Analysis of nanoindentation load-displacement loading curves

S. V. Hainsworth*, H. W. Chandler, T. F. Page

*Corresponding author for this work

Research output: Contribution to journalArticle

228 Citations (Scopus)

Abstract

Nanoindentation load-displacement curves provide a "mechanical fingerprint" of a materials response to contact deformation. Over the last few years, much attention has been focused on understanding the factors controlling the detailed shape of unloading curves so that parameters such as true contact area, Young's modulus, and an indentation hardness number can be derived. When the unloading curve is well behaved (by which we mean approximating to linear behavior, or alternatively, fitting a power-law relationship), then this approach can be very successful. However, when the test volume displays considerable elastic recovery as the load is removed [e.g., for many stiff hard materials and many inhomogeneous systems (e.g., those employing thin hard coatings)], then the unloading curve fits no existing model particularly well. This results in considerable difficulty in obtaining valid mechanical property data for these types of materials. An alternative approach, described here, is to attempt to understand the shapes of nanoindentation loading curve and thus quantitatively model the relationship between Young's modulus, indentation hardness, indenter geometry, and the resultant maximum displacement for a given load. This paper describes the development and refinement of a previous approach by Loubet et al.1 originally suggested for a Vickers indenter, but applied here to understand the factors that control the shape of the loading curve during nanoindentation experiments with a pointed, trigonal (Berkovich) indenter. For a range of materials, the relationship P = Kmδ2 was found to describe the indenter displacement, δ, in terms of the applied load P. For each material, Km can be predicted from the Young's modulus (E) and the hardness (H). The result is that if either E or H is known, then the other may be calculated from the experimental loading curve. This approach provides an attractive alternative to finite element modeling and is a tractable approach for those cases where analysis of unloading curves is infeasible.

Original languageEnglish
Pages (from-to)1987-1995
Number of pages9
JournalJournal of Materials Research
Volume11
Issue number8
DOIs
Publication statusPublished - Aug 1996

Fingerprint

Nanoindentation
nanoindentation
Unloading
unloading
curves
Elastic moduli
Hardness
Indentation
modulus of elasticity
hardness
indentation
Hard coatings
Recovery
Mechanical properties
Geometry
recovery
mechanical properties
coatings
Experiments
geometry

ASJC Scopus subject areas

  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Analysis of nanoindentation load-displacement loading curves. / Hainsworth, S. V.; Chandler, H. W.; Page, T. F.

In: Journal of Materials Research, Vol. 11, No. 8, 08.1996, p. 1987-1995.

Research output: Contribution to journalArticle

Hainsworth, S. V. ; Chandler, H. W. ; Page, T. F. / Analysis of nanoindentation load-displacement loading curves. In: Journal of Materials Research. 1996 ; Vol. 11, No. 8. pp. 1987-1995.
@article{62bacc73708b4adc8385172239324816,
title = "Analysis of nanoindentation load-displacement loading curves",
abstract = "Nanoindentation load-displacement curves provide a {"}mechanical fingerprint{"} of a materials response to contact deformation. Over the last few years, much attention has been focused on understanding the factors controlling the detailed shape of unloading curves so that parameters such as true contact area, Young's modulus, and an indentation hardness number can be derived. When the unloading curve is well behaved (by which we mean approximating to linear behavior, or alternatively, fitting a power-law relationship), then this approach can be very successful. However, when the test volume displays considerable elastic recovery as the load is removed [e.g., for many stiff hard materials and many inhomogeneous systems (e.g., those employing thin hard coatings)], then the unloading curve fits no existing model particularly well. This results in considerable difficulty in obtaining valid mechanical property data for these types of materials. An alternative approach, described here, is to attempt to understand the shapes of nanoindentation loading curve and thus quantitatively model the relationship between Young's modulus, indentation hardness, indenter geometry, and the resultant maximum displacement for a given load. This paper describes the development and refinement of a previous approach by Loubet et al.1 originally suggested for a Vickers indenter, but applied here to understand the factors that control the shape of the loading curve during nanoindentation experiments with a pointed, trigonal (Berkovich) indenter. For a range of materials, the relationship P = Kmδ2 was found to describe the indenter displacement, δ, in terms of the applied load P. For each material, Km can be predicted from the Young's modulus (E) and the hardness (H). The result is that if either E or H is known, then the other may be calculated from the experimental loading curve. This approach provides an attractive alternative to finite element modeling and is a tractable approach for those cases where analysis of unloading curves is infeasible.",
author = "Hainsworth, {S. V.} and Chandler, {H. W.} and Page, {T. F.}",
year = "1996",
month = "8",
doi = "10.1557/JMR.1996.0250",
language = "English",
volume = "11",
pages = "1987--1995",
journal = "Journal of Materials Research",
issn = "0884-2914",
publisher = "Cambridge University Press",
number = "8",

