Investigation of Hertz Theory Using Finite Element Nanoindentation of Isotropic Elastic Copper

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Investigation of Hertz Theory Using Finite
Element Nanoindentation of Isotropic Elastic
Copper

• Brendan Donohue

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Outline

• Hertz Theory
• Problem
• Technique
• Results
• Future Work
• Questions

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Background Hertz Theory

• Hertz Theory describes load-displacement behavior
  of indentation
• Assumptions rigid spherical indenter, elastic
  isotropic material, frictionless contact

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Hertz Theory contd

• Load is also described by effective modulus and
  effective radius of the indenter

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Problem

• Constant k takes some parameters
• Validate finite element model with respect to the
  Hertz Model.
• Parameters size of the grain relative to the
  indenter, number and type of elements in both
  indenter and grain, density of mesh near indent,
  effective modulus of material

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Technique The Setup

• Hemispherical rigid indenter, flat grain
• 4700 grain elements
• 2400 indenter elements
• Displacement boundary condition

R13.5 um
3R
4R
7
The Setup
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Results
FEM fails to predict Hertz behavior for low
displacement
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Future Work

• Revise FEM for flat grain to better approach
  Hertz Theory
• Validate Hertz Theory for cyclic loading
• Check the influence of the indenter radius by
  varying it