Methods of obtaining instantaneous modulus of viscoelastic solids using displacement-controlled instrumented indentation with axisymmetric indenters of arbitrary smooth profiles

Yang Tse Cheng; Che Min Cheng; Wangyang Ni

doi:10.1016/j.msea.2005.09.134

Methods of obtaining instantaneous modulus of viscoelastic solids using displacement-controlled instrumented indentation with axisymmetric indenters of arbitrary smooth profiles

Yang Tse Cheng, Che Min Cheng, Wangyang Ni

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

We derive a relationship between the initial unloading slope, contact depth, and the instantaneous relaxation modulus for displacement-controlled indentation in linear viscoelastic solids by a rigid indenter with an arbitrary axisymmetric smooth profile. While the same expression is well known for indentation in elastic and in elastic-plastic solids, we show that it is also true for indentation in linear viscoelastic solids, provided that the unloading rate is sufficiently fast. When the unloading rate is slow, a "hold" period between loading and unloading can be used to provide a correction term for the initial unloading slope equation. Finite element calculations are used to illustrate the methods of fast unloading and "hold-at-the-maximum-indenter-displacement" for determining the instantaneous modulus using spherical indenters.

Original language	English
Pages (from-to)	2-7
Number of pages	6
Journal	Materials Science and Engineering: A
Volume	423
Issue number	1-2
DOIs	https://doi.org/10.1016/j.msea.2005.09.134
State	Published - May 15 2006

Bibliographical note

Funding Information:
The authors would like to thank Mike Lukitsch, Yue Qi, Tom Perry, and Wes Capehart, Lou Hector, and Mark W. Verbrugge for valuable discussions. C.-M. Cheng would like to acknowledge partial support from NSF of China, Project No.10372101.

Keywords

Indentation
Instantaneous modulus
Viscoelastic solids

ASJC Scopus subject areas

General Materials Science
Condensed Matter Physics
Mechanics of Materials
Mechanical Engineering

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10.1016/j.msea.2005.09.134

Cite this

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title = "Methods of obtaining instantaneous modulus of viscoelastic solids using displacement-controlled instrumented indentation with axisymmetric indenters of arbitrary smooth profiles",

abstract = "We derive a relationship between the initial unloading slope, contact depth, and the instantaneous relaxation modulus for displacement-controlled indentation in linear viscoelastic solids by a rigid indenter with an arbitrary axisymmetric smooth profile. While the same expression is well known for indentation in elastic and in elastic-plastic solids, we show that it is also true for indentation in linear viscoelastic solids, provided that the unloading rate is sufficiently fast. When the unloading rate is slow, a {"}hold{"} period between loading and unloading can be used to provide a correction term for the initial unloading slope equation. Finite element calculations are used to illustrate the methods of fast unloading and {"}hold-at-the-maximum-indenter-displacement{"} for determining the instantaneous modulus using spherical indenters.",

keywords = "Indentation, Instantaneous modulus, Viscoelastic solids",

author = "Cheng, {Yang Tse} and Cheng, {Che Min} and Wangyang Ni",

note = "Funding Information: The authors would like to thank Mike Lukitsch, Yue Qi, Tom Perry, and Wes Capehart, Lou Hector, and Mark W. Verbrugge for valuable discussions. C.-M. Cheng would like to acknowledge partial support from NSF of China, Project No.10372101.",

year = "2006",

month = may,

day = "15",

doi = "10.1016/j.msea.2005.09.134",

language = "English",

volume = "423",

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Methods of obtaining instantaneous modulus of viscoelastic solids using displacement-controlled instrumented indentation with axisymmetric indenters of arbitrary smooth profiles. / Cheng, Yang Tse; Cheng, Che Min; Ni, Wangyang.
In: Materials Science and Engineering: A, Vol. 423, No. 1-2, 15.05.2006, p. 2-7.

Research output: Contribution to journal › Article › peer-review

TY - JOUR

T1 - Methods of obtaining instantaneous modulus of viscoelastic solids using displacement-controlled instrumented indentation with axisymmetric indenters of arbitrary smooth profiles

AU - Cheng, Yang Tse

AU - Cheng, Che Min

AU - Ni, Wangyang

N1 - Funding Information: The authors would like to thank Mike Lukitsch, Yue Qi, Tom Perry, and Wes Capehart, Lou Hector, and Mark W. Verbrugge for valuable discussions. C.-M. Cheng would like to acknowledge partial support from NSF of China, Project No.10372101.

PY - 2006/5/15

Y1 - 2006/5/15

N2 - We derive a relationship between the initial unloading slope, contact depth, and the instantaneous relaxation modulus for displacement-controlled indentation in linear viscoelastic solids by a rigid indenter with an arbitrary axisymmetric smooth profile. While the same expression is well known for indentation in elastic and in elastic-plastic solids, we show that it is also true for indentation in linear viscoelastic solids, provided that the unloading rate is sufficiently fast. When the unloading rate is slow, a "hold" period between loading and unloading can be used to provide a correction term for the initial unloading slope equation. Finite element calculations are used to illustrate the methods of fast unloading and "hold-at-the-maximum-indenter-displacement" for determining the instantaneous modulus using spherical indenters.

AB - We derive a relationship between the initial unloading slope, contact depth, and the instantaneous relaxation modulus for displacement-controlled indentation in linear viscoelastic solids by a rigid indenter with an arbitrary axisymmetric smooth profile. While the same expression is well known for indentation in elastic and in elastic-plastic solids, we show that it is also true for indentation in linear viscoelastic solids, provided that the unloading rate is sufficiently fast. When the unloading rate is slow, a "hold" period between loading and unloading can be used to provide a correction term for the initial unloading slope equation. Finite element calculations are used to illustrate the methods of fast unloading and "hold-at-the-maximum-indenter-displacement" for determining the instantaneous modulus using spherical indenters.

KW - Indentation

KW - Instantaneous modulus

KW - Viscoelastic solids

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SN - 0921-5093

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EP - 7

JO - Materials Science and Engineering: A

JF - Materials Science and Engineering: A

IS - 1-2

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Methods of obtaining instantaneous modulus of viscoelastic solids using displacement-controlled instrumented indentation with axisymmetric indenters of arbitrary smooth profiles

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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