skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: In situ frustum indentation of nanoporous copper thin films

Journal Article · · International Journal of Plasticity
 [1];  [2];  [3];  [4];  [4];  [1]
  1. Georgia Inst. of Technology, Atlanta, GA (United States). The Woodruff School of Mechanical Engineering
  2. Univ. of Nevada, Reno, NV (United States). Chemical and Materials Engineering
  3. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Integrated Nanotechnologies (CINT)
  4. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

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 paper 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 νp 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. Finally, 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.

Research Organization:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Georgia Institute of Technology, Atlanta, GA (United States)
Sponsoring Organization:
USDOE Office of Science (SC); National Science Foundation (NSF)
Grant/Contract Number:
AC52-06NA25396; CMMI-1351705
OSTI ID:
1416294
Alternate ID(s):
OSTI ID: 1549660
Report Number(s):
LA-UR-17-27378
Journal Information:
International Journal of Plasticity, Vol. 98; ISSN 0749-6419
Publisher:
ElsevierCopyright Statement
Country of Publication:
United States
Language:
English
Citation Metrics:
Cited by: 15 works
Citation information provided by
Web of Science

References (70)

On couple-stress elasto-plastic constitutive frameworks for glassy polymers journal February 2016
Size effects in ductile cellular solids. Part II: experimental results journal December 2001
Experimental observations of deformation behavior of bulk metallic glasses during wedge-like cylindrical indentation journal September 2006
Deformation behavior of a zirconium based metallic glass during cylindrical indentation: in situ observations journal March 2005
Controlled nanoporous Pt morphologies by varying deposition parameters journal August 2009
Analysis of elastic and plastic deformation associated with indentation testing of thin films on substrates journal January 1988
Nanoporous Au: A high yield strength material journal January 2005
Size Effects on the Mechanical Behavior of Nanoporous Au journal October 2006
Surface-chemistry-driven actuation in nanoporous gold journal November 2008
Mechanical properties of bulk single crystalline nanoporous gold investigated by millimetre-scale tension and compression testing journal January 2014
The effect of indenter geometry on the elastic response to indentation journal June 1994
Geometrically necessary dislocation density measurements associated with different angles of indentations journal March 2014
Effect of double ion implantation and irradiation by Ar and He ions on nano-indentation hardness of metallic alloys journal July 2013
Modelling the combined effect of grain size and grain shape on plastic anisotropy of metals journal May 2012
Isotropic constitutive models for metallic foams journal June 2000
Hydrogen sensing of nanoporous palladium films supported by anodic aluminum oxides journal December 2006
The stress on an elastic half-space due to sectionally smooth-ended punch journal October 1981
A simple predictive model for spherical indentation journal February 1993
Solution of the Contact Problem of a Rigid Conical Frustum Indenting a Transversely Isotropic Elastic Half-Space journal September 2013
Fluid and Resistive Tethered Lipid Membranes on Nanoporous Substrates journal September 2015
Density dependence of the compressive properties of porous copper over a wide density range journal April 2007
Mechanical strength of nanoporous gold fabricated by dealloying journal June 2007
Electrochemical actuation of nanoporous Ni in NaOH solution journal March 2012
Size effects in twinned nanopillars journal July 2014
Characterization and Mechanical Behavior of Nanoporous Gold journal September 2006
Deforming nanoporous metal: Role of lattice coherency journal May 2009
Determination of the effective zero-point and the extraction of spherical nanoindentation stress–strain curves journal August 2008
Inkjet printed electronics using copper nanoparticle ink journal January 2010
Extended expanding cavity model for measurement of flow properties using instrumented spherical indentation journal October 2013
Electrochemically dealloyed platinum with hierarchical pore structure as highly active catalytic coating journal January 2015
Nanoporous metal/oxide hybrid electrodes for electrochemical supercapacitors journal February 2011
Investigation of sharp contact at rigid–plastic conditions journal April 2001
Defect structures and hardening mechanisms in high dose helium ion implanted Cu and Cu/Nb multilayer thin films journal May 2012
Synthesis of transversely isotropic nanoporous platinum journal April 2012
A relation between relative density, alloy composition and sample shrinkage for nanoporous metal foams journal December 2012
A relationship between the geometrical structure of a nanoporous metal foam and its modulus journal April 2013
Mechanical properties of nanocrystalline nanoporous platinum journal January 2016
Synthesis and mechanical behavior of nanoporous nanotwinned copper journal December 2013
Elastic and plastic Poisson’s ratios of nanoporous gold journal January 2016
On the intrinsic hardness of a metallic film/substrate system: Indentation size and substrate effects journal July 2012
Nanoporous Gold—Testing Macro-scale Samples to Probe Small-scale Mechanical Behavior journal September 2015
Topology-dependent scaling laws for the stiffness and strength of nanoporous gold journal October 2016
A FIB-nanotomography method for accurate 3D reconstruction of open nanoporous structures journal April 2016
The contact problem of a rigid cylinder on an elastic layer journal January 1968
Spherical indentation of elastic–plastic solids
  • Mesarovic, Sinisa Dj.; Fleck, Norman A.
  • Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, Vol. 455, Issue 1987 https://doi.org/10.1098/rspa.1999.0423
journal July 1999
Size effects in indentation response of thin films at the nanoscale: A molecular dynamics study journal November 2008
Indentation of elastically soft and plastically compressible solids journal July 2015
An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments journal June 1992
Size effects in ductile cellular solids. Part I: modeling journal December 2001
Studying grain boundary regions in polycrystalline materials using spherical nano-indentation and orientation imaging microscopy journal August 2011
Compressive response of vertically aligned carbon nanotube films gleaned from in situ flat-punch indentations journal November 2012
Importance of surface preparation on the nano-indentation stress-strain curves measured in metals journal March 2009
Coarsening of nanoporous Au: Relationship between structure and mechanical properties journal October 2015
Nanoporous metal as a platform for electrochemical and optical sensing journal January 2014
Mechanical behavior of mesoporous titania thin films journal June 2014
Sensitivity of the residual topography to single crystal plasticity parameters in Berkovich nanoindentation on FCC nickel journal February 2016
Indentation of metals by a flat-ended cylindrical punch journal September 2004
Crystal plasticity analysis of cylindrical indentation on a Ni-base single crystal superalloy journal December 2013
The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile journal May 1965
Oxygen reduction in nanoporous metal–ionic liquid composite electrocatalysts journal October 2010
The Tension of Metallic Films Deposited by Electrolysis journal May 1909
A multi-step dealloying method to produce nanoporous gold with no volume change and minimal cracking journal May 2008
Effect of Precursor Stoichiometry on the Morphology of Nanoporous Platinum Sponges journal June 2014
Studies of grain boundary regions in deformed polycrystalline aluminum using spherical nanoindentation journal June 2016
Effect of elastic surface deformation on the relation between hardness and yield strength journal December 2004
Thermo-mechanical strain gradient plasticity with energetic and dissipative length scales journal March 2012
Nanoporous Metals by Alloy Corrosion: Formation and Mechanical Properties journal August 2009
Platinum-plated nanoporous gold: An efficient, low Pt loading electrocatalyst for PEM fuel cells journal February 2007
Indentation of a hard film on a soft substrate: Strain gradient hardening effects journal January 2007
Dislocation dynamics simulations of plasticity in polycrystalline thin films journal March 2012

Cited By (2)

A Review of Nanoporous Metals in Interconnects journal August 2018
Multi-scale progressive failure mechanism and mechanical properties of nanofibrous polyurea aerogels journal January 2018