Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-17T19:18:33.315Z Has data issue: false hasContentIssue false
  • English
  • Français

Determination of shear creep compliance of linear viscoelastic solids by instrumented indentation when the contact area has a single maximum

Published online by Cambridge University Press:  09 May 2012

Guangjian Peng ,
Taihua Zhang ,
Yihui Feng  and
Rong Yang
Guangjian Peng
Affiliation:
State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China; and Graduate University of Chinese Academy of Sciences, Beijing 100049, China
Taihua Zhang*
Affiliation:
State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
Yihui Feng
Affiliation:
State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
Rong Yang
Affiliation:
State Key Laboratory of Nonlinear Mechanics (LNM), Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
*
a)Address all correspondence to this author. e-mail: zhangth@lnm.imech.ac.cn
Get access

Abstract

Lee and Radok [J. Appl. Mech.27, 438 (1960)] derived the solution for the indentation of a smooth rigid indenter on a linear viscoelastic half-space. They had pointed out that their solution was valid only for regimes where contact area did not decrease with time. In this article, a large number of finite element simulations and one typical experiment demonstrate that Lee-Radok solution is approximately valid for the case of reducing contact area. Based on this finding, three semiempirical methods, i.e., Step-Ramp method, Ramp-Ramp method and Sine-Sine method, are proposed for determination of shear creep compliance using the data of both loading and unloading segments. The reliability of these methods is acceptable within certain tolerance.

Type
Articles
Information
Journal of Materials Research , Volume 27 , Issue 12 , 28 June 2012 , pp. 1565 - 1572
Copyright
Copyright © Materials Research Society 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Oliver, W.C. and Pharr, G.M.: An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, 1564 (1992).CrossRefGoogle Scholar
2.Ngan, A.H.W. and Tang, B.: Viscoelastic effects during unloading in depth-sensing indentation. J. Mater. Res. 17, 2604 (2002).CrossRefGoogle Scholar
3.Feng, G. and Ngan, A.H.W.: Effects of creep and thermal drift on modulus measurement using depth-sensing indentation. J. Mater. Res. 17, 660 (2002).CrossRefGoogle Scholar
4.Tang, B. and Ngan, A.H.W.: Accurate measurement of tip–sample contact size during nanoindentation of viscoelastic materials. J. Mater. Res. 18, 1141 (2003).CrossRefGoogle Scholar
5.Cheng, Y.T. and Cheng, C.M.: Relationships between initial unloading slope, contact depth, and mechanical properties for spherical indentation in linear viscoelastic solids. Mater. Sci. Eng. A 409, 93 (2005).CrossRefGoogle Scholar
6.Cheng, Y.T. and Cheng, C.M.: General relationship between contact stiffness, contact depth, and mechanical properties for indentation in linear viscoelastic solids using axisymmetric indenters of arbitrary profiles. Appl. Phys. Lett. 87, 111914 (2005).CrossRefGoogle Scholar
7.Cheng, Y.T., Ni, W.Y., and Cheng, C.M.: Determining the instantaneous modulus of viscoelastic solids using instrumented indentation measurements. J. Mater. Res. 20, 3061 (2005).CrossRefGoogle Scholar
8.Cheng, Y.T., Cheng, C.M., and Ni, W.Y.: Methods of obtaining instantaneous modulus of viscoelastic solids using displacement-controlled instrumented indentation with axisymmetric indenters of arbitrary smooth profiles. Mater. Sci. Eng. A 423, 2 (2006).CrossRefGoogle Scholar
9.Lu, H., Wang, B., Ma, J., Huang, G., and Viswanathan, H.: Measurement of creep compliance of solid polymers by nanoindentation. Mech. Time-Depend. Mater. 7, 189 (2003).CrossRefGoogle Scholar
10.Oyen, M.L.: Spherical indentation creep following ramp loading. J. Mater. Res. 20, 2094 (2005).CrossRefGoogle Scholar
11.Oyen, M.L.: Analytical techniques for indentation of viscoelastic materials. Philos. Mag. 86, 5625 (2006).CrossRefGoogle Scholar
12.Tweedie, C.A. and Van Vliet, K.J.: Contact creep compliance of viscoelastic materials via nanoindentation. J. Mater. Res. 21, 1576 (2006).CrossRefGoogle Scholar
13.Huang, G. and Lu, H.: Measurements of two independent viscoelastic functions by nanoindentation. Exp. Mech. 47, 87 (2006).CrossRefGoogle Scholar
14.Vandamme, M. and Ulm, F.: Viscoelastic solutions for conical indentation. Int J. Solids Struct. 43, 3142 (2006).CrossRefGoogle Scholar
15.Huang, G. and Lu, H.: Measurement of Young’s relaxation modulus using nanoindentation. Mech. Time-Depend. Mater. 10, 229 (2007).CrossRefGoogle Scholar
16.Menčík, J. and Beneš, L.: Determination of viscoelastic properties by nanoindentation. J. Optoelectron. Adv. Mater. 10, 3288 (2008).Google Scholar
17.Cheng, Y.T. and Yang, F.Q.: Obtaining shear relaxation modulus and creep compliance of linear viscoelastic materials from instrumented indentation using axisymmetric indenters of power-law profiles. J. Mater. Res. 24, 3013 (2009).CrossRefGoogle Scholar
18.Lee, E.H. and Radok, J.R.M.: The contact problem for viscoelastic bodies. J. Appl. Mech. 27, 438 (1960).CrossRefGoogle Scholar
19.Hunter, S.C.: The Hertz problem for a rigid spherical indenter and a viscoelastic half-space. J. Mech. Phys. Solids 8, 219 (1960).CrossRefGoogle Scholar
20.Graham, G.A.C.: The contact problem in the linear theory of viscoelasticity. Int. J. Eng. Sci. 3, 27 (1965).CrossRefGoogle Scholar
21.Ting, T.C.T.: Contact stresses between a rigid indenter and a viscoelastic half-space. J. Appl. Mech. 33, 845 (1966).CrossRefGoogle Scholar
22.Greenwood, J.A.: Contact between an axisymmetric indenter and a viscoelastic half-space. Int. J. Mech. Sci. 52, 829 (2010).CrossRefGoogle Scholar
23.ABAQUS (HKS Inc, Pawtucket, RI).Google Scholar