# Inaccuracies in Sneddon`s solution for elastic indentation by a rigid cone and their implications for nanoindentation data analysis

## Abstract

Methods currently used for analyzing nanoindentation load-displacement data to determine a material`s hardness and elastic modulus are based on Sneddon`s solution for the indentation of an elastic half-space by a rigid axisymmetric indenter. Although this solution is widely used, no attempts have been made to determine how well it works for conditions of finite deformation, as is the case in most nanoindentation experiments with sharp indenters. Analytical and finite element results are presented which show that corrections to Sneddon`s solution are needed if it is to be accurately applied to the case of deformation by a rigid cone. Failure to make the corrections results in an underestimation of the load and contact stiffness and an overestimation of the elastic modulus, with the magnitude of the errors depending on the angle of the indenter and Poisson`s ratio of the half-space. For a rigid conical indenter with a half-included tip angle of 70.3{degrees}, i.e., the angle giving the same area-to-depth ratio as the Berkovich indenter used commonly in nanoindentation experiments, the underestimation of the load and contact stiffness and overestimation of the elastic modulus may be as large as 13%. It is shown that a simple first order correction can be achievedmore »

- Authors:

- Publication Date:

- Research Org.:
- Rice Univ., Houston, TX (United States)

- Sponsoring Org.:
- USDOE, Washington, DC (United States)

- OSTI Identifier:
- 230354

- Report Number(s):
- CONF-960401-16

ON: DE96009404; TRN: 96:002999

- DOE Contract Number:
- AC05-96OR22464

- Resource Type:
- Conference

- Resource Relation:
- Conference: Spring meeting of the Materials Research Society (MRS), San Francisco, CA (United States), 8-12 Apr 1996; Other Information: PBD: 1996

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING NOT INCLUDED IN OTHER CATEGORIES; HARDNESS; MEASURING METHODS; ANALYTICAL SOLUTION; FINITE ELEMENT METHOD; MATERIALS TESTING; ELASTICITY

### Citation Formats

```
Bolshakov, A, and Pharr, G M.
```*Inaccuracies in Sneddon`s solution for elastic indentation by a rigid cone and their implications for nanoindentation data analysis*. United States: N. p., 1996.
Web.

```
Bolshakov, A, & Pharr, G M.
```*Inaccuracies in Sneddon`s solution for elastic indentation by a rigid cone and their implications for nanoindentation data analysis*. United States.

```
Bolshakov, A, and Pharr, G M. Wed .
"Inaccuracies in Sneddon`s solution for elastic indentation by a rigid cone and their implications for nanoindentation data analysis". United States. https://www.osti.gov/servlets/purl/230354.
```

```
@article{osti_230354,
```

title = {Inaccuracies in Sneddon`s solution for elastic indentation by a rigid cone and their implications for nanoindentation data analysis},

author = {Bolshakov, A and Pharr, G M},

abstractNote = {Methods currently used for analyzing nanoindentation load-displacement data to determine a material`s hardness and elastic modulus are based on Sneddon`s solution for the indentation of an elastic half-space by a rigid axisymmetric indenter. Although this solution is widely used, no attempts have been made to determine how well it works for conditions of finite deformation, as is the case in most nanoindentation experiments with sharp indenters. Analytical and finite element results are presented which show that corrections to Sneddon`s solution are needed if it is to be accurately applied to the case of deformation by a rigid cone. Failure to make the corrections results in an underestimation of the load and contact stiffness and an overestimation of the elastic modulus, with the magnitude of the errors depending on the angle of the indenter and Poisson`s ratio of the half-space. For a rigid conical indenter with a half-included tip angle of 70.3{degrees}, i.e., the angle giving the same area-to-depth ratio as the Berkovich indenter used commonly in nanoindentation experiments, the underestimation of the load and contact stiffness and overestimation of the elastic modulus may be as large as 13%. It is shown that a simple first order correction can be achieved by redefining the effective angle of the indenter in terms of the elastic constants. Implications for the interpretation of nanoindentation data are discussed.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1996},

month = {5}

}