Flat indentation of a viscoelastic polymer film on a rigid substrate

Abstract A systematic method of flat indentation was developed to measure the elastic and viscoelastic properties of polymer films. A flat indentation problem on an elastic film perfectly bonded to a rigid substrate was revisited, from which the relationship between the applied force and the penetration depth was obtained in a simple form. Application of the elastic–viscoelastic correspondence principle converts the force–depth relationship for elastic films to the Laplace transform of that for viscoelastic films. Indentation experiments with a flat diamond tip were performed on polymer films (SU-8 and NR4-8000P). Analysis of the measured data with the viscoelastic force–depth relationship provides the shear moduli, Poisson’s ratios, and relaxation moduli of these films. Viscoplastic deformations produced in the films that underwent the flat indentation process were quantified by measuring the residual deformation after unloading with an atomic force microscope.

[1]  G. Graham,et al.  The contact problem in the linear theory of viscoelasticity , 1965 .

[2]  H. Y. Yu,et al.  The effect of substrate on the elastic properties of films determined by the indentation test — axisymmetric boussinesq problem , 1990 .

[3]  En-Jui Lee,et al.  The Contact Problem for Viscoelastic Bodies , 1960 .

[4]  L. E. Scriven,et al.  Flat‐punch indentation of viscoelastic material , 2000 .

[5]  G. Pharr,et al.  An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments , 1992 .

[6]  S. C. Hunter.  The Hertz problem for a rigid spherical indenter and a viscoelastic half-space , 1960 .

[7]  A. Hult,et al.  Viscoelasticity in Polymer Films on Rigid Substrates , 2003 .

[8]  K. Zeng,et al.  Extracting the mechanical properties of a viscoelastic polymeric film on a hard elastic substrate , 2004 .

[9]  W. Hayes,et al.  A mathematical analysis for indentation tests of articular cartilage. , 1972, Journal of biomechanics.

[10]  R. Cook,et al.  Indentation responses of time-dependent films on stiff substrates , 2004 .

[11]  N. N. Lebedev,et al.  Axisymmetric contact problem for an elastic layer , 1958 .

[12]  Fuqian Yang,et al.  Indentation of an incompressible elastic film , 1998 .

[13]  John S. Villarrubia,et al.  Nanoindentation of polymers: an overview , 2001 .

[14]  I. N. Sneddon.  The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile , 1965 .

[15]  Stefan Carlsson,et al.  On Microindentation of Viscoelastic Polymers , 1998 .

[16]  G. Gladwell.  Contact Problems in the Classical Theory of Elasticity , 1980 .

[17]  S. R. Lee,et al.  Measurement of time-dependent adhesion between a polymer film and a flat indenter tip , 2008 .

[18]  R. Christensen,et al.  Theory of Viscoelasticity , 1971 .