  stable stresses in the vicinity of the crack.

• Subjects / Keywords

  • Anti-plane deformations
  • Interface cracks
  • Plane deformations
  • First Order Surface Effects
  • Size-dependent stress distributions
  • Cauchy singular integro-differential equations
  • Linear elastic fracture mechanics

• Graduation date

  Fall 2012

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3XH1S

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.