In situ frustum indentation of nanoporous copper thin films

Ran Liu, Siddhartha Pathak, William M. Mook, J. Kevin Baldwin, Nathan Mara, Antonia Antoniou

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


Mechanical properties of thin films are often obtained solely from nanoindentation. At the same time, such measurements are characterized by a substantial amount of uncertainty, especially when mean pressure or hardness are used to infer uniaxial yield stress. In this work we demonstrate that indentation with a pyramidal flat tip (frustum) indenter near the free edge of a sample can provide a significantly better estimate of the uniaxial yield strength compared to frequently used Berkovich indenter. This is first demonstrated using a numerical model for a material with an isotropic pressure sensitive yield criterion. Numerical simulations confirm that the indenter geometry provides a clear distinction of the mean pressure at which a material transitions to inelastic behavior. The mean critical pressure is highly dependent on the plastic Poisson ratio vνp so that at the 1% offset of normalized indent depth, the critical pressure pmc normalized to the uniaxial yield strength σ0 is 1 < pmc0 < 1.3 for materials with 0<νp<0.5. Choice of a frustum over Berkovich indenter reduces uncertainty in hardness by a factor of 3. These results are used to interpret frustum indentation experiments on nanoporous (NP) Copper with struts of typical diameter of 45 nm. An estimate of the yield strength of NP Copper is obtained 230 MPa < σ0 < 300 MPa. Edge indentation further allows one to obtain in-plane strain maps near the critical pressure. Comparison of the experimentally obtained in-plane strain maps of NP Cu during deformation and the strain field for different plastic Poisson ratios suggest that this material has a plastic Poisson ratio of the order of 0.2-0.3. However, existing constitutive models may not adequately capture post-yield behavior of NP metals.

Original languageEnglish (US)
Pages (from-to)139-155
Number of pages17
JournalInternational Journal of Plasticity
StatePublished - Nov 2017

Bibliographical note

Publisher Copyright:
© 2017 Elsevier Ltd. All rights reserved.


  • Methods: electron microscopy
  • Methods: finite elements
  • Methods: mechanical testing
  • Physical phenomena: yield condition
  • Problem description: constitutive behavior
  • Problem description: porous material


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