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.
|Number of pages||6|
|Journal||Materials Science and Engineering A|
|State||Published - May 15 2006|
Bibliographical noteFunding 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.
- Instantaneous modulus
- Viscoelastic solids
ASJC Scopus subject areas
- Materials Science (all)
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering