Size-Dependent Bending of Thin Metallic Films

  • H.X. Zhu
  • B.L. Karihaloo
Conference paper
Part of the Iutam Bookseries book series (IUTAMBOOK, volume 10)


Size-dependent pure bending of thin metallic films has been analytically studied taking into account the associated strengthening mechanisms at different thickness scales. The classical plasticity theory is applicable to films thicker than 100 microns. Consequently, their bending capacity is governed by the competition between the material hardening and the thickness reduction. For films with a thickness ranging from fractions of a micron to a few microns, in addition to the above mechanisms, the strain gradient effect plays an important role and introduces an internal length scale. When the film thickness reduces to the nano-scale, the strain gradient effect is gradually replaced by the dominant surface stress/energy effect.


Thin films strain gradient effect surface stress bending stiffness 


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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • H.X. Zhu
    • 1
  • B.L. Karihaloo
  1. 1.School of EngineeringCardiff UniversityUK

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