}

TY - JOUR

T1 - Analysis of nanoindentation load-displacement loading curves

AU - Hainsworth, S. V.

AU - Chandler, H. W.

AU - Page, T. F.

PY - 1996/8

Y1 - 1996/8

N2 - Nanoindentation load-displacement curves provide a "mechanical fingerprint" of a materials response to contact deformation. Over the last few years, much attention has been focused on understanding the factors controlling the detailed shape of unloading curves so that parameters such as true contact area, Young's modulus, and an indentation hardness number can be derived. When the unloading curve is well behaved (by which we mean approximating to linear behavior, or alternatively, fitting a power-law relationship), then this approach can be very successful. However, when the test volume displays considerable elastic recovery as the load is removed [e.g., for many stiff hard materials and many inhomogeneous systems (e.g., those employing thin hard coatings)], then the unloading curve fits no existing model particularly well. This results in considerable difficulty in obtaining valid mechanical property data for these types of materials. An alternative approach, described here, is to attempt to understand the shapes of nanoindentation loading curve and thus quantitatively model the relationship between Young's modulus, indentation hardness, indenter geometry, and the resultant maximum displacement for a given load. This paper describes the development and refinement of a previous approach by Loubet et al.1 originally suggested for a Vickers indenter, but applied here to understand the factors that control the shape of the loading curve during nanoindentation experiments with a pointed, trigonal (Berkovich) indenter. For a range of materials, the relationship P = Kmδ2 was found to describe the indenter displacement, δ, in terms of the applied load P. For each material, Km can be predicted from the Young's modulus (E) and the hardness (H). The result is that if either E or H is known, then the other may be calculated from the experimental loading curve. This approach provides an attractive alternative to finite element modeling and is a tractable approach for those cases where analysis of unloading curves is infeasible.

AB - Nanoindentation load-displacement curves provide a "mechanical fingerprint" of a materials response to contact deformation. Over the last few years, much attention has been focused on understanding the factors controlling the detailed shape of unloading curves so that parameters such as true contact area, Young's modulus, and an indentation hardness number can be derived. When the unloading curve is well behaved (by which we mean approximating to linear behavior, or alternatively, fitting a power-law relationship), then this approach can be very successful. However, when the test volume displays considerable elastic recovery as the load is removed [e.g., for many stiff hard materials and many inhomogeneous systems (e.g., those employing thin hard coatings)], then the unloading curve fits no existing model particularly well. This results in considerable difficulty in obtaining valid mechanical property data for these types of materials. An alternative approach, described here, is to attempt to understand the shapes of nanoindentation loading curve and thus quantitatively model the relationship between Young's modulus, indentation hardness, indenter geometry, and the resultant maximum displacement for a given load. This paper describes the development and refinement of a previous approach by Loubet et al.1 originally suggested for a Vickers indenter, but applied here to understand the factors that control the shape of the loading curve during nanoindentation experiments with a pointed, trigonal (Berkovich) indenter. For a range of materials, the relationship P = Kmδ2 was found to describe the indenter displacement, δ, in terms of the applied load P. For each material, Km can be predicted from the Young's modulus (E) and the hardness (H). The result is that if either E or H is known, then the other may be calculated from the experimental loading curve. This approach provides an attractive alternative to finite element modeling and is a tractable approach for those cases where analysis of unloading curves is infeasible.

UR - http://www.scopus.com/inward/record.url?scp=0030216784&partnerID=8YFLogxK

U2 - 10.1557/JMR.1996.0250

DO - 10.1557/JMR.1996.0250

M3 - Article

VL - 11

SP - 1987

EP - 1995

JO - Journal of Materials Research

JF - Journal of Materials Research

SN - 0884-2914

IS - 8

ER -