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Finite element analysis and experimental investigation of the Hertzian assumption on the characterization of initial plastic yield

Published online by Cambridge University Press:  31 January 2011

Li Ma ,
Dylan J. Morris ,
Stefhanni L. Jennerjohn ,
David F. Bahr  and
Lyle Levine
Li Ma
Affiliation:
National Institute of Standards and Technology, Materials Science and Engineering Laboratory, Gaithersburg, Maryland 20899-8520; and Department of Chemical Physics, Kent State University, Kent, Ohio 44242
Dylan J. Morris
Affiliation:
National Institute of Standards and Technology, Materials Science and Engineering Laboratory, Gaithersburg, Maryland 20899-8520
Stefhanni L. Jennerjohn
Affiliation:
National Institute of Standards and Technology, Materials Science and Engineering Laboratory, Gaithersburg, Maryland 20899-8520; and Department of Chemical Physics, Kent State University, Kent, Ohio 44242
David F. Bahr
Affiliation:
Mechanical and Materials Engineering, Washington State University, Pullman, Washington 99164
Lyle Levine
Affiliation:
National Institute of Standards and Technology, Materials Science and Engineering Laboratory, Gaithersburg, Maryland 20899-8520
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Abstract

Sudden displacement excursions during load-controlled nanoindentation of relatively dislocation-free surfaces of metals are frequently associated with dislocation nucleation, multiplication, and propagation. Insight into the nanomechanical origins of plasticity in metallic crystals may be gained through estimation of the stresses that nucleate dislocations. An assessment of the potential errors in the experimental measurement of nucleation stresses, especially in materials that exhibit the elastic–plastic transition at small indentation depths, is critical. In this work, the near-apex shape of a Berkovich probe was measured by scanning probe microscopy. This shape was then used as a “virtual” indentation probe in a 3-dimensional finite element analysis (FEA) of indentation on 〈100〉-oriented single-crystal tungsten. Simultaneously, experiments were carried out with the real indenter, also on 〈100〉-oriented single-crystal tungsten. There is good agreement between the FEA and experimental load–displacement curves. The Hertzian estimate of the radius of curvature was significantly larger than that directly measured from the scanning probe experiments. This effect was replicated in FEA simulation of indentation by a sphere. These results suggest that Hertzian estimates of the maximum shear stresses in the target material at the point of dislocation nucleation are a conservative lower bound. Stress estimates obtained from the experimental data using the Hertzian approximation were over 30% smaller than those determined from FEA.

Keywords

DislocationsNanoindentation
Type
Articles
Information
Journal of Materials Research , Volume 24 , Issue 3 , March 2009 , pp. 1059 - 1068
Copyright
Copyright © Materials Research Society 2009

